View Full Version : Time dilation ll
In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
What do people think he meant by the phrase "...must go more slowly..."?
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
********************
On the (probably erroneous) basis that some people may agree that he did I follow that up with the question - On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”?
Pretty obvious questions - I know - however they are leading to a conclusion but my previous attempt started at the wrong end of Einstein’s section 4 STR depictions leading to confusion.
neopolitan
Mar25-09, 03:33 AM
In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
What do people think he meant by the phrase "...must go more slowly..."?
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
********************
On the (probably erroneous) basis that some people may agree that he did I follow that up with the question - On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”?
Pretty obvious questions - I know - however they are leading to a conclusion but my previous attempt started at the wrong end of Einstein’s section 4 STR depictions leading to confusion.
Might not be relevant, but it might.
A spinning mass is not spherical. It is fatter at the equator than at the poles.
The clock at the pole at sea level will be closer to the centre of mass of the earth than a clock on the equator at sea level is.
I am pretty sure that the overall effect is that when comparing clocks at sea level, all clocks will run at the same rate. I wouldn't like to have to do the maths, perhaps someone else can :smile:
If the earth was a perfect sphere, then yes, the clock at the equator would run slow compared to the clock at the pole (but the rotation of this perfectly spherical earth would be terribly unstable).
neopolitan
Might not be relevant, but it might.
A spinning mass is not spherical. It is fatter at the equator than at the poles.
The clock at the pole at sea level will be closer to the centre of mass of the earth than a clock on the equator at sea level is.
I am pretty sure that the overall effect is that when comparing clocks at sea level, all clocks will run at the same rate. I wouldn't like to have to do the maths, perhaps someone else can :smile:
If the earth was a perfect sphere, then yes, the clock at the equator would run slow compared to the clock at the pole (but the rotation of this perfectly spherical earth would be terribly unstable).
neopolitan
Although you appear to be suggesting that this section of special theory is wrong I am of the opinion that Einstein's stipulation "..under otherwise identical conditions." would provide for that factor perhaps placing the polar clock on top of a tall tower whereby it is then the same distance from the center of gravity as the equatorial clock however it is not the validity of Einstein's presentation to which my posting applies but to its conclusion.
Furthermore, the argument you present has no relevance to his previous depiction "...one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A..." which is analogous to an astronaut making an out-and-return trip into space.
Having stated (albeit perhaps erroneously) that an equatorial clock will 'go more slowly' than a polar clock i am of the opinion that the clock that is made to travel in a closed curve around another clock will similarly 'go more slowly' than the 'stationary' clock.
We assume, theoretically, that both systems are in an otherwise empty space whereby there is no question that the central clocks are moving as there is nothing with which a state of motion can be determined.
I am of the opinion that his comment "must go more slowly" means that the equatorial clock and the clock that is moving in a closed curve will respectively be ticking over at slower rates than (i.e. incurring time dilation relatively to) the 'stationary' polar-central clocks.
An astronaut blasts off from the planet and travels out into space continuously firing a lateral rocket and moves in a closed curve returning to the planet. According to Einstein's section 4 STR depiction his clock (A) 'must go more slowly' than his twin's clock (B) and upon arriving home he finds that his clock lags behind his twin's clock.
Having read and accepted special theory (in particular section 4) as well as Einstein's 1918 Naturwissennschaften article (in which he stated that it is only the clock that incurs acceleration that ticks over at the slower time not the 'stationary' clock) the astronaut should be entitled to conclude that his clock lags behind clock B because, whilst he was moving, his clock went more slowly (i.e. ticked over at a slower rate than) his twin's clock regardless of the fact that his clock appears to be ticking over at it's 'normal' rate.
The alternative is that he is of the opinion that, whilst he was traveling, the Earth clock (and the entire universe) ticked over at a faster rate than his own clock.
I am of the opinion that the idea that a clock can be made to tick over at a faster rate than it was before another clock started moving (i.e. universal time contraction)was an anathema to Einstein and it is his work to which my postings apply not interpretations of same.
neopolitan
Mar25-09, 10:08 PM
Nowhere in my post did I say SR is wrong in any section. Nothing in my post should be taken as suggesting that SR is wrong is any section.
Setting up two towers, so that a clock is at the same separation from the centre of mass of the earth has the same effect as placing two clocks on a rotating perfect sphere, without the issue of rotational instability.
Highlighting words will not change what I have written above.
In light of your clarification, ie your interpretation of "under otherwise identical conditions" to mean "with same separation from the earth's centre of mass" rather than "at sea level", then I would answer your question, viz:
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
with a yes. The clock on a suitable tower at the equator will run more slowly than the clock on a suitable tower at the pole and - yes - that is what I think, in essence, Einstein meant.
Similarly, if you are inertial and have a clock in orbit around you, or moving in a closed curve around you, then that clock would run more slowly than any identical clock that you held.
Furthermore, if you are essentially in orbit around a point mass (stand on the surface of the Earth and that is what you are doing - you are in geosynchronous orbit around the Earth, normally referred to as "standing still") and there is a clock on a tower above you, that clock will be affected by the greater effective orbital velocity relative to you, and as a result it will run slower than an identical clock held by you. That effect must, however, be considered together with the effect of your being deeper in the gravity well, which means that your clock is running slower than clocks less deep in the gravity well.
These effects are considered in the calculations required to make GPS work (because GPS works on triangulation performed by comparing the times on clocks) - check wikipedia (http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity)if you don't believe me.
Note that this third scenario is generalised version of the second scenario, whereas in the third scenario the radius of the closed curve is r=R, in the second scenario r=0. The first scenario is also a generalised version of the second scenario, but there is a lateral offset of the closed curve which is zero in the second scenario and R in the first. R is the radius of the Earth.
cheers,
neopolitan
.In light of your clarification, ie your interpretation of "under otherwise identical conditions" to mean "with same separation from the earth's centre of mass" rather than "at sea level", then I would answer your question, viz:
"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"
with a yes.
Is a person located alongside a clock at the equator entitled to be of the opinion that his clock is ticking over at a slower rate than the depicted clock at the pole?
neopolitan
Mar26-09, 03:50 AM
Is a person located alongside a clock at the equator entitled to be of the opinion that his clock is ticking over at a slower rate than the depicted clock at the pole?
No. The person at the equator (in the tower) is not inertial.
No. The person at the equator (in the tower) is not inertial.
It is my opinion that Einstein suggested that a clock at the equator "....must go more slowly..." (i.e. tick over at a slower rate) than a clock at one of the poles ("...under otherwise identical conditions.") because the [clock] at that location is not inertial relatively to the 'stationary' (i.e. inertial) clock at the pole (on the hypothetical basis that this system is contained in an otherwise empty universe relatively to which no velocity of the planet can be determined).
According to Einstein, a clock at the equator will go more slowly than a clock at one of the poles (under otherwise identical conditions ergo there is no reason whatsoever to refer to any tower).
Why would the person at the equator disagree with Einstein insisting that his clock is not 'going more slowly' (i.e. ticking over at a slower rate) than a clock at one of the poles?
On what basis would that person insist that Einstein was wrong?
A person who is, in accordance with Einstein's section 4 depiction, moving in a closed curve around another clock knows that his is not an inertial reference frame and that the clock which has, in Einstein's terms, remained at rest is inertial and because of that fact his clock will, as Einstein pointed out, 'go more slowly' than the inertial clock.
That person is, in my opinion, entitled to agree with Einstein thus realize that his clock is ticking over at a slower rate than it was before he started moving.
neopolitan
Mar26-09, 09:32 PM
Why would the person at the equator disagree with Einstein insisting that his clock is not 'going more slowly' (i.e. ticking over at a slower rate) than a clock at one of the poles?
On what basis would that person insist that Einstein was wrong?
As you've defined it, that person would have no reason to insist that Einstein was wrong, because his clock would run more slowly.
A person who is, in accordance with Einstein's section 4 depiction, moving in a closed curve around another clock knows that his is not an inertial reference frame and that the clock which has, in Einstein's terms, remained at rest is inertial and because of that fact his clock will, as Einstein pointed out, 'go more slowly' than the inertial clock.
That person is, in my opinion, entitled to agree with Einstein thus realize that his clock is ticking over at a slower rate than it was before he started moving.
I am pretty sure that what you have written here says what I said.
Are you going to get towards a situation where the planet is in empty space but still rotating, with nothing to reference against and claim that it is impossible to judge which is moving in a closed curve around the other?
In that instance, you will still have one clock experiencing centripetal acceleration and the other one not. They are distinguishable.
If you try taking the planet away, you will have taken away too much, since your mechanism for one clock moving around the other in a closed curve was the planet and will have to be replaced. Whatever mechanism you replace it with will give one clock centripetal acceleration and not the other (unless you make them co-orbit something, in which case they both experience centripetal acceleration, but the situation is no longer analogous).
cheers,
neopolitan
matheinste
Mar26-09, 10:24 PM
In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
What do people think he meant by the phrase "...must go more slowly..."?
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
********************
On the (probably erroneous) basis that some people may agree that he did I follow that up with the question - On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”?
Pretty obvious questions - I know - however they are leading to a conclusion but my previous attempt started at the wrong end of Einstein’s section 4 STR depictions leading to confusion.
Because the reference is to the Special Theory of Relativity I would imagine that Einstein was not taking into account the effects of gravity. In SR, an inertial clock shows or measures maximum proper time. Any non inertial clock moving in a closed curve relative to it will experience or show or measure less proper time. So in the example quoted the clock moving around the equator will show less time elapsed and so can be deemed to have ticked more slowly. If gravity is ignored then the pole and the equator are irrelevant and the only important thing is that one clock remains inertial and one is non inertial, that is has moved in a closed curve.
Matheinste.
As you've defined it, that person would have no reason to insist that Einstein was wrong, because his clock would run more slowly.
Is he allowed to know that his clock is, as Einstein stated, running more slowly than it would if he were located at one of the poles?
Are you going to get towards a situation where the planet is in empty space but still rotating, with nothing to reference against and claim that it is impossible to judge which is moving in a closed curve around the other?
In that instance, you will still have one clock experiencing centripetal acceleration and the other one not. They are distinguishable.
It would be very much appreciated if you did not make erroneous assumptions.
I have no reason whatsoever to suggest that if the planet was in empty space that it is impossible to judge which is moving in a closed curve around the other. The planet is, although spinning, not moving in a closed curve!
If you try taking the planet away, you will have taken away too much, since your mechanism for one clock moving around the other in a closed curve was the planet and will have to be replaced. Whatever mechanism you replace it with will give one clock centripetal acceleration and not the other (unless you make them co-orbit something, in which case they both experience centripetal acceleration, but the situation is no longer analogous).
cheers,
neopolitan
In section 4 STR Einstein 'took the planet away' in the preceding depiction wherein he wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow."
If you do respond in the positive to the question, above, asking if you accept that the person at the equator is allowed to know that his clock is, as Einstein stated, running more slowly than it would if he were located at one of the poles do you also accept that the person traveling in a closed curve around another clock is entitled to insist that his clock is, as Einstein suggested, ticking over at a slower rate than the 'at rest' (inertial reference frame) clock?
Because the reference is to the Special Theory of Relativity I would imagine that Einstein was not taking into account the effects of gravity. In SR, an inertial clock shows or measures maximum proper time. Any non inertial clock moving in a closed curve relative to it will experience or show or measure less proper time. So in the example quoted the clock moving around the equator will show less time elapsed and so can be deemed to have ticked more slowly. If gravity is ignored then the pole and the equator are irrelevant and the only important thing is that one clock remains inertial and one is non inertial, that is has moved in a closed curve.
Matheinste.
(In fact Einstein could have been taking into account the effects of gravity in accordance with his comment "under otherwise identical conditions" whereupon the polar clock could be located at the top of a very tall tower thereby placing it the same distance from the planet's center of gravity as the equatorial clock.)
My next question is - on the basis that a clock at the equator is (according to Einstein's section 4 STR presentation) ticking over at a slower rate than a polar clock - is a person located at the equator entitled to be of the opinion that, as Einstein suggested, his clock is physically ticking over at a slower rate than it would be if he were at one of the poles?
Alternatively, if he were originally located at one of the poles and moved to the equator would he be entitled to realize that his clock is then physically ticking over at a slower rate than it was before he made that trip?
neopolitan
Mar27-09, 01:03 AM
Is he allowed to know that his clock is, as Einstein stated, running more slowly than it would if he were located at one of the poles?
Yes. That person can perform experiments which show that he is not inertial but rather undergoing some form of acceleration (and even that that acceleration is centripetal). The coriolis effect should be sufficient to convince him of this.
It would be very much appreciated if you did not make erroneous assumptions.
I have no reason whatsoever to suggest that if the planet was in empty space that it is impossible to judge which is moving in a closed curve around the other. The planet is, although spinning, not moving in a closed curve!
I asked a question and preempted one possible answer. The planet's movement in a closed curve or lack of it is irrelevant since anyone anywhere on the surface will share that component of the motion. You did say you were leading to a conclusion. I'm beginning to lose my curiosity as to what that conclusion might be.
In section 4 STR Einstein 'took the planet away' in the preceding depiction wherein he wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow."
If you do respond in the positive to the question, above, asking if you accept that the person at the equator is allowed to know that his clock is, as Einstein stated, running more slowly than it would if he were located at one of the poles do you also accept that the person traveling in a closed curve around another clock is entitled to insist that his clock is, as Einstein suggested, ticking over at a slower rate than the 'at rest' (inertial reference frame) clock?
Yes. For the same reasons above. The person moving in a closed curve will be able to perform tests which show that he is undergoing acceleration and that that acceleration is centripetal.
Perhaps if you say what it is that you are actually aiming towards, you might be able to get your concern resolved.
cheers,
neopolitan
I asked a question and preempted one possible answer. The planet's movement in a closed curve or lack of it is irrelevant since anyone anywhere on the surface will share that component of the motion. You did say you were leading to a conclusion. I'm beginning to lose my curiosity as to what that conclusion might be.
C'est la vie.
Yes. For the same reasons above. The person moving in a closed curve will be able to perform tests which show that he is undergoing acceleration and that that acceleration is centripetal.
Perhaps if you say what it is that you are actually aiming towards, you might be able to get your concern resolved.
cheers,
neopolitan
On the basis that a person moving in a closed curve is entitled to be of the opinion that, as Einstein pointed out, his clock is physically ticking over at a slower rate than it was before he started moving then would you agree that in section 4 [where Einstein wrote - "If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv^2/c^2 .... t being the time occupied in the journey from A to B."] that A is entitled to conclude that, whilst he is moving, his clock physically ticks over at a slower rate than it did before he started moving?
Unlike his later depictions of a clock that is moving in a closed curve around another clock there is, in this polygonal line trip, no continuous acceleration as A moves toward B with uniform velocity as intimated by the factor 'v' in his equation ergo, during that trip, is an observer accompanying clock A entitled to be of the opinion that, as indicated by Einstein's equation, his clock is physically ticking over at a slower rate than it was before he started moving?
Einstein's section 4 depiction of a clock that is made to move toward another clock is, in my opinion, analogous to his 1918 Naturwissenschaften article wherein he stated that it is only the clock that experiences a force of acceleration that physically incurs time dilation whilst the other clock (the stationary, inertial, clock B) does not incur variations in it's rate of operation ergo it does not, as some people insist, tick over at a faster rate than it did before A started moving.
neopolitan
Mar27-09, 07:58 AM
cos,
This is analogous to the twin paradox. The accelerated twin, I believe is justified in thinking that his clock has slowed. His observations while in the inertial phase will not conform to that since other clocks which were previously synchronised will now appear to run slow. However, if the travelling twin stops (after a deceleration) and performs a synchronisation with the stationary twin, the travelling (accelerated) twin will find that it was his clock that ran slow.
It's reasonably simple to do the maths to show how all the observations match up as long as you use the right equations.
Neither of the twins will observe the other's clock speed up.
The only way you could do that, to my knowledge, is to put one twin into orbit, moving him out from the gravity well and reducing the GR effect of gravity. But I think that is outside your scenario.
cheers,
neopolitan
This is analogous to the twin paradox. The accelerated twin, I believe is justified in thinking that his clock has slowed. His observations while in the inertial phase will not conform to that since other clocks which were previously synchronised will now appear to run slow.
Einstein's 1918 Naturwissenschaften article was an attempt to negate the 'twin paradox' explaining why it is that both clocks do not tick over at a slower rate than each other; that the accelerated clock is 'the moving clock' to which opponents referred when they asked "Which is the moving clock?"
He described, in that article, two clocks that are moving past each other and pointed out that the only way that the time indicated by those clocks can only be accurately compared would be if they were stationary alongside each other and for this to take place one of them would have to decelerate, come to a stop and accelerate toward the other clock, again coming to a stop.
Einstein insisted that it is only the clock that experiences forces of acceleration that incurs time dilation not the 'at rest' clock.
The second leg of that journey - the clock accelerating toward the other one and coming to a stop alongside it - is precisely the same phenomenon as Einstein described in section 4 where clock A moves to B's location ergo, in my opinion, his 1918 article was effectively a reiteration of what he had previously indicated in section 4.
I feel that it is interesting to note that when Galileo prepared his book 'Two New Sciences' he had already been castigated by authorities as a result of his support for the non-geocentric universe thus wrote that manuscript in the form of a 'purely hypothetical' dialogue between a teacher and two of his students.
Having apparently been castigated by his colleagues for suggesting - in the introduction to general theory - that the law of the constancy of the speed of light required modification - I am of the opinion that Einstein similarly wrote his 1918 article in the form of a 'hypothetical' discussion between a relativist and a skeptic perhaps (having referred to acceleration in order to 'justify' his argument) in an attempt to prevent additional criticism.
You wrote "...other clocks which were previously synchronised will now appear to run slow." Run slow relatively to what? To the accelerated twin's clock?
On the basis that the accelerated twin is justified in thinking that, as Einstein suggested, his clock is now ticking over at a slower rate than it was before he started moving how can his 'observations' (calculations) show him that the previously synchronized inertial clock B is also running slow (presumably compared to his clock)?
However, if the travelling twin stops (after a deceleration) and performs a synchronisation with the stationary twin, the travelling (accelerated) twin will find that it was his clock that ran slow.
That is what Einstein pointed out in section 4 STR as I have previously cited.
It's reasonably simple to do the maths to show how all the observations match up as long as you use the right equations.
I happen to agree with Einstein that -
"As far as the propositions of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality."
Observer A moves to B's location in a polygonal line and arrives to find that his clock lags behind B. He is, apparently, permitted to realize that, whilst he was moving, his clock was ticking over at a slower rate than it was before he started accelerating (and at a slower rate than clock B) irrespective of the fact that it 'appeared' to have been ticking over at its normal rate but when he 'does the math' involving the 'certain' (i.e. fully self-consistent) Lorentz transformations he 'determines' that B is ticking over at a slower rate than his own clock.
Neither of the twins will observe the other's clock speed up.
There are those who insist that because A is of the opinion that his clock's rate of operation has (seemingly) remained unchanged and there is no experiment that he can carry out during that trip to determine otherwise then he 'will' be of the opinion that the eventual difference between the clocks is due to clock B ticking over at a faster rate than it did before he started moving.
One interpretation that I read several years ago showing "how all the observations match up as long as you use the right equations." insisted that when an astronaut is returning to the planet he can 'do math' which 'shows' him that his twin sister is, by his judicious application of the accelerator, physically retro-aging by a factor of sixty years!
When I argued that the sister could have died during that period - thus his calculations would 'show' him that she came back to life and, along with millions of other people, emerged from her grave - that author insisted that the astronaut could be of that opinion on the basis that this is what his math shows him is taking place. I'm afraid that I have little faith in such 'certainties'.
A worthy opponent in this group in response to my previous thread pointed out that from the point of view of a third observer (C) clocks A and B could, initially, have been moving past him at v thus when A accelerates then moves with uniform velocity it would be stationary alongside C whilst, from his point of view, B continues to move past him at v so in his opinion B is ticking over at a slower rate than A. He would thereby determine that when A pulls up alongside B it will not lag behind B but B will lag behind A!
It is my belief that 'reality' is determined in the reference frame where the event takes place so if C accelerates toward and comes to a stop alongside B he will see that B does not lag behind A as indicated by his 'internally balanced' mathematical equations but that A lags behind B. Of what value his 'determinations' or 'predictions'?
He should be allowed to realize that what he assumed to be taking place was not taking place in reality thus that his observations, determinations, predictions, were affected by his relative rate of travel.
"Knowledge is one-dimensional, the proper application of knowledge is multi-dimensional. Only the extremely wise, and the exceptionally foolish, are not prepared to change." (Confucius)
neopolitan
Mar27-09, 10:06 PM
"As far as the propositions of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality."
Interestingly enough, that quotation is used on this web page (http://www.lhup.edu/~dsimanek/philosop/logic.htm)on the use and misuse of logic (my emphasis).
And that is what this is. A misuse of logic.
As soon as you mention "worthy opponents" the misuse of logic makes more sense.
If you are not prepared to work through the mathematics which shows how both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow, then there is little more to be going on with.
Using the correct frames and equations, all the predictions and determinations made by either twin will be reconcilable with those of the other.
Throwing more words at the "problem" won't make it a real problem.
As for Einstein, I suspect a quotation taken out of context, but even if he was wrong that is no great issue, he was a man as subject to error as the rest of us. It's just that the things he was right about were of such great consequence.
cheers,
neopolitan
Einstein's section 4 depiction of a clock that is made to move toward another clock is, in my opinion, analogous to his 1918 Naturwissenschaften article wherein he stated that it is only the clock that experiences a force of acceleration that physically incurs time dilation whilst the other clock (the stationary, inertial, clock B) does not incur variations in it's rate of operation ergo it does not, as some people insist, tick over at a faster rate than it did before A started moving.It seems like you're suggesting that something physically happens to the clocks. This is simply not the case. The rate that a clock ticks is simply a frame dependent quantity. It's different for different reference frames. Saying that a clock actually changes its "ticking rate" is like saying that a car "slowed down" because its relative speed is different for different observers in relative motion. And the fact that the cars relative speed depends on reference frame doesn't mean that the observers disagree, they will agree that the relative speed of the car frame dependent.
And Einstein's 1918 paper does not claim that the time dilation is not reciprocal between inertial frames. It is simply a resolution taking the accelerated frame into account during the turnaround. During each inertial leg, each clock runs slow as observed from the other frame. Only during the turnaround acceleration, the earth's clock runs fast as observed from the accelerated frame.
And it's never a matter of opinion what any clock reads in any frame in SR. Every observer will agree on the facts. No clock is running slower than another in any absolute sense. Which clock runs slower than the other depends on which frame the observation is made from. No observer in any inertial frame ever observes a clock in relative motion to run faster than his own, or his own clock to run slower than one in relative motion.
This is true in Einstein's 1918 paper as well. It is only with respect to the accelerated frame of the ship during turnaround that a clock in relative motion runs fast compared to a clock at rest in that frame, and that's not an inertial frame. During all inertial motion, in each frame, the clock in motion runs slow compared to the clock at rest in that frame. This is reciprocal time dilation.
DaleSpam
Mar28-09, 01:47 AM
"Which is the moving clock?"The question more correctly should be "Which is the inertial clock". Which clock is moving is a frame-dependent question, but which clock is inertial is frame-independent. All frames (inertial or not) will agree that the inertial clock's worldline is longest, although they may disagree about which is "ticking fastest" (relative to coordinate time) at any given moment. All frames agree that each clock ticks at the rate of 1 s/light-second along their worldline.
Whether one clock "physically" ticks at a different rate than normal depends on if you consider experimentally-measurable coordinate-dependent quantities to be "physical".
All frames agree that each clock ticks at the rate of 1 s/light-second along their worldline. I'm sure that's a typo, but that would mean the clock was traveling at c. :!!)
DaleSpam
Mar28-09, 10:22 AM
That is not a typo. The Minkowski norm of any 4-velocity is c, so a particle at rest can indeed be considered to "travel" at c in the time direction.
If you are not prepared to work through the mathematics which shows how both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow, then there is little more to be going on with.
You agree with me as well as with Einstein's comment regarding mathematical 'certainty' and 'reality'!
During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.
If the traveler repeats that same journey he could calculate (determine) that his twin's clock appears to be running slow however in accordance with the result of the first experiment he knows that. in reality, it is his clock that is running slow! Of what value his totally contradictory mathematical determination?
matheinste
Mar28-09, 08:16 PM
Hello cos.
You seem to be neglecting the comments of DaleSpam and Al68.
Matheinste.
It seems like you're suggesting that something physically happens to the clocks. This is simply not the case.
"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.
If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
In the first paragraph Einstein states -
"...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."
In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.
In the third paragraph Einstein states -
"...a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles."
In other words, according to Einstein, something is physically happening to to the equatorial clock - it is ticking over at a slower rate than the polar clock ("under otherwise identical conditions.")
Perhaps it is your opinion that nothing physically happens to either of the clocks however it is Einstein's opinion to which my posting applies!
And Einstein's 1918 paper does not claim that the time dilation is not reciprocal between inertial frames. It is simply a resolution taking the accelerated frame into account during the turnaround. During each inertial leg, each clock runs slow as observed from the other frame. Only during the turnaround acceleration, the earth's clock runs fast as observed from the accelerated frame.
When the clock in Einstein's 1918 paper decelerates and comes to a stop it is analogous to Einstein's section 4 depiction -
"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B."
Having come to a stop (ergo then being in the same reference frame as clock B) clock A can be synchronized with clock B then having accelerated and moved to B's location A will be found to lag behind B on the basis that it must 'go more slowly' (i.e. tick over at a slower rate) than the inertial clock.
According to your depiction that "...during the turnaround acceleration, the earth's clock runs fast as observed from the accelerated frame." the astronaut must be of the opinion that something has physically made the Earth clock run faster than it did before he started accelerating.
Not only is the Earth clock, in his opinion, running fast - time itself, for the Earth must also be 'running fast'. Earth clock seconds, minutes, hours and days 'have' contracted hence the planet would, whilst he is accelerating, be spinning faster on its axis than it was before he started accelerating!
The claim that, during the turnaround acceleration, the Earth clock runs fast is usually accompanied by the claim that when the astronaut stops accelerating Earth time resorts to its normal (some insist slower) rate so at the very instant that the astronaut takes his foot off the gas pedal the Earth's faster axial spin immediately reverts to normal! No gradual slowing down but immediate return to normal!
And it's never a matter of opinion what any clock reads in any frame in SR. Every observer will agree on the facts. No clock is running slower than another in any absolute sense. Which clock runs slower than the other depends on which frame the observation is made from. No observer in any inertial frame ever observes a clock in relative motion to run faster than his own, or his own clock to run slower than one in relative motion.
This is true in Einstein's 1918 paper as well. It is only with respect to the accelerated frame of the ship during turnaround that a clock in relative motion runs fast compared to a clock at rest in that frame, and that's not an inertial frame. During all inertial motion, in each frame, the clock in motion runs slow compared to the clock at rest in that frame. This is reciprocal time dilation.
In Einstein's section 4 he points out that, in each example, when clock A is compared with clock B it is found that A lags behind B.
Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.
I am of the opinion that your comment that an astronaut accompanying clock A in Einstein's depictions (of clock A initially accelerating toward clock B) would see clock B 'running faster' is only as a result of Doppler shift however he sees almost precisely the same amount of Doppler shift when he stops accelerating as he did at the very instant that he removes his foot from the gas pedal.
There is, I suggest, nothing in special theory which shows that any action performed by the astronaut - accelerating, decelerating, moving toward or away from another clock at any velocity - will have a physical affect on that other clock - only on what it appears to be doing.
The idea (during the astronaut's period of acceleration following turn around) that the stationary clock incurs time contraction (i.e. 'is' ticking over at a faster rate than it was before he accelerated) was, for Einstein, an anathema and it it is his depictions to which I refer not interpretations arrived at by anybody else.
Whether one clock "physically" ticks at a different rate than normal depends on if you consider experimentally-measurable coordinate-dependent quantities to be "physical".
When Einstein wrote that a clock at the equator 'must go more slowly' than a clock at one of the poles (under otherwise identical conditions) was he indicating that the the equatorial clock physically 'goes more slowly' than the polar clock or was he considering 'experimentally-measurable coordinate-dependent quantities to be "physical."'?
Hello cos.
You seem to be neglecting the comments of DaleSpam and Al68.
Matheinste.
Give me a break!
I do have a life apart from this group furthermore I usually refuse to communicate with fanatics who have, in other postings, applied ad hominem attacks.
matheinste
Mar28-09, 10:02 PM
Hello cos.
I do not see where Einstein says or implies that anything physical happens to the clocks.
All that clocks do is measure time. In all the examples used in thought experiments the clocks are assumed ideal, that is their physical tmekeeping processes are not affected by their state of motion. As clocks merely measure time and their physical workings are unaffected by motion, it is concluded, as a basic consquence of the postulates of SR that it is time itself which undergoes a change of rate which is reflected in the rate of "ticking" and hence the accumulated time on the clock.
As others have made clear, an inertial clock will accumulate more time than a clock that has experienced non inertial motion, in this case having moved around a closed path.
Again, as others have said, if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own, having of course discounted any visual effects due to the relative motion. The effect is reciprocal and wll be agreed upon by both observers.
Matheinste.
neopolitan
Mar28-09, 10:50 PM
You agree with me as well as with Einstein's comment regarding mathematical 'certainty' and 'reality'!
Probably not since I at no point gave a definition of certainty and reality. I agree that models simple enough to understand are not fully descriptive of reality, and any model which was fully descriptive would be too complex to do much with (except live in, perhaps, since a fully descriptive model of the universe would be .... the universe).
Again, if you refuse to go through the maths, you won't understand.
During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.
Appears only when taking everything into account. Naively, on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other.
If you truly want to think about this, rather than push a barrow, then you might want to consider the twin paradox with each twin firing photons at each other during the journey at a rate determined by their on board clock. Consideration of when and where each twin interacts with the incoming photons will show you how it all works out such that both clocks appear to run slow with respect to each other while they are in motion with respect to each other, but the accelerated twin (the one with more than one inertial frame) will experience less elapsed time.
But until you do something like that, you're not learning anything and neither are we.
If the traveler repeats that same journey he could calculate (determine) that his twin's clock appears to be running slow however in accordance with the result of the first experiment he knows that. in reality, it is his clock that is running slow! Of what value his totally contradictory mathematical determination?
If he is committing to do as much mathematics to arrive at his mathematical determination as you are, no value at all. I keep repeating it, because it's the only way forward for you, do the maths, then come back. There are plenty of people willing to help you work through it, if you need it.
cheers,
neopolitan
DaleSpam
Mar28-09, 11:18 PM
When Einstein wrote that a clock at the equator 'must go more slowly' than a clock at one of the poles (under otherwise identical conditions) was he indicating that the the equatorial clock physically 'goes more slowly' than the polar clock or was he considering 'experimentally-measurable coordinate-dependent quantities to be "physical."'?Einstein didn't use the word "physical" to describe time dilation, but if I had to guess then I would guess that at that time he considered such experimentally-measurable coordinate-dependent quantities to be "physical".
I do not see where Einstein says or implies that anything physical happens to the clocks.
In section 4 STR Einstein wrote that clock A physically moves to B's location. He also states that a clock that is made to move in a closed curve relative to an 'at rest' clock will 'go more slowly' than the stationary clock. It follows that by 'going more slowly' than the previously synchronous clock that the moving clock is physically 'going more slowly' than it was before it started moving - a rate of operation that is comparable to the stationary clock's rate of operation - whether or not clock A is moving in a polygonal line or in a closed curve.
Having suggested that clock A is then ticking over at a slower rate than it did before it started moving what gives you the impression that Einstein did not imply that something physical happens to clock A?
All that clocks do is measure time. In all the examples used in thought experiments the clocks are assumed ideal, that is their physical timekeeping processes are not affected by their state of motion. As clocks merely measure time and their physical workings are unaffected by motion, it is concluded, as a basic consquence of the postulates of SR that it is time itself which undergoes a change of rate which is reflected in the rate of "ticking" and hence the accumulated time on the clock.
The Hafele-Keating was obviously not a thought experiment and it is said to ratify Einstein's suggestion that a clock that is made to move in a closed path around another clock will tick over at a slower rate than the other clock i.e. at a slower rate than it did before it started moving.
As others have made clear, an inertial clock will accumulate more time than a clock that has experienced non inertial motion, in this case having moved around a closed path.
As Einstein, in my opinion, 'made clear' - a non-inertial clock will 'go more slowly' (i.e. tick over at a slower rate) than an inertial clock (and tick at a slower rate than it was before it started moving). He did not suggest, and I believe would not have tolerated the idea, that the inertial clock will 'accumulate more time' than it would if the other clock had not been made to move. The rate of operation of the inertial clock physically remains unchanged irrespective of the distance traveled through spacetime by another clock.
Again, as others have said, if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own, having of course discounted any visual effects due to the relative motion. The effect is reciprocal and wll be agreed upon by both observers.
An observer accompanying clock A in Einstein's section 4 STR depiction (in accordance with his mathematical calculations) 'sees' (or 'determines') that clock B 'is' ticking over at a slower rate than his own clock yet arrives at B's location to find that B does not lag behind his clock as he calculated (i.e. 'determined' or 'predicted') it will but that his clock lags behind B!
Having arrived at B's location and having determined that his clock lags behind clock B due to the fact that, whilst he was moving, his clock was ticking over at a slower rate than it was before he started moving (i.e. 'going more slowly' than it was before he started moving) A could return to his original location and repeat the experiment during which his calculations will, again, 'show' him that clock B 'is' ticking over at a slower rate than his own clock (i.e at a slower rate than it was before he started moving) however the reality determined by the results of the first leg of the experiment - that his clock was ticking over at slower rate than it was before he started moving - challenges the validity of those calculations (i.e. 'determinations or 'predictions' arrived at via those calculations). They do not refer to reality and that, in my opinion, is what Einstein stated.
Your comment ".. if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own." applies specifically to special theory prior to section 4 which does not refer to those observers moving with inertial motion but to one observer that has (having accelerated) incurred non-inertial motion.
It is, in my opinion, 'misleading' (to say the very least) for anyone to stipulate events depicted in the previous sections of special theory and not to allow for Einstein's comments in section 4.
Probably not since I at no point gave a definition of certainty and reality. I agree that models simple enough to understand are not fully descriptive of reality, and any model which was fully descriptive would be too complex to do much with (except live in, perhaps, since a fully descriptive model of the universe would be .... the universe).
You wrote that the mathematics "...shows how both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow."
Are you suggesting that the mathematics are not 'certain' - that they are not self consistent?
Are you suggesting that when they both see that A lags behind B that this is NOT reality?
I made no suggestion whatsoever that you 'gave a definition of certainty and reality' but that, in my opinion, you provided examples OF 'certainty' and 'reality'.
Again, if you refuse to go through the maths, you won't understand.
Again, on the basis that I am of the opinion that mathematics does not refer to reality what would be the point of my going through the maths when I refuse to believe that what they determine is reality?
Your next comment makes no sense on the basis that you removed my statement -
"During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.
Appears only when taking everything into account.
There is only one aspect to be taken into account, the astronaut's rate of travel and it's incorporation as 'v' in the Lorentz' transformations.
[QUOTE=neopolitan;2137819]Naively, on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other.
You wrote, above, that "...both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow."
Your "..on the way back in..." is analogous to Einstein's section reference to one clock (A) that is made to move to B's location.
Let us imagine that the journey you depict is the second trip of an astronaut away from and back toward the planet. As a result of the fact that at the conclusion of that first experiment 'both will agree that the accelerated twin's clock ran slow' when it accelerated following turn around would it not be feasible for both observers to realize that precisely the same phenomenon is taking place during the second, identical experiment?
I am of the opinion that whilst the astronaut is 'on the way out' that his clock will also 'go more slowly' than it did prior to his departure in accordance with Einstein's .5tv^2/c^2 equation.
You wrote, above, "...on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other." This, I believe, is only due to the Doppler effect wheras the mathematical determinations of both observers is in accordance with the Lorentz transformations which do NOT incorporate or allow for Doppler shift.
The fact that I see the light emitted by a clock toward, or away from, which I am moving blueshifted or redshifted does NOT mean that it IS ticking over at a faster, or slower, rate than it was before I started moving but that it appears to be ticking over at a different rate.
I am of the opinion that Einstein's comment that the accelerated clock ticks over at a slower rate than the inertial clock has absolutely nothing whatsoever to do with Doppler shift!
If you truly want to think about this, rather than push a barrow, then you might want to consider the twin paradox with each twin firing photons at each other during the journey at a rate determined by their on board clock. Consideration of when and where each twin interacts with the incoming photons will show you how it all works out such that both clocks appear to run slow with respect to each other while they are in motion with respect to each other, but the accelerated twin (the one with more than one inertial frame) will experience less elapsed time.
I find it galling that you continue to resort to snide, belittling remarks.
Each twin firing photons at each other is precisely the same as each of them looking at the other clock i.e. 'receiving photons fired at them' so your depiction is, once again, in relation to the Doppler effect albeit a complicated version of same.
The accelerated twin will, according to Einstein, "...experience less elapsed time." due to the fact that (when he arrives at B's location and finds that his clock lags behind B) he realizes that his clock was, as you have agreed, running slow.
Einstein didn't use the word "physical" to describe time dilation, but if I had to guess then I would guess that at that time he considered such experimentally-measurable coordinate-dependent quantities to be "physical".
I did not suggest that he did, however, thank you for that agreement.
neopolitan
Mar29-09, 03:08 AM
cos,
I don't know what you are after. I have made plenty of snide and belittling comments in my time, but what you claim was snide and belittling wasn't intended to be.
Your position is inconsistent since in part it is based on maths and then you say maths doesn't reflect reality. Additionally, what you are arguing seems to be based on an appeal to authority (Einstein said something, so what I interpret him to have said must be true). I don't think that Einstein expected to be believed just because he said something.
He'd probably suggest that you work through the maths, which he certainly didn't reject as you seem to.
cheers,
neopolitan
cos,
I don't know what you are after. I have made plenty of snide and belittling comments in my time, but what you claim was snide and belittling wasn't intended to be.
I was, for 30 years, married to an alcoholic who constantly belittled me and the next day tearfully insisted that she didn't intend to but, that same evening, did the same thing. This caused me to suffer from chronic and severe reactive depression however I put up with it on the basis of my marriage vows but I will not tolerate such behavior from anyone!
Your position is inconsistent since in part it is based on maths and then you say maths doesn't reflect reality. Additionally, what you are arguing seems to be based on an appeal to authority (Einstein said something, so what I interpret him to have said must be true). I don't think that Einstein expected to be believed just because he said something.
My 'position' is not, in any part, based on maths but is based solely on Einstein's section 4 STR comments in which he based his depictions on maths.
I am of the opinion that clock A ticks over at a slower rate than it did prior to it's acceleration NOT because that's what the maths shows but that the slower rate of operation is, according to Einstein, in accordance with that equation.
[QUOTE=neopolitan;2138035]He'd probably suggest that you work through the maths, which he certainly didn't reject as you seem to.
I am of the opinion that Einstein obviously did not reject maths but that he insisted that it does not refer to reality.
I do NOT reject mathematics on the basis that it is an absolutely indispensable aspect of science and, indeed, of everyday life however I do NOT accept that what it shows is reality.
Where 'reality' indicates that a mathematical proposition does not take place as indicated by an equation I am of the opinion that reality takes precedence.
neopolitan
Mar29-09, 07:20 AM
cos,
It appears that you have had some misfortune, but it is not relevant to the discussion.
I am of the opinion that Einstein obviously did not reject maths but that he insisted that it does not refer to reality.
This is central.
You are taking one quote and misrepresenting it terribly.
You should try to take Einstein's comments in context. In 1917 he found that his equations showed that the universe is expanding. He then spent quite a few years trying to fit a cosmological constant in order to make the universe static. In other words, the mathematics were telling him that the universe is expanding and "reality" was telling him it isn't.
Edwin Hubble came to the rescue with observations which showed that the universe is in fact expanding and Einstein's maths were correct, not his perception of what must be real.
So, I put it to you again, try the maths. The maths worked for Einstein. In 1918, to be honest, his attitude about what "must be right" wasn't working. He later called his search for a cosmological constant his greatest blunder.
You would probably be better off if you search for one of his papers or essays written after 1929.
cheers,
neopolitan
DaleSpam
Mar29-09, 09:10 AM
I did not suggest that he did, however, thank you for that agreement.You are quite welcome, but you should be aware that I am open-minded on the subject of the meaning of the word "physical". I am willing to take either position for the sake of communication. Also, I suspect (again just guessing) that Einstein's opinion changed after Minkowski.
However, since your opinion appears to be firm that frame-dependent quantities can be considered "physical", then it should come as no surprise that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation. The same thing happens with all other frame-variant "physical" quantities like energy, momentum, speed, etc. (e.g. clock A can "physically" have more speed than clock B in one frame and vice versa in another frame).
So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.
neopolitan
Mar29-09, 08:43 PM
So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.
I think cos is moving towards something like this:
"if the slowing down of clocks is supposed to real or physical, then something is amiss, and if results (like the twin paradox) suggest that only one clock ran slow, then the mathematics should be suspected, rather than the reality or physical results"
cos,
I am not saying categorically that that is your contention, it is merely what I think you are saying.
However, I should point out that you have to take into account everything in a situation like the twin's paradox. Specifically, you need to consider simultaneity (I say this even though this is not my favoured approach). Both twins will calculate that the other twin's clock ran slow during the inertial phases. What the twins will not agree on is how long those inertial phases lasted.
So the results will be (time on a slow clock running for a longer time) and (time on a slow clock running for a shorter time). The change in direction was an event that was colocal with the acelerated twin, but not colocal with the twin who was inertial throughout, which means that - taking into account simultaneity - the stationary twin will calculate that the travelling twin turned around later than travelling twin calculated. This is totally in agreement with the fact that the travelling twin's clock ran slow compared to the stationary twin.
So if you like, both clocks really ran slow, the travelling twin really turned around later than was said on his clock and at the end of the journey one clock will really show more time elapsed than shown on the other - and both clocks are showing the real time elapsed for that clock.
cheers,
neopolitan
cos,
It appears that you have had some misfortune, but it is not relevant to the discussion.
It is relevant to the discussion inthat, in the discussion you made what I considered to be snide and belittling comments which were themselves not relevant to the discussion.
"I am of the opinion that Einstein obviously did not reject maths but that he insisted that it does not refer to reality."
This is central.
You are taking one quote and misrepresenting it terribly.
You should try to take Einstein's comments in context. In 1917 he found that his equations showed that the universe is expanding. He then spent quite a few years trying to fit a cosmological constant in order to make the universe static. In other words, the mathematics were telling him that the universe is expanding and "reality" was telling him it isn't.
Edwin Hubble came to the rescue with observations which showed that the universe is in fact expanding and Einstein's maths were correct, not his perception of what must be real.
It is my understanding that Hubble argued that the greater redshift of the more distant galaxies was not an indication that the universe is expanding thus he would not have accepted the veracity of Einstein's calculations that it is!
So, I put it to you again, try the maths. The maths worked for Einstein......
Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.
According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!
HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?
You are, I believe, confusing Einstein's depiction of a non-inertial observer with his previously depicted inertial observer.
You would probably be better off if you search for one of his papers or essays written after 1929.
I assume that you have read his papers and essays written after 1929 and to save time not only for myself but also for others that may be following this thread perhaps you would be so kind as to nominate just one of those papers showing that he recanted or amended his section 4 STR comments.
Albert Einstein's 1905 article 'On the Electrodynamics of Moving Bodies' is said to be the foundation of modern-day physics and in that article he indicates that inertial observers that are moving relative to each other will both determine that the other person's clock will be running slower than their own however in section 4 of that same article he shows that an observer who has accelerated will not find that the other clock is ticking over at a slower rate than their own clock but at a faster rate!
DaleSpam
Mar29-09, 09:41 PM
According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!
HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?His math is fine and does not give an erroneous answer, you just made a mistake. Clock A is non-inertial, so the acompanying observer correctly determines that the other clock "physically" runs faster overall. In fact, all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average.
matheinste
Mar29-09, 09:49 PM
Hello cos.
Probably of no consequence but in an early traslation of about 1920 part of your quoted text reads:-
-----From this, we conclude that a clock placed at the equator must be slower by a very small amount than a similarly constructed clock which is placed at the pole, all other conditions being identical.-----
The words "be slower" are used rather than "gone more slowly". The words "balance clock" do not appear. This may of course be due to the transators M.N. Saha and S.N. Bose.
I am not drawing any conclusions from this, it is just a point of interest.
Mateinste
His math is fine and does not give an erroneous answer, you just made a mistake. Clock A is non-inertial, so the acompanying observer correctly determines that the other clock "physically" runs faster overall. In fact, all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average.
On the assumption that "..the accompanying observer correctly determines that the other clock "physically" runs faster overall." and on the assumption that he is an enquiring scientist is it not possible that he might ask himself what force has made clock B PHYSICALLY run faster than it did before he started moving?
He is an astronaut returning to the planet following turn-around; he 'sees' Earth clocks ticking over at a faster rate than they did before he started accelerating hence he 'sees' shorter Earth seconds than he did before he started moving thus he must also 'see' Earth minutes, hours and days to also 'be' ticking over at a faster rate than they were before he started moving ergo he 'sees' the Earth spinning on its axis and orbiting the sun at a considerably faster rate than it did before he started moving.
Is he not likely to ask himself what physical force has made the planet spin faster on its axis and orbit the sun at a much faster rate than it did before he started his return journey?
Although he 'determines' that the Earth clock 'is' running faster than it did before he started moving and that the planet 'is' spinning faster on its axis than they did before he started accelerating is he not likely to realize that this is nothing more than a (mathematically generated) illusion created by his non-inertial motion?
In section 4 STR Einstein pointed out, in effect, that clock A, having moved to clock B's location will lag behind clock B due to the fact that clock A 'goes more slowly' (i.e. ticks over at a slower rate) than clock B not that clock B would leap ahead of clock A thus that clock B would incur time contraction which I believe was for Einstein an anathema.
You wrote "... all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average." and i agree with that comment; clock B does 'run faster' than A due to the fact that, as Einstein pointed out, clock A runs slower than B however for them to be of the opinion that clock B runs faster than it did before A started moving is erroneous - according to Einstein's section 4 STR.
According to Einstein - clock A ticks over at a slower rate than it did before it started moving NOT that B starts ticking over at a faster rate. Clock A accelerates and it is, according to Einstein, this factor that physically causes it to tick over at the slower rate. There is no force, no action on it's behalf which causes clock B to physically tick over at a faster rate than it did before A started moving.
So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.
It is not simply a disagreement over the words "physical" and "reality" but a disagreement over those words as they apply to Einsteins section 4 STR depictions.
Hello cos.
Probably of no consequence but in an early traslation of about 1920 part of your quoted text reads:-
-----From this, we conclude that a clock placed at the equator must be slower by a very small amount than a similarly constructed clock which is placed at the pole, all other conditions being identical.-----
The words "be slower" are used rather than "gone more slowly". The words "balance clock" do not appear. This may of course be due to the transators M.N. Saha and S.N. Bose.
I am not drawing any conclusions from this, it is just a point of interest.
Mateinste
My reference was specifically in relation to Einstein's 1905 paper not any other translation.
In section 4 he wrote -
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
neopolitan
Mar29-09, 11:38 PM
cos,
I assume that you are refering to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks" since that section ends with:
Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.
Shortly before, in that same section:
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2 tv2/c2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Now it should be remembered that this is Einstein. If I wrote something similar on this forum, I would probably be appropriatedly chastised for an inaccuracy - perhaps not for being incorrect, but for not clearly stating something.
The time t is the time occupied in the journey from A to B, in the frame of the clock which remains stationary. According to the stationary clock, the clock which was moved travelled a distance of x = v.t.
I'd say that the time t' on the moving clock at the end of that journey would be:
\gamma ( t - x.v / c^{2} ) = \gamma ( t - t.v^{2} / c^{2} ) = \gamma t (1 - v^{2} / c^{2} ) = t / \gamma
The difference is therefore \Delta = t - t' = t ( 1 - 1 / \gamma) \approx 1/2t . v^{2} / c^{2} .
When that moving clock stops, there are a number of ticks from the "stationary" clock still travelling to catch up, x/(c-v) = vt/(c-v) worth. Those ticks in transit will, when added to the ticks already received, show that the more time has elapsed has elapsed on the stationary clock, even though that time elapsed at a slower rate.
So Einstein's answer, while possibly not immediately intuitive, is not erroneous.
cheers,
neopolitan
neopolitan
Mar29-09, 11:55 PM
My reference was specifically in relation to Einstein's 1905 paper not any other translation.
In section 4 he wrote -
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
I have to admit that I laughed out aloud at this.
Einstein's paper was written in German. The original text can be seen here (http://de.wikibooks.org/wiki/A._Einstein:_Kommentare_und_Erl%C3%A4uterungen:_Zu r_Elektrodynamik_bewegter_K%C3%B6rper:_Kinematisch er_Teil:_%C2%A74).
The 1920 translation is of the same paper. A translation today (using more modern language) would be a translation of the same paper.
cheers,
neopolitan
DaleSpam
Mar30-09, 12:50 AM
On the assumption that "..the accompanying observer correctly determines that the other clock "physically" runs faster overall." and on the assumption that he is an enquiring scientist is it not possible that he might ask himself what force has made clock B PHYSICALLY run faster than it did before he started moving?
He is an astronaut returning to the planet following turn-around; he 'sees' Earth clocks ticking over at a faster rate than they did before he started accelerating hence he 'sees' shorter Earth seconds than he did before he started moving thus he must also 'see' Earth minutes, hours and days to also 'be' ticking over at a faster rate than they were before he started moving ergo he 'sees' the Earth spinning on its axis and orbiting the sun at a considerably faster rate than it did before he started moving.
Is he not likely to ask himself what physical force has made the planet spin faster on its axis and orbit the sun at a much faster rate than it did before he started his return journey?Certainly. And the answer would be the fictitious forces present in his non-inertial frame.
I don't mind how you use the word "physical", but you need to be self-consistent. You cannot claim that frame-variant quantities, like the rate of a clock, are "physical" and then exclude the frame-variant fictitious forces from being "physical" also. In a non-inertial reference frame fictitious forces can do work, can have potential energy, can cause mechanical stress and strain, and have many other measurable effects.
Although he 'determines' that the Earth clock 'is' running faster than it did before he started moving and that the planet 'is' spinning faster on its axis than they did before he started accelerating is he not likely to realize that this is nothing more than a (mathematically generated) illusion created by his non-inertial motion?Yes, that is why they are called fictitious forces. That is also why he is not likely to try to do the analysis in his non-inertial rest frame, but is more likely to do the analysis in some inertial frame.
You wrote "... all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average." and i agree with that comment; clock B does 'run faster' than A due to the fact that, as Einstein pointed out, clock A runs slower than B however for them to be of the opinion that clock B runs faster than it did before A started moving is erroneous - according to Einstein's section 4 STR.
According to Einstein - clock A ticks over at a slower rate than it did before it started moving NOT that B starts ticking over at a faster rate. Clock A accelerates and it is, according to Einstein, this factor that physically causes it to tick over at the slower rate. There is no force, no action on it's behalf which causes clock B to physically tick over at a faster rate than it did before A started moving.Your explanation is correct only in the inertial reference frame where B is at rest. In other reference frames there will be other explanations. But all reference frames will agree on the conclusion.
cos,
I assume that you are refering to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks" since that section ends with:
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
On the basis that this precisely the comment to which I refer I fail to see how you could possibly be of the opinion that I may not have been '...referring to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks."'
It would be very much appreciated if we could adhere to relevant matters.
Shortly before, in that same section:
"From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2 tv2/c2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."
Now it should be remembered that this is Einstein. If I wrote something similar on this forum, I would probably be appropriatedly chastised for an inaccuracy - perhaps not for being incorrect, but for not clearly stating something.
You may not have noticed but Einstein's comments have been criticized in this forum! Einstein has, somewhat belatedly, been chastised!
The time t is the time occupied in the journey from A to B, in the frame of the clock which remains stationary. According to the stationary clock, the clock which was moved travelled a distance of x = v.t.
And according to the traveler the distance he travels is less than the distance from A to B as measured by the stationary observer.
When that moving clock stops, there are a number of ticks from the "stationary" clock still travelling to catch up, x/(c-v) = vt/(c-v) worth. Those ticks in transit will, when added to the ticks already received, show that the more time has elapsed has elapsed on the stationary clock, even though that time elapsed at a slower rate.
What on Earth does "...there are a number of ticks from the 'stationary' clock still travelling to catch up." mean?
When the moving clock stops, A and B could press switches whereupon both clocks stop ticking so any 'ticks in transit' would be out of luck. Their time will have expired and they can no affect on the times registered by clocks A and B.
So Einstein's answer, while possibly not immediately intuitive, is not erroneous.
I made no suggestion whatsoever that Einstein's answer is erroneous!
Certainly. And the answer would be the fictitious forces present in his non-inertial frame.
My references are to reality and I am of the opinion that fictitious forces do not come under that category.
I don't mind how you use the word "physical", but you need to be self-consistent. You cannot claim that frame-variant quantities, like the rate of a clock, are "physical" and then exclude the frame-variant fictitious forces from being "physical" also. In a non-inertial reference frame fictitious forces can do work, can have potential energy, can cause mechanical stress and strain, and have many other measurable effects.
Yes, that is why they are called fictitious forces. That is also why he is not likely to try to do the analysis in his non-inertial rest frame, but is more likely to do the analysis in some inertial frame.
So if something cannot be logically identified or physically determined it comes under the heading of a 'fictitious force'? It was a fictitious force that many years ago exchanged my tooth for a dime.
The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.
People who believe in God are criticized by others for their faith in a 'fictitious force' yet apparently some people are apparently of the opinion that a non-material 'force' can result in an equal and opposite reaction provided the results supply the solution they seek.
Your explanation is correct only in the inertial reference frame where B is at rest. In other reference frames there will be other explanations. But all reference frames will agree on the conclusion.
Einstein indicated that clock A will lag behind B due to the fact that, whilst it is moving, clock A 'goes more slowly' (ticks over at a slower rate) than clock B.
It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.
C moves to B's location and comes to a stop alongside A and B and finds, much to his consternation, that B does not lag behind A as indicated by his 'calculations' or 'determinations' or 'predictions' but that A lags behind B!
neopolitan
Mar30-09, 04:43 AM
I made no suggestion whatsoever that Einstein's answer is erroneous!
Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.
According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!
HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?
????
What on Earth does "...there are a number of ticks from the 'stationary' clock still travelling to catch up." mean?
When the clocks are not colocated it takes time for the information from one clock to reach the other. The information travels at the speed of light. If the moving clock "looked" back at the stationary clock (as per Einstein's scenario), just before stopping, it would see only the time on the stationary clock that happened, in the moving clock's frame, x'/c ago (where x' is the separation that the moving clock thinks that it has from the stationary clock based on the travelling time). There will be more information still in transit.
Given that we can't agree as to whether you are saying Einstein's maths was erroneous or not, or that what he said matches with his maths, I don't feel this is going anywhere.
If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.
cheers,
neopolitan
C moves to B's location and comes to a stop alongside A and B and finds, much to his consternation, that B does not lag behind A as indicated by his 'calculations' or 'determinations' or 'predictions'
Then why don't you help C with his predictions? Let the movement be sinusoidal, and let the "clock rate" be adjusted by -1/2 v². Sometimes a decent calculation saves many lines of philosophical debate.
"...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."
In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.
No, that's not why they're no longer in synch.
Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.
No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than earth's clock in earth's frame.
When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than earth's clock, he knew all along that the ship's clock ran slower than earth's clock in earth's frame.
The idea (during the astronaut's period of acceleration following turn around) that the stationary clock incurs time contraction (i.e. 'is' ticking over at a faster rate than it was before he accelerated) was, for Einstein, an anathema and it it is his depictions to which I refer not interpretations arrived at by anybody else.The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.
It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.
DaleSpam
Mar30-09, 07:53 AM
My references are to reality and I am of the opinion that fictitious forces do not come under that category.That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.
The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.
It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.
What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not. The reason that the ship's clock readings coincide with the end result of elapsed time is because the ship's clock is local to every relevant event and therefore represents the proper elapsed time for the ship for every event in every frame. That is not true of earth's clock. Earth's clock is local to the departure and return only, so only those readings represent proper time for the earth twin in a different frame. For events not local to earth, the earth clock represents proper time in earth's frame only. Clocks in relative motion only read proper time locally, not at a distance. So an earth clock reading in the ship's frame does not represent the proper time in earth's frame for any event not local to earth, like the ship's turnaround.
If that's what you mean by not being "reality", then just say so and I think everyone would agree.
HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his mathHe got no erroneous answer. All of his math gave correct answers. And it's not contradictory because he didn't confuse reciprocal time dilation between the twins' clocks with the non-symmetrical elapsed time of the clocks.
You would probably be better off if you search for one of his papers or essays written after 1929.
Hi, neopolitan,
I think Einstein's best work was prior to 1929, despite not being perfect.
His 1918 paper on the twins paradox is nothing like the way cos is interpreting it. The only difference between it and standard resolutions is that instead of using an instantaneous turnaround with earth's clock "jumping" ahead suddenly, he uses a realistic acceleration turnaround with earth's clock "running fast" in the ship's frame during the turnaround. It's essentially the same as the standard resolutions, at least as far as this topic is concerned.
I think cos is moving towards something like this:
"if the slowing down of clocks is supposed to real or physical, then something is amiss, and if results (like the twin paradox) suggest that only one clock ran slow, then the mathematics should be suspected, rather than the reality or physical results"
cos,
I am not saying categorically that that is your contention, it is merely what I think you are saying.
However, I should point out that you have to take into account everything in a situation like the twin's paradox. Specifically, you need to consider simultaneity (I say this even though this is not my favoured approach). Both twins will calculate that the other twin's clock ran slow during the inertial phases. What the twins will not agree on is how long those inertial phases lasted.
(I missed this posting; perhaps because it was a response to jtbell.)
I assume that you are here referring to an astronaut's out-and-return journey. You wrote "...during the inertial phases." There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.
So the results will be (time on a slow clock running for a longer time) and (time on a slow clock running for a shorter time). The change in direction was an event that was colocal with the acelerated twin, but not colocal with the twin who was inertial throughout, which means that - taking into account simultaneity - the stationary twin will calculate that the travelling twin turned around later than travelling twin calculated. This is totally in agreement with the fact that the travelling twin's clock ran slow compared to the stationary twin.
"This is totally in agreement with the fact that the travelling twin's clock ran slow compared to the stationary twin." that's what I'm saying!
So if you like, both clocks really ran slow, the travelling twin really turned around later than was said on his clock and at the end of the journey one clock will really show more time elapsed than shown on the other - and both clocks are showing the real time elapsed for that clock.
"...both clocks really ran slow..." In his 1918 article Einstein attempted to overcome the paradox that 'both clocks run slow' suggesting that it is only the clock that experiences a force of acceleration that incurs time dilation not the stationary clock ergo, according to that article which, in my opinion, directly complies with his 1905 depiction of A moving in a polygonal path to B's location, both clocks do NOT 'run slow'.
I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!
You are quite welcome, but you should be aware that I am open-minded on the subject of the meaning of the word "physical". I am willing to take either position for the sake of communication. Also, I suspect (again just guessing) that Einstein's opinion changed after Minkowski.
I would really appreciate it if we could limit the discussion to facts rather than suppositions.
However, since your opinion appears to be firm that frame-dependent quantities can be considered "physical", then it should come as no surprise that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation. The same thing happens with all other frame-variant "physical" quantities like energy, momentum, speed, etc. (e.g. clock A can "physically" have more speed than clock B in one frame and vice versa in another frame).
The idea "that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation.." Is I believe the 'paradox' that Einstein attempted to solve in his 1918 article wherein he presented that it is only the clock that experiences forces of acceleration that ticks over at the slower rate not the clock that has remained inertial thus that, according to that article (which I believe was merely an extension of his section 4 comments), Einstein effectively pointed out that clock B does not tick over at a slower rate than A.
Perhaps you could show me where, in your opinion, Einstein's shows in section 4 STR or his 1918 article that the inertial clock, B, ticks over at a slower rate than A. Prior to section 4 STR he does show that clock A ticks over at a slower rate than clock B in one frame whilst clock B ticks over at a slower rate than clock A in another frame however it is specifically his section 4 depiction to which I refer.
On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!
Mentz114
Mar30-09, 08:39 PM
On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!
You've repeated this a number of times.
So what ? I'm not in the least perturbed. When I look in a mirror left and right are reversed, if I look through a telescope things look nearer. Nothing to lose sleep over.
Then why don't you help C with his predictions? Let the movement be sinusoidal, and let the "clock rate" be adjusted by -1/2 v². Sometimes a decent calculation saves many lines of philosophical debate.
Why should I 'help C with his predictions'?
Why should I let his movement be in the nature of a curve having the form of a sine wave? Why can't he, as most sensible astronaut's would, travel in a direct route to C's location?
Sometimes a 'decent calculation' can create obfuscation.
matheinste
Mar30-09, 08:40 PM
Cos
To observers in relative inertial motion each will see the others clock running slow due to the effects time dilation. This is fundamental to Einstein and SR. In the example you give, Enstein's clock moving in a closed path is non inertial and so factors other than time dilation must be taken into account. The non-inertial clock will show less accumulated time on its return. That is fact. Beacuse it shows a reading which lags behind that of the inertial clock you could perhaps say either that it has ticked slower for the same amount of time or that it has ticked at the same rate for a shorter length of time. I am unsure of your interpretation but I suspect the former would be what you describe as a physical change. Perhaps that is what your question boils down to i.e ticking slower for the same time as the inertial clock or ticking at the same rate as the inertial clock for less time than the inertial clock.
There is no scenario in which two clocks can separate and reunite with both having remained in inertial motion throughout. So the scenario Einstein descibes is not a denial of reciprocal time dilation.
Matheinste.
On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!
As long as you stick to inertial frames, all frames will always agree about what two clocks read when they meet each other (and therefore whose time is behind), in spite of the fact that they may disagree about which clock was ticking slower at a given moment. Are you suggesting otherwise?
neopolitan
Mar30-09, 08:46 PM
There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.
I was perhaps unclear about what I meant about "inertial phase", there are four or five inertial phases and I was only referring to two, the inertial phases in which the twins are not at rest with respect to each other. There are two or three more inertial phases: at rest together before, at rest with respect to each other in the middle and at rest together after. The other phases are when one twin accelerates (first in one direction and then in the other direction ,possibly in two stages, and finally in the first direction again to decelerate). The other twin remains inertial throughout.
"This is totally in agreement with the fact that the travelling twin's clock ran slow compared to the stationary twin." that's what I'm saying!
But my comment was directly after a passage in which I said that during inertial phases (as defined above) both twins' clocks run slow with respect to the other. That is not what you seem to be agreeing to.
I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!
I am going to make a huge assumption here. You are monolingual.
If you were fluently bilingual, or multilingual, you could not possibly believe that a paper could be translated from German into English without being interpreted. A word for word transliteration would be nigh on impossible to read and impossible to understand. What would be easy to comprehend when transliterated from German to English would be the mathematics, which I find rather amusing.
Perhaps I am wrong and you are fluent in German, in which case, you may be better off working directly from the German rather than the 1922 translation by W. Perrett and G.B. Jeffery, which I took to be your source (and this is why I posted words from it earlier, because there are apparently other translations). But so long as you quote English words and claim Einstein wrote them, you are just making yourself look silly.
cheers,
neopolitan
I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!
Physics is not like literature or history, in which "original sources" have primary importance.
With all due respect to Einstein, one should not attach any more weight to his writings about relativity than to those of the many physicists who have refined, tested, and extended his ideas during the past century. His papers are not the last word about SR, and not the "bible" of SR. I consider them to be mainly of historical interest today.
Similarly, we don't consider Newton's "Principia Mathematica" as having precedence over all other works on classical mechanics, nor do we consider Maxwell's works as uniquely defining for classical electrodynamics.
When the clocks are not colocated it takes time for the information from one clock to reach the other.
Nothing that I have written (nor, in my opinion, to which Einstein referred in his section 4 depiction) says anything about the time that it takes for the information from one clock to reach the other!
If the moving clock "looked" back at the stationary clock (as per Einstein's scenario), just before stopping...
To which of Einstein's scenario are you now referring? I can only assume that you are referring to an astronaut who has traveled out into space who, 'just before stopping' (i.e. just before coming to a stop at the end of his outward bound journey) 'looks back' at his twin's clock yet I see nothing in Einstein's section 4 depictio where he refers to that scenario.
In Einstein's initial polygonal line trip the traveler looks ahead to the stationary clock however I am of the opinion that his 'determination' (that B is, as has been claimed, ticking over at a slower rate than his own clock) is based on his calculations not on his perception of what clock B appears to be doing.
it would see only the time on the stationary clock that happened, in the moving clock's frame, x'/c ago (where x' is the separation that the moving clock thinks that it has from the stationary clock based on the travelling time). There will be more information still in transit.
You are, here, apparently referring to light travel time which I thought we had agreed the astronaut allows for!
Given that we can't agree as to whether you are saying Einstein's maths was erroneous or not, or that what he said matches with his maths, I don't feel this is going anywhere.
If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.
My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!
If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.[/QUOTE]
On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.
My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!
No, the fact that one clock lags behind is not proof that it was ticking more slowly--you're forgetting to take into account the relativity of simultaneity (http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html). In some frames clock B may be ticking slower than clock A and yet clock A will still be behind when they meet, because A and B did not start out in sync in the first place in these frames. Consider Einstein's example in section 4 of the 1905 paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/):
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.
Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.
neopolitan
Mar30-09, 10:44 PM
If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.
On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.
Don't you love language?
I agree with Jtbell, at least in part. This is not a physics discussion.
I disagree with Jtbell, at least in part. This is not a philosophy discussion.
Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind - an example, totally not about physics but toally unhinged is here (http://www.geocities.com/Baja/5692/). Your increasing use of bold, and underline, concerns me.
No matter what emphasis you place on an inherently incorrect statement, it will remain an inherently incorrect statement.
If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.
So, I put it to you again, try the maths. The maths worked for Einstein......
Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.
According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!
HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?
[cos] "...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."
In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.
[A168]No, that's not why they're no longer in synch.
I did NOT refer to WHY they're no longer in synch but pointed out that according to Einstein they ARE no longer in synch.
In his 1918 article (which, in my opinion, was effectively an extension of his 1905 section 4 depiction) Einstein points out that the clocks are 'no longer in synch' because one of them (clock A in his section 4 depiction) has undergone acceleration!
You may have your own interpretation of why those clocks ar no longer in synch however I'm referring to Einstein's explanation.
[cos]Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.
No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than earth's clock in earth's frame.
I find it particularly galling that some people take phenomenon out of context.
In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.
When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than earth's clock,
Having come to a stop (analagous to Einstein's section 4 clock A moving to B's location) his clock will, according to Einstein, lag behind the previously synchronous Earth clock.
He allows for light travel time whereupon he eventually notices that the Earth clock is ahead of his own clock (although now ticking over at the same rate as his own clock).
He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.
Alternatively, there could be a clock located at the point where he comes to a stop that is synchronous with the Earth clock (it's mechanism compensates for it's location in a much weaker gravitational tidal area) whereupon he finds that his clock lags behind that clock. He can either assume that this clock physically ticked over at faster rate than it did before he started moving toward it (in total contradiction of what his calculations 'showed' him is taking place) OR that, as Einstein suggested, his clock was 'going more slowly' than it was before he left the planet ergo is ticking over at a slower rate than this clock.
he knew all along that the ship's clock ran slower than earth's clock in earth's frame.
Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.
[QUOTE=Al68;2139532]The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.
The relative rate may well be 'frame-dependent' on the basis of the calculations made by observers in those frames however the physical rate of clocks is not frame-dependant. All clocks will tick over at their own rate regardless of the opinions expressed, or determinations arrived at, by other frames.
Nothing changed with Earth clock during the turn-around nor when the astronaut previously accelerates away from the planet nor when he was moving away at uniform vleocity nor when he slows down nor when he turns his ship around nor when he accelerates back to the planet nor when he moves with uniform velocity nor when he decelerates prior to landing!
Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!
[QUOTE=Al68;2139532]It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.
That's precisely what I'm saying!
That clock's rate of operation does not change!
Ergo when a traveler 'determines' that the inertial clock 'is' running slower or faster than his own clock he is deluding himself if he believes that the inertial clock's rate of operation has physically changed in lieu of accepting that it is his clock's rate of operation that has changed.
When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.
In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.
He is obviously not saying that the accelerated clock is ticking more slowly at every instant, since at any given instant you can pick an inertial frame where the accelerated clock has a smaller velocity and thus is ticking faster. Presumably in section 4 he's talking about something like the average rate of ticking of the accelerated clock, either between the time it departs from and returns to a non-accelerating clock, or over the course of a complete orbit in the case of the clock which is accelerating because it's at the equator of a rotating sphere. All inertial frames will agree in these cases that the average rate of ticking of the accelerated clock is slower, even though in a given inertial frame there may be periods of time where it is ticking faster.
[cos]My references are to reality and I am of the opinion that fictitious forces do not come under that category.
That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.
Does your comment "That is fine by me." mean that you agree with me that fictitious forces do not come under the heading of reality?
[cos]The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.
This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.
In my opinion this means that unless I accept the 'reality' of purely hypothetical, non-existent, fictitious forces I cannot, in a non-inertial frame, do any analysis.
[cos]It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.
No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.
What 'second leg of the trip'?
A accelerates toward and comes to a stop alongside B. There is only one leg of that trip unless of course you are referring to periods of acceleration as being 'legs' of that trip.
A does not, from C's point of view 'travel at a faster speed than B'.
In C's frame A decelerates and comes to a stop alongside C whilst B keeps moving at it's original speed ergo B is moving whilst A has 'come to a stop'.
On the basis that A has come to a stop alongside C it cannot, from C's point of view, be experiencing any time dilation! A is then ticking over at the same rate as C!
Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!
This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.
A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?
Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!
What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not.
According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!
According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.
According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.
Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind -
In my case it is a result of sheer frustration.
Correspondence terminated.
neopolitan
Mar31-09, 12:55 AM
In my case it is a result of sheer frustration.
Correspondence terminated.
Desperation perhaps.
My final advice to you may sound familiar: try working through the maths.
Final comment: the (applied) mathematics does actually reflect the reality. The reality and the mathematics underlying the physics involved are not separate such that one can be ignored in favor of the other, irrespective of what anyone may say, be it Einstein, Gandhi, Queen Elizabeth, Jesus, Mohammed, Buddha or, believe it or not, you.
cheers,
neopolitan
According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!
According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.
Again, on average only. At any given instant, there is no objective truth about which clock is ticking slower, it's obvious Einstein would not disagree with this since the basic postulate of relativity is that the laws of physics are the same in all frames, and basic calculations show that all inertial frames will agree about average rates of ticking between two points where clocks meet, while disagreeing about instantaneous rates of ticking.
He is obviously not saying that the accelerated clock is ticking more slowly at every instant, since at any given instant you can pick an inertial frame where the accelerated clock has a smaller velocity and thus is ticking faster. Presumably in section 4 he's talking about something like the average rate of ticking of the accelerated clock, either between the time it departs from and returns to a non-accelerating clock, or over the course of a complete orbit in the case of the clock which is accelerating because it's at the equator of a rotating sphere. All inertial frames will agree in these cases that the average rate of ticking of the accelerated clock is slower, even though in a given inertial frame there may be periods of time where it is ticking faster.
Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving.
Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.
His observations would not negate Einstein's comment that, whilst it is moving, clock A will 'go more slowly' than it did before it started moving.
matheinste
Mar31-09, 07:56 AM
Cos.
As nothing anyone says seems to be of any help, perhaps the only way forward is for you to undertake an even deeper study of the subject of relativity and then you may be able to answer your own question.
Matheinste.
DaleSpam
Mar31-09, 08:04 AM
In my opinion this means that unless I accept the 'reality' of purely hypothetical, non-existent, fictitious forces I cannot, in a non-inertial frame, do any analysis.That is correct. If you want to use a non-inertial frame then you must also use fictitious forces, they go together. The fictitious forces are every bit as "real" and "physical" as their corresponding non-inertial frames. Therefore, if you object to fictitious forces then you cannot use non-inertial frames.
What 'second leg of the trip'?Isn't A the travelling twin and B the home twin of a standard twins scenario? If so, then A clearly has two legs of his trip, the outbound and the inbound leg. If this is not a standard twins scenario then what is the scenario? There are too many A and B scenarios in Einstein's paper for me to be sure which one you mean.
Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving.
As Einstein makes clear in sections 1 and 2 of the 1905 paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/), in order to talk about any inertial frame you must at least hypothetically be able to imagine a network of rulers and clocks at rest in that frame which can be used to assign coordinates to events. Of course, once we accept relativity we can use other types of observations to figure out what such a network would measure even if we haven't actually physically constructed it.
Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.
Sure it does, it gives you the correct predictions about what the clocks read when they meet, given that frame's definition of simultaneity which tells you their initial times at the moment before clock A is accelerated towards clock B. There is no "objective" sense in which they both read the same time at the moment before A was accelerated, that is only true in one particular frame, the frame where they were both initially at rest before the acceleration. In other frames, A and B were initially out-of-sync, and thus B could be ahead of A when they meet even though B was the one ticking more slowly after A accelerated.
His observations would not negate Einstein's comment that, whilst it is moving, clock A will 'go more slowly' than it did before it started moving.
Einstein was only saying A goes more slowly in one particular frame, the "stationary frame" K. The observations in another frame certainly negate your idea (not Einstein's) that A will "go more slowly" in some objective sense, since they show that it is equally valid to say that A ticks more quickly after it accelerates (and in this frame, it stops moving when it accelerates). If both frames make exactly the same physical predictions about what A and B will read when they meet, what possible basis could there be for considering one frame's perspective more valid than any other's? If you think Einstein would ever consider one frame more valid than another, you need to re-read section 2 of the paper, the whole point of the first postulate is that all inertial frames are equally valid (you might also re-read section 1 which shows there can be no objective truth about whether the two clocks are synchronized prior to A's acceleration).
I did NOT refer to WHY they're no longer in synch but pointed out that according to Einstein they ARE no longer in synch.That's right.
In his 1918 article (which, in my opinion, was effectively an extension of his 1905 section 4 depiction) Einstein points out that the clocks are 'no longer in synch' because one of them (clock A in his section 4 depiction) has undergone acceleration!That's right.
In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.That's right except that it's not a matter of opinion that "the other clock 'is' ticking over at a slower rate than his own clock".Having come to a stop (analagous to Einstein's section 4 clock A moving to B's location) his clock will, according to Einstein, lag behind the previously synchronous Earth clock.That's right.
He allows for light travel time whereupon he eventually notices that the Earth clock is ahead of his own clock (although now ticking over at the same rate as his own clock).
That's right.
He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.Or he can realize that the earth clock was ticking slower than his in the ship's frame, and that after he comes to rest at the turnaround point his clock reads less time than earth's. Alternatively, there could be a clock located at the point where he comes to a stop that is synchronous with the Earth clock (it's mechanism compensates for it's location in a much weaker gravitational tidal area) whereupon he finds that his clock lags behind that clock. He can either assume that this clock physically ticked over at faster rate than it did before he started moving toward it (in total contradiction of what his calculations 'showed' him is taking place) OR that, as Einstein suggested, his clock was 'going more slowly' than it was before he left the planet ergo is ticking over at a slower rate than this clock.Or he can correctly conclude that the clock at the turnaround point represents proper time in earth's frame, and that the earth clock cannot read the same as the clock at the turnaround point in the ship frame because they read the same in earth's frame.Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.That's not what Einstein said. The clock goes the same speed it always did in its own rest frame. Nothing changed with Earth clock during the turn-around nor when the astronaut previously accelerates away from the planet nor when he was moving away at uniform vleocity nor when he slows down nor when he turns his ship around nor when he accelerates back to the planet nor when he moves with uniform velocity nor when he decelerates prior to landing!
Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!That's correct. The same can be said of the ship's clock. Nothing physically happened to either clock.
When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.Earth's clock did tick faster than the ship's clock in earth's frame, but not because anything physically happened to either clock.
A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?It will be slower than the ship's clock in the ship's frame all the way up until the ship accelerates. After the ship comes to a stop, the earth clock will read more than the ship's. In Einstein's 1918 paper, the earth clock runs very fast in the ship's frame during the turnaround, enough so that it starts out reading less than the ship clock, and ends up reading more than the ship clock.
Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!Reality, but he doesn't confuse that with the greater lapse in proper time by the earth clock.According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!I misspoke. I should have said reciprocal.
According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.This is true in earth's frame, which is the frame both twins end up in.
According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest. That is only true if you're referring specifically to earth's frame. Which is a reasonable thing to do, since that's the frame in which the twins will reunite and compare clocks.
Another thing to remember is that in STR, two clocks separated by a distance that are synchronized in one frame (like an earth clock and one at the turnaround point at rest with earth) are not in synch in any other frame. So the two clocks would have different readings in the ship frame. It is the clock local to the ship that reads the proper time of the event in earth's frame. The earth clock reading in the ship's frame does not represent the proper time of the turnaround event in earth's frame. The math is not erroneous, unless it's misapplied to suggest that the time on a non-local clock in relative motion represents proper time for any event in the frame of that clock.
It seems that perhaps you are using the word "reality" to mean clock readings that represent the proper time in each frame, and "illusion" to mean clock readings that do not represent proper time. If that's the case, then what you're calling reality is called proper time in SR, and what you're calling illusion is called coordinate time. It's coordinate time that is frame dependent and reciprocal, not the proper time elapsed between events. Proper time is not frame dependent.
DaleSpam
Mar31-09, 06:26 PM
It seems that perhaps you are using the word "reality" to mean clock readings that represent the proper time in each frame, and "illusion" to mean clock readings that do not represent proper time. If that's the case, then what you're calling reality is called proper time in SR, and what you're calling illusion is called coordinate time. It's coordinate time that is frame dependent and reciprocal, not the proper time elapsed between events. Proper time is not frame dependent.I think you are correct in this. It is difficult to know since cos has not been completely explicit, but I believe that he most commonly uses the word "reality" to refer to frame-invariant measurements whereas the word "physical" applies to frame-variant measurements in inertial frames and "illusion" refers to frame-variant measures in non-inertial frames. I think that is reasonable usage since those terms are not well-defined.
cos, can you confirm that usage or would you prefer to amend it?
Again, on average only. At any given instant, there is no objective truth about which clock is ticking slower, it's obvious Einstein would not disagree with this since the basic postulate of relativity is that the laws of physics are the same in all frames, and basic calculations show that all inertial frames will agree about average rates of ticking between two points where clocks meet, while disagreeing about instantaneous rates of ticking.
"At any given instant" neither of the clocks are ticking. I agree wholeheartedly.
When Einstein wrote that the accelerated clock 'must go more slowly' than the at rest clock to what was he referring?
I assume that he was talking about the slower average rate of the accelerated clock as compared to the average rate of the stationary clock.
That is correct. If you want to use a non-inertial frame then you must also use fictitious forces, they go together. The fictitious forces are every bit as "real" and "physical" as their corresponding non-inertial frames. Therefore, if you object to fictitious forces then you cannot use non-inertial frames.
In special theory Einstein points out that because we cannot determine any form of absolute rest ("...the phenomena of electrodynamics as well as of mechanics possess no properies corresponding to the idea of [same]") hence "...an absolutely sttionary space..." can be ignored with respect to ".. the view here to be developed."
Some authors point out that because we cannot detect an 'edge' to the universe then there is no 'edge' in accordance with the special theory-quantum physics basis that 'observation creates reality'.
Other than it's 'effect' on other objects this fictitious force cannot be detected
What is that creates this 'fictitious force' that cannot be detected - a fictitious force generator that, itself, cannot be detected?
What fuels this fictitious force generator? Ex nihilo gas?
In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.
Isn't A the travelling twin and B the home twin of a standard twins scenario? If so, then A clearly has two legs of his trip, the outbound and the inbound leg. If this is not a standard twins scenario then what is the scenario? There are too many A and B scenarios in Einstein's paper for me to be sure which one you mean.
That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.
In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.
"At any given instant" neither of the clocks are ticking. I agree wholeheartedly.
You can certainly talk about instantaneous rate of ticking, just like you can talk about instantaneous velocity; by considering average rate of ticking/average speed over some finite time interval, and then considering the limit as the size of the time interval approaches zero.
In any case, we don't have to worry about instantaneous quantities if we just consider segments of the non-inertial clock's worldline in which it is traveling at constant velocity, like a single "leg" of the non-inertial twin's journey in the twin paradox, or the time interval where clock A is moving at constant velocity towards clock B after having been accelerated in section 4 of Einstein's 1905 paper. Would you dispute that for any such segment, there is no objective truth about whether the clock that was accelerated is ticking faster or slower than the clock that wasn't?
When Einstein wrote that the accelerated clock 'must go more slowly' than the at rest clock to what was he referring?
I assume that he was talking about the slower average rate of the accelerated clock as compared to the average rate of the stationary clock.
Well, if you're just talking about average rate of ticking for a non-inertial clock between the times it departs from and returns to an inertial clock, then you aren't saying anything controversial if you say that the non-inertial clock has a slower average rate of ticking between these events, since this is true in all frames. I thought you were saying something more, that the clock A in his example in section 4 was objectively ticking slower than clock B during the after it was accelerated to the time it met clock B; that would be incorrect, but if you didn't mean to suggest this, please clarify.
[cos]Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.
Sure it does, it gives you the correct predictions about what the clocks read when they meet, given that frame's definition of simultaneity which tells you their initial times at the moment before clock A is accelerated towards clock B.
Although the frame to which you refer may be able to determine 'correct predictions' I refuse to accept that his observations will have any physical affect whatsoever on clock A's rate of operation! His observations only provide him with an appearance of what that clock seems to be doing. His observations do not make that clock physically tick over at a faster or slower rate.
There is no "objective" sense in which they both read the same time at the moment before A was accelerated, that is only true in one particular frame, the frame where they were both initially at rest before the acceleration. In other frames, A and B were initially out-of-sync, and thus B could be ahead of A when they meet even though B was the one ticking more slowly after A accelerated.
I wrote -
"Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving."
Apart from observers A and B there are no other observers who can determine that A and B are 'initially out-of-synch'.
It is observer A's point of view (determinations) whilst he is moving to which my posting refers not to any other observer's points of view!
Einstein was only saying A goes more slowly in one particular frame, the "stationary frame" K.
On the basis that A arrives at Bs location to find that his clock lags behind B he is fully entitled to be of the opinion that this was due to the fact that, as Einstein pointed out, his clock 'went more slowly' (i.e. ticked over at a slower rate) than B.
His alternative is to assume that clock B physically ticked over at a faster rate than it did before he started moving however on the basis that, in my opinion, his actions can have absolutely no physical affect whatsoever on the rate of operation of that clock A can only conclude that his assumption is erroneous!
The observations in another frame certainly negate your idea (not Einstein's) that A will "go more slowly" in some objective sense, since they show that it is equally valid to say that A ticks more quickly after it accelerates (and in this frame, it stops moving when it accelerates). If both frames make exactly the same physical predictions about what A and B will read when they meet, what possible basis could there be for considering one frame's perspective more valid than any other's? If you think Einstein would ever consider one frame more valid than another, you need to re-read section 2 of the paper, the whole point of the first postulate is that all inertial frames are equally valid (you might also re-read section 1 which shows there can be no objective truth about whether the two clocks are synchronized prior to A's acceleration).
There are, in this otherwise empty universe, no observers in any other frame however even if there were then their observations do NOT negate my idea in the same way that my observations have no affect whatsoever on their 'ideas' or determinations!
On the basis that "...the whole point of the first postulate is that all inertial frames are equally valid." then that other observer should be able to accept that my observations are just as valid as his observations ergo that his observations do not negate mine!
In section 4 Einstein stipulates that the two clocks are synchronised prior to A's acceleration.
Having read, and fully accepted, special theory your observer could realize that whilst in his opinion A and B are seemingly not synchronized he should be able to apply special theory thus determine that in their reference frame they are synchronized thus that it is only his relative rate of travel to that system which has made them appear not to be synchronized.
He therefore cannot believe that his relative rate of travel has physically caused them to not be synchronous in their own reference frame!
I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/
I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.
I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/
I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.
In my browser it appears that the url in my post is not coming through properly. the missing word is "Articles"
Although the frame to which you refer may be able to determine 'correct predictions' I refuse to accept that his observations will have any physical affect whatsoever on clock A's rate of operation! His observations only provide him with an appearance of what that clock seems to be doing. His observations do not make that clock physically tick over at a faster or slower rate.
The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking, if "physical" is taken to mean something objective that doesn't depend on an arbitrary choice of coordinate system (which is how physicists usually use the word 'physical'). Similarly, there is no "physical" truth about which of two objects has a greater x-coordinate; it depends on what coordinate system you use, where you place the origin and how you orient the x-axis of that system. Perhaps you are just using a different definition of "physical"? Would you say that a "physical" truth need not be frame-invariant, but can be relative to one's choice of coordinate system. If so, I would certainly agree that in the frame where A and B were initially at rest, it is a physical truth that A ticked more slowly after accelerating. But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.
I wrote -
"Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving."
Apart from observers A and B there are no other observers who can determine that A and B are 'initially out-of-synch'.
It is observer A's point of view (determinations) whilst he is moving to which my posting refers not to any other observer's points of view!
Of course, an "observer" is just a shorthand for talking about a certain coordinate system; in reality, an intelligent observer is perfectly capable of determining the coordinates of events in a system other than his own rest frame. However, if you are only talking about what's true in the frame where A and B were initially at rest, I agree that in this frame A was ticking more slowly after accelerating.
On the basis that A arrives at Bs location to find that his clock lags behind B he is fully entitled to be of the opinion that this was due to the fact that, as Einstein pointed out, his clock 'went more slowly' (i.e. ticked over at a slower rate) than B.
Only if he acknowledges that this "fact" is specific to a particular (arbitrary) choice of coordinate system, just like the "fact" that A's velocity increased rather than decreased after accelerating, or the "fact" that A may have had a greater x-coordinate than B before accelerating due to a particular choice of how to orient the x-axis of whatever coordinate system he chose.
His alternative is to assume that clock B physically ticked over at a faster rate than it did before he started moving
There is no inertial frame where B was ticking faster than A before A accelerated, so this has nothing to do with what I was arguing.
There are, in this otherwise empty universe, no observers in any other frame however even if there were then their observations do NOT negate my idea in the same way that my observations have no affect whatsoever on their 'ideas' or determinations!
On the basis that "...the whole point of the first postulate is that all inertial frames are equally valid." then that other observer should be able to accept that my observations are just as valid as his observations ergo that his observations do not negate mine!
Again, these are not physical "observations" as most physicists would define the term; you're not talking about what the observer sees with their eyes (i.e. local facts about when light from various events reaches their position), but about the coordinates they assign to events using certain calculations. For example, if when my clock reads 20 seconds I see the light from an explosion, that is a local physical fact which all frames agree occurred. Likewise, if the explosion happened next to the 5 light-second mark on my ruler, and I am next to the 0 light-second mark on my ruler, those are also local physical facts. On the other hand, if I say that the light from the explosion must have taken 5 seconds to reach me and therefore must have been simultaneous with the event of my clock reading 15 seconds even though I didn't see it until later, that is a calculation based on certain assumptions about the coordinate system I want to use, I could equally well use some different assumptions and calculate the explosion happened simultaneously with my clock reading 14 seconds or 16 seconds.
But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower, or which events were simultaneous, or which event had a greater x-coordinate. If that's all you're saying then I would agree.
In section 4 Einstein stipulates that the two clocks are synchronised prior to A's acceleration.
He specifically stated that this was only true relative to one particular choice of coordinate system: "If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous"
Having read, and fully accepted, special theory your observer could realize that whilst in his opinion A and B are seemingly not synchronized he should be able to apply special theory thus determine that in their reference frame they are synchronized thus that it is only his relative rate of travel to that system which has made them appear not to be synchronized.
He therefore cannot believe that his relative rate of travel has physically caused them to not be synchronous in their own reference frame!
Of course I was never arguing that they were not synchronized in their own reference frame, just that this is not an objective "physical" truth. According to the usual way of speaking, there is no physical truth about whether they were synchronized or not, because simultaneity is a coordinate-dependent quantity. But as I said, maybe you are using a different definition of "physical truth" from the usual one in which there can be "physical truths" about coordinate-dependent notions like which of two objects has a greater x-coordinate.
DaleSpam
Mar31-09, 10:44 PM
In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.
That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.
In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.
In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.
That's right except that it's not a matter of opinion that "the other clock 'is' ticking over at a slower rate than his own clock".
Semantics! The astronaut makes his calculations as a result of which he is of the opinion (or 'accepts' or 'believes') that this is taking place. His opinion is that it is taking place. He is entitled to be of that opinion!
He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.
Or he can correctly conclude that the clock at the turnaround point represents proper time in earth's frame, and that the earth clock cannot read the same as the clock at the turnaround point in the ship frame because they read the same in earth's frame.
Having arrived at the turnaround point thus having obviously come to a stop alongside a clock (B') at that location (which he knows to be synchronous with the Earth clock) he finds that his clock lags behind that clock.
It makes no difference whatsoever if, during that trip, he is of the opinion that B and B' are no longer synchronized on the basis that, having learned STR he ca determine that in their reference frame they are synchronized.
During that trip he determines that B' is ticking over at a slower rate than his clock whereupon he predicts that B' will resultantly lag behind his own clock yet he arrives at that location to find that B' does not lag behind his clock but that his clock lags behind B'.
Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.
That's not what Einstein said. The clock goes the same speed it always did in its own rest frame.
The clock appears to be ticking over at the same rate as it always has and this determination is based on the fact that there is no evidence - no internal dynamic experiment that he can conduct - that indicates otherwise however having arrived at the location of B' and found that his clock lags behind that clock he can conclude that this is due to the fact that, as Einstein stated, his clock 'went more slowly' than it did before he left the planet.
In his 1918 article (which I believe was merely an extension of his section 4 STR depictions) Einstein pointed out that it is ONLY the clock that experiences forces of acceleration (i.e. his section 4 clock A) that incurs a variation in it's rate of operation (a slower tick rate) NOT the unaccelerated inertial reference frame clock (i.e. his section 4 clock B).
He would, I believe, have been appalled if anyone had suggested (as do some people) that the accelerated clock does not incur time contraction but that the unaccelerated clock incurred time contraction!
Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!
That's correct. The same can be said of the ship's clock. Nothing physically happened to either clock.
The ship's clock accelerated; the Earth clock did not! According to Einstein's 1918 extension of his section 4 depiction - the accelerated clock ticks over at a slower rate than the unaccelerated clock and it is for that reason, according to Einstein, that the unaccelerated clock ticks over at a slower rate than it did before it started accelerating and at a slower rate than the unaccelerated clock.
When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.
Earth's clock did tick faster than the ship's clock in earth's frame, but not because anything physically happened to either clock.
This is, of course reciprocal. The ship's clock can tick slower than the Earth clock in the ship's frame. The ship's clock has. as Einstein pointed out, accelerated thus it is, according to Einstein, the accelerated ship's clock that incurs time dilation - the Earth clock does not incur time contraction.
A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?
It will be slower than the ship's clock in the ship's frame all the way up until the ship accelerates. After the ship comes to a stop, the earth clock will read more than the ship's.
(In an attempt to overcome confusion on my behalf I assume that when you say that the ship accelerates it is incurring negative acceleration i.e. it is slowing down.)
I've seen and heard of some fantastic claims but this one is a beauty.
The astronaut is moving at a velocity that generates a gamma factor of 400 000. He 'sees' or 'determines' that his clock is ticking over at the rate of 400 000 seconds for each of clock B' seconds (i.e. B is ticking over at a slower rate than his clock) but at the very moment that he puts his foot on the gas pedal to power up his retrorockets clock B stops
ticking over at that slower rate and instantaneously starts ticking over the faster rate of 400 000 seconds for each of his seconds. is it not possible that he would believe that such an enormous rate of instantaneous reversal would have some affect on that clock's mechanism?
That clock instantaneously reverses its rate of operation from being 400 000 times slower than his clock to being 400 000 times faster?
If you believe that I've got a bridge you might be interested in buying.
Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!
Reality, but he doesn't confuse that with the greater lapse in proper time by the earth clock.
If you know somebody who believes that is reality please let him know that I've got other bridges for sale.
According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.
This is true in earth's frame, which is the frame both twins end up in.
I don't care in which frame the observations are made. In my opinion nothing that any frame 'observes' can physically affect the rate of operation of any clock!
The astronaut comes to a stop alongside clock B' and is then 'in the Earth's frame'. He sees that his clock lags behind B' and on the assumption that he does not believe that B' was ticking over at the rate of 1 second for each of his own 400 000 seconds and that it instantaneously reverts to 400 000 seconds for each of his seconds I do not believe that any sensible person would believe that what they 'determined' was reality!
According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.
That is only true if you're referring specifically to earth's frame. Which is a reasonable thing to do, since that's the frame in which the twins will reunite and compare clocks.
See above.
Another thing to remember is that in STR, two clocks separated by a distance that are synchronized in one frame (like an earth clock and one at the turnaround point at rest with earth) are not in synch in any other frame.
This has been covered above.
It seems that perhaps you are using the word "reality" to mean......
I am using the word 'reality' in the same way as did Einstein in section 4 wherein he wrote that a clock at the equator "...must go more slowly..." than a clock at one of the poles. I don't care which frame makes the observation or determination; none of their findings will have any affect whatsoever on the tick rate of that clock.
I think you are correct in this. It is difficult to know since cos has not been completely explicit, but I believe that he most commonly uses the word "reality" to refer to frame-invariant measurements whereas the word "physical" applies to frame-variant measurements in inertial frames and "illusion" refers to frame-variant measures in non-inertial frames. I think that is reasonable usage since those terms are not well-defined.
cos, can you confirm that usage or would you prefer to amend it?
I am saying that because, according to Einstein in section 4 STR, a clock at the equator 'must go more slowly' than a clock at one of the poles then a person located at the equator could be of the opinion that Einstein may have ben right; that his clock is ticking over at a slower rate than a polar clock.
I am further saying that because of Einstein's analogy to a clock (A) that has been made to travel in a polygonal line to another clock's location (B) then A will also 'go more slowly' than that 'at rest' clock.
Translate those comments into your own 'frame'. I fail to see that they are overly complicated for you.
In his 1918 article (which I believe was merely an extension of his section 4 STR depictions) Einstein pointed out that it is ONLY the clock that experiences forces of acceleration (i.e. his section 4 clock A) that incurs a variation in it's rate of operation (a slower tick rate) NOT the unaccelerated inertial reference frame clock (i.e. his section 4 clock B).
He would, I believe, have been appalled if anyone had suggested (as do some people) that the accelerated clock does not incur time contraction but that the unaccelerated clock incurred time contraction!
No one has suggested that that the unaccelerated "inertial reference frame clock" experiences a variation in its rate of ticking, at least not in any inertial reference frame (if we consider non-inertial coordinate systems, virtually anything can be true about the rate of ticking of any clock). The point is just that although the accelerated clock does change its rate of ticking in almost every inertial frame (except the frame where its direction changes but its speed stays the same), there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after. Do you disagree with this?
DaleSpam
Apr1-09, 08:03 AM
cos, Einstein never used the word "physical" to refer to time dilation and he never used the word "real" or "illusion" at all. So the question remains, what do you mean by those words? I have suggested what I think you mean (although you are not consistent in your usage), but you haven't even had the courtesy to say yes or no to it. I don't care how you use those words, but just define them and use them consistently so that we can communicate.
I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/
I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.
Your contribution to the discussion may have been unneccesary if you had gone through previous postings wherein I made no suggestion that relativity does not work.
cos post;
In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve
with constant velocity until it returns to A, the journey lasting
t seconds, then by the clock which has remained at rest the
travelled clock on its arrival at A will be a .5tv^2/c^2 second
slow. Thence we conclude that a balance-clock at the equator must
go more slowly, by a very small amount, than a precisely similar
clock situated at one of the poles under otherwise identical
conditions."
What do people think he meant by the phrase "...must go more
slowly..."?
Does anyone agree that he meant that the moving clock will tick
over at a slower rate than (i.e. incur time dilation relatively
to) the other clock?
********************
On the (probably erroneous) basis that some people may agree that
he did I follow that up with the question - On the basis of his
depiction of a clock that is made to move in a closed curve around
another clock is it correct for me to assume that Einstein meant
that the clock that is moving in a closed curve will “go more
lowly”(i.e. tick over at a slower rate) than the clock “which has
remained at rest.”?
The A clock must accelerate to leave the B clock, move at a
constant speed for most of the path, then decelerate to reunite
with the B clock. Since A initiated the trip, and traveled a
greater distance than B, in the same amount of elapsed B time, A
would have an average speed greater than B. Time dilation is a
functon of speed, therefore the A clock experiences more time
dilation than B. When reunited, A clock is lagging behind B clock.
This is not about perception of clocks, but the physics of clock
function according to light propagation. Each will
observe/perceive the others clock to be running faster or slower,
depending on direction of motion.
This is a repeat of my reply for the your first thread.
[quote=phyti;1913665]Here is a quote from the Max Born book, page 257, which you have (A and B swapped).
"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."
Because A & B are synchronized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.[quote]
I can only add, time dilation is a real factor affecting particle accelerators and gps systems.
The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking....
So when Einstein wrote that clock A 'must go more slowly' than clock B he was not describing a 'physical' fact (or truth)?
But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.
By the comment ".... A ticked more rapidly after accelerating." I take it that you mean that A ticked more rapidly whilst it was moving with uniform velocity (i.e. after accelerating)?
By "ticked more rapidly" did you mean that A ticks over at a faster rate than it did before it accelerated (or whilst it is accelerating) or that because A, applying the Lorentz transformations, 'determines' that B is ticking over at a slower rate than itself?
The idea of time contraction was, I believe, an unacceptable concept as far as Einstein was concerned.
You wrote, below, "...I agree that in this frame A was ticking more slowly after accelerating." It was 'this frame' to which I have consistently been referring.
Of course, an "observer" is just a shorthand for talking about a certain coordinate system; in reality, an intelligent observer is perfectly capable of determining the coordinates of events in a system other than his own rest frame. However, if you are only talking about what's true in the frame where A and B were initially at rest, I agree that in this frame A was ticking more slowly after accelerating.
"After accelerating"? I am of the opinion that the v in Einstein's equation .5tv^2/c^2 can be his instantaneous velocity whilst accelerating.
The slower rate of operation of clock A is not affected by the fact that he takes his foot off the gas pedal at any given instant.
But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower......
So A, having arrived at B's location, is, apparently, entitled to be of the opinion that his clock lags behind B due to the fact that whilst he was moving his clock was 'going more slowly' (i.e. ticking over at a slower rate) than B?
In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.
That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.
They apparently not only assumed that I understood Newtonian mechanics but that the potentially millions of other people who were to read those books and articles also understood Newtonian mechanics!
Somewhat presumptuous of them wouldn't you agree?
You state that fictitious forces are not 'Einstein'. Do you mean that they are not special theory?
If they are incorporated in STR perhaps you would be so kind as to point out where in STR Einstein refers, or alludes to, fictitious forces?
That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.
In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.
Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.
There is NO observer C in Einstein's section 4 STR depiction and the introduction of same is nothing more than a deliberate obfuscation!
Determinations made by a hypothetical observer C can have no effect whatsoever on what is taking place as far as A or B are concerned nor on the rates of operation of their clocks!
In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.
That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.
They apparently not only assumed that I understood Newtonian mechanics but that the potentially millions of other people who were to read those books and articles also understood Newtonian mechanics!
On the basis that a majority of those items were popularization works this attitude would be somewhat presumptuous of those authors wouldn't you agree?
You state that fictitious forces are not 'Einstein'. Do you mean that they are not special theory?
If they are incorporated in STR perhaps you would be so kind as to point out where in STR Einstein refers, or alludes to, fictitious forces?
That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.
In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.
Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.
There is NO observer C in Einstein's section 4 STR depiction and the introduction of same is nothing more than a deliberate obfuscation!
Determinations made by a hypothetical observer C can have no effect whatsoever on what is taking place as far as A or B are concerned nor on the rates of operation of their clocks!
No one has suggested that that the unaccelerated "inertial reference frame clock" experiences a variation in its rate of ticking, at least not in any inertial reference frame (if we consider non-inertial coordinate systems, virtually anything can be true about the rate of ticking of any clock). The point is just that although the accelerated clock does change its rate of ticking in almost every inertial frame (except the frame where its direction changes but its speed stays the same), there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after. Do you disagree with this?
Some people insist that after A accelerates (and is then moving with uniform velocity toward B) observer A 'determines', in accordance with the Lorentz transformations, that B is ticking over at a slower rate than it was before A started moving.
I wholeheartedly agree that "...there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after." The point that I'm trying to make is that irrespective of what those frames 'say' or 'determine' their observations have absolutely no affect whatsoever on clocks A or B!
As I have also pointed out, the systems that Einstein depicted could be contained in an otherwise empty universe in which there are obviously no other frames!
cos, Einstein never used the word "physical" to refer to time dilation and he never used the word "real" or "illusion" at all. So the question remains, what do you mean by those words? I have suggested what I think you mean (although you are not consistent in your usage), but you haven't even had the courtesy to say yes or no to it. I don't care how you use those words, but just define them and use them consistently so that we can communicate.
It is not important what I think about the words 'physical' or 'real' but what Einstein meant by the words 'must go more slowly'!
I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowly (i.e. ticks over at a slower rate) than a clock at one of the poles or, analogously, than a clock around which it has moved in a closed curve or, analogously, relative to which it has moved in any polygonal line including it's original trip to B's location.
What do you believe he meant by the words 'must go more slowly'?
So when Einstein wrote that clock A 'must go more slowly' than clock B he was not describing a 'physical' fact (or truth)?
Not if "physical truth" is defined to mean something that is true regardless of your choice of conventions about coordinate systems, and as I said before, this is how most physicists nowadays use the word "physical". If you want to use a different definition that's fine, it's just semantics, but I would ask that you spell out what you mean by physical. That's what DaleSpam asked you in post #90 above, and I also asked you about this in post #85 which you were responding to here:
The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking, if "physical" is taken to mean something objective that doesn't depend on an arbitrary choice of coordinate system (which is how physicists usually use the word 'physical'). Similarly, there is no "physical" truth about which of two objects has a greater x-coordinate; it depends on what coordinate system you use, where you place the origin and how you orient the x-axis of that system. Perhaps you are just using a different definition of "physical"? Would you say that a "physical" truth need not be frame-invariant, but can be relative to one's choice of coordinate system? If so, I would certainly agree that in the frame where A and B were initially at rest, it is a physical truth that A ticked more slowly after accelerating. But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.
Could you please answer these questions? Specifically, do you want to define "physical" differently from how most physicists define it, so that it no longer implies coordinate-invariance? If so, do you acknowledge that under such a nonstandard definition, there could also be a "physical truth" about which of two objects has a greater x-coordinate, even though this truth can obviously only be decided relative to a particular (arbitrary) choice of how to orient our coordinate axes?
By the comment ".... A ticked more rapidly after accelerating." I take it that you mean that A ticked more rapidly whilst it was moving with uniform velocity (i.e. after accelerating)?
Yes, in the frame where it came to rest after accelerating.
By "ticked more rapidly" did you mean that A ticks over at a faster rate than it did before it accelerated (or whilst it is accelerating) or that because A, applying the Lorentz transformations, 'determines' that B is ticking over at a slower rate than itself?
Since A accelerated, A does not have a single rest frame, so the meaning of "applying the Lorentz transformations" is ambiguous--what frame would you have A use, the frame where A was at rest before the acceleration, or the frame where A was at rest after the acceleration? I was thinking of the inertial frame where A was at rest after acceleration, and in this frame both of your above statements are true; in this frame A ticks faster after acceleration than before acceleration, and in this frame B ticks more slowly than A after A has accelerated.
The idea of time contraction was, I believe, an unacceptable concept as far as Einstein was concerned.
I don't understand what you mean by "time contraction", can you explain this? No clocks rate of ticking is faster than the rate coordinate time is passing in any inertial frame, if that's what you mean; it can only be ticking at the same rate as coordinate time (if it's at rest in the chosen frame), or slower than coordinate time (if it's moving in this frame).
"After accelerating"? I am of the opinion that the v in Einstein's equation .5tv^2/c^2 can be his instantaneous velocity whilst accelerating.
Please note that Einstein's equation above is an amount of time, not an instantaneous rate of ticking, and certainly not an instantaneous velocity. It's meant to tell you how much a moving clock will lag behind a non-moving clock in a given frame after some time t has passed in that frame. Also, it is only an approximation; the non-approximate equation would be t*(1 - \sqrt{1 - v^2/c^2}). For example, if clock A is moving at 0.6c and clock B is at rest in a certain frame, and they start off showing the same time, then after t=10 seconds of coordinate time have passed in that frame, clock A will lag behind clock B by 10*(1 - \sqrt{1 - 0.6^2}) = 10*(1 - 0.8) = 2 seconds. If you use Einstein's approximation you predict that clock A lags behind clock B by 0.5*10*0.6^2 = 1.8 seconds, which is close to the correct value of 2 seconds although a little off.
The slower rate of operation of clock A is not affected by the fact that he takes his foot off the gas pedal at any given instant.
It's true that if you accept the notion of "instantaneous rate of ticking" (which you objected to earlier), then the instantaneous rate of ticking in a given frame depends solely on the instantaneous velocity in that frame, it doesn't depend on whether the clock is accelerating or moving at constant speed. In any case, in most thought-experiments in SR we just assume the accelerations are instantaneous.
But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower......
So A, having arrived at B's location, is, apparently, entitled to be of the opinion that his clock lags behind B due to the fact that whilst he was moving his clock was 'going more slowly' (i.e. ticking over at a slower rate) than B?
It is meaningless to state an "opinion" about clock rates without specifying what coordinate system you want to use, and of course A is "entitled" to use absolutely any frame he wants, even one where neither he nor B have been at rest at any point during the experiment. If A wishes to calculate things relative to the inertial frame where B is at rest, then in this frame it is certainly true that A lagged behind because A ticked more slowly after accelerating. But again, you always have to specify a choice of frame you use when talking about rates of ticking, to do otherwise would be like saying "it's my opinion that Earth has a greater x-coordinate than the Sun" without specifying where you want the origin of your coordinate system to be and which direction the x-axis is pointing relative to this origin.
I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowly (i.e. ticks over at a slower rate) than a clock at one of the poles
But you're still haven't defined what you mean by words like "physically", "really", or "actually"! It is true that relative to a particular choice of coordinate system A ticks more slowly, but we understand that this choice is an arbitrary one and the universe doesn't care which coordinate system we use, nothing in the laws of physics justifies the idea that one coordinate system's point of view is somehow more correct than another's. Similarly, if you pick a coordinate system where the origin is at the center of the Sun and the positive x-direction is pointed towards the Earth, it's true in this coordinate system that the Earth has a greater x-coordinate than the Sun...but would you say that the Earth "physically" or "really" or "actually" has a greater x-coordinate than the Sun, in spite of the fact that we are obviously free to use a coordinate system where the origin is at a different position? Please answer this question about whether you would use words like "physical" to describe statements about which of two objects has a greater x-coordinate, and it will help me to understand what you mean by the word "physical" when you talk about clock rates.
In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve
with constant velocity until it returns to A, the journey lasting
t seconds, then by the clock which has remained at rest the
travelled clock on its arrival at A will be a .5tv^2/c^2 second
slow. Thence we conclude that a balance-clock at the equator must
go more slowly, by a very small amount, than a precisely similar
clock situated at one of the poles under otherwise identical
conditions."
What do people think he meant by the phrase "...must go more
slowly..."?
Does anyone agree that he meant that the moving clock will tick
over at a slower rate than (i.e. incur time dilation relatively
to) the other clock?
********************
On the (probably erroneous) basis that some people may agree that
he did - I follow that up with the question - On the basis of his
depiction of a clock that is made to move in a closed curve around
another clock is it correct for me to assume that Einstein meant
that the clock that is moving in a closed curve will “go more
slowly” (i.e. tick over at a slower rate) than the clock “which has
remained at rest.”?
The A clock must accelerate to leave the B clock, move at a
constant speed for most of the path, then decelerate to reunite
with the B clock. Since A initiated the trip, and traveled a
greater distance than B, in the same amount of elapsed B time, A
would have an average speed greater than B. Time dilation is a
function of speed, therefore the A clock experiences more time
dilation than B. When reunited, A clock is lagging behind B clock.
This is not about perception of clocks, but the physics of clock
function according to light propagation. Each will
observe/perceive the others clock to be running faster or slower,
depending on direction of motion.
In Einstein's section 4 depiction of an equatorial clock which 'must go more slowly' than a polar clock there is no relationship to "...the physics of clock function according to light propagation."
"The physics of clock function according to light propagation." is solely in relation to Doppler shift and light travel time which, I believe, has absolutely no physical effect whatsoever on any clocks physical rate of operation.
As you point out, above, "...Time dilation is a function of speed." It is not a function of Doppler shift or light travel time which, although bought about by relative speed, only create an illusion of time variations.
You wrote "...Since A initiated the trip, and traveled a greater distance than B..." Clock B travels no distance! It has, according to Einstein, remained at rest!
You wrote "..therefore the A clock experiences more time dilation than B." Clock B, in Einstein's depiction "...has remained at rest..." ergo it incurs no time dilation!
This is a repeat of my reply for the your first thread.
[quote=phyti;1913665]Here is a quote from the Max Born book, page 257, which you have (A and B swapped).
"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."
My interpretation of that comment is that every internal process in A's system (including the rate of operation of his clocks) must take place more slowly (i.e. his clocks must 'go more slowly') than the same process (i.e. the rate of operation of the clocks) in system B.
Because A & B are synchronized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.[quote]
I wholeheartedly agree - the time effect (i.e. the slower rate of operation of A's clock compared to it's rate of operation before he started moving) is, according to Einstein, caused by the motion and as you point out above "Time dilation is a function of speed, therefore the A clock experiences [sic. more] time dilation."
[QUOTE=phyti;2143042]I can only add, time dilation is a real factor affecting particle accelerators and gps systems.
Irrelevant, I made no suggestion whatsoever that time dilation (as depicted by Einstein's section 4 STR comments) is not 'a real factor'!
DaleSpam
Apr1-09, 11:27 PM
You state that fictitious forces are not 'Einstein'. Do you mean that they are not special theory?Correct, the concept of fictitious forces predates Einstein by more than 100 years.
There is NO observer C in Einstein's section 4 STR depiction and the introduction of same is nothing more than a deliberate obfuscation!
Determinations made by a hypothetical observer C can have no effect whatsoever on what is taking place as far as A or B are concerned nor on the rates of operation of their clocks!That is a bit of an extreme reaction. The whole point of relativity is that you can use any inertial reference frame you choose. The results will always be the same, as I explained.
Anyway, I only introduced C because you already refused to use non-inertial reference frames like A's. If you only admit B's reference frame (because A's is non-inertial and because no other inertial frame is explicitly mentioned) then it is hard to see what you are objecting to.
Not if "physical truth" is defined to mean something that is true regardless of your choice of conventions about coordinate systems, and as I said before, this is how most physicists nowadays use the word "physical". If you want to use a different definition that's fine, it's just semantics, but I would ask that you spell out what you mean by physical. That's what DaleSpam asked you in post #90 above, and I also asked you about this in post #85 which you were responding to here:
You have allowed this thread to deteriorate into a totally in appropriate philosophical discussion.
When Einstein wrote that the equatorial clock 'must go more slowly' than a clock at one of the poles did he mean that the equatorial clock goes more slowly than a polar clock?
DaleSpam
Apr1-09, 11:31 PM
I made no suggestion that relativity does not work.Then what is the discussion about?
You have allowed this thread to deteriorate into a totally in appropriate philosophical discussion.
When Einstein wrote that the equatorial clock 'must go more slowly' than a clock at one of the poles did he mean that the equatorial clock goes more slowly than a polar clock?
As I said, I think he meant the average over an entire orbit, and I believe it would be true in all inertial frames that over a complete orbit an equatorial clock would tick less than a clock at the pole. Can we focus on the other situation Einstein discusses in section 4 where clock A and clock B are initially some distance apart, then A is briefly accelerated and afterwards moves inertially towards B? Do you assert that in this example A is "physically", "really", or "actually" ticking slower than B between the time it's accelerated and the time it reaches B, in spite of the fact that there are perfectly valid inertial frames where it is B that's ticking slower during this period of time? I just want to understand if you use words like "physically", "really" and "actually" to mean something that there is a single correct answer about, or if you just use these words to refer to the perspective of particular frames, so that you would be equally fine with saying that it is B that "physically", "really", and "actually" ticks slower than A in certain choices of frames.
DaleSpam
Apr2-09, 07:15 AM
It is not important what I think about the words 'physical' or 'real' but what Einstein meant by the words 'must go more slowly'!
I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowlyThe problem is that because you refuse to define "physical", "real", etc. I still don't know what you mean by that last. I cannot tell if we agree or disagree, and I don't know what words to use to clearly communicate my position back to you. It is, in fact, important what you think about those words because you are the one I am trying to communicate with. I even made it easy for you and suggested some definitions, all you have to do is say yes or no.
I think it is rather hypocritical that you accused me of "deliberate obfuscation" above.
matheinste
Apr2-09, 08:44 AM
This doesn't answer the question but may be of some interest for those like me who have not seen it before.
http://www.sigmapisigma.org/radiations/2005/electrodynamics_fall05.pdf
"--------If there are two synchronously running clocks at A, and one of them is moved along a closed curve with constant velocity until it has returned to A, which takes, say, t sec, then,on its arrival at A, this clock will lag ½t(v R /c)2 sec [to lowest order in v R /c] behind the clock that has not been moved. From this we conclude that a balance-wheel clock located at the Earth’s equator must, under otherwise identical conditions, run more slowly by a very small amount than an absolutely identical clock located at one of the Earth’s poles.---------”
There are legion experimental demonstrations of time dilation, such as the ubiquitous muons-in-cosmic-rays example that appears in all the textbooks. When time could be measured to nanosecond precision fifty years after Einstein wrote these preceding lines, an experiment was done that recalled Einstein’s prediction explicitly:
Hay’s experiment as described J. Bronowski, The Ascent of Man, Little & Brown (1973), p. 255.
The experiment was done by a young man called H.J. Hay at Harwell. He imagined the earth squashed flat into a plate, so that the North Pole is at the centre and the equator runs round the rim. He put a radio-active clock on the rim and another at the center of the plate and let it turn. The clocks measure time statistically by counting the number of radio-active atoms that decay. And sure enough, the clock at the rim of Hay’s plate keeps time more slowly than the clock at the centre. This goes on in every spinning plate, on every turntable. At this moment, in every revolving gramophone disc, the centre is ageing faster than the rim with every turn
Matheinste.
cos,
you have repeatedly been asked to explain what you mean by "physically", "really", or "actually". You might think these words are obvious and require no further explanation, but in relativity things that seemed obvious in Newtonian theory are no longer so. If you describe something as "physically slower" (for example), you need to explain what measurements or calculations you would perform to decide whether something is "physically slower" or not.
You often refer to a clock "ticking more slowly" but you fail to say slower than what and as measured by whom. In relativity these are not optional extras: different observers get different answers. It makes sense to assert "A ticks more slowly than B as measured by C". If we shorten this to "A ticks more slowly than B" this only makes sense (for instantaneous tick rates) in a context where the "as measured by C" is understood -- often the context is "as measured by B". To say "A ticks more slowly" makes no sense at all unless everyone implicitly understands what B and C are.
Note that in relativity it is possible for
"A ticks (instantaneously) more slowly than B as measured by B"
"B ticks (instantaneously) more slowly than A as measured by A"
to be simultaneously true. It's not a contradiction because A & B use different measurement procedures.
But "A actually ticks slower" (without mention of a B or C) means nothing. Can you give an unambiguous operational definition (what numbers you would measure or calculate) of what you think it means?
When Einstein wrote that the equatorial clock 'must go more slowly' than a clock at one of the poles did he mean that the equatorial clock goes more slowly than a polar clock?He meant the equatorial clock ticks more slowly than a polar clock as measured by a polar clock.
============
Note: everything above applies to "instantaneous" clock rates. If you are talking about average clock rates where clocks A and B are initially together, separate and come back together again, everyone will agree which clock ticked fewer ticks than the other over the whole round-trip journey, but then at least one of the clocks must have accelerated (I'm assuming Special Relativity in the absence of gravity), so simple inertial frame analysis is not sufficient.
Jesse, post 81
Well, if you're just talking about average rate of ticking for a non-inertial clock between the times it departs from and returns to an inertial clock, then you aren't saying anything controversial if you say that the non-inertial clock has a slower average rate of ticking between these events, since this is true in all frames. I thought you were saying something more, Well, if you're just talking about average rate of ticking for a non-inertial clock between the times it departs from and returns to an inertial clock, then you aren't saying anything controversial if you say that the non-inertial clock has a slower average rate of ticking between these events, since this is true in all frames. I thought you were saying something more, that the clock A in his example in section 4 was objectively ticking slower than clock B during the after it was accelerated to the time it met clock B; that would be incorrect, but if you didn't mean to suggest this, please clarify. that would be incorrect, but if you didn't mean to suggest this, please clarify.
that the clock A in his example in section 4 was objectively ticking slower than clock B during the after it was accelerated to the time it met clock B
If it wasn't, when or where in the trip does the difference in time occur?
Please don't use the 1st postulate as a defense, it get's old fast!
If it wasn't, when or where in the trip does the difference in time occur?
In a frame where the clock A that was accelerated was not ticking slower than B (because A and B initially had a nonzero speed and A's speed decreased after accelerating, from the perspective of this frame), the reason A was behind B when they met was because they were not synchronized in the first place (always remember the relativity of simultaneity (http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html)!). In this frame B's time was always ahead of A's time by a constant amount prior to A accelerating, and after A accelerated its reading was "gaining on" B's reading, but not fast enough for it to surpass B's time by the time they met. If A was allowed to continue on at constant velocity past B after they crossed paths, then in this frame A's time would eventually surpass B's time.
Note that I gave a numerical example that worked like this back in post #64:
Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.
Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.
When Einstein wrote that the equatorial clock 'must go more slowly' than a clock at one of the poles did he mean that the equatorial clock goes more slowly than a polar clock?
As I said, I think he meant the average over an entire orbit, and I believe it would be true in all inertial frames that over a complete orbit an equatorial clock would tick less than a clock at the pole.
On the basis that the equatorial clock does, on average over an entire orbit, 'go more slowly' than the polar clock I am of the impression that during this orbit the equatorial clock also 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock.
On the basis that, after one orbit, the equatorial clock is slower than (i.e lags behind) the polar clock then in my opinion it must, during that orbit, have ticked over at a slower rate than it would had it been located alongside the polar clock.
I think there is a distinction between the idea that the equatorial clock is slower than (i.e. lags behind) a polar clock after an entire orbit and that it 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock.
Can we focus on the other situation Einstein discusses in section 4 where clock A and clock B are initially some distance apart, then A is briefly accelerated and afterwards moves inertially towards B? Do you assert that in this example A is "physically", "really", or "actually" ticking slower than B between the time it's accelerated and the time it reaches B, in spite of the fact that there are perfectly valid inertial frames where it is B that's ticking slower during this period of time?
I agree that "...in this example A is "physically", "really", or "actually" ticking slower than B between the time it's accelerated and the time it reaches B." however I do not accept that "...there are perfectly valid inertial frames where it is B that's ticking slower during this period of time."
In my opinion B's rate of operation can in no way be affected by A's acceleration or deceleration or rate of uniform travel toward (or away from) B!
So when you say that it is B that's ticking slower during this period of time this is nothing more than a comparison of the calculated rate of operation of B to that of the rate of operation of clock A thus clock A 'is' ticking over at a faster rate than it was before it started accelerating however I am of the understanding that the concept of time contraction was, for Einstein, unacceptable.
Ergo, on that basis, A is not ticking over at a faster rate (time contraction) than it was before it started accelerating and on the basis that A's actions of any kind have no affect whatsoever on B's rate of operation A cannot be of the opinion that B is ticking over at a slower rate than it was before he started accelerating but can only conclude that B appears (according to his calculations) to be ticking over at a faster rate than it was previously.
In my opinion, which is probably controversial, clock A's instantaneous velocity can be substituted for v in the Lorentz transformations.
A is accelerating toward B and has attained a instantaneous velocity of s. He switches his rockets off and at that very instant is moving at the same (albeit, now) uniform velocity of s (i.e he is moving toward B at the same speed as he was at the very instant the rocket shut down).
I fail to see why the calculated rate of operation of clock A from B's point of view (or the calculated rate of clock B from A's point of view) will be any different if A has attained an instantaneous velocity of s or is moving toward B with a uniform velocity of s.
I just want to understand if you use words like "physically", "really" and "actually" to mean something that there is a single correct answer about, or if you just use these words to refer to the perspective of particular frames, so that you would be equally fine with saying that it is B that "physically", "really", and "actually" ticks slower than A in certain choices of frames.
Saying that B 'is' ticking slower (or faster) than A in certain choices of frames is NOT the same as saying that B ticks over at slower (or faster) rates than it did before A started moving (or accelerating). I reiterate - I am of the opinion that B's rate of operation is not affected by A's actions of any kind, it merely appears, from A's point of view (in accordance with his calculations), to change!
An astronaut has come to a stop at the end of his outward bound trip. He accelerates and attains an instantaneous velocity whereby a gamma factor of 400 000 is attained. He 'sees' (or 'determines' or 'calculates') the Earth clock ticking over at a fsater rate than his own clock by a factor of one second Earth time for each 400 000 seconds of his own time.
He flicks a switch extinguishing his rocket and at that very instant 'sees' (or 'determines' or 'calculates') that the Earth clock is no longer ticking over at that faster rate than his own clock but is immediately ticking over at a slower rate than his own clock by a factor of 400 000 seconds for each of his own seconds.
Is he not likely to ask himself what affect this would have on the clock (and on all of the planet's inhabitants) which instantaneously reverts from being 400 000 times faster than his clock to being 400 000 times slower?
Does he truly believe that this takes place because he flicked that switch?
I won't bother detailing the following but on the basis of the identical nature of time contraction and length contraction he would 'see' the planet instantaneously change from being shaped like a pancake of around 32 meters thick at the center (tapering to almost zero at its perimeter) to being more than 5 billion kilometers deep (in his direction of travel).
Would he not be of the opinion that this instantaneous and somewhat considerable change in that dimension could have a detrimental affect on the planet and a devastating effect on its inhabitants.
In fact, as his instantaneous velocity increases, so too 'does' the distance from him to the planet (as 'does' the rate of operation of the Earth clock) but when he flicks that switch the (seemingly increasing) distance to the planet instantaneously reverts to a close proximity to the plant - simply because he flicked a switch?
It is not important what I think about the words 'physical' or 'real' but what Einstein meant by the words 'must go more slowly'!
I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowly.
The problem is that because you refuse to define "physical", "real", etc. I still don't know what you mean by that last.
OK; what do you think Einstein meant by the phrase "...must go more slowly...."?
My opinion is that he was saying that a clock at the equator must tick over at a slower rate than it would if it were located at one of the poles or that it ticks over at a slower rate than a polar clock.
I cannot tell if we agree or disagree, and I don't know what words to use to clearly communicate my position back to you. It is, in fact, important what you think about those words because you are the one I am trying to communicate with. I even made it easy for you and suggested some definitions, all you have to do is say yes or no.
Your response to the question above might indicate whether or not we agree or disagree.
I think it is rather hypocritical that you accused me of "deliberate obfuscation" above.
The term 'hypocritical' implies that you are of the opinion that I have introduced 'deliberate obfuscation'.
Whilst my responses, or lack thereof, may have created obfuscation this was not my intention!
cos,
you have repeatedly been asked to explain what you mean by "physically", "really", or "actually". You might think these words are obvious and require no further explanation, but in relativity things that seemed obvious in Newtonian theory are no longer so. If you describe something as "physically slower" (for example), you need to explain what measurements or calculations you would perform to decide whether something is "physically slower" or not.
When Einstein wrote in section 4 STR that an equatorial clock 'must go more slowly' he, I believe, related this to his equation .5tv^2/c^2 . having referred to that same equation in my postings I assumed that readers would automatically apply that same equation.
As to what measurements or calculations I would perform (as distinct from applying) I am of the opinion that Einstein did not explain what measurements or claculations he would perform (as distinct from applying) so perhaps you point should be directed to his depiction.
You often refer to a clock "ticking more slowly" but you fail to say slower than what and as measured by whom. In relativity these are not optional extras: different observers get different answers. It makes sense to assert "A ticks more slowly than B as measured by C". If we shorten this to "A ticks more slowly than B" this only makes sense (for instantaneous tick rates) in a context where the "as measured by C" is understood -- often the context is "as measured by B". To say "A ticks more slowly" makes no sense at all unless everyone implicitly understands what B and C are.
Perhaps you could provide a reference as to where I referred to a clock that is ticking more slowly but where I failed to say to what it is ticking more slowly than?
I do not care who makes the measurement. In my opinion a clock's intrinsic rate of operation will remain unchanged regardless of the point of view, or the determinations of, an observer.
Note that in relativity it is possible for
"A ticks (instantaneously) more slowly than B as measured by B"
"B ticks (instantaneously) more slowly than A as measured by A"
This may well be true of the previous sections of relativity however in section 4 Einstein points out that a clock at the equator must go more slowly than a clock at one of the poles and it is my understanding that from the point of view of observer B (at one of the poles) A does not 'tick more slowly' than his own clock as per you statement above ("A ticks (instantaneously) more slowly than B as measured by B") but faster!
[QUOTE=DrGreg;2144031]to be simultaneously true. It's not a contradiction because A & B use different measurement procedures.
It matters not that A and B "...use different measurement procedures." Nothing that any of them 'measure' or 'calculate' or 'determine' or 'predict' will have any affect whatsoever on a clock's intrinsic rate of operation.
But "A actually ticks slower" (without mention of a B or C) means nothing. Can you give an unambiguous operational definition (what numbers you would measure or calculate) of what you think it means?
He meant the equatorial clock ticks more slowly than a polar clock as measured by a polar clock.
And as measured by the equatorial observer!
He determines that his clock is 'going more slowly' than the polar clock; he realizes that his having moved to the equator has had no affect whatsoever on the rate of operation of the polar clock which is still ticking over at the same rate as it was when he was at the same location.
In order to qualify that suggestion - neither of the observers can actually see what the other clock is doing but on the basis that the equatorial observer has read, and agrees with, Einstein's section 4 depiction he could agree with Einstein that his clock is 'going more slowly' than the polar clock and at a slower rate than it was before he moved to the equator.
Note: everything above applies to "instantaneous" clock rates. If you are talking about average clock rates where clocks A and B are initially together, separate and come back together again, everyone will agree which clock ticked fewer ticks than the other over the whole round-trip journey, but then at least one of the clocks must have accelerated (I'm assuming Special Relativity in the absence of gravity), so simple inertial frame analysis is not sufficient.
Most of the above applies to Einstein's section 4 STR depiction of equatorial and polar clocks where the the clocks are not separated and come back together again however observer A, as i pointed out in other message, could initially have been located at one of the poles where his clock was ideally synchronous with an identical clock. He moves to the equator then back to the pole (i.e. travels in a closed curve relative to the polar clock) whereupon he finds, as Einstein depicted in his description of a clock that moves in a closed curve relative to another clock, that his clock now lags behind that clock ergo he should be able to conclude, as Einstein pointed out, that his clock (progressively) went more slowly (i.e.ticked over at a slower rate) than the polar clock.
DaleSpam
Apr3-09, 12:34 AM
OK; what do you think Einstein meant by the phrase "...must go more slowly...."?I think that he meant that A's proper time is slower than the coordinate time \left(\frac{dt}{d\tau}>1\right) in system K, the reference frame where A and B were initially at rest and synchronized. I believe that he understood that this is a frame-variant statement, which was the reason why he clearly identified frame K.
The term 'hypocritical' implies that you are of the opinion that I have introduced 'deliberate obfuscation'.
Whilst my responses, or lack thereof, may have created obfuscation this was not my intention!I will accept this statement at face value and not impugn your motives. I would ask that you show me the courtesy of doing the same.
By the way, I would appreciate it if you would try not to underline so many words. I often go back through a thread looking for a link, and they are very hard to find with so many non-links in underlined font. Italics and bold are much preferable (as you have done in this quoted post).
On the basis that the equatorial clock does, on average over an entire orbit, 'go more slowly' than the polar clock I am of the impression that during this orbit the equatorial clock also 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock.
Only on average over the whole orbit, not necessarily at every moment, depending what frame you choose. In certain frames there will be periods of time where the equatorial clock has a smaller speed than the polar clock, so during these periods of time the polar clock must be ticking slower in such a frame.
I agree that "...in this example A is "physically", "really", or "actually" ticking slower than B between the time it's accelerated and the time it reaches B."
You "agree"? I did not say that was what I thought.
however I do not accept that "...there are perfectly valid inertial frames where it is B that's ticking slower during this period of time."
So do you disagree with the math in the second paragraph in my example from post #64 below?
Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.
Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.
Unless you think the math is wrong in the second paragraph, the second paragraph is saying that in the frame where A and B were initially moving at 0.6c, it must be true that at the moment A accelerates (and we can assume the acceleration is instantaneously brief), A reads t=0 seconds and B reads t=36 seconds, and at the moment B and A meet, A reads 80 seconds and B reads 100 seconds. So B ticked forward by 64 seconds, while A ticked forward by 80 seconds, therefore B was ticking slower during this period, from the perspective of this frame. If you don't disagree with the math--and I can show you that these numbers follow directly from applying the Lorentz transformation to the scenario described in the first paragraph from the perspective of B's rest frame--then how can you say you disagree with the statement that "there are perfectly valid inertial frames where it is B that's ticking slower during this period of time"?
In my opinion B's rate of operation can in no way be affected by A's acceleration or deceleration or rate of uniform travel toward (or away from) B!
No one said anything about B's rate of operation being accelerated by A's acceleration! In the frame described by the second paragraph, B is always ticking at a rate of 0.8 ticks per second of coordinate time, both before and after A accelerates. Before A accelerates A is also ticking at 0.8 ticks per second of coordinate time, but then after accelerating A comes to rest in this frame, and is now ticking at 1 tick per second of coordinate time. Here are a few numbers to make this clear:
At coordinate time of t=-30 seconds in this frame, A reads -24 seconds, B reads 12 seconds
At coordinate time of t=-20 seconds in this frame, A reads -16 seconds, B reads 20 seconds
At coordinate time of t=-10 seconds in this frame, A reads -8 seconds, B reads 28 seconds
At coordinate time of t=0 seconds in this frame (the moment that A accelerates), A reads 0 seconds, B reads 36 seconds
At coordinate time of t=10 seconds in this frame, A reads 10 seconds, B reads 44 seconds
At coordinate time of t=20 seconds in this frame, A reads 20 seconds, B reads 52 seconds
At coordinate time of t=30 seconds in this frame, A reads 30 seconds, B reads 60 seconds
...So, you can see that for each interval of 10 seconds of coordinate time prior to A's acceleration, B advances forward by 8 seconds (from 20 to 28 seconds between t=-20 and t=-10 seconds, for example), and A also advances forward by 8 seconds (from -16 to -8 seconds between t=-20 and t=-10). On the other hand, for each interval of 10 seconds of coordinate time after A's acceleration, B still advances forward by the same amount of 8 seconds (from 44 to 52 seconds between t=10 and t=20, for example), while A now advances forward at the faster rate of 10 seconds (from 10 to 20 seconds between t=10 and t=20). So B's rate of ticking never changes in this frame, only A's rate of ticking changes, from ticking at the same rate as B before it accelerates to ticking faster than B afterwards. Again, do you disagree that these are the numbers we get if we apply the Lorentz transformation to the scenario as it was described in B's rest frame, or do you agree with the math but think that the description in B's rest frame describes what "really", "actually" happens while the description in this second frame is some sort of illusion?
So when you say that it is B that's ticking slower during this period of time this is nothing more than a comparison of the calculated rate of operation of B to that of the rate of operation of clock A thus clock A 'is' ticking over at a faster rate than it was before it started accelerating however I am of the understanding that the concept of time contraction was, for Einstein, unacceptable.
You still have never explained what "time contraction" means. You can see in the above scenario that even though A speeds up after accelerating, its rate of ticking can never be faster than the rate that coordinate time is passing--is that what you mean by time contraction? Or do you just think relativity forbids a clock's rate from ever speeding up at all after it changes velocities? If the latter, you're incorrect, if a clock changes velocities in such a way that its speed becomes smaller in a given frame, then its rate of ticking will get faster than what it was before changing velocities, from the perspective of that frame.
In my opinion, which is probably controversial, clock A's instantaneous velocity can be substituted for v in the Lorentz transformations.
Sure, if you want to figure out what things look like in the frame where A is instantaneously at rest at that instant (but in this frame A was not always at rest if it is accelerating; by definition an inertial frame must travel at the same constant velocity forever).
A is accelerating toward B and has attained a instantaneous velocity of s. He switches his rockets off and at that very instant is moving at the same (albeit, now) uniform velocity of s (i.e he is moving toward B at the same speed as he was at the very instant the rocket shut down).
Of course, did you think I had suggested otherwise?
I fail to see why the calculated rate of operation of clock A from B's point of view (or the calculated rate of clock B from A's point of view) will be any different if A has attained an instantaneous velocity of s or is moving toward B with a uniform velocity of s.
In SR we're only calculating things from the "point of view" of particular inertial coordinate systems, I don't know what it means to calculate things "from A's point of view" since A changes velocity at a certain point. If you want to calculate things from the point of view of the inertial frame where A is at rest after accelerating, that is exactly what I was doing in the second paragraph of my numerical example above.
Saying that B 'is' ticking slower (or faster) than A in certain choices of frames is NOT the same as saying that B ticks over at slower (or faster) rates than it did before A started moving (or accelerating).
As I point out above, I have never claimed this, so I don't know why you're making this point. When I said "...there are perfectly valid inertial frames where it is B that's ticking slower during this period of time", I thought it was fairly clear from the context that I meant B is ticking slower than A during this period of time, not that B is ticking slower than B was ticking prior to A's acceleration. Perhaps you misunderstood my meaning? If so, now that I have clarified, do you disagree that "there are perfectly valid inertial frames where it is B that's ticking slower than A during this period of time" (i.e. the period of time between A accelerating and A and B meeting)? If you don't disagree, then would you say that B is "physically", "really", and "actually" ticking slower than A during this period of time, from the perspective of these frames?
OK; what do you think Einstein meant by the phrase "...must go more slowly...."?
I think that he meant that A's proper time is slower than the coordinate time \left(\frac{dt}{d\tau}>1\right) in system K, the reference frame where A and B were initially at rest and synchronized. I believe that he understood that this is a frame-variant statement, which was the reason why he clearly identified frame K.
His comment "...must go more slowly...." was not in relation to "...in system K, the reference frame where A and B were initially at rest and synchronized." but to his later reference to a clock at the equator which, he insisted 'must go more slowly' than a clock at one of the poles.
For the purpose of edification I submit his section 4 comments -
"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.
If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
I will accept this statement at face value and not impugn your motives. I would ask that you show me the courtesy of doing the same.
Noted - but I also trust that you will not impugn my motives in relation to any other of my postings and I will reciprocate
By the way, I would appreciate it if you would try not to underline so many words. I often go back through a thread looking for a link, and they are very hard to find with so many non-links in underlined font. Italics and bold are much preferable (as you have done in this quoted post).
"Sorry 'bout that Chief."
On the basis that the equatorial clock does, on average over an entire orbit, 'go more slowly' than the polar clock I am of the impression that during this orbit the equatorial clock also 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock.
Only on average over the whole orbit, not necessarily at every moment, depending what frame you choose. In certain frames there will be periods of time where the equatorial clock has a smaller speed than the polar clock, so during these periods of time the polar clock must be ticking slower in such a frame.
On the basis that in my opinion this may well be the crux of the matter I make no apology for the fact that, although having read same, I have removed the remainder of your posting on the basis of my physical disabilities which severely restricts the time that I am able to devote to my responses.
"Depending what frame "?
There are, as I have previously stipulated, only [I]two frames in this otherwise empty universe - that of the polar observer and that of the equatorial observer.
The planet could, as I have also previously stipulated, be replaced by a large rotating, transparent, massless sphere.
Apart from rotating, the sphere is not moving. From both points of view the equatorial clock is always moving at the same speed relative to the polar clock i.e. 1600K-h.
At no time does "...the equatorial clock [have] a smaller speed than the polar clock..."
There are, as I have previously stipulated, only two frames in this otherwise empty universe - that of the polar observer and that of the equatorial observer.
First of all, frames are just coordinate systems. They don't depend on what objects happen to be present in the universe, you can certainly assign coordinates to events using a coordinate system where no object in the universe happens to be at rest. So, regardless of what objects happen to be present in the universe, you have an infinite number of different inertial frames you can use.
Second, in SR we usually stick to talking about inertial frames. The object at the equator does not remain at rest in any inertial frame, because it's moving non-inertially. You can think about non-inertial coordinate systems if you wish, but the usual rules of inertial frames, like light always moving at c or moving clocks running slow by a factor of \sqrt{1 - v^2/c^2}, no longer apply in non-inertial coordinate systems, so it's easier to just use inertial ones.
Finally, If you don't want to reply to my entire post that's fine, but could I request that you clarify what you meant when you said (speaking of the A-B thought experiment rather than the equatorial and polar clock thought experiment) that you do not agree with my statement that "...there are perfectly valid inertial frames where it is B that's ticking slower during this period of time"? Did you misunderstand what I meant by "it is B that's ticking slower", thinking I was saying that B's rate of ticking slowed down after A accelerated in some inertial frame? If so, please note that I didn't mean to imply any change in B's rate of ticking, I just meant that there are inertial frames where B is ticking slower than A after A accelerates, because in these frames A's rate of ticking speeds up after it accelerates (since its speed decreases in these frames) while B's rate of ticking remains unchanged. So with that clarification, would you still disagree that "there are perfectly valid inertial frames where it is B that's ticking slower than A during this period of time (the period after A accelerates)", or would you now agree with it? I'm not asking for a detailed answer here, just a simple "agree" or "disagree".
So, regardless of what objects happen to be present in the universe, you have an infinite number of different inertial frames you can use.
On the basis of my presentation that the sphere is located in an otherwise empty universe thus a universe in which there is not an infinite number of frames and your continued insistence on an infinite number of frames - which, in my opinion, is a reprehensible attitude - this discussion is terminated.
matheinste
Apr3-09, 04:56 AM
cos
Maybe for frames you mean rest frames.
In a universe empty except for ANY number of objects there are an infinite number of frames. This applies equally well to a universe containing only one object or our populated universe. However, there is at most only one frame in which any individual object can be at rest at any instant. So in the two clock scenario there are an infinite number of frames but for each clock there is only one frame in which it is at rest at any instant.
Matheinste
DaleSpam
Apr3-09, 07:39 AM
His comment "...must go more slowly...." was not in relation to "...in system K, the reference frame where A and B were initially at rest and synchronized." but to his later reference to a clock at the equator which, he insisted 'must go more slowly' than a clock at one of the poles.Then I suggest that you misunderstood him. He postulated the equivalence of inertial reference frames and then he derived the relativity of simultaneity earlier in the paper. From then on he was repeatedly careful to identify the reference frame in which his analysis held. I don't know how you can read that work and come to any conclusion other than that he understood simultaneity, time dilation, and length contraction to be frame-variant effects.
Why do you think he repeatedly identified the reference frame in his later analysis if he believed that his results were frame-invariant?
During that trip he determines that B' is ticking over at a slower rate than his clockyes. whereupon he predicts that B' will resultantly lag behind his own clockNo, he would make no such prediction. yet he arrives at that location to find that B' does not lag behind his clock but that his clock lags behind B'.Which is what he would have predicted. Note that B' is only synchronized with the earth clock in earth's frame, not in the ship's frame. In earth's frame B and B' both read zero when the ship leaves earth. In the ship's frame, B read zero when the ship left earth, but B' did not. B' runs faster than the ship's clock in the ship's frame during the initial acceleration at earth.
In his 1918 article (which I believe was merely an extension of his section 4 STR depictions) Einstein pointed out that it is ONLY the clock that experiences forces of acceleration (i.e. his section 4 clock A) that incurs a variation in it's rate of operation (a slower tick rate) NOT the unaccelerated inertial reference frame clock (i.e. his section 4 clock B).He says no such thing in his 1918 paper.
The ship's clock has. as Einstein pointed out, accelerated thus it is, according to Einstein, the accelerated ship's clock that incurs time dilation - the Earth clock does not incur time contraction.Again, he says no such thing in his 1918 paper.
The astronaut is moving at a velocity that generates a gamma factor of 400 000. He 'sees' or 'determines' that his clock is ticking over at the rate of 400 000 seconds for each of clock B' seconds (i.e. B is ticking over at a slower rate than his clock) but at the very moment that he puts his foot on the gas pedal to power up his retrorockets clock B stops
ticking over at that slower rate and instantaneously starts ticking over the faster rate of 400 000 seconds for each of his secondsThis is exactly the claim made by Einstein in his 1918 paper (except it would be much greater than 400,000 to one in your example during the turnaround). Referring to the ship's non-inertial rest frame: "the clock U1(earth clock), going at a velocity v, runs indeed at a slower pace than the resting clock U2(at rest with ship). However, this is more than compensated by a faster pace of U1(earth clock) during partial process 3 (turnaround acceleration)....The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4. This consideration completely clears up the paradox that you brought up."
That clock instantaneously reverses its rate of operation from being 400 000 times slower than his clock to being 400 000 times faster?No, nothing happens to his clock. The rate of earth's clock is frame dependent and he is changing frames.
If you believe that I've got a bridge you might be interested in buying.What I believe is irrelevant. This is what SR predicts and what Einstein claims in his 1918 paper.
I don't care in which frame the observations are made. In my opinion nothing that any frame 'observes' can physically affect the rate of operation of any clock!
Nothing physically happens to any clock. In fact the assumption is that each clock keeps proper time and is not affected by acceleration. And the rate of each clock is frame dependent. In other words the rate of a clock on earth is different for different reference frames, although the clock doesn't change. This is the primary revelation Einstein made in 1905.
On the basis of my presentation that the sphere is located in an otherwise empty universe thus a universe in which there is not an infinite number of frames and your continued insistence on an infinite number of frames - which, in my opinion, is a reprehensible attitude - this discussion is terminated.
Again, a "frame" is just a coordinate system, not something physical. Where did you get the idea that we are only allowed to assign x,y,z,t coordinates to events using a coordinate system where some physical object in the universe is at rest?
cos;
Irrelevant, I made no suggestion whatsoever that time dilation (as depicted by Einstein's section 4 STR comments) is not 'a real factor'!
I'm not saying you did. Those comments just reinforce that is is a real phenomena.
Particle physicists would not report things they did not observe, and gps satellites would not be corrected if they functioned accurately.
In a universe empty except for ANY number of objects there are an infinite number of frames. This applies equally well to a universe containing only one object or our populated universe. However, there is at most only one frame in which any individual object can be at rest at any instant. So in the two clock scenario there are an infinite number of frames but for each clock there is only one frame in which it is at rest at any instant.
Matheinste
So is an observer standing alongside Einstein's section 4 equatorial clock entitled to realize that, as Einstein pointed out, his clock is 'going more slowly' (i.e. ticking over at a slower rate) than it would if he were at that pole?
If he were to be initially located at one of the poles and were to move to the equator would he be entitled to conclude that his clock is then ticking over at a slower rate than it was before he moved away from the pole?
A168
For some reason I have been unable to respond to #121; when I hit the 'quote' button it brings up someone else's message however in an attempt to save time for both of us let's get back to basics.
In section 4 STR Einstein wrote -
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
I am of the opinion that by his comment "...must go more slowly...." he was saying that the equatorial clock ticks over at a slower rate than the polar clock.
Do you agree with my opinion?
cos, you terminated the discussion with me because of my "reprehensible attitude" that one is free to use any one of an infinite number of inertial frames regardless of how many physical objects are present in the universe, but you are continuing to talk to matheinste even though he argues exactly the same thing:
In a universe empty except for ANY number of objects there are an infinite number of frames. This applies equally well to a universe containing only one object or our populated universe.
I am sure if you asked anyone else on this thread they would agree that frames are just coordinate systems and you don't need any objects to be at rest in a frame in order to calculate what things look like from the perspective of that frame (and this perspective is as valid as the perspective of any other frame in SR)--even if you think this is incorrect somehow, given that it's a widespread opinion it's a point worth discussing, no? So, would you be willing to reconsider your termination of our previous discussion?
cos, you terminated the discussion with me because of my "reprehensible attitude" that one is free to use any one of an infinite number of inertial frames regardless of how many physical objects are present in the universe, but you are continuing to talk to matheinste even though he argues exactly the same thing:
I am responding to your posting on the basis that as far as i am concerned it is off thread.
I several times requested that you did not refer to a number of inertial frames however on the basis of your continued insistence upon doing so I terminated our discussion.
To the best of my knowledge i have not requested matheinste to 'cease and desist' however my attitude to our correspondence may well depend on his response to my recent message to him.
Irrelevant, I made no suggestion whatsoever that time dilation (as depicted by Einstein's section 4 STR comments) is not 'a real factor'!
I'm not saying you did. Those comments just reinforce that is is a real phenomena.
You find me at a disadvantage - to what do you refer by the phrase "Those comments."?
Are you referring to Einstein's comments in section 4? If so, then do you agree with me that his statement that the equatorial clock "...must go more slowly..." (i.e. must tick over at a slower rate) than a clock at the equator means that it will tick over at a slower rate than it would if it were located at that pole - that this is a 'real phenomena'?
An observer is located at one of the poles; do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
I am responding to your posting on the basis that as far as i am concerned it is off thread.
But the question of which clock is ticking slower at a given moment (as opposed to average rate of ticking over the entire orbit) does depend on your choice of frame, so the fact that in relativity you are free to analyze things from the perspective of a frame where no physical object is at rest is relevant to what's being discussed on the thread, as far as I can tell. If you think it's incorrect that you can use a given frame even if there's no object in the universe at rest in that frame, that's a perception of yours that I think everyone else on this thread would disagree with, so it's worth discussing why you believe that you're right and everyone else is wrong.
I several times requested that you did not refer to a number of inertial frames however on the basis of your continued insistence upon doing so I terminated our discussion.
Again, all questions of "which clock is ticking slower at a given moment" depend on which frame you're using, and a lot of times you use language that makes it sound like you believe there's a single correct answer to questions about which clock is ticking slower, rather than a number of different possible answers depending on what frame you choose. You could avoid discussion of multiple frames if you modify your question to something like "which clock is ticking slower in the rest frame of the polar observer" (or 'in the rest frame of clock B' in the case of the other thought-experiment), and then no one would have reason to dispute your claim about which clock is ticking slower. But it is you who seem to be consciously refusing to qualify your statements about clock rates in a way that shows you understand the answer is specific to a particular choice of frame (why do you insist on phrasing your question in a way that doesn't refer to any specific frame?), and I think it's this refusal that leads many people here to think you are misunderstanding something about the SR...so, it's only natural that people will respond to you by pointing out that the question of which clock ticks slower at a given moment depends on what frame you choose, and that it is equally valid to analyze things from the perspective of any inertial frame. If you do already understand and accept this point, then just say so and no one will need to bring up the issue of multiple possible inertial frames again on this thread. If you don't understand/agree with this, then people will keep bringing up this point, because a failure to understand this is a major misunderstanding of SR.
matheinste
Apr4-09, 03:08 AM
I am responding to your posting on the basis that as far as i am concerned it is off thread.
I several times requested that you did not refer to a number of inertial frames however on the basis of your continued insistence upon doing so I terminated our discussion.
To the best of my knowledge i have not requested matheinste to 'cease and desist' however my attitude to our correspondence may well depend on his response to my recent message to him.
Whether you talk to JesseM after your interpretation of his perfectly legitimate comment as "reprehensible" is entirely up to you. I do not wish to shoulder the responsibility for your action and so will not reply to your recent message in which you say ."---however my attitude to our correspondence may well depend on his response (matheinste's) to my recent message to him.----"
Matheinste.
DaleSpam
Apr4-09, 07:02 AM
do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?Come on cos! I, and others, have asked you several times what do you mean by this? What does "actually (really)" mean to you? Can something be "actually (really)" true if it depends on the coordinate system? This is the crux of the entire thread!
neopolitan
Apr4-09, 08:26 AM
An observer is located at one of the poles; do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
I know you have terminated discussions with me, but perhaps someone else can pick up on this point.
The clocks do measure a rate. It's a pretty simple rate, one second per second, or one minute per minute, or if you have a more accurate clock, one microsecond per microsecond.
It seems that you are dividing time up into different types. If you want to measure a rate of "seconds at the equator per second at the pole", then you might get a much different answer to plain "seconds per second" which by default would be "seconds where I am, doing what I am doing per second where I am, doing what I am doing" which is a rate that would never change.
Is your argument that a clock at the equator runs at a rate of "seconds at the equator per second at the pole" which is "really" slower than the clock at pole which runs at "seconds at the pole per second at the pole" - and that this is "real" because the rate "seconds at the pole per second at the equator" is greater than the rate "seconds at the equator per second at the pole"?
Further, are you implying that when you have two frames which are inertial (A and B) where potential clock rates are:
seconds at A per second at A = seconds at B per second at B
and
seconds at A per second at B = seconds at B per second at A
where
seconds at A per second at A != (does not equal) seconds at B per second at A
then there is something illusory happening?
These are supposed to be clarifying questions. If you are not saying any of these things, it is helpful to know that you aren't.
cheers,
neopolitan
You find me at a disadvantage - to what do you refer by the phrase "Those comments."?
Are you referring to Einstein's comments in section 4? If so, then do you agree with me that his statement that the equatorial clock "...must go more slowly..." (i.e. must tick over at a slower rate) than a clock at the equator means that it will tick over at a slower rate than it would if it were located at that pole - that this is a 'real phenomena'?
An observer is located at one of the poles; do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
Those comments were regarding particle accelerators and gps, actual cases of time dilation effects.
In the case where one clock moves away from the first, travels on a closed path, then rejoins it, and you are comparing the clocks in the same frame you started with, the difference in readings must be explained by the motion of the clock that traveled, which requires acceleration (+ and -) at the beginning and end of the trip. There is nothing else to be used as a cause.
This case is then depicted/extended to the earth rotation example. The conclusion is the same.
The clock that takes the longest closed path, records the least amount of time.
The equatorial clock would run slower according to any earth bound clock not on the equator.
Regarding another poster related to this:
Since the ratio of the earth diameter to distance traveled in a 24 hr day is approx. 8/1500,
any other position on the earth surface is always moving faster than the pole, in the sun reference frame. And as mentioned, in the earth frame, it doesn't matter. The rotation is constant (disregarding small fluctuations).
Jesse,
Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity.
Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.
The difference is 60(.6)(.8)/(1-.36) = 45 sec. The separation is 60 lsec. They cannot detect length change in their own frame, just as they can't detect their slower clocks.
A records arrival of B at 60/.6 = 100 sec. B records .8(100) =80 sec due to time dilation. Because of the shortened time, B thinks the distance is also short, i.e. .8(60) = 48 lsec.
(At this point why do you dilate A's time again, to 64 sec).
For A: t1=0, t2=100, elapsed time =100 sec
For B: t1=45, t2=125, elapsed time = 80 sec
Even though clock A lags clock B, B runs slower than A.
It's the elapsed times that are compared for unsynchronized clocks.
This scenario introduces a third rest frame with A and B moving at .6c. The original example involved two synchronized clocks with one moving in an arbitrary closed path to rejoin the other. The purpose is to demonstrate the clock taking the longer path records less time. They are not equivalent examples.
cos;
do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking at it's proper rate for the speed it has) would actually be ticking at a slower rate than it was at the pole?
My changes are in blue.
Is my translation of your quote correct?
Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.
Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.
The difference is 60(.6)(.8)/(1-.36) = 45 sec.
Difference between what and what? Where are you getting that formula?
The separation is 60 lsec.
Separation between what and what?
They cannot detect length change in their own frame, just as they can't detect their slower clocks.
Not sure what you mean by "their own frame", or what you mean by "cannot detect length contraction". In the frame where A comes to rest after accelerating, the distance between A and B when A accelerates is certainly less than 60 light-seconds, an ruler-clock system at rest in this frame would measure the distance as 48 light-seconds.
A records arrival of B at 60/.6 = 100 sec. B records .8(100) =80 sec due to time dilation. Because of the shortened time, B thinks the distance is also short, i.e. .8(60) = 48 lsec.
You seem to have the notation backwards, B is the one who shows a time of 100 seconds upon meeting with A, A is the one who shows a time of 80 seconds when they meet. And the time has nothing to do with why the distance is 48 light-seconds in the frame where A is at rest after accelerating, 48 light-seconds is what would be measured by an actual ruler-clock system at rest in that frame; if you had a ruler with a rest length of 48 light-seconds which was at rest in that frame, with clocks at either end that are synchronized in that frame, then if one end of the ruler is passing next to A when the clock there reads T (at some time before A accelerates), that means that when the clock at the other end reads T at the moment it is passing next to B, showing that A and B are 48 light-seconds apart at time T in this frame.
(At this point why do you dilate A's time again, to 64 sec).
Again you seem to have the notation confused, it is B that only elapses 64 seconds between the event of A accelerating and the event of B meeting A, as measured in the frame where A is at rest and B is moving at 0.6c. The reason has to do with the relativity of simultaneity--do you understand this concept? Remember, in B's rest frame, B read t=0 at the moment that A accelerated (when we assume A read t=0 too, because A and B were initially synchronized in B's rest frame), which means that in the other frame where B is moving at 0.6c, B does not read t=0 at the moment A accelerated, instead it already reads 36 seconds. In general if two clocks are synchronized in their own rest frame and a distance L apart in this frame, then in a frame where the clocks are moving at speed v, they will be out-of-sync by vL/c^2. Here L=60 light-seconds (the initial distance between A and B in B's rest frame) and v=0.6c (B's velocity in the frame where B is moving at 0.6c), so in the frame where B is moving at 0.6c, A and B must be out-of-sync by (60)(0.6)/1 = 36 seconds, so B must already read t=36 seconds at the moment A reads t=0 seconds in this frame. And of course, you can also use the time dilation formula to show that in the frame where A is at rest after accelerating while B is moving at 0.6c, then if A elapses some amount of time T after the moment A accelerates, B must only elapse T * \sqrt{1 - 0.6^2} after the moment A accelerates in this frame. So, if A elapses 80 seconds between accelerating and meeting B, in this frame B must elapse 80*\sqrt{1 - 0.36} = 64 seconds between the time on B that's simultaneous with A accelerating (according to this frame's definition of simultaneity, that's the moment of B reading 36 seconds) and the time on B when it meets up with A (when it reads 100 seconds).
For A: t1=0, t2=100, elapsed time =100 sec
For B: t1=45, t2=125, elapsed time = 80 sec
I don't understand where these numbers are supposed to come from. I already stated the scenario in such a way that in B's rest frame, A and B both read t=0 at the moment that A accelerates, and they are a distance of 60 light-seconds apart in this frame at that moment. Do you disagree that with that assumption, if A is moving at 0.6c towards B after accelerating in this first frame, then it will take 100 seconds of coordinate time for A to catch up with B in this frame? Do you disagree that with A moving at 0.6c for 100 seconds it will only elapse 80 seconds in this first frame due to time dilation, and that since B remains at rest in this frame it will elapse 100 seconds, so A will read 80 seconds and B will read 100 seconds when they meet? Do you disagree that in the second frame where A is at rest after accelerating while B is moving at 0.6c, the event of A accelerating will be simultaneous with the event of B reading t=36 seconds?
Even though clock A lags clock B, B runs slower than A.
It's the elapsed times that are compared for unsynchronized clocks.
In what frame? In B's rest frame, where A was initially at rest too before accelerating, A and B were synchronized up until the moment A accelerated--that was how I defined the problem. In the frame where A was at rest after accelerating (and A and B were moving at 0.6c before A changed velocity), they were out-of-sync by 36 seconds until A accelerated.
This scenario introduces a third rest frame with A and B moving at .6c.
"Third"? I only mentioned two frames:
1) the frame where A and B were initially at rest, then after A accelerated it was moving at 0.6c while B remained at rest
2) the frame where A and B were initially moving at 0.6c, then after A accelerated it came to rest while B continued to move at 0.6c
What other frame are you thinking of?
The original example involved two synchronized clocks with one moving in an arbitrary closed path to rejoin the other.
Einstein assumed clock A and B were initially at rest with respect to one another and synchronized in their rest frame, then A was moved at constant velocity towards B; that's exactly what I assumed in my example too. Read what he wrote again:
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Do you think my example differs in any way from this? If so, how?
Are you referring to Einstein's comments in section 4? If so, then do you agree with me that his statement that the equatorial clock "...must go more slowly..." (i.e. must tick over at a slower rate) than a clock at the equator means that it will tick over at a slower rate than it would if it were located at that pole - that this is a 'real phenomena'?
An observer is located at one of the poles; do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
In the case where one clock moves away from the first, travels on a closed path, then rejoins it, and you are comparing the clocks in the same frame you started with, the difference in readings must be explained by the motion of the clock that traveled, which requires acceleration (+ and -) at the beginning and end of the trip. There is nothing else to be used as a cause.
I appreciate that you have answered my question in relation to 'those comments' however my questions in relation to the equatorial clock's variation in it's rate of operation were not in relation to any eventual "...difference in readings..." nor any "cause" of that phenomenon.
This case is then depicted/extended to the earth rotation example. The conclusion is the same.
The clock that takes the longest closed path, records the least amount of time.
The equatorial clock would run slower according to any earth bound clock not on the equator.
This doesn't answer my question viz -
"An observer is located at one of the poles; do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?"
As an analogy - an observer is located on a mountain-top, he descends the mountain; is he entitled to be of the opinion that his clock is then ticking over at a slower rate than it was before he moved down the mountain?
I provide this as being an analogy on the basis of the principle of equivalence.
do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking over at it's 'normal' rate) would actually (really) be ticking over at a slower rate than it was before he left that location?
do you agree with me that if he moves to the equator he would be entitled to realize that his clock (although ticking at it's proper rate for the speed it has) would actually be ticking at a slower rate than it was at the pole?
My changes are in blue.
Is my translation of your quote correct?
On the basis of some of the responses I have received then, with trepidation - yes.
A168
For some reason I have been unable to respond to #121; when I hit the 'quote' button it brings up someone else's message however in an attempt to save time for both of us let's get back to basics.
In section 4 STR Einstein wrote -
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
I am of the opinion that by his comment "...must go more slowly...." he was saying that the equatorial clock ticks over at a slower rate than the polar clock.
Do you agree with my opinion?Yes, but in a relative sense, not in an absolute sense. Yes, in an absolute sense if you are referring to the proper time elapsed on each clock between two specified events, since proper time is not frame dependent.
It seems like you are referring to proper time when you use the terms "real" and "physical", since proper time is not frame dependent. And it seems you are using the term "illusion" to refer to coordinate time. If that's the case, then this whole misunderstanding can be cleared up by the simple statement that the reciprocal time dilation between clocks in relative motion refers to coordinate time, not proper time.
In section 4 STR Einstein wrote -
"Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
I am of the opinion that by his comment "...must go more slowly...." he was saying that the equatorial clock ticks over at a slower rate than the polar clock.
Do you agree with my opinion?
Yes, but in a relative sense, not in an absolute sense. Yes, in an absolute sense if you are referring to the proper time elapsed on each clock between two specified events, since proper time is not frame dependent.
I am not referring to any time "...elapsed on each clock..." nor, in my opinion, was Einstein referring to any time "...elapsed on each clock..."
Einstein was, in my opinion, stating that the equatorial clock "..must go more slowly..." than the polar clock (i.e. that the equatorial clock is ticking over at a slower rate than the polar clock) on the basis that the equatorial clock is moving relative to the 'stationary' (in an otherwise empty universe) polar clock in the same way as the clocks aboard the aircraft in the Hafele-Keating experiment were 'going more slowly' (i.e. ticking over at a slower rate) than the laboratory clocks.
It seems like you are referring to proper time when you use the terms "real" and "physical", since proper time is not frame dependent. And it seems you are using the term "illusion" to refer to coordinate time.
I believe that to be a correct assumption. My interpretation of what is 'real' or 'physical' or 'actual' or 'normal' is what takes place in an observer's reference frame not what appears to be taking place from the point of view of a person who is moving relative to that reference frame i.e. a point of view that is frame dependent.
If that's the case, then this whole misunderstanding can be cleared up by the simple statement that the reciprocal time dilation between clocks in relative motion refers to coordinate time, not proper time.
There is NO reciprocal time dilation IN Einstein's section 4!
His equatorial clock 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock! The polar clock does not, reciprocally, 'go more slowly' than the equatorial clock!
The concept of 'reciprocal time dilation between clocks in relative motion' is sections 1 through 3 of STR not section 4!
The 'reciprocal time dilation between clocks in relative motion' applies to one inertial reference frame clock that is moving past another inertial reference frame clock. There is, in Einstein's depictions, only one clock (A) that is (having accelerated) moving whilst the other clocks (B), as Einstein pointed out, have 'remained at rest'.
As you pointed out - "...the reciprocal time dilation between clocks in relative motion refers to coordinate time, not proper time." So although the other clock appears on the basis of my determinations (which are based solely on the Lorentz transformations) to be ticking over at a slower rate than my clock it is not, in reality, physically ticking over at a slower rate than my clock however, in section 4 STR Einstein stipulated that clock A is 'going more slowly' than B ergo the proper time rate of A is not the same as the proper time rate of B.
Einstein's closed curve section 4 depiction could be applied to one observer (A) stationary alongside and some distance from B.
A accelerates and, continually firing his lateral rocket, moves in a closed curve around B and, having extinguished his main drive system, is then orbiting B at v.
From B's point of view A is moving (thus incurring time dilation) but from A's point of view B is not moving! (B could be spinning on it's axis thereby consistently presenting its face to A whereupon A determines that B is not moving whilst he, on the other hand experiencing g forces determines that he is centripetally accelerating).
B has, from A's point of view, remained at rest as Einstein stipulated he does.
I believe that to be a correct assumption. My interpretation of what is 'real' or 'physical' or 'actual' or 'normal' is what takes place in an observer's reference frame not what appears to be taking place from the point of view of a person who is moving relative to that reference frame i.e. a point of view that is frame dependent.
Isn't this second person also "an observer", so isn't what they measure in fact "what takes place in an observer's reference frame"? (this point is independent of the other point that you refuse to discuss, namely that there is no need to have a physical observer actually at rest in a given frame in order to consider how things look from the perspective of that frame, and that in SR this perspective is just as valid as the perspective of any other frame).
There is NO reciprocal time dilation IN Einstein's section 4!
His equatorial clock 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock! The polar clock does not, reciprocally, 'go more slowly' than the equatorial clock!
As has been discussed, that's probably because he was talking about total time elapsed over an entire orbit. Unless Einstein wished to deny the selfsame theory he had set out in sections 1-3 (which would be a silly way to read him), of course he would not deny that at a given instant, the polar clock ticks more slowly than the equatorial clock in the instantaneous inertial rest frame of the equatorial clock at that instant.
Einstein's closed curve section 4 depiction could be applied to one observer (A) stationary alongside and some distance from B.
A accelerates and, continually firing his lateral rocket, moves in a closed curve around B and, having extinguished his main drive system, is then orbiting B at v.
In that section Einstein also discusses the simpler example where A and B are initially at rest with respect to one another, then A is moved at constant velocity (i.e. constant speed in a straight line rather than a curve) towards B. Why aren't you willing to consider things from the perspective of A's inertial rest frame during the phase where A is moving towards B? Is A not an inertial observer?
DaleSpam
Apr6-09, 08:08 AM
I believe that to be a correct assumption. My interpretation of what is 'real' or 'physical' or 'actual' or 'normal' is what takes place in an observer's reference frame not what appears to be taking place from the point of view of a person who is moving relative to that reference frame i.e. a point of view that is frame dependent.So, do I understand this correctly? If A and B are in relative motion you would describe A in terms of A's rest frame and B in terms of B's rest frame and call that "real" etc. Any description of A from B's rest frame or B from A's rest frame would be "illusion" etc. Is that correct?
I assume this is correct in the case where A and B are both inertial observers, but what about non-inertial observers? You didn't seem to like non-inertial frames earlier, so would you hold to the same definition of "real" in the case that one or both of A and B are non-inertial?
Jesse; re: post 136
In your scenario, there is a C rest frame in which A and B, separated by 60 ls (light seconds), are moving to the right at .6c, with A in the lead. A changes to zero speed in the C frame ( change made arbitrarily brief and ignored). A's clock reads t. At a previous time, using the synchronization convention of sending a signal from half the distance between A and B to both, the B clock is ahead of the A clock by xbg = 45 sec, with x=60,b=.6, g=1.25.
The separation x is not 48 because when both were moving at .6c, they were equivalent to one object, therefore as long as each has the same velocity, their spacing is constant at 60 ls. That is their rest frame spacing, and is what they would measure at any other common speed. Only outside observers measure the separation between them differently.
(This is where you recite postulate 1.)
A's clock now reads t, B's clock reads t+45.
Now is when A and B see the spacing differently, because of the speed difference.
A sees B move to him in 60/.6 = 100 sec.
Because of time dilation, B's clock advances .8*100 = 80 sec.
A's clock now reads t+100, B's clock reads t+125.
The clock that experiences the least amount of time is not the one with the smallest reading, but the one with the longest path.
"Third"? I only mentioned two frames:
According to the relativity police, when both A and B move at .6c, it must be in reference to a specific frame! Follow your own rules!
In defense of cos, your responses are long and cluttered, with side excursions to things that aren't relevant to the original question, and are actually distracting. Post 1, was a simple example with two clocks at one (approx.) location, with one moving away and returning. The question was essentially, can Einstein's statement about the time difference be taken literally.
There was no question regarding other frames or what ifs. When people ask basic questions, they need answers in terms they can understand, not a course in 4-dimensional donut theory.
Referring to post 1:
If it isn't obvious that one clock is moving relatively to the other (no other clocks are mentioned), and the difference in time readings is attributed to the motion of the 'moving' clock, and Einstein is not known to lie about scientific experimentation, then there's a problem with comprehension, and getting meaning from the context of the writing.
If I offer you $1000, and deliver it in 100's, would you reject it just because you were expecting it in 50's?
I still recommend a good dictionary as your first information source.
matheinste
Apr6-09, 05:52 PM
In the thread "Twin paradox negation" at the end of 2008 the original discussion deteriorated into the present discussion regarding section 4 clocks. It was eventually locked by jtbell in #220 with the words
------It looks like neither side is going to budge and the participants are simply getting testier and testier, so there is no useful purpose in continuing this discussion. -------
Matheinste.
Jesse; re: post 136
In your scenario, there is a C rest frame in which A and B, separated by 60 ls (light seconds), are moving to the right at .6c, with A in the lead.
No, I specified that A and B had an initial separation of 60 ls in frame #1 where they were initially at rest before A accelerated (read post #64 again, where I said 'Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K', which Einstein had defined as the frame where A and B were initially at rest). In frame #2 where A and B are initially moving at 0.6c, the initial separation between them is not 60 ls, it is 48 light-seconds, due to length contraction.
A changes to zero speed in the C frame ( change made arbitrarily brief and ignored). A's clock reads t. At a previous time, using the synchronization convention of sending a signal from half the distance between A and B to both, the B clock is ahead of the A clock by xbg = 45 sec, with x=60,b=.6, g=1.25.
No, if the two clocks were synchronized using the Einstein synchronization convention in the frame #1 where they were at rest, then in the frame where they are both moving at 0.6c, they will be out-of-sync by 36 seconds. Where do you get the idea that they will be out-of-sync by xbg? Maybe this relates to your misunderstanding about which frame they are 60 light-seconds apart in--it's true that if two clocks were a distance of x apart in the frame where they are moving at speed b, and the clocks are synchronized in their own rest frame, then in the frame where they're moving at speed b they'll be out-of-sync by xbg/c^2 (and we're using units where c=1 here). However, if two clocks are a distance of x apart in their own rest frame, and they are synchronized in their rest frame, then in a frame where they're moving at speed b they'll be out-of-sync by xb/c^2, and again I had specified that the 60 light-second separation was in their own rest frame. You can verify that xb/c^2 is the correct formula in this case using the Lorentz transformation. Suppose that in frame #1, A is at rest at position x=0 before accelerating, and B is at rest at position x=60. A accelerates at time t=0, and at that moment A reads 0 seconds and B reads 0 seconds. As long as each clock is at rest its reading matches with coordinate time; for example, at coordinate time t=-10, A reads -10 seconds and B reads -10 seconds. After A accelerates to 0.6c, its reading no longer matches with coordinate time in this frame, but B's continues to do so since it remains at rest; at t=10 seconds B reads 10 seconds, and at t=36 seconds B reads 36 seconds.
So, the event of B reading 36 seconds happens at position x=60, time t=36 in this frame, while the event of A reading 0 seconds (and instantaneously accelerating) happens at x=0, t=0 in this frame. Now we transform to frame #2 which is moving at 0.6c relative to frame #1; in this frame A and B were initially moving at 0.6c in the -x' direction, then A came to rest while B continued to move at the same speed and eventually caught up with A. If we know the coordinates x,t of an event in frame #1 and we want to know the coordinates x',t' of the same event in frame #2, then with gamma = 1.25, the Lorentz transformation equations are:
x' = 1.25 * (x - 0.6c*t)
t' = 1.25 * (t - 0.6c*x/c^2)
If you plug in x=0 and t=0 into this transformation, for the event of A reading 0 seconds and accelerating, you get x'=0 and t'=0 in frame #2. Now plug in the event of B reading 36 seconds, which has coordinates x=60 and t=36 in frame #1. This gives:
x' = 1.25 * (60 - 0.6*36) = 1.25 * (60 - 21.6) = 1.25 * 38.4 = 48
t' = 1.25 * (36 - 0.6*60) = 1.25 * (36 - 36) = 0
So, you can see that the event of B reading 36 seconds happens at t'=0 in this frame, and is thus simultaneous with the event of A reading 0 seconds which also happens at t'=0 in this frame. And you can also see that the spatial separation between A and B at this moment is 48 light-seconds in this frame.
We could also show that at any moment prior to A's acceleration, it's still true in this frame #2 that B is 36 seconds ahead and that the two clocks are 48 light-seconds apart. For example, consider the event of A reading -100 seconds, which in the unprimed frame #1 happens at x=0 and t=-100. In the primed frame #2 the coordinates of this event are:
x' = 1.25 * (0 - 0.6*-100) = 1.25 * (60) = 75
t' = 1.25 * (-100 - 0.6*0) = 1.25 * (-100) = -125
I claim that in frame #2, this event is simultaneous with the event of B reading -64 seconds. In the unprimed frame #1, B reads -64 seconds at x=60, t=-64, so in the primed frame #2 the coordinates of this event are:
x' = 1.25 * (60 - 0.6*-64) = 1.25 * (60 + 38.4) = 1.25 * (98.4) = 123
t' = 1.25 * (-64 - 0.6*60) = 1.25 * (-64 - 36) = 1.25 * (-100) = -125
So you can see that in frame #2 these events are indeed simultaneous, since they both happen at t'=-125. You can also see that the distance between A and B at this moment is 123 - 75 = 48 light-seconds, just as before.
The separation x is not 48 because when both were moving at .6c, they were equivalent to one object, therefore as long as each has the same velocity, their spacing is constant at 60 ls. That is their rest frame spacing, and is what they would measure at any other common speed. Only outside observers measure the separation between them differently.
The frame where both are moving at 0.6c is by definition not their "rest frame"! I specified that they had a separation of 60 light-seconds in the frame #1 where they were both initially at rest until A accelerated. This means that in the frame #2 where they were both moving at 0.6c until A accelerated, their separation is 48 light-seconds. Either you just misunderstood what frame the 60 light-second figure was supposed to refer to, or you are misunderstanding something more basic about the term "rest frame" and how length in the rest frame is related to length in other frames by the length contraction equation.
"Third"? I only mentioned two frames:
1) the frame where A and B were initially at rest, then after A accelerated it was moving at 0.6c while B remained at rest
2) the frame where A and B were initially moving at 0.6c, then after A accelerated it came to rest while B continued to move at 0.6c
According to the relativity police, when both A and B move at .6c, it must be in reference to a specific frame! Follow your own rules!
Of course it's in reference to a specific frame, the second of the two frames I mentioned--that's the primed frame #2 in the Lorentz transformation above, and also the one I put in bold in the quote from the previous post. So what is the third frame that you think is needed? Perhaps you are suggesting there needs to be a third object C which is at rest in frame #2...but this would be the same mistake cos made, in SR there is absolutely no need to have an object at rest in a given frame in order to analyze things from the perspective of that frame, a "frame" is just a coordinate system for assigning space and time coordinates to events. In any case, even if we do introduce an object C which is at rest in frame #2, there are still only two inertial frames to consider, because A and B would share the same inertial rest frame before A accelerated, and A and C would share the same inertial rest frame after A accelerated.
In defense of cos, your responses are long and cluttered, with side excursions to things that aren't relevant to the original question, and are actually distracting. Post 1, was a simple example with two clocks at one (approx.) location, with one moving away and returning. The question was essentially, can Einstein's statement about the time difference be taken literally.
There was no question regarding other frames or what ifs. When people ask basic questions, they need answers in terms they can understand, not a course in 4-dimensional donut theory.
But his whole question is about where there is a real physical truth about which clock is "actually" ticking slower at a given moment. I specifically mentioned that of course there was a real physical truth about which clock ticked more in total over the course of the two clocks departing and returning, but he made clear that he did not just want to talk about total time elapsed or average rate of ticking over the course of an extended trip, he wanted to talk about the relative rate of ticking at a single instant or a very brief time-interval. And if he doesn't understand that there is no single correct answer to the question of which clock is ticking slower at a given instant--that different inertial frames disagree about which is ticking slower at a given instant (because they disagree about which clock has a greater instantaneous velocity at that instant), and that all frames' perspectives are considered equally valid, and that to try to say there's a single correct answer is equivalent to introducing some notion of absolute time, which is the opposite of what relativity says. So, I think bringing up different frames is pretty critical to making sure he's not misunderstanding something very basic about SR.
If it isn't obvious that one clock is moving relatively to the other (no other clocks are mentioned), and the difference in time readings is attributed to the motion of the 'moving' clock, and Einstein is not known to lie about scientific experimentation, then there's a problem with comprehension, and getting meaning from the context of the writing.
Again, if you read cos' subsequent posts, it's clear he's not just talking about total time elapsed on each clock, he wants to talk about whether we can say one clock is ticking slower at any given moment. And the answer in relativity is "not in any frame-independent sense; different frames have different opinions about which clock is ticking slower at a given moment, and all inertial frames are considered equally valid in SR."
Einstein was, in my opinion, stating that the equatorial clock "..must go more slowly..." than the polar clock (i.e. that the equatorial clock is ticking over at a slower rate than the polar clock) on the basis that the equatorial clock is moving relative to the 'stationary' (in an otherwise empty universe) polar clock in the same way as the clocks aboard the aircraft in the Hafele-Keating experiment were 'going more slowly' (i.e. ticking over at a slower rate) than the laboratory clocks.Right, assuming we ignore gravity.
I believe that to be a correct assumption. My interpretation of what is 'real' or 'physical' or 'actual' or 'normal' is what takes place in an observer's reference frame not what appears to be taking place from the point of view of a person who is moving relative to that reference frame i.e. a point of view that is frame dependent.OK, you're simply using a definition of "real" that others on this forum do not. No problem.
His equatorial clock 'goes more slowly' (i.e. ticks over at a slower rate) than the polar clock! The polar clock does not, reciprocally, 'go more slowly' than the equatorial clock!Right, because the equatorial clock does not stay in a single inertial frame. The standard time dilation equations can't be used in the non-inertial frame that the equatorial clock remains at rest in.Einstein's closed curve section 4 depiction could be applied to one observer (A) stationary alongside and some distance from B.
A accelerates and, continually firing his lateral rocket, moves in a closed curve around B and, having extinguished his main drive system, is then orbiting B at v.Not if we're still ignoring gravity. Without gravity, A would have to continuously fire his rocket in order to maintain a circular path around B.From B's point of view A is moving (thus incurring time dilation) but from A's point of view B is not moving! (B could be spinning on it's axis thereby consistently presenting its face to A whereupon A determines that B is not moving whilst he, on the other hand experiencing g forces determines that he is centripetally accelerating).
B has, from A's point of view, remained at rest as Einstein stipulated he does.Well, notice that in the non-inertial frame that A is at rest in while circling B, the relative velocity between the two clocks is zero. Both clocks are stationary with respect to this rotating reference frame.
This would be similar to a spinning wheel in deep space with negligible gravity, and a clock in the center, and a clock attached to the rim. If we're referring to the non-inertial reference frame in which the "rim" clock is at rest, then there is no relative motion between the clocks. Both clocks are at rest in this frame. The standard SR time dilation equations can't be used. This doesn't mean there is no time dilation, it just means that you can't use the standard SR equations to analyze non-inertial reference frames. We could use the gravitational time dilation equations to calculate the difference in the rates of each clock in this frame, and we'd get the same answer as we would by considering the center clock at rest in an inertial frame and the circling clock as in relative motion. That's no coincidence.
An (accelerating) observer at rest with and local to the circling clock would observe the center clock to run faster than his own, since he is accelerating toward the center clock continuously.
Einstein was, in my opinion, stating that the equatorial clock "..must go more slowly..." than the polar clock (i.e. that the equatorial clock is ticking over at a slower rate than the polar clock) on the basis that the equatorial clock is moving relative to the 'stationary' (in an otherwise empty universe) polar clock in the same way as the clocks aboard the aircraft in the Hafele-Keating experiment were 'going more slowly' (i.e. ticking over at a slower rate) than the laboratory clocks.
Right...
Having made the comment "Right" can I take it that you agree that an equatorial clock is ticking over at a slower rate than a polar clock ("...under otherwise identical conditions.")?
This would be similar to a spinning wheel in deep space with negligible gravity, and a clock in the center, and a clock attached to the rim.
We have a large wheel in space that, initially, is not spinning; ignoring any effects of the wheel's mass a clock at the center would be ticking over at the same rate as an identical clock at the rim.
The wheel starts spinning. According to Einstein's section 4 depiction - the rim clock (A) that is now moving around the central clock (B) is then 'going more slowly' (i.e. ticking over at a slower rate) than B which has, according to Einstein, remained at rest.
An observer located at the center of the wheel sees clock A ticking over at a slower rate than his own clock (and, obviously, at a slower rate than it was before the wheel started spinning).
Having read and accepted Einstein's section 4 STR depiction of a clock that is made to move in a closed curve relative to another clock (and which will, as a result, incur time dilation relative to the 'at rest' clock) observer B realizes that clock A is ticking over at a slower rate than it was before the wheel started spinning due to the fact that it is now moving whilst he has remained at rest.
I am of the opinion that observer B could be aware of the fact that if he were to move to the rim of this wheel his own clock would then also be ticking over at a slower rate than it is whilst he remains at the center of the wheel; that the 'law' of physics that caused A to start ticking over at a faster rate than it was before the wheel started spinning will also apply to his clock.
An (accelerating) observer at rest with and local to the circling clock would observe the center clock to run faster than his own, since he is accelerating toward the center clock continuously.
I am of the opinion that he does not "observe the center clock to run faster than his own, [because] he is accelerating toward the center clock continuously." but he observes the central clock to be running faster than his own clock for the simple reason that it, having remained at rest, is physically ticking over at a faster rate than his own clock.
The observer I depicted moves to the rim thus then sees the clock at the center of the wheel ticking over at a faster rate than his own clock however on the basis that he can find no reason whatsoever as to why that clock would now be ticking over at a faster rate than it was before he moved to the rim of the wheel he can only(sensibly) conclude that his clock has slowed down in the same way as did clock A when the wheel started spinning.
He should be able to realize that the 'law' of physics that caused clock A to start ticking over at a slower rate when the wheel started spinning applies equally to his clock - his reference frame.
He is unable to carry out any experiment to confirm that his clock is ticking over at a slower rate than it was prior to his relocation - his heart-beat has also slowed down as have his mental processes however his intelligence has (presumably; hopefully) not been impaired.
Having made the comment "Right" can I take it that you agree that an equatorial clock is ticking over at a slower rate than a polar clock ("...under otherwise identical conditions.")?
Note to Al68: keep in mind that cos seems to be trying to lead people into saying that the equatorial clock is ticking slower at every instant, not just over the course of an entire orbit, and not just visually when an observer next to one of the clocks looks at the other. I'm sure you'd agree that at any given moment, we can pick an inertial frame where the equatorial clock's instantaneous velocity is smaller than the polar clock's, and that it would therefore be the polar clock that is ticking slower at this moment in this frame (which is just as good as any other inertial frame).
cos
The complication in considering rotating frames is that this is an advanced topic in special relativity, halfway towards the mathematics of general relativity.
I'm going to modify your scenario slightly and consider a wheel rolling along a road. As always we ignore gravity.
Clock A is fixed to the wheel rim.
Clock B is fixed to the wheel centre.
Clock C is fixed to the road.
If the wheel is stationary, all 3 clocks agree that they are ticking at the same rate as each other. Now let the wheel roll.
We consider what is happening just at the moment that the wheel rolls over clock C in such a way that clocks A and C are momentarily at the same place.
From the point of view of inertial clock B, A and C are both ticking at the same rate as each other, both slower than B.
From the point of view of inertial clock C, A is ticking at the same rate as C, B is ticking slower than A and C.
From the point of view of accelerating clock A, C is ticking at the same rate as A, B is ticking faster than A and C.
Now how do you explain those 3 points of view in terms of "physically ticking", whatever that means?
Having made the comment "Right" can I take it that you agree that an equatorial clock is ticking over at a slower rate than a polar clock ("...under otherwise identical conditions.")?Yes, in the rest frame of the polar clock, and in the accelerated frame of the equatorial clock, if we ignore gravity. Note again that this is not standard time dilation between inertial frames. Both clocks are stationary in the "rotating" reference frame. Relative velocity between the clocks is zero in this frame.
We have a large wheel in space that, initially, is not spinning; ignoring any effects of the wheel's mass a clock at the center would be ticking over at the same rate as an identical clock at the rim.
The wheel starts spinning. According to Einstein's section 4 depiction - the rim clock (A) that is now moving around the central clock (B) is then 'going more slowly' (i.e. ticking over at a slower rate) than B which has, according to Einstein, remained at rest.That's right.
An observer located at the center of the wheel sees clock A ticking over at a slower rate than his own clock Yes.(and, obviously, at a slower rate than it was before the wheel started spinning).Yes, in the center observers rest frame. But not for an observer stationary at clock A. In his non-inertial frame, clock A runs at the same rate it always did, and the center clock B started running at a faster rate when the wheel started spinning.
Having read and accepted Einstein's section 4 STR depiction of a clock that is made to move in a closed curve relative to another clock (and which will, as a result, incur time dilation relative to the 'at rest' clock) observer B realizes that clock A is ticking over at a slower rate than it was before the wheel started spinning due to the fact that it is now moving whilst he has remained at rest.Yes, if you're referring to the inertial frame in which clock B is spinning, and clock A is in relative motion. If you're referring to the rotating reference frame in which both clocks are stationary after the wheel starts spinning, then the difference in clock rates is not due to relative motion, since there is none. In the rotating frame, the difference in clock rates is due to proper acceleration. This is simply a matter of which perspective you choose, the result is the same.
I am of the opinion that observer B could be aware of the fact that if he were to move to the rim of this wheel his own clock would then also be ticking over at a slower rate than it is whilst he remains at the center of the wheel; that the 'law' of physics that caused A to start ticking over at a faster rate than it was before the wheel started spinning will also apply to his clock.No single clock changes its own rate in its own rest frame ever. If it does, then it doesn't qualify as a good time keeper in SR. That being said, if clock B were moved to the rim, it would run slow relative to a third clock "C" that was at the center and remained there.
I am of the opinion that he does not "observe the center clock to run faster than his own, [because] he is accelerating toward the center clock continuously." but he observes the central clock to be running faster than his own clock for the simple reason that it, having remained at rest, is physically ticking over at a faster rate than his own clock.
In the frame of clock A, both clocks are at rest. Both clocks are stationary in the accelerated frame of clock A.
The observer I depicted moves to the rim thus then sees the clock at the center of the wheel ticking over at a faster rate than his own clock however on the basis that he can find no reason whatsoever as to why that clock would now be ticking over at a faster rate than it was before he moved to the rim of the wheel he can only(sensibly) conclude that his clock has slowed down in the same way as did clock A when the wheel started spinning.He has plenty of basis. He is no longer in an inertial frame. He can't use the standard time dilation equations in his frame. Light doesn't even travel at c in his accelerated reference frame. The standard lorentz transformations do not apply in this frame. He can prove to himself that he is not at rest in an inertial frame by the simple fact that if he releases his clock into freefall it will not stay near him. The clock must be accelerated to stay in the frame.
He should be able to realize that the 'law' of physics that caused clock A to start ticking over at a slower rate when the wheel started spinning applies equally to his clock - his reference frame.Again, any clock that changes its own rate in its own frame does not qualify as a valid clock in SR.
He is unable to carry out any experiment to confirm that his clock is ticking over at a slower rate than it was prior to his relocation - his heart-beat has also slowed down as have his mental processes however his intelligence has (presumably; hopefully) not been impaired.Well, his heartrate may very well be different under different circumstances. But if he has a watch that chimes every hour according to his clock A before the wheel started spinning, it will chime every hour according to clock A afterward as well.
Note to Al68: keep in mind that cos seems to be trying to lead people into saying that the equatorial clock is ticking slower at every instant, not just over the course of an entire orbit, and not just visually when an observer next to one of the clocks looks at the other. I'm sure you'd agree that at any given moment, we can pick an inertial frame where the equatorial clock's instantaneous velocity is smaller than the polar clock's, and that it would therefore be the polar clock that is ticking slower at this moment in this frame (which is just as good as any other inertial frame).Hi JesseM,
Sure, but if I understand cos correctly, he wants to analyze things from the accelerated rest frame of the equatorial clock, ignoring gravity. Basically the one reference frame in which both clocks are stationary.
The complication in considering rotating frames is that this is an advanced topic in special relativity, halfway towards the mathematics of general relativity.
I'm going to modify your scenario slightly and consider a wheel rolling along a road. As always we ignore gravity.
Clock A is fixed to the wheel rim.
Clock B is fixed to the wheel centre.
Clock C is fixed to the road.
If the wheel is stationary, all 3 clocks agree that they are ticking at the same rate as each other. Now let the wheel roll.
We consider what is happening just at the moment that the wheel rolls over clock C in such a way that clocks A and C are momentarily at the same place.
From the point of view of inertial clock B, A and C are both ticking at the same rate as each other, both slower than B.
From the point of view of inertial clock C, A is ticking at the same rate as C, B is ticking slower than A and C.
From the point of view of accelerating clock A, C is ticking at the same rate as A, B is ticking faster than A and C.
Now how do you explain those 3 points of view in terms of "physically ticking", whatever that means?
In all 3 of those points of view the word "physically" can be placed in front of every "ticking".
On the basis that the wheel is initially at rest then starts rolling along the road your clock C is then Einstein's section 4 STR clock B (to differentiate let's call his clock B') which remains at rest whilst your clock B (Einstein's A') ticks over at a slower rate than it did before it accelerated ergo your clock C (Einstein's B') ticks over at a faster rate than your clock B (Einstein's A') not at a slower rate as you present above.
I won't bother dissecting the rest of your depictions; it's tiresome and uneccessary but perhaps I could save both of us a lot of work -
A person is located at the center of a stationary (neither moving nor spinning) hypothetically zero-mass disc in an imaginary otherwise empty universe. There is, at the rim of this disc, a large clock (A) identical to his own clock (B).
The disc starts spinning; according to Einstein's section 4 depiction - clock A (now moving in a closed curve around the stationary clock B) will tick over at a slower rate than B.
The person located at the center of the wheel will see clock A continuously ticking over at a slower rate than his own clock and on the basis that observation (determination) creates reality he is fully entitled to be of the opinion that clock A is ticking over at a slower rate than his own clock.
He has every right to anticipate that if he then moves to the rim of the disc his clock will be subjected to the same 'law' of physics that caused clock A to tick over at the slower rate than his own clock when A started moving thus that when he moves to the rim his clock will also be ticking over at a slower rate than a clock at the center of the disc.
Being located on the rim of the disc he would observe that the central clock is ticking over at a faster rate than his own clock however for him to assume that his clock has not been subjected to the same 'law' of physics as was clock A but that the central clock's rate of operation increased he, presumably being a scientist, should ask himself what indeterminable force - what phenomenon - caused the central clock to physically undergo an increase it's rate of operation?
It is my understanding that the idea of the central clock's rate of operation increasing (i.e. time contraction) was, for Einstein, an anathema.
Your depiction of a wheel rolling along a road complies with sections 1 through 3 of STR.
My depiction of a disc rotating in space complies with section 4 of STR.
"Thus, while the static observers in the cylindrical chart admits a unique family of orthogonal hyperslices T = T0, the Langevin observers admit no such hyperslices." http://en.wikipedia.org/wiki/Born_coordinates
Is quoted statement correct, and if so, is it applicable to this discussion?
A person is located at the center of a stationary (neither moving nor spinning) hypothetically zero-mass disc in an imaginary otherwise empty universe. There is, at the rim of this disc, a large clock (A) identical to his own clock (B).
The disc starts spinning; according to Einstein's section 4 depiction - clock A (now moving in a closed curve around the stationary clock B) will tick over at a slower rate than B.This is correct, but doesn't depend on whether or not the wheel was previously spinning or not.
The person located at the center of the wheel will see clock A continuously ticking over at a slower rate than his own clock and on the basis that observation (determination) creates reality he is fully entitled to be of the opinion that clock A is ticking over at a slower rate than his own clock.Also correct, but it's not just his opinion, it is objectively true in his rest frame.
He has every right to anticipate that if he then moves to the rim of the disc his clock will be subjected to the same 'law' of physics that caused clock A to tick over at the slower rate than his own clock when A started moving thus that when he moves to the rim his clock will also be ticking over at a slower rate than a clock at the center of the disc.Also correct, if he also accelerates continuously to stay stationary with clock A (and clock B) after he gets to the rim. (if he instead just moves to the rim and becomes inertial, the central clock will run slow relative to his, as he would be moving in a straight line tangent to the rim, in inertial motion, and would soon be far away.)
Being located on the rim of the disc he would observe that the central clock is ticking over at a faster rate than his own clock however for him to assume that his clock has not been subjected to the same 'law' of physics as was clock A but that the central clock's rate of operation increased he, presumably being a scientist, should ask himself what indeterminable force - what phenomenon - caused the central clock to physically undergo an increase it's rate of operation?The fact that he is now accelerating toward the central clock (just like clock A is) caused the central clock's rate to increase relative to his, the central clock's rate doesn't change in its own frame, or in any absolute sense. If this observer's clock is running slower than the central clock then the central clock is running faster than his. The "increased" rate of the central clock is only a relative increase-relative to the observer's clock. The observer never sees his own clock change its rate of ticking. The central clock doesn't tick faster than it used to in any sense whatsoever, except relative to the observer's clock.
And again, no clock ever changes its own rate of operation in its own frame. Any clock that does is "broken" in SR.
And it's still important to note that in the rotating rest frame in which clock A is stationary, clock B is also stationary, and the relative velocity between them is zero. Obviously we can't attribute the time dilation to velocity in this frame, because there is none. But attributing the time dilation to gravitational time dilation in the accelerated frame is mathematically equivalent to attributing it to relative velocity in the inertial frame in which the central clock is stationary and the rim clock is in relative motion.
Having made the comment "Right" can I take it that you agree that an equatorial clock is ticking over at a slower rate than a polar clock ("...under otherwise identical conditions.")?
Yes, in the rest frame of the polar clock, and in the accelerated frame of the equatorial clock, if we ignore gravity. Note again that this is not standard time dilation between inertial frames. Both clocks are stationary in the "rotating" reference frame. Relative velocity between the clocks is zero in this frame.
You do not need to continuously refer to the fact that we ignore gravity nor do you need to point out, 'again', that this is not standard time dilation between reference frames.
Relative velocity is not zero in the picture referred to. The equatorial clock is moving in a closed curve around the polar clock as is Einstein's analogous clock that is made to move in a closed curve around an at rest clock.
An observer located at the center of the wheel sees clock A ticking over at a slower rate than his own clock (and, obviously, at a slower rate than it was before the wheel started spinning).
Yes, in the center observers rest frame. But not for an observer stationary at clock A. In his non-inertial frame, clock A runs at the same rate it always did, and the center clock B started running at a faster rate when the wheel started spinning.
An observer located alongside clock A is not moving relative to clock A but is orbiting clock B.
When the wheel starts spinning that person is then subjected to a g force thus knows that his is no longer an inertial reference frame.
The central clock is not 'running at a faster rate' when the wheel starts spinning.
It is, from that person's point of view, ticking over at a faster rate than his own clock but to suggest that the central clock is ticking over at a faster rate than it was before the wheel started turning requires 'something' - some force or phenomenon - that has physically created this faster rate of operation however that observer has no reason whatsoever to be of the opinion that the central clock (other than appearing to be spinning on its axis which could be eliminated by it's being mounted on a free-spinning base) is moving.
There is no discernible force that has engendered a suitable equal and opposite reaction.
Having read and accepted Einstein's section 4 STR depiction of a clock that is made to move in a closed curve relative to another clock (and which will, as a result, incur time dilation relative to the 'at rest' clock) observer B realizes that clock A is ticking over at a slower rate than it was before the wheel started spinning due to the fact that it is now moving whilst he has remained at rest.
Yes, if you're referring to the inertial frame in which clock B is spinning, and clock A is in relative motion. If you're referring to the rotating reference frame in which both clocks are stationary after the wheel starts spinning, then the difference in clock rates is not due to relative motion....
I am of the opinion that it should be blatantly obvious that I am referring to the frame wherein clock A is in relative motion not to the rotating...(etc.)
I am of the opinion that observer B could be aware of the fact that if he were to move to the rim of this wheel his own clock would then also be ticking over at a slower rate than it is whilst he remains at the center of the wheel; that the 'law' of physics that caused A to start ticking over at a faster rate than it was before the wheel started spinning will also apply to his clock.
No single clock changes its own rate in its own rest frame ever. If it does, then it doesn't qualify as a good time keeper in SR. That being said, if clock B were moved to the rim, it would run slow relative to a third clock "C" that was at the center and remained there.
That's precisely what I said!
I am of the opinion that he does not "observe the center clock to run faster than his own, [because] he is accelerating toward the center clock continuously." but he observes the central clock to be running faster than his own clock for the simple reason that it, having remained at rest, is physically ticking over at a faster rate than his own clock.
In the frame of clock A, both clocks are at rest. Both clocks are stationary in the accelerated frame of clock A.
The central observer sees clock A orbiting around him; he is obviously of the opinion that clock A is moving; he moves to A's location and, for some reason, decides that he and clock A are no longer moving?
My depiction is not in relation to what clock A determines but what the previously centrally located observer (having moved to A's location) determines.
The observer I depicted moves to the rim thus then sees the clock at the center of the wheel ticking over at a faster rate than his own clock however on the basis that he can find no reason whatsoever as to why that clock would now be ticking over at a faster rate than it was before he moved to the rim of the wheel he can only(sensibly) conclude that his clock has slowed down in the same way as did clock A when the wheel started spinning.
He has plenty of basis. He is no longer in an inertial frame.
How does the fact that he is no longer in an inertial frame provide a reason for the central clock ticking over at a faster rate than it did before he moved to the rim?
He can't use the standard time dilation equations in his frame.
How would using the standard time dilation equations provide him with an identification of an indeterminable force?
Light doesn't even travel at c in his accelerated reference frame.
Light emanating from the central light clock does reach him at c in precisely the same way that light from the sun reaches us at c.
The standard lorentz transformations do not apply in this frame.
I'm not sure to which frame you are referring however Einstein pointed out that the slower rate of operation of the clock on the rim is in accordance with the equation .5tv^2/c^2.
He can prove to himself that he is not at rest in an inertial frame by the simple fact that if he releases his clock into freefall it will not stay near him. The clock must be accelerated to stay in the frame.
Having moved from the centre of the wheel to it's rim he already knows that he is not at rest in an inertial reference frame.
Again, any clock that changes its own rate in its own frame does not qualify as a valid clock in SR.
In section 4 Einstein pointed out that a clock that moves to another clock's location does change it's own rate. It, according to Einstein, 'goes more slowly' than it did before it started moving.
In sections 1 through 3 of SR "...any clock that changes its own rate in its own frame does not qualify as a valid clock in SR." however in section 4 Einstein introduced a clock that does 'change it's own rate' - by moving!
He is unable to carry out any experiment to confirm that his clock is ticking over at a slower rate than it was prior to his relocation - his heart-beat has also slowed down as have his mental processes however his intelligence has (presumably; hopefully) not been impaired.
Well, his heartrate may very well be different under different circumstances.
And your reason for making that comment was...? I really don't believe that it contributed anything.
But if he has a watch that chimes every hour according to his clock A before the wheel started spinning, it will chime every hour according to clock A afterward as well.
Is it not feasible that because his seconds are shorter than they were before he started moving that his hours are also shorter?
DaleSpam
Apr10-09, 02:23 PM
I believe that to be a correct assumption. My interpretation of what is 'real' or 'physical' or 'actual' or 'normal' is what takes place in an observer's reference frame not what appears to be taking place from the point of view of a person who is moving relative to that reference frame i.e. a point of view that is frame dependent.So, do I understand this correctly? If A and B are in relative motion you would describe A in terms of A's rest frame and B in terms of B's rest frame and call that "real" etc. Any description of A from B's rest frame or B from A's rest frame would be "illusion" etc. Is that correct?If my understanding is correct then I think this entire thread is pretty easy to resolve.
What you describe as "real" is what is usually called "proper" (e.g. an observer's proper time is the time displayed on a clock carried by the observer which is thus at rest in the observer's frame). As you mention, proper quantities (proper time, proper length, proper acceleration, proper mass, etc.) are not frame dependent. This is one good reason for classifying "proper" quantities as "real".
Now, looking at the scenarios of interest here, we know that between when A and B start and when they meet A accumulates less proper time than B. This is a frame-invariant fact and involves only descriptions of each clock in its own rest frame. All frames agree on this, and this is what you would call "real".
However, as soon as you begin comparing the rate of one clock to another clock then you are talking about "what appears to be taking place from the point of view of a person who is moving relative to that reference frame". This is not "real" according to your definition above, and therefore it should not be surprising that different reference frames disagree on the details since they are all just "illusions" anyway. You simply cannot make any "real" statements about the relative rates of A and B.
Relative velocity is not zero in the picture referred to. The equatorial clock is moving in a closed curve around the polar clock as is Einstein's analogous clock that is made to move in a closed curve around an at rest clock.Relative velocity between the clocks is zero in the rotating reference frame, not any inertial frame.
The central clock is not 'running at a faster rate' when the wheel starts spinning.Not in an absolute sense, or relative to any inertial frame. It does run fast relative to clock A in the accelerated frame of clock A.
The central observer sees clock A orbiting around him; he is obviously of the opinion that clock A is moving; he moves to A's location and, for some reason, decides that he and clock A are no longer moving?He decides he is no longer moving relative to clock A. The relative velocity of both clocks is now zero relative to him.
How does the fact that he is no longer in an inertial frame provide a reason for the central clock ticking over at a faster rate than it did before he moved to the rim? The central clock didn't change its rate, it always ticked at a faster rate than a clock accelerating toward it in the accelerating clock's frame.
Light emanating from the central light clock does reach him at c in precisely the same way that light from the sun reaches us at c.Light from the sun doesn't reach us at precisely c. Light only travels at c relative to inertial reference frames.
I'm not sure to which frame you are referring however Einstein pointed out that the slower rate of operation of the clock on the rim is in accordance with the equation .5tv^2/c^2.Right, in the inertial frame of the center clock. But this equation can't be used in accelerated frames. If it was used, it would say that clock B ticked at the same rate as clock A in A's frame, which is clearly wrong.
In section 4 Einstein pointed out that a clock that moves to another clock's location does change it's own rate. It, according to Einstein, 'goes more slowly' than it did before it started moving.It 'goes more slowly' than the stationary clock, not necessarily more slowly that it did before. We could easily say that the "moving" clock is "going faster than it did before" relative to a third clock at rest with it after it starts moving. How does a single clock slow down and speed up at the same time? Because nothing happened to the clock itself, its rate is frame dependent. In sections 1 through 3 of SR "...any clock that changes its own rate in its own frame does not qualify as a valid clock in SR." however in section 4 Einstein introduced a clock that does 'change it's own rate' - by moving!The clock never changed its own rate, it always had different rates in different reference frames because its rate was always frame dependent.
Anytime Einstein speaks of a clock running slow relative to another, his assumption is that nothing physical is different about, or happening to the clocks. They are simply both keeping proper time. It is time itself that passes at different rates for observers in relative motion, and their clocks are just tools that record this, assuming that each clock works identically regardless of its own state of motion.
If we define two events, less proper time will elapse for the rim clock than for the center clock between those two events. The clocks just measure this effect, they don't cause the effect by "changing their rate of operation". The effect isn't caused by anything happening to the clocks.
Anytime Einstein speaks of a clock running slow relative to another, his assumption is that nothing physical is different about, or happening to the clocks. They are simply both keeping proper time. It is time itself that passes at different rates for observers in relative motion, and their clocks are just tools that record this, assuming that each clock works identically regardless of its own state of motion.
Time is the tick rate of the clock, which is a function of the ratio of its speed to light speed. It's also the rate of activity for all material objects composed of basic particles, because light is the mediator of energy transitions. Proper time occurs when the clock and observer have no relative motion, thus the observer cannot detect the change. The clock function is a real, physical effect. Clocks don't measure time since time is a relationship of events. The clock only provides a standard event to measure the rate of activity. An observer with a clock that ticks at half the rate of a 2nd clock merely records twice as many (external to their frame) events in an interval as the 2nd observer. The number of external events remains constant.
Being located on the rim of the disc he would observe that the central clock is ticking over at a faster rate than his own clock however for him to assume that his clock has not been subjected to the same 'law' of physics as was clock A but that the central clock's rate of operation increased he, presumably being a scientist, should ask himself what indeterminable force - what phenomenon - caused the central clock to physically undergo an increase it's rate of operation?
The fact that he is now accelerating toward the central clock (just like clock A is) caused the central clock's rate to increase relative to his, the central clock's rate doesn't change in its own frame, or in any absolute sense. If this observer's clock is running slower than the central clock then the central clock is running faster than his. The "increased" rate of the central clock is only a relative increase-relative to the observer's clock. The observer never sees his own clock change its rate of ticking. The central clock doesn't tick faster than it used to in any sense whatsoever, except relative to the observer's clock. And again, no clock ever changes its own rate of operation in its own frame. Any clock that does is "broken" in SR
In section 4 STR Einstein implied that a clock on the rim of the wheel (i.e. a clock that is moving in a closed curve around another clock) will 'go more slowly' (i.e. will tick over at a slower rate) than the 'at rest' clock by a factor of .5tv^2/c^2.
The v in that equation is, of course, the speed at which the moving clock is orbiting the stationary clock.
The traveler would 'see' the stationary clock ticking over at a faster rate than his clock in accordance with that equation yet there is nothing in that equation which refers to his centripetal acceleration toward the other clock!
The traveler 'sees' the central clock 'ticking over at a faster rate than it was before he started moving' thus assumes that it has changed it's own rate of operation ergo that clock is "broken".
No action taken by the traveler - accelerating or decelerating; moving at any uniform velocity toward or away from the stationary clock - has any physical effect whatsoever on that clock's rate of operation! For him to be of the opinion that it is ticking over at a faster rate than it was before he moved to the rim he must be of the opinion that it is his having moved to the rim that has caused the central tick to tick over at a faster rate than it was when he was at that location!
In section 4 Einstein effectively, analogously, wrote that the 'going more slowly' (i.e. time dilation) of the rim observer is dependent upon his rate of travel around the stationary clock. You are, in my opinion, insinuating that from the point of view of your, now, rim observer Einstein was wrong - that the moving clock does not 'go more slowly' (i.e. ticks over at a slower rate) than the stationary clock but that the stationary clock 'goes more quickly' (i.e. ticks over at a faster rate - time contraction) than the accelerated clock.
It is my understanding that the idea of time contraction was, for Einstein, an anathema.
The traveler maintaining an identical distance from the central clock (i.e. being anchored to the rim of the wheel) is analogous to an astronaut whose ship is up against an invisible immovable barrier in space some distance from a clock. He fires his rockets yet cannot move toward that clock. The fact that he fires his rocket does not increase the rate of operation of that clock!
He can pour as much power as he likes into his rocket (analogous to the rim observer increasing his rate of travel around the central clock whilst maintaining a constant distance from same i.e. the wheel is turning faster) but this will have no affect whatsoever on that clock's rate of operation yet in the case of the rim observer, the central clock's rate of operation 'does' increase (in reality, his clock 'goes [even] more slowly' than it did before the rate of spin of the wheel increased).
You wrote "If this observer's clock is running slower than the central clock then the central clock is running faster than his." and I have consistently agreed with that comment however for the traveler to be of the opinion that the central clock has undergone a change in it's rate of operation and that it is now ticking over at a faster rate than it was when he was at that location indicates to me not only a challenge to Einstein's section 4 depiction but also an indication of his gross ignorance and stupidity!
And it's still important to note that in the rotating rest frame in which clock A is stationary, clock B is also stationary, and the relative velocity between them is zero. Obviously we can't attribute the time dilation to velocity in this frame, because there is none. But attributing the time dilation to gravitational time dilation in the accelerated frame is mathematically equivalent to attributing it to relative velocity in the inertial frame in which the central clock is stationary and the rim clock is in relative motion.
Whilst it well may be "...important to note that in the rotating rest frame in which clock A is stationary, clock B is also stationary, and the relative velocity between them is zero." for the observer at the center of the wheel to be of the opinion that when he moves to it's rim he will be stationary is, in my opinion, asinine!
The wheel is spinning at perhaps several hundred thousand Ks a second. Having moved to the rim he feels a tremendous 'force' attempting to pull him away from the wheel - a force to which he was not being subjected at the center of the wheel.
Assuming that he is of the opinion that he is 'stationary' is he not likely to ask himself what is creating this 'pull'?
Is he incapable of realizing either before, during or after his relocation that being on the rim of the wheel he will be moving at the same velocity as was a clock at the rim before he moved?
Relative velocity is not zero in the picture referred to. The equatorial clock is moving in a closed curve around the polar clock as is Einstein's analogous clock that is made to move in a closed curve around an at rest clock.
Relative velocity between the clocks is zero in the rotating reference frame, not any inertial frame.
You are fully aware of the fact that I am not referring to 'the rotating reference frame'!
I am talking about the point of view of an observer who initially sees a clock on the wheel's rim (moving at perhaps several hundred thousands of kilometers a second) and who then moves to the rim whereupon, experiencing tremendous g forces, knows that he is then moving at the same velocity as the wheel's rim.
The central clock is not 'running at a faster rate' when the wheel starts spinning.
Not in an absolute sense, or relative to any inertial frame. It does run fast relative to clock A in the accelerated frame of clock A.
I have consistently agreed with this comment however for the observer to be of the opinion that the central clock is ticking over at a faster rate than it was before he moved to the rim, is in my opinion, as I have also pointed out, asinine and contradicts Einstein's statement that the accelerated clock is 'going more slowly' than the stationary clock.
The central observer sees clock A orbiting around him; he is obviously of the opinion that clock A is moving; he moves to A's location and, for some reason, decides that he and clock A are no longer moving?
He decides he is no longer moving relative to clock A. The relative velocity of both clocks is now zero relative to him.
Totally irrelevant and deliberately misleading. You are fully aware of the fact that my astronaut possesses intelligence thus is fully aware of the fact that, having moved to the rim and experiencing a tremendous g force, he is now moving at the same orbital speed as clock A!
How does the fact that he is no longer in an inertial frame provide a reason for the central clock ticking over at a faster rate than it did before he moved to the rim?
The central clock didn't change its rate, it always ticked at a faster rate than a clock accelerating toward it in the accelerating clock's frame.
Having moved to the rim and seeing the central clock ticking over at a faster rate than his own clock (i.e seemingly at a faster rate than it was before he moved) the observer can only assume that the central clock has changed it's rate of operation.
Light emanating from the central light clock does reach him at c in precisely the same way that light from the sun reaches us at c.
Light from the sun doesn't reach us at precisely c. Light only travels at c relative to inertial reference frames.
You wrote, above, "Relative velocity between the clocks is zero in the rotating reference frame..."
I'm not sure to which frame you are referring however Einstein pointed out that the slower rate of operation of the clock on the rim is in accordance with the equation .5tv^2/c^2.
Right, in the inertial frame of the center clock. But this equation can't be used in accelerated frames. If it was used, it would say that clock B ticked at the same rate as clock A in A's frame, which is clearly wrong.
In section 4 STR Einstein used that equation in relation to several accelerated frames!
Clock B, in all of his depictions is not accelerated ergo his equation, which only applies to accelerated frames, does not apply to clock B!
In section 4 Einstein pointed out that a clock that moves to another clock's location does change it's own rate. It, according to Einstein, 'goes more slowly' than it did before it started moving.
It 'goes more slowly' than the stationary clock, not necessarily more slowly that it did before. We could easily say that the "moving" clock is "going faster than it did before" relative to a third clock at rest with it after it starts moving. How does a single clock slow down and speed up at the same time? Because nothing happened to the clock itself, its rate is frame dependent. The clock never changed its own rate, it always had different rates in different reference frames because its rate was always frame dependent.
The stationary clock's rate of operation remains unchanged! In accordance with your statement that the (non-inertial) clock "'goes more slowly' than the stationary clock..." then, on the basis that the traveler knows that the stationary clock's rate of operation remains unchanged and that his clock is 'going more slowly than the unchanged stationary clock he can only assume that his clock is 'going more slowly' than it was before he started accelerating!
Anytime Einstein speaks of a clock running slow relative to another, his assumption is that nothing physical is different about, or happening to the clocks.
On the basis that one clock is ticking over at a slower rate than another clock something physical is different about those clocks! They are ticking over at different rates!
If a clock at sea-level is ticking over at a slower rate than a clock on top of a mountain something physical is creating this variation. One of them is in a stronger gravitational tidal area than the other one!
When Hafele and Keating carried out the first leg of their experiment something physical did happen to the clocks in the aircraft! They were 'going more slowly' (i.e. ticking over at a slower rate) than the laboratory clocks. The laboratory clocks remained unchanged!
Clifford M Will pointed out in Was Einstein Right? that the clocks in the aircraft should more correctly have been compared with a (relatively 'stationary') master clock at the center of the planet which (gravitational effects being allowed for) is ticking over at the same rate as Einstein's polar clock.
During that flight Hafele and Keating were analogous to a person moving from a point part-way across the rotating wheel (A') to the rim of that wheel who (erroneously) assumes that his clock is not ticking over at a slower rate than it was when he was at A's location but that A' has started ticking over at a faster rate than it was when he was at that location.
Hafele and Keating could also have been (but presumably were not) of the opinion that their clocks did not slow down when they 'moved to that more distant location on the spinning wheel' but that the laboratory clocks (clock A') ticked over at a faster rate than they did before the flight commenced ergo that the laboratory cloks changed their rate of operation!
They are simply both keeping proper time. It is time itself that passes at different rates for observers in relative motion, and their clocks are just tools that record this, assuming that each clock works identically regardless of its own state of motion.
According to Einstein - a clock that has been accelerated 'goes more slowly' (i.e.ticks over at a slower rate) than a clock that has remained at rest!
If we define two events, less proper time will elapse for the rim clock than for the center clock between those two events. The clocks just measure this effect, they don't cause the effect by "changing their rate of operation". The effect isn't caused by anything happening to the clocks.
Less proper time elapses for the rim clock than for the center clock because the rim clock is 'going more slowly' (i.e. ticking over at a slower rate) than the center clock!
I have made no suggestion to the effect that the clocks will cause the times between when those events occur to vary.
In section 4 Einstein effectively, analogously, wrote that the 'going more slowly' (i.e. time dilation) of the rim observer is dependent upon his rate of travel around the stationary clock. You are, in my opinion, insinuating that from the point of view of your, now, rim observer Einstein was wrong - that the moving clock does not 'go more slowly' (i.e. ticks over at a slower rate) than the stationary clock but that the stationary clock 'goes more quickly' (i.e. ticks over at a faster rate - time contraction) than the accelerated clock.
It is my understanding that the idea of time contraction was, for Einstein, an anathema.
If you are just comparing the rates of the two clocks to one another in given frame, then the contrast you're trying to draw here doesn't make sense--if clock X is ticking slower than Y, then of course Y is ticking faster than X, these are just two ways of saying the same thing (just like there's no difference between the statements 'Dave is taller than Stan' and 'Stan is shorter than Dave'). On the other hand, if you are talking about the rate a clock is ticking relative to coordinate time in a given frame, then it's true that in inertial frames there is no "time contraction"--a clock at rest in an inertial frame ticks at the same rate as coordinate time, while all moving clocks tick slower than coordinate time. But in a non-inertial frame like the rotating frame where the clock at the equator is at rest and ticking at the same rate as coordinate time, it is perfectly possible for a clock to tick faster than coordinate time, so in this sense "time contraction" can occur in non-inertial frames.
The wheel is spinning at perhaps several hundred thousand Ks a second. Having moved to the rim he feels a tremendous 'force' attempting to pull him away from the wheel - a force to which he was not being subjected at the center of the wheel.
Assuming that he is of the opinion that he is 'stationary' is he not likely to ask himself what is creating this 'pull'?
In non-inertial frames, G-forces which an inertial observer would attribute to acceleration are instead explained as a consequence of a "pseudo-gravitational field"--see the equivalence principle analysis (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html) from the twin paradox page (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html).
In section 4 STR Einstein used that equation in relation to several accelerated frames!
That's interesting if he did so.
In section 4 STR Einstein used that equation in relation to several accelerated frames!
That's interesting if he did so.
You can read section 4 here (http://www.fourmilab.ch/etexts/einstein/specrel/www/), nowhere does Einstein refer (explicitly or implicitly) to any non-inertial frames, although he does analyze the time on accelerating clocks from the perspective of inertial frames.
You can read section 4 here (http://www.fourmilab.ch/etexts/einstein/specrel/www/), nowhere does Einstein refer (explicitly or implicitly) to any non-inertial frames, although he does analyze the time on accelerating clocks from the perspective of inertial frames.
Thanks! Very standard stuff (for our times) then.
In section 4 STR Einstein used that equation in relation to several accelerated frames!
That's interesting if he did so.
In all but his reference to a clock at the equator he points out that each clock A starts off at rest then moves to another location and although he does not specifically refer to acceleration per se I believe that a relocation of clock A requires acceleration.
In section 4 STR Einstein implied that a clock on the rim of the wheel (i.e. a clock that is moving in a closed curve around another clock) will 'go more slowly' (i.e. will tick over at a slower rate) than the 'at rest' clock by a factor of .5tv^2/c^2.Yes, if the equation is used in the inertial frame in which the center clock is at rest.The v in that equation is, of course, the speed at which the moving clock is orbiting the stationary clock.Yes, again in the inertial frame in which the center clock is at rest.The traveler would 'see' the stationary clock ticking over at a faster rate than his clock in accordance with that equation yet there is nothing in that equation which refers to his centripetal acceleration toward the other clock!That's because the equation isn't used in the "traveler's" rest frame.The traveler 'sees' the central clock 'ticking over at a faster rate than it was before he started moving' thus assumes that it has changed it's own rate of operation ergo that clock is "broken".Not if he understands SR.
In section 4 Einstein effectively, analogously, wrote that the 'going more slowly' (i.e. time dilation) of the rim observer is dependent upon his rate of travel around the stationary clock. You are, in my opinion, insinuating that from the point of view of your, now, rim observer Einstein was wrong - that the moving clock does not 'go more slowly' (i.e. ticks over at a slower rate) than the stationary clock but that the stationary clock 'goes more quickly' (i.e. ticks over at a faster rate - time contraction) than the accelerated clock.If A>B then B<A.
You wrote "If this observer's clock is running slower than the central clock then the central clock is running faster than his." and I have consistently agreed with that comment however for the traveler to be of the opinion that the central clock has undergone a change in it's rate of operation and that it is now ticking over at a faster rate than it was when he was at that location indicates to me not only a challenge to Einstein's section 4 depiction but also an indication of his gross ignorance and stupidity!The faster rate is relative, not absolute.
Whilst it well may be "...important to note that in the rotating rest frame in which clock A is stationary, clock B is also stationary, and the relative velocity between them is zero." for the observer at the center of the wheel to be of the opinion that when he moves to it's rim he will be stationary is, in my opinion, asinine!Stationary with respect to the rim clock, not in any other sense.
The wheel is spinning at perhaps several hundred thousand Ks a second. Having moved to the rim he feels a tremendous 'force' attempting to pull him away from the wheel - a force to which he was not being subjected at the center of the wheel.
Assuming that he is of the opinion that he is 'stationary' is he not likely to ask himself what is creating this 'pull'?
Is he incapable of realizing either before, during or after his relocation that being on the rim of the wheel he will be moving at the same velocity as was a clock at the rim before he moved?If he's moving at the same velocity as the rim clock, in the center clock's frame, then he is stationary with respect to the rim clock. The "pull" he feels is evidence of proper acceleration, not velocity.
Having moved to the rim and seeing the central clock ticking over at a faster rate than his own clock (i.e seemingly at a faster rate than it was before he moved) the observer can only assume that the central clock has changed it's rate of operation.That would be like saying that the car driving in front of me "sped up" because its speed relative to me increased when I hit my brakes.
In section 4 STR Einstein used that equation in relation to several accelerated frames!He certainly did not. He used the equation for clocks that have accelerated, not for accelerated reference frames.
Here's a question: Let's call the clock that moves from the center to join the rim clock clock "C". The statement that clock C runs slower at the rim than it did at the center is simply not true in every reference frame. For example, let's say I'm in inertial motion at the rim, local to and momentarily co-moving with the rim clock. In my frame, clock C is running faster than it did at the center. What caused clock C to "speed up its rate of operation"?
In all but his reference to a clock at the equator he points out that each clock A starts off at rest then moves to another location and although he does not specifically refer to acceleration per se I believe that a relocation of clock A requires acceleration.
But again, he's analyzing things from the perspective of an inertial frame, not from the perspective of A's non-inertial rest frame. Do you understand the difference between 1) analyzing an accelerating object from the perspective of an inertial frame, and 2) using a non-inertial frame?
Time is the tick rate of the clock, which is a function of the ratio of its speed to light speed.That ratio is always zero for the inertial rest frame of the clock.
In section 4 STR Einstein implied that a clock on the rim of the wheel (i.e. a clock that is moving in a closed curve around another clock) will 'go more slowly' (i.e. will tick over at a slower rate) than the 'at rest' clock by a factor of .5tv^2/c^2.
Yes, if the equation is used in the inertial frame in which the center clock is at rest.
So the observer is located at the center of the wheel; he determines that the rim clock (A) is moving around him at v and, applying Einstein's section 4 STR equation (i.e. "...the equation is used in the inertial frame in which the center clock is at rest."), he calculates the slower rate at which the rim clock is ticking compared to his own clock's rate of operation (i.e. clock B).
Still located at the center of the wheel is he not entitled to be of the opinion that if he moved to A's location that his clock would, then, also be ticking over at the same slower rate than a central clock?
Is he not entitled to be of the opinion that the same 'law' of physics that causes clock A to tick over at a slower rate than B would equally affect his clock?
If he sends another clock, that is synchronous with his clock, out to A's location would he not, then, see that clock ticking over at a slower rate than it was before it moved?
I am of the opinion that this is the very crux of the discussion so at this stage will delay responding to the rest of your post until I receive a response to this message.
I hope that doesn't sound pretentious - it was not intended to be; it is merely an attempt to save both of us some time.
Still located at the center of the wheel is he not entitled to be of the opinion that if he moved to A's location that his clock would, then, also be ticking over at the same slower rate than a central clock?
There isn't really room for differing "opinions" in SR, there are just statements of fact about what is true in a given frame, no one ever disagrees about what's true in a specific frame. It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel. But without the context of a particular frame, it's meaningless to offer "opinions" about which clock is ticking slower at a given moment.
So the observer is located at the center of the wheel; he determines that the rim clock (A) is moving around him at v and, applying Einstein's section 4 STR equation (i.e. "...the equation is used in the inertial frame in which the center clock is at rest."), he calculates the slower rate at which the rim clock is ticking compared to his own clock's rate of operation (i.e. clock B).
Still located at the center of the wheel is he not entitled to be of the opinion that if he moved to A's location that his clock would, then, also be ticking over at the same slower rate than a central clock?Yes, but it's not just his opinion, it's objective fact in his frame.
Is he not entitled to be of the opinion that the same 'law' of physics that causes clock A to tick over at a slower rate than B would equally affect his clock?Yes, he is.
If he sends another clock, that is synchronous with his clock, out to A's location would he not, then, see that clock ticking over at a slower rate than it was before it moved?Yes, he would. But not everyone would. Some hypothetical observers would see that same clock tick at a faster rate than it did before it moved. Because in some reference frames, it "runs slower" and in some frames it "runs faster" than it did when it was at the center.
Jesse;
To avoid the complications of too many words, here is a drawing.
Here A and B are initially at rest in the F-frame. When clock F reads 0, A and B clocks read 0, and A and B accelerate (instantly) to speed v. Per synch convention, clock B concludes clock A is ahead by d, for the duration t as indicated on A and B clocks. At the end of t, both decelerate (instantly) to zero in the F-frame. Clock A reads t + d, clock B reads t.
Do you think this scenario is correct, specifically the clock readings?
Jesse;
To avoid the complications of too many words, here is a drawing.
Here A and B are initially at rest in the F-frame. When clock F reads 0, A and B clocks read 0, and A and B accelerate (instantly) to speed v. Per synch convention, clock B concludes clock A is ahead by d, for the duration t as indicated on A and B clocks. At the end of t, both decelerate (instantly) to zero in the F-frame. Clock A reads t + d, clock B reads t.
Do you think this scenario is correct, specifically the clock readings?
No. If two clocks are initially in sync in the F frame, and then simultaneously in the F frame they both accelerate to velocity v, and later come to rest simultaneously in the F frame, then they will naturally remain synchronized in the F frame because their velocities are the same at every moment in this frame and thus their rate of ticking (=the rate they are accumulating proper time) is also the same at every moment in this frame.
If you want to look at the frame F' in which they are at rest during the phase where they were moving at velocity v in the F frame, then if we look at the prior phase where both were at rest in the F frame, in the F' frame both clocks were moving at velocity v during this phase and the time on B's clock was ahead of the time on A's clock by some constant amount vx/c^2 (where x is the distance between them in the F frame). In frame F' B comes to rest before A comes to rest (another consequence of the relativity of simultaneity), so B is then ticking faster than A and the difference between their readings increases, then A comes to rest too and the difference between their readings remains constant for a bit, and then a little later B accelerates away from rest again before A accelerates away from rest, so during this period A is ticking faster than B and the difference between their readings is decreasing, with the net result that once A accelerates and they are both moving at constant velocity in frame F' again, the time difference between their readings in frame F' will once again have returned to vx/c^2.
An illustration, in the F frame (left) and the F' frame (right)
Thanks for the illustration DrGreg! Did you use any special graphing program to put those together or just make it in a drawing program? I'd like to find some simple program to put together spacetime diagrams quickly, they'd come in handy on a lot of these threads...
Thanks for the illustration DrGreg! Did you use any special graphing program to put those together or just make it in a drawing program? I'd like to find some simple program to put together spacetime diagrams quickly, they'd come in handy on a lot of these threads...No, I just used Microsoft Powerpoint as a drawing tool (the 2007 version conveniently is able to export as PNG which I can then crop to size before uploading, otherwise I could have done a screen dump).
In the past I've used the specialist software MATLAB to draw accurate graphs, but that was using someone else's computer. I think you could use Microsoft Excel, or other graph-plotting software, in a similar way. But in this case I just drew some lines and circles and arranged them by eye.
So the observer is located at the center of the wheel; he determines that the rim clock (A) is moving around him at v and, applying Einstein's section 4 STR equation (i.e. "...the equation is used in the inertial frame in which the center clock is at rest."), he calculates the slower rate at which the rim clock is ticking compared to his own clock's rate of operation (i.e. clock B).
Still located at the center of the wheel is he not entitled to be of the opinion that if he moved to A's location that his clock would, then, also be ticking over at the same slower rate than a central clock?
Yes, but it's not just his opinion, it's objective fact in his frame.
Thank you.
Is he not entitled to be of the opinion that the same 'law' of physics that causes clock A to tick over at a slower rate than B would equally affect his clock?
Yes, he is.
Ditto.
If he sends another clock, that is synchronous with his clock, out to A's location would he not, then, see that clock ticking over at a slower rate than it was before it moved?
Yes, he would. But not everyone would. Some hypothetical observers would see that same clock tick at a faster rate than it did before it moved. Because in some reference frames, it "runs slower" and in some frames it "runs faster" than it did when it was at the center.
So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.
Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?
Are any of the numerous hypothetical observers entitled to realize that whilst that relocated clock is, from their point of view (in accordance with their mathematical calculations, determinations, predictions,*******) ticking over at a slower rate (or faster rate) than it was when it was at the center of the wheel that in the original observer's frame the relocated clock is ticking over at a slower rate than it was before it moved?
Does anything that those hypothetical observers determine have any affect whatsoever on that clock?
I suggest that they do not!
For all intents and purposes, as far as the real observer, is concerned those hypothetical observers are just that!
For all intents and purposes, as far as the real observer is concerned, those hypothetical observers do not exist!
Having determined the objective fact that a clock at the rim is ticking over at a slower rate than his own clock and having sent a clock to A's location and determined the objective fact that it is then ticking over at a slower rate than his own clock he moves to A's location.
Before he moves from the center of the wheel - you agree with me that he can determine that when he moves to the rim his clock will then be subjected to the same 'law' of physics that caused the rim clock to be ticking over at a slower rate than his centrally located clock - that his clock will be ticking over at a slower rate than it is whilst he is still at the center of the wheel.
He moves to A's location; is he then not entitled to be of the opinion that the same 'law' of physics that caused the rim clock to be ticking over at a slower rate than the central clock no longer applies to him and his clock?
Prior to moving from the center of the wheel he notices that a clock at that location is stationary alongside him. It is (relative to him) not spinning on an axis and he is not being subjected to any g force (he is actually spinning very slowly - it is a wheel of enormous diameter - but cannot feel that he is on the basis that it is an otherwise empty universe).
He moves to the wheel rim which he knows is spinning around it's hub on the basis that, having arrived at that location, he is now looking at a central clock that is spinning on it's axis but, more importantly, he is then being subjected to an enormous g force attempting to move him further away from the center of the wheel ergo he knows that his is not an inertial frame.
He knows (having previously determined the speed at which a clock on the rim is spinning around the center of the wheel) that his clock is moving at that same speed ergo applies Einstein's equation and determines the, then, slower rate of operation of his clock.
It is ticking over at it's 'proper' time but he knows that it is (as is Einstein's section 4 clock traveling in a closed curve around an at rest clock) moving and that in accordance with section 4 (as well as his determination of an objective fact whilst he was at the center of the wheel) it is 'going more slowly' than it was before he moved to the rim.
I'm not suggesting that he must or that he should arrive at this conclusion but that he could!
Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?
Yes.
Does anything that those hypothetical observers determine have any affect whatsoever on that clock?
No.
I'm not suggesting that he must or that he should arrive at this conclusion but that he could!
I can arrive at any conclusion I want any time.
Proposed answers only. If they don't make sense, read what JesseM has to say!:smile:
So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.
Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?Well, like I pointed out, that's only an objective fact in his frame. Those other hypothetical observers agree with the objective fact that clock "C" slowed down in the frame of your observer.
The same laws of physics that caused the clock to "slow down" in your observer's frame also caused the same clock to "speed up" in other frames, whether actual observers are present or not. After all, your observer is hypothetical as well.
Whether or not the clock slowed down or sped up is frame dependent, not observer dependent or a matter of opinion.
So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.
Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?
Again, it is meaningless to talk about clock rates without specifying a choice of frame. He believes that the clock at the edge of the wheel is ticking slower in the frame where he is at rest, and so does the hypothetical observer at rest in a different frame. Likewise, the hypothetical observer B at rest in the other frame believes that the clock at the center is ticking slower than the clock at the edge (at some specific moment) in the frame where that observer B is at rest, and the observer at the center of the wheel agrees. Either observer can make determinations/predictions/calculations in any frame they choose, and as long as they specify which frame a particular statement about clock rates is meant to apply in, their statements will be objective facts that all observers should agree on. On the other hand, if you talk about clock rates without specifying a choice of frame, your statements are too ill-defined to be judged true or false.
He knows (having previously determined the speed at which a clock on the rim is spinning around the center of the wheel) that his clock is moving at that same speed ergo applies Einstein's equation and determines the, then, slower rate of operation of his clock.
It is ticking over at it's 'proper' time but he knows that it is (as is Einstein's section 4 clock traveling in a closed curve around an at rest clock) moving and that in accordance with section 4 (as well as his determination of an objective fact whilst he was at the center of the wheel) it is 'going more slowly' than it was before he moved to the rim.
I'm not suggesting that he must or that he should arrive at this conclusion but that he could!
He can certainly conclude that his clock is now going more slowly in the inertial rest frame where the center of the wheel is at rest, and every possible observer would agree with that statement. But if you don't add that qualifier about which frame you mean your statements to apply to, but just say something like "my opinion is that his clock is moving more slowly once he's at the rim of the wheel", then you aren't making well-defined statements about physics.
He moves to the wheel rim which he knows is spinning around it's hub on the basis that, having arrived at that location, he is now looking at a central clock that is spinning on it's axis but, more importantly, he is then being subjected to an enormous g force attempting to move him further away from the center of the wheel ergo he knows that his is not an inertial frame.
Now that he's moved to the rim, hasn't the inertial observer at the centre become hypothetical? If hypothetical observers and the frames that one may associate with them are disallowed, how is he supposed to determine that his clock is ticking more slowly in the inertial frame associated with the hypothetical observer at the centre of the wheel? If that particular hypothetical observer and associated inertial frame is allowed, how then would other hypothetical observers and their frames be disallowed?
Again, I defer to JesseM on all serious matters.
So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.
Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?
Well, like I pointed out, that's only an objective fact in his frame. Those other hypothetical observers agree with the objective fact that clock "C" slowed down in the frame of your observer.
Those other hypothetical observers can realize that in my observer's frame his clock does slow down!
The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!
According to Einstein's section 4 the rate of operation of clock C depends on whether it accelerates or clock B accelerates and it would very much be appreciated (but I believe I am wasting my time pointing out) that my postings relate solely to section 4 STR!!!
The same laws of physics that caused the clock to "slow down" in your observer's frame also caused the same clock to "speed up" in other frames, whether actual observers are present or not.
My postings are specifically in relation to what my observer determines not what other observers determine. I repeat - The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!
After all, your observer is hypothetical as well.
A childish and valueless comment!
Whether or not the clock slowed down or sped up is frame dependent, not observer dependent or a matter of opinion.
And it is exclusively my observer's frame to which my postings specifically apply!
He moves to the wheel rim which he knows is spinning around it's hub on the basis that, having arrived at that location, he is now looking at a central clock that is spinning on it's axis but, more importantly, he is then being subjected to an enormous g force attempting to move him further away from the center of the wheel ergo he knows that his is not an inertial frame.
Now that he's moved to the rim, hasn't the inertial observer at the centre become hypothetical?
What inertial observer at the center? In my posting I make no reference to an inertial observer that has remained at the center of the wheel when my observer moves to the rim.
My observer moves to the rim as a result of which there is no observer at the center of the wheel. There is only a clock with which he compares rates of operation.
If hypothetical observers and the frames that one may associate with them are disallowed, how is he supposed to determine that his clock is ticking more slowly in the inertial frame associated with the hypothetical observer at the centre of the wheel? If that particular hypothetical observer and associated inertial frame is allowed, how then would other hypothetical observers and their frames be disallowed?
If you seek to contribute something worthwhile to this thread you could at least try to get your facts straight.
What inertial observer at the center? In my posting I make no reference to an inertial observer that has remained at the center of the wheel when my observer moves to the rim.
My observer moves to the rim as a result of which there is no observer at the center of the wheel. There is only a clock with which he compares rates of operation.
If you seek to contribute something worthwhile to this thread you could at least try to get your facts straight.
You are funny! :rofl:
BTW, are the clocks at the centre and the rim (Einstein?) synchronizable?
Those other hypothetical observers can realize that in my observer's frame his clock does slow down!Yes they would.
The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!That's right. The equations give the exact same answer regardless of what any observer thinks (including yours).
According to Einstein's section 4 the rate of operation of clock C depends on whether it accelerates or clock B accelerates and it would very much be appreciated (but I believe I am wasting my time pointing out) that my postings relate solely to section 4 STR!!!
Well, since section 4 doesn't contradict any other section, I don't see the problem.
My postings are specifically in relation to what my observer determines not what other observers determine. I repeat - The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!That's right. Whatever the answer is is objectively true in that frame and doesn't even need any observer present to be true.
And it is exclusively my observer's frame to which my postings specifically apply!That's what I thought, which is why a lot of my answers were yes with the caveat "in his frame".
The only reason I pointed out that whether or not clock C "slows down" or "speeds up" is frame dependent is just to make it clear that nothing is actually "physically happening" to the clock in any universal sense.
I know it seems pedantic to always state the frame that the velocity (and therefore the relative tick rate) of the clock is relative to, but the factor [sqrt(1-v^2/c^2) is different for different values of v, and v is different for different reference frames.
And the reason it's called relativity is because each result obtained is relative to a particular frame, and not true in any other (absolute) sense.
Rindler, http://books.google.com/books?id=fUj_LW51GfQC&printsec=frontcover#PPA185,M1
Hmmm, if I'm reading Rindler's discussion beginning from the bottonm of p185 correctly, then the clock at the centre and the rim can be made Einstein synchronous, in which case it could be said to be ticking more slowly in a frame independent manner. If I remember correctly, clocks stationary in two different Lorentz inertial frames cannot be Einstein synchronized, hence "ticking more slowly" in that case only has a frame dependent meaning. Just thinking intuitively here, is this actually correct?
It seems like you're suggesting that something physically happens to the clocks. This is simply not the case. The rate that a clock ticks is simply a frame dependent quantity. It's different for different reference frames. Saying that a clock actually changes its "ticking rate" is like saying that a car "slowed down" because its relative speed is different for different observers in relative motion. And the fact that the cars relative speed depends on reference frame doesn't mean that the observers disagree, they will agree that the relative speed of the car frame dependent. .
Hi Al68.
I swear that I am not singling you out. I was browsing other threads and this caught my attention.
You say that the rate that a clock ticks is simply a frame dependent quantity. Really? Correct me if I am wrong, but are not all clocks man made machines that are designed to tick or move at a predetermined rate that is determined by man? A clock is not some thing that motivated to tick or count off numbers by some outside influence, a clock is not motivated by some exterior force that move it’s inner workings. A clock is just a machine designed to move or count off numerical increments according to how it was made. A clock will tick at the same rate in any frame of reference, how that is perceived by man is another story. A clock's motion is not dependent on a frame of reference, it will always move or count off numbers at a predetermined rate that can only be changed by changing the amount of energy applied to the actual structure or inner workings of the clock. Right?
Alright, I have read though most of this thread and have seen a few outpoints that need to be resolved regarding time dilation.
First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock?
If No, than please explain or give a reference on how a clock move or changes without any energy being involved.
If yes, than what types of energy can be used to motivate the machine called a clock?
Can electricity be used? Yes
Can spring tension be used? Yes
Can the motion of mass (as in a water clock, an atomic clock) be used? Yes
I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.
You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.
If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.
In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.
So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.
If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing that is a form of energy is absurd.
Physics does not define time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.
You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.
Let the discussion begin.
matheinste
Apr12-09, 04:06 AM
Alright, I have read though most of this thread and have seen a few outpoints that need to be resolved regarding time dilation.
First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock?
If No, than please explain or give a reference on how a clock move or changes without any energy being involved.
If yes, than what types of energy can be used to motivate the machine called a clock?
Can electricity be used? Yes
Can spring tension be used? Yes
Can the motion of mass (as in a water clock, an atomic clock) be used? Yes
I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.
You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.
If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.
In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.
So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.
If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing that is a form of energy is absurd.
Physics does not define time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.
You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.
Let the discussion begin.
Any elementary textbook on Special Relativity or even Wikipedia will explain these things.
Matheinste.
BTW, are the clocks at the centre and the rim (Einstein?) synchronizable?
They are synchronized before the wheel starts spinning.
cos
Let me present an analogy to show why your obsession with which clock is "really" ticking slower, regardless of frame, is misguided.
Two astronauts Alice and Bob are travelling together in deep space (far from any gravity) and on their travels they encounter a number of pairs of objects. As they find each pair, they both take a photo, simultaneously. The results are below: the top row are Alice's photos; the bottom row are Bob's.
(Note: this is assumed to take place in a Newtonian universe. Ignore relativistic distortions to the photos.)
Now, looking at the first pair of photos on the left, which line has the steepest slope (or steepest gradient, if you prefer)? In Alice's photo, it looks like the blue line. But it Bob's photo, it looks like the red line. cos, which of the two lines really, physically, actually has the steepest slope?
Similarly, for the middle pair of photos, which line, the red or the blue, really, physically, actually has the steepest slope?
Similarly, for the rightmost pair (which is supposed to be a 3D blue helix wrapped around a red axis) which line, the red or the blue, really, physically, actually has the steepest slope?
If you say these are all nonsense questions, that is exactly my point.
Here, slope is a ratio of two distances, vertical height divided by horizontal width. The analogy is with your example of a ratio of two times.
A clock's motion is not dependent on a frame of reference, it will always move or count off numbers at a predetermined rate that can only be changed by changing the amount of energy applied to the actual structure or inner workings of the clock. Right?Are you aware that energy is frame dependent, even in classical physics? So the "amount of energy applied to the actual structure or inner workings of the clock" would itself depend on the reference frame.
And when I say that the rate a clock ticks is frame dependent, that's within SR assuming that the clock keeps perfect time. Mathematically, the value of [sqrt(1-v^2/c^2)] will be different for different values of v, and v for any specific clock is different for different reference frames.
I won't bother claiming that SR is correct, so just assume that anything I've said in this thread has the caveat "according to SR", since that's the theory being discussed.
Rindler, http://books.google.com/books?id=fUj_LW51GfQC&printsec=frontcover#PPA185,M1
Hmmm, if I'm reading Rindler's discussion beginning from the bottonm of p185 correctly, then the clock at the centre and the rim can be made Einstein synchronous, in which case it could be said to be ticking more slowly in a frame independent manner.Well if you just alter the clock at the rim to run at the same rate as the center clock in the rim clock's frame, they would stay in synch just because then the rim clock would not be keeping proper time. ie it would run slow relative to its own proper time and relative to a "good" local clock stationary with it.
There isn't really room for differing "opinions" in SR, there are just statements of fact about what is true in a given frame, no one ever disagrees about what's true in a specific frame. It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel. But without the context of a particular frame, it's meaningless to offer "opinions" about which clock is ticking slower at a given moment.
Einstein had opinions, and derived the theory you are discussing!
The 'opinion' in the quoted post by cos is 'drawing a conclusion based on fact'.
He is merely repeating the experiment as stated, and according to postulate 1 (your favorite), expects consistent physics. Per your reply, you agree.
It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel.
The context is there (if you take time to read it), and your last statement isn't needed.
... Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.
Let the discussion begin.
Energy is transferred at light speed via photons. Unlike material particles, light moves independently of its source and at a constant speed. If an object moves, the internal process of energy transfer takes longer on average. Time is not a thing, it's a relationship between events. The observer matches an event to a clock event (tick), the same as matching the end of an object to a mark on a ruler, i.e. measurement. The rate of ticks therefore depends on the speed of the clock. Anything that has a uniform periodic rate, your pulse, the earth rotation, yearly cycle, atomic vibrations, etc. can be used, depending on the precision required.
Einstein had opinions, and derived the theory you are discussing!
I said "no rooms for differing opinions within SR", meaning among those who already accept the theory and are discussing conclusions made using the theory.
It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel.
The context is there (if you take time to read it), and your last statement isn't needed.
cos did eventually say he was talking about the frame of the observer at the center of the wheel, but it took a lot of prodding from other people before he did so. And it's still not completely clear to me that he would agree with the following:
1. That conclusions in all inertial frames are equally valid, even ones in which no observer happens to be at rest
2. That different observers never have differing opinions on any statements as long as the context of what frames they're talking about is clear
3. That an observer is not "naturally" required to use the frame where he is at rest when making statements about clock rates
Well if you just alter the clock at the rim to run at the same rate as the center clock in the rim clock's frame, they would stay in synch just because then the rim clock would not be keeping proper time. ie it would run slow relative to its own proper time and relative to a "good" local clock stationary with it.
And is it true that such a thing couldn't be done with two clocks moving at different constant velocities relative to a Lorentz inertial frame?
In addition to whether two particular clocks can be (rate?, Einstein?) synchronized, there is the question of whether that synchronization agrees with slow clock transport. Jammer refers to Rumpf's study on this: http://books.google.com/books?id=vuTXBPvswOwC&printsec=frontcover#PPA288,M1.
We can design the clocks to emit flashes of light at hourly intervals. Position an observer M above the center clock on the axis of the orbit, and assume a 24 hr orbit. A real world scenario will include a distant star as a reference for one orbit. M will count 24 flashes per orbit from the center clock. M will count less than 24 flashes per orbit from the moving clock, per time dilation.
The distance is constant between flashes and M for each clock, thus no doppler effect. The frequency of events/flashes matches the frequency of perception/detection. If M moves relative to the two clock system, the perceived frequency of flashes will change, but the clock event frequencies will not.
The motion of M alters his perception but not the physics of clock function.
I specifically make a distinction between event (light emission) and perception (light detection), in case it's causing any confusion for cos specifically, and anyone else in general.
Even Einstein ignored this, using them interchangably. An astronomer would not show you one of those beautiful Hubble photos of star fields and galaxies, and try to convince you they are all the same distance from here.
And the reason it's called relativity is because each result obtained is relative to a particular frame, and not true in any other (absolute) sense.
In section 4 STR Einstein pointed out that a clock (A) which, having accelerated, moves to the location of another clock (B) clock A will, whilst A is moving, 'go more slowly' (i.e. tick over at a slower rate) than the stationary clock.
Observers A and B will eventually both agree that A lags behind B and I see no reason why they cannot both agree that A ticked over at a slower rate than B thereby creating this lag.
I'm not talking about what either of them 'sees' or 'calculates' or 'predicts' or ‘determines’ during that trip but about what they agree to after the trip.
If A accepts that Einstein was right - that his clock did tick over at a slower rate than B as Einstein suggests it will then he could also, upon repeating that experiment, be of the opinion that whilst he is moving his clock is ticking over at a slower rate than clock B irrespective of the fact that it's rate of operation has seemingly remained unchanged.
Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.
Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?
Some people insist that whilst A is accelerating B was, according to his calculations, ticking over at a faster rate than his own clock but that when A takes his foot off the gas pedal B is instantaneously ticking over at a slower rate than his own clock.
He accelerates to an experimentally maximum attained instantaneous velocity thereby generating a gamma factor of 400 000. At that instant clock B ‘is’, according to his calculations, ticking over at the rate of 400 000 seconds for each of his own seconds.
He flicks a switch extinguishing his rockets and at that very instant clock B reverts from being 400 000 times faster than his own clock and [i]instantaneously[i/] reverts to being 400 000 times slower than his clock!
Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?
On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.
To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).
People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).
Proponents of that ‘logic’ (?) point out that the faster rate of B’s ‘tick’ during periods of acceleration exceed the slower rate of B’s tick whilst A is moving with uniform velocity thus this is, they insist, the reason why A and B find that A ultimately lags behind B.
If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.
It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!
I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).
That clock arrives at the sphere’s equator whereupon it is then ticking over at the same rate as the original equatorial clock ergo at a slower rate than my own clock.
I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock in precisely the same way as the clock I previously dispatched ticked over at a progressively slower rate i.e. the law of physics that physically altered the dispatched clock’s rate of operation as it accelerated will equally apply to my reference frame and to my clock.
I suspect that somebody will respond that from the point of view of observer XYPG on planet Poplex which is in a deadly spiral toward a black hole my clock will not progressively slow down however the views expressed, or opinions held, or determinations made, by that observer have absolutely no affect whatsoever on my observations or determinations and it is MY determinations and predictions to which my postings apply not those of potentially countless hypothetical observers.
People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).
Let me present an analogy to show why your obsession with which clock is "really" ticking slower, regardless of frame, is misguided.
<snip>
If you say these are all nonsense questions, that is exactly my point.
I am of the opinion that they are irrelevant questions.
In section 4 Einstein stated that a clock that moves toward (or is made to move in a closed curve around) another clock will 'go more slowly' (i.e. will tick over at slower rate) than the stationary clock.
If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.
It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!
I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).
That clock arrives at the sphere’s equator whereupon it is then ticking over at the same rate as the original equatorial clock ergo at a slower rate than my own clock.
I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock in precisely the same way as the clock I previously dispatched ticked over at a progressively slower rate i.e. the law of physics that physically altered the dispatched clock’s rate of operation as it accelerated will equally apply to my reference frame and to my clock.
I am of the opinion that they are irrelevant questions. The point of my post was to illustrate that that there are some questions (such as "which way is 'up' when there's no gravity?") to which there is no "real" answer, only an answer relative to a frame, and different frames may disagree on what their answer is.
If you are interested only in a single frame, and you choose to describe measurements in that frame as "real", then there's nothing to discuss.
Observers A and B will eventually both agree that A lags behind B and I see no reason why they cannot both agree that A ticked over at a slower rate than B thereby creating this lag.
Only if they both agree to use the frame in which they are currently at rest to make statements about clock rates. There is nothing that prevents them from using some other frame, it's a matter of arbitrary choice. You're talking as though an observer's inertial rest frame can somehow be taken as intrinsically representing that observer's "perspective", but there's no real basis for that; why are you so resistant to actually spelling out what frame you want the observers to use when you make statements like this?
I'm not talking about what either of them 'sees' or 'calculates' or 'predicts' or ‘determines’ during that trip but about what they agree to after the trip.
It's misleading to use the word "sees" as if it were synonymous with the other ones which refer to frame-dependent calculations. What you see visually is determined by when the light from different events strikes you, unlike frame-dependent calculations this is not a matter of arbitrary choice, all frames will agree in their predictions about what time shows on your clock when you first see the light from a distant event. The rate you see a clock ticking is in general different from the rate you calculate it to be ticking in the frame where you're at rest--for example, as A is approaching B, B will see A's clock ticking faster than his own, even though in B's rest frame A's clock is really ticking slower than his own. In order to determine when things happen in a given frame, you have to take the times you saw events and do some abstract calculations in order to determine when the events "really" happened in that frame, and it's just as easy to do the calculations using a frame where you are not at rest as it is to do the calculations for the frame where you are at rest.
Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.
This is exactly what is true in one particular non-inertial frame where A was at rest throughout this process, there's nothing silly about it, it's just a matter of how you define your coordinate system. Probably this is why physicists typically use words like "real" "physical" to refer only to coordinate-independent facts, because it would sound kind of silly to say that there was a real, physical change in the pulsar's rate of spinning at the moment A accelerated; but if you wish to defy convention and use these words to refer to coordinate-dependent facts, then you have to say that there was a real, physical change in the pulsar's rate of spinning in A's non-inertial rest frame (unless you want to specify that 'real' and 'physical' can refer only to coordinate-dependent statements made in inertial frames, but in that case you won't be able to make any statements about which of two clocks is 'really' ticking faster if the clocks are at different locations in curved spacetime, like clocks at the top and bottom of a mountain, since all coordinate systems in non-infinitesimal regions of curved spacetime are non-inertial).
Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
He doesn't say a single thing about non-inertial frames in section 4. If you disagree, please quote some part of section 4 that you think is referring to non-inertial frames.
Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?
He didn't use the words "goes more slowly" but rather said A "lags behind" B, which might be taken merely to mean that A's reading is less than B's reading when they meet. But even if you interpret "lags behind" to mean "goes more slowly", he did refer to a specific frame in that section, the "stationary" frame K in which the clocks A and B were initially at rest and synchronized:
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Note that in this translation Einstein routinely uses the word "system" to refer to what we have been calling a "frame", and he also made clear that K referred to a coordinate system in section 3.
He accelerates to an experimentally maximum attained instantaneous velocity thereby generating a gamma factor of 400 000. At that instant clock B ‘is’, according to his calculations, ticking over at the rate of 400 000 seconds for each of his own seconds.
He flicks a switch extinguishing his rockets and at that very instant clock B reverts from being 400 000 times faster than his own clock and instantaneously reverts to being 400 000 times [i]slower than his clock!
Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?
You don't appear to appreciate that non-inertial coordinate systems make exactly the same predictions about frame-independent facts as inertial ones in SR, so any purely local predictions you could make about the "clock's mechanism" or an "observer" (like whether any part of the clock breaks, or whether the observer is injured) will be exactly the same in a non-inertial frame as an inertial one. Keep in mind that in a non-inertial coordinate system, coordinate accelerations (even very large ones) need not be accompanied by G-forces as would be true in an inertial frames, because there can be "pseudo-gravitational forces" to cancel them out--again, please read this section (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html) of the twin paradox page (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html).
On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.
To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).
People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).
Yes, these things will be true in one particular non-inertial coordinate system--what's your objection, aside from some sort of aesthetic distaste? As long as one properly applies the laws of physics in this non-inertial coordinate system, all predictions made about coordinate-independent facts (the facts most physicists would refer to as 'physical' ones, even if you don't) will be exactly the same as those made using an inertial coordinate system.
If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.
It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from [i]my point of view, not his!
Only if you choose to define "your point of view" as "your inertial rest frame". Again, unlike what an observer sees visually which is intrinsic to his worldline, what happens in an observer's rest frame is a matter of abstract calculations, they could just as easily do the calculations from the perspective of a frame where they are moving at 0.99c and choose to refer to that as adopt the arbitrary convention that this frame shall be referred to as "their point of view".
I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).
And again, the rate you see it ticking will be different than the rate it's ticking in your inertial rest frame (although they will both be slower than your clock).
I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock
You have a "right" to assume that if you want to continue to calculate things from the perspective of the inertial frame where you were at rest at the pole even once you have started moving from the pole. On the other hand, if you want to calculate things from the perspective of a frame moving relative to the pole--perhaps your instantaneous inertial rest frame as you are in motion--then you have an equal "right" to assume your clock is ticking faster than a clock at the pole. Both statements are correct given that you make clear which frame you want to use, but if you don't make it clear, these statements are simply too ill-defined to be right or wrong.
I suspect that somebody will respond that from the point of view of observer XYPG on planet Poplex which is in a deadly spiral toward a black hole my clock will not progressively slow down however the views expressed, or opinions held, or determinations made, by that observer have absolutely no affect whatsoever on my observations or determinations and it is MY determinations and predictions to which my postings apply not those of potentially countless hypothetical observers.
No, YOU can make determinations from whatever frame you choose, you don't have to use the inertial frame where you are at rest. And even if you want to (arbitrarily) define "your determinations" as determinations made using inertial frame where you are at rest while at the pole, why don't you then also want to define "your observations" once you have started moving relative to the pole as determinations made in the inertial frame where you are instantaneously at rest at that moment, or even using the non-inertial frame where you have remained at rest throughout the whole journey?
People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).
That's fine as long as you understand this is an arbitrary matter of choice, there is no intrinsic reason a given observer has to calculate things from the perspective of the inertial frame where they happen to be at rest (and as I said it's puzzling why you continue to refer to the pole's rest frame as 'my' frame even once you have started moving relative to the pole). Aside from this, you have made some statements about non-inertial frames which definitely suggest confusion between coordinate-dependent facts and coordinate-independent ones (like suggesting that a large coordinate acceleration in a non-inertial frame would somehow imply a clock or observer would be damaged).
that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
A statement like this would be true in B's inertial frame. I don't understand what you mean by A's non-inertial reference frame. It is clear that you have specified A to be a non-inertial observer, but how are you specifying A's non-inertial reference frame?
Do you intend Eq. 3, 4 of http://relativity.livingreviews.org/Articles/lrr-2003-1/?
Or do you intend Eq 2 of http://journals.iut.ac.ir/ijpr/efullv5n3y2005p63-67.pdf?
If any case how are you defining simultaneity in order to compare rates of spatially separated clocks at the "same time"? Are you using constant coordinate time, or hypersurfaces orthogonal to a 4-vector in the spacetime direction of the A's worldline?
The point of my post was to illustrate that that there are some questions (such as "which way is 'up' when there's no gravity?") to which there is no "real" answer, only an answer relative to a frame, and different frames may disagree on what their answer is.
The point of my OP was to show that having arrived at B's location and having found that his clock lags behind clock B observer A is entitled to agree with Einstein that his clock 'went more slowly' (i.e. ticked over at a a slower rate) than clock B so if he repeats that experiment he is further entitled to be of the opinion that whilst his clock is ticking over at it's normal rate (e.g. at the same rate as his heart-beat) it is in reality ticking over at a slower rate than it was before he started moving as evidenced by that previous experiment and will lag behind clock B no matter when he looks at his clock.
Midway through his journey his clock will lag behind B by some 50% of the amount by which it lag behind B when he arrives at B's location on the basis that the t in Einstein's equation .5tv^2/c^2 is 50% of the total time for the journey.
In his book Was Einstein Right? Clifford M Will depicted a variation of Einstein's Principle of Simultaneity describing a train passenger moving past three people on the embankment A, B and C. (251, Oxford,1990)
A and C are equidistant from B. At the moment that the passenger (having moved past A) is directly in line with B that person illuminates a light the beams from which reach A and C simultaneously at which instant they synchronize their clocks but, according to Will, from the passenger's point of view that light will reach C before it reaches A thus, from the passenger's point of view, the clocks are not synchronized.
The passenger gets off at the next station and catches a cab back to the scene and finds, to his immense surprise, that in reality the clocks are synchronized!
He can argue until he's blue in the face that the clock's are not synchronized thus that somebody has played a trick on him by resetting one of those clocks however the simple fact is he is denying reality!
The opinions expressed, or determinations arrived at, by countless other reference frames have absolutely no bearing whatsoever on A's determinations nor on the rate of operation of his clock in the same way that the observations made by Will's train passenger does not prevent the clocks from being synchronized.
You wrote that in a gravity free location there is no "real" answer to the question as to which way is 'up'. There is a gathering of transparent space ships all at different angles to each other and all stationary. A command goes out to all ships to place a specific item in their upper bunks.
I, for one, would be very surprised if I saw Fred, in a ship that is 'upside down' to me, place his item in a bunk at his floor level not at the other one near his eye-level as is mine in my ship.
If you are interested only in a single frame, and you choose to describe measurements in that frame as "real", then there's nothing to discuss.
I have, all along, endeavored to point out that I am only interested in a single frame! A's frame!
that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
A statement like this would be true in B's inertial frame. I don't understand what you mean by A's non-inertial reference frame. It is clear that you have specified A to be a non-inertial observer, but how are you specifying A's non-inertial reference frame?
He powers up his main drive system and hits the gas pedal; he feels a force pushing him into his seat thus realizes that his is now an non-inertial reference frame. That's how I'm specifying that A's is a non-inertial reference frame and I believe that it is simple enough to stand on it's own without the application of any mathematical equation.
If any case how are you defining simultaneity in order to compare rates of spatially separated clocks at the "same time"? Are you using constant coordinate time, or hypersurfaces orthogonal to a 4-vector in the spacetime direction of the A's worldline?
An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".
He powers up his main drive system and hits the gas pedal; he feels a force pushing him into his seat thus realizes that his is now an non-inertial reference frame. That's how I'm specifying that A's is a non-inertial reference frame and I believe that it is simple enough to stand on it's own without the application of any mathematical equation.
No, all that that specifies is that A is a non-inertial observer. It does not specify a frame. A frame is a method of assigning four numbers to every point in spacetime.
An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".
Curiously the way you define things here, no frame is needed - all frames inertial and non-inertial will give the same answer.
I haven't calculated, so I'm going to guess and defer to Al68, JesseM, DaleSpam, DrGreg or anyone else that might have actually done the calculation. Consider two standard clocks (ie. clocks that will tick at the same rate when they are in the same place), one is stationary in an inertial frame K, and the other moves with constant speed relative to the inertial frame K in a circle centered on the stationary clock. The stationary clock sends out light pulses separated by delta of its proper time. The moving clock will receive those pulses at less than delta of its proper time. If one wishes to specify using t and v (as Einstein did) the amount by which the moving clock has gone slow, then one will need to use the inertial frame K (colloquially called the inertial frame of the stationary clock).
If A accepts that Einstein was right - that his clock did tick over at a slower rate than B as Einstein suggests it will then he could also, upon repeating that experiment, be of the opinion that whilst he is moving his clock is ticking over at a slower rate than clock B irrespective of the fact that it's rate of operation has seemingly remained unchanged.
He could be of any opinion he likes. Einstein never made any prediction about anyone's opinion. It's objective fact that clock B ticks slower than clock A in both B's inertial frame and the rotating frame.
Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving.... Einstein didn't say this. He said clock A would tick slower than clock B, and his calculation was in the rest frame of clock B.he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.
Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate. relative to clock B, that's right. Because in A's non-inertial frame, clock B is slower than clock A. (even though this is not shown in section 4, section 4 only shows the calculation from B's inertial frame.)
Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B? He was referring to B's inertial frame. That's clear from his calculation.
Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B? He can have any opinion he wants, but SR predicts what a clock would read if it works at the same rate regardless of such forces.
On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.
To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).
People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict). Who's claiming that the second hand of earth's clock is spinning fast in earth's frame?
Proponents of that ‘logic’ (?) point out that the faster rate of B’s ‘tick’ during periods of acceleration exceed the slower rate of B’s tick whilst A is moving with uniform velocity thus this is, they insist, the reason why A and B find that A ultimately lags behind B. Do you mean proponents like Einstein in his 1918 paper where he says "However, this is more than compensated by a faster pace of U1 (earth clock) during partial process 3 (acceleration).....The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4 (inertial motion). This consideration completely clears up the paradox that you brought up" ?
People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).Well, if you're just saying the same thing the rest of us are saying, I don't quite see your point in this thread.
DaleSpam
Apr13-09, 07:21 AM
I have, all along, endeavored to point out that I am only interested in a single frame! A's frame!How can you possibly be interested in A's frame? It is non-inertial and you reject non-inertial frames. You cannot have it both ways, if you want to do an analysis in a non-inertial frame then you must be willing to use fictitious forces in the analysis. They are an inescapable feature of non-inertial frames. This is not Einstein's requirement, but predates him by centuries.
Are you aware that energy is frame dependent, even in classical physics? So the "amount of energy applied to the actual structure or inner workings of the clock" would itself depend on the reference frame. .
I am not aware of this. Are you suggesting frames of reference emanate energy? If so, how far out does this energy emanate from a given reference frame?
What type of energy is being applied? Electromagnetic?
For example, I am driving in my car in the city, I am driving in a straight line at a constant velocity, are you suggesting that the frame of reference that I occupy is physically applying energy to the people on the street, the people in their buildings, the objects all around me, all the objects in the buildings, and depending on how far this energy can influence other things, could I include planes in the sky, boats on the ocean and other more distant things and people as those things that are influenced or having energy applied to them by my frame of reference?
Really, I am not aware of this notion that energy is frame dependent. If my example is incorrect then could you please give an example, or refer me to something that gives an example. I am familiar with Einstein’s book on relativity, if there is an example in there could you please give me the chapter.
One last thing just to be clear. Do you think that this notion of frame dependent energy is a real physical phenomenon that actually occurs in this universe on a daily basis?
If so, man I would really like you to tell me what type of energy this is or where I can research it more.
Thank you.
Energy is transferred at light speed via photons. Unlike material particles, light moves independently of its source and at a constant speed. If an object moves, the internal process of energy transfer takes longer on average. Time is not a thing, it's a relationship between events. The observer matches an event to a clock event (tick), the same as matching the end of an object to a mark on a ruler, i.e. measurement. The rate of ticks therefore depends on the speed of the clock. Anything that has a uniform periodic rate, your pulse, the earth rotation, yearly cycle, atomic vibrations, etc. can be used, depending on the precision required.
Thank you for your input. I do not want to be picky here, but not all energy is transferred at the speed of light. If I drop a ball the potential energy is converted to kinetic energy and that kinetic energy is transferred to the ground at whatever the velocity of the ball was when it contacted the ground. But that is a minor point.
I am much more interested in what you said about time. You said time is not a thing, I agree. So in this whole theory of time dilation, what do you think is actually being dilated? If time is not a thing, then what is being dilated do you think? Or are you of the mindset, like me, that time dilation is not a real physical occurrence?
I am not aware of this. Are you suggesting frames of reference emanate energy? If so, how far out does this energy emanate from a given reference frame?
The point is that there is no single objective truth about "how much energy there is" at a single instant, each frame has its own definition of the amount of energy in the world (or in any finite part of it) at any given time, but it works out that the amount of energy calculated in each inertial frame will remain constant from one moment to the next. Similarly, there is no objective truth about "how fast an object is moving"--for example, if you and I have a relative velocity of 20 meters/second, then in my rest frame I am at rest while you have a velocity of 20 m/s, while in your rest frame you are at rest while I have a velocity of 20 m/s, velocity is inherently frame-dependent. Since the kinetic energy of an object is a function of its velocity (equal to (1/2)mv^2 in Newtonian mechanics, equal to (\frac{1}{\sqrt{1 - v^2/c^2}} - 1)*mc^2 in relativity, the two being approximately equal when v is small compared to c), so the fact that velocity is frame-dependent may help you see why energy would be frame-dependent too.
Also, do you understand that a "frame" is just a coordinate system for assigning spatial coordinates x,y,z and time coordinate t to arbitrary events? It isn't a physical thing, it's just a way of labelling points in space and time, which then allows you to express the laws of physics as equations telling you how the positions of different objects are expected to change as a function of time in that system of coordinates. This is true in Newtonian physics as well as relativity (as is the fact that both velocity and energy are frame-dependent).
Consider two standard clocks (ie. clocks that will tick at the same rate when they are in the same place), one is stationary in an inertial frame K, and the other moves with constant speed relative to the inertial frame K in a circle centered on the stationary clock. The stationary clock sends out light pulses separated by delta of its proper time. The moving clock will receive those pulses at less than delta of its proper time. If one wishes to specify using t and v (as Einstein did) the amount by which the moving clock has gone slow, then one will need to use the inertial frame K (colloquially called the inertial frame of the stationary clock).
You may aware that your depiction is effectively identical to Einstein's section 4 STR picture of a clock (A) that is made to travel in an eccentric closed curve relative to the clock which has remained at rest (B) but that your version is more related to Einstein's polar-equatorial clock depiction (which is determined on the basis of "under otherwise identical conditions." i.e. the polar clock could be mounted an a tower placing it at the same distance from the Earth's center of gravity as is the equatorial clock).
An observer located alongside clock B that "...is stationary in an inertial frame K...." notices that clock A is ticking over at a slower rate than his own clock and determines "...using t and v (as Einstein did)" the amount by which the moving clock goes slow.
Observer B sends another clock (B1) to A's location whereupon he finds that clock B1 is then ticking over at the same rate as clock A ergo at a slower rate than it was before it moved to the rim and at an identically slower rate than his own clock. As that clock moves away from him (ergo it is orbiting him at increasing speeds) he notices that it's rate of operation decreases accordingly.
Having read, and accepted, Einstein's section 4 depictions of a clock that has been made to travel in a closed curve relative to a stationary clock and an equatorial clock relative to a polar clock observer B knows that it is the factor v in Einstein's equation that has determined the actual variation in the rate of operation of clock B1 ergo it is the speed at which B1 is now moving that has determined it's slower rate of operation.
Observer B moves to the rim.
He knows that his speed is increasing (he is accelerating) thus that at any given instant his velocity is greater than it was the previous instant so when he applies his v to Einstein's equation he determines the amount by which his clock is then ticking over at a specific slower rate than it was when he was stationary at the center of the wheel.
He looks at his own clock which is ticking over at it's normal rate so when he looks at the central clock and determines that it is ticking over at a faster rate than his own clock he can either assume that some indeterminable force has made that clock tick over at a faster rate than it was when he was alongside same OR that his clock is (indeterminably) ticking over at a slower rate than it was before he started moving as did the previously dispatched clock B1.
Prior to the above situation the wheel is not spinning; there are clocks (and observers) that are Einstein's section 4 "...stationary clocks at the points A and B of K which, viewed in the stationary system, are synchronous."
The wheel is made to spin.
Observer A on the rim experiences a force of acceleration thus knows that his is the moving clock which Einstein stipulated "...must go more slowly..." (i.e. tick over at a slower rate) than the stationary clock.
If that observer (now moving at a constant speed around B thus experiencing a force as the result of his centripetal acceleration) is of the opinion that he has not started moving but that it is clock B that has started spinning on it's axis (as a result of which it is, in his opinion, now ticking over at faster rate than it was before it started spinning) he is, in my opinion, not only contradicting Einstein's section 4 but is indicating gross stupidity.
There is, I submit, nothing in Einstein's section 4 presentation (or for that matter in any of the previous STR sections) which suggest that a clock that is made to spin on it's axis will tick over at a faster rate than it did before it started spinning!
If anything it should tick over at a slower rate than it was before it started spinning however that is not what observer A 'determines'.
To be honest, I don't know really what Einstein was thinking (too many reasonable possibilities). But on the basis of your definition of "An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"." in post #207, for this particular pair of clocks (A circling, B "stationary"), A sees B run fast (time dilation), and B sees A run slow (transverse Doppler), so A and B can consistently say that B runs slow compared to A by your definition for comparing rates. And yes, the circling clock is the one that slowed, not the "stationary" one, if we stipulate quite reasonably that inertial clocks in special relativity do not change their rate of ticking. And as far as I can tell, your definition is an operational definition in terms of frame independent quantities.
So now what is the problem about "If anything it should tick over at a slower rate than it was before it started spinning however that is not what observer A 'determines'."? Also, do you mean spinning or orbiting?
Ok, I see that you do mean "spinning". I am very tempted to say an ideal clock is a point, so it doesn't spin.
Anyway, instead of using ""An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"" which you defined in post #207, another inequivalent way of defining what A determines is to set up a non-inertial frame in which the time coordinate along A's wordline is A's proper time. There are several ways of doing this, and several ways of defining "same time" and comparing "rates". Non-inertial frames usually give me a headache, and asking frame dependent questions is just a matter of definitions which don't yield different predictions regarding experimental results. I can also use any inertial frame to make predictions of experimental results, and since global inertial frames exist in special relativity, I and A can use them if they are more convenient. A frame is just a way of addressing spacetime points/events. For example, we can say the White House's address is 1600 Pennsylvania Ave, or 38.898648N, 77.037692W. It shouldn't bother us that 1600 >> 38.9. We can use any address we want - it doesn't change the physical location of the White House.
If A accepts that Einstein was right - that his clock did tick over at a slower rate than B as Einstein suggests it will then he could also, upon repeating that experiment, be of the opinion that whilst he is moving his clock is ticking over at a slower rate than clock B irrespective of the fact that it's rate of operation has seemingly remained unchanged.
He could be of any opinion he likes.
Although condescending I appreciate that you have granted this permission.
Einstein never made any prediction about anyone's opinion.
Totally irrelevant albeit suitably disparaging comment! I made no suggestion that he did!
It's objective fact that clock B ticks slower than clock A in both B's inertial frame and the rotating frame.
Huh? Typo or total contradiction of Einstein's section 4? I'll assume that you meant to write that clock A ticks slower than clock B in both B's inertial frame and the rotating frame.
Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving....
Einstein didn't say this. He said clock A would tick slower than clock B, and his calculation was in the rest frame of clock B.
Einstein 'said' that clock A would tick slower than clock B (which I take it corrects your typo above) because A is made to move relative to clock B!
he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.
Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
relative to clock B, that's right. Because in A's non-inertial frame, clock B is slower than clock A. (even though this is not shown in section 4, section 4 only shows the calculation from B's inertial frame.)
In A's non-inertial frame clock B is faster than his own clock (A) not slower!
When A, in Einstein's closed curve depiction, arrives back at B's location he finds that his clock lags behind clock B!
Having, as you suggest, determined that B is ticking over at a slower rate than his own clock whilst he is moving how does he, having arrived at B's location, explain the precisely contradictory result?
Your comment that "...in A's non-inertial frame, clock B is slower than clock A." complies with you previous comment that "It's objective fact that clock B ticks slower than clock A in both B's inertial frame and the rotating frame." ergo I now get the impression that the latter was not a typo'.
Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?
He was referring to B's inertial frame. That's clear from his calculation.
You wrote above (including my corrections of what I assume was a typo') "It's objective fact that clock [A] ticks slower than clock [B] in both B's inertial frame and the rotating frame."
According to your comment, he was not only referring to B's inertial frame but also to A's non-inertial frame.
Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?
He can have any opinion he wants, but SR predicts what a clock would read if it works at the same rate regardless of such forces.
So SR 'predicts' (or can be shown to) that a clock can instantaneously revert from being 400 000 times slow to being 400 000 times fast and we are expected to believe that because SR says this that it can take place in reality?
"As far as the propositions of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."
I read that as indicating that Einstein may have been of the opinion that whilst the fully internally balanced, self-sufficient, mathematical propositions of SR can be shown to indicate that this will take place without totally destroying that clock in reality the clock will be destroyed!
Unlike some people I live in this universe.
On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.
To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).
People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).
Who's claiming that the second hand of earth's clock is spinning fast in earth's frame?
According to Robert Katz in An Introduction to the Special Theory of Relativity (36, Affiliated East-West Press, 1964) "In physics what is real is identical with what is measured."
I am of the understanding that, in physics, the word 'real' can be substituted by the words 'determined' or 'predicted' or 'observed' ergo Mendelssohn's flare on the sun does 'not' take place eight minutes before it is observed and that the moon 'physically' ceases to exist if no-one looks at it.
An astronut who determines (calculates or predicts) that the Earth clock is ticking over at the rate of 400 000 secods for each of his own seconds is of the opinion that it is ticking over at the rate of 400 000 secods for each of his own seconds.
If he determines that, in it's own reference frame, the Earth clock is not ticking over at a rate of 400 000 seconds for each of his own seconds (or at the rate of one second for each of his own 400 0000 seconds depending on his direction of travel and location of his foot relative to the gas pedal) why would he be of the opinion that it is ticking over at a faster (or slower) rate than his own clock?
Do you mean proponents like Einstein in his 1918 paper where he says "However, this is more than compensated by a faster pace of U1 (earth clock) during partial process 3 (acceleration).....The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4 (inertial motion). This consideration completely clears up the paradox that you brought up" ?
Yeah - that's right - people like Einstein who also said, 3 years later "As far as...." but you already know the rest.
His phrase "....the propositions of mathematics..." in that comment applies, in my opinion, to his reference above to "The calculation..."
Well, if you're just saying the same thing the rest of us are saying, I don't quite see your point in this thread.[/QUOTE]
From what I can see you are making completely opposing comments about A's and B's respective rates of operations hance i can see no agreement on my behalf to those conflicting comments.
atyy,
Allow me to quote relevant sections of my OP:
*********************
"In section 4 STR Einstein wrote -
"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."
What do people think he meant by the phrase "...must go more slowly..."?
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
On the (probably erroneous) basis that some people may agree that he did I follow that up with the question - On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”?
*********************
An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
My opinion :rofl: is that Einstein meant the second of your proposed interpretations ("incur time dilation"), which is a frame dependent interpretation. However, I think you have cunningly shown that your first interpretation ("An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"."), a frame independent one, is also plausible. Deciding between the interpretations is a matter of literary analysis, and asking whether he meant "on average" or "exclusively" etc.
An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".
Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?
My opinion is that Einstein meant the second of your proposed interpretations ("incur time dilation"), which is a frame dependent interpretation.
As far as i am concerned there is no distinction between my interpretations.
The observer in the first paragraph is the one (A) depicted in Einstein's section 4 who, having accelerated, is now moving toward clock B.
In section 4 Einstein effectively, analogously, suggested that clock A, having been made to move to clock B's location, is ticking over at a slower rate than it was before it started moving.
I (vainly and tremulously) take the part of observer A prior to commencing the trip. I see clock B ticking over at the same rate as my clock. I accelerate then move toward clock B at uniform velocity.
Prior to making this trip I have read and accepted Einstein's section 4 suggestion that my clock will be ticking over at a slower rate than clock B.
As far as I am concerned it makes no difference whatsoever if I 'look' at this event from a frame dependent point of view or a frame independent point of view I take Einstein's word for it that my clock is ticking over at a slower rate than clock B.
In fact I do not 'look' at this event from a frame dependent point of view or a frame independent point of view but sit back serenely, confidently, of the opinion that Einstein was right; that my clock is ticking over at a slower rate than it was before I started moving.
However, I think you have cunningly shown that your first interpretation ("An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"."), a frame independent one, is also plausible. Deciding between the interpretations is a matter of literary analysis, and asking whether he meant "on average" or "exclusively" etc.
I am of the opinion that you have, using the word 'cunningly', deliberately disparaged my comments.
cos, atyy is distinguishing between what an observer sees visually and what they calculate is true in a given frame, the same issue I was talking about in post 204 when I wrote:
It's misleading to use the word "sees" as if it were synonymous with the other ones which refer to frame-dependent calculations. What you see visually is determined by when the light from different events strikes you, unlike frame-dependent calculations this is not a matter of arbitrary choice, all frames will agree in their predictions about what time shows on your clock when you first see the light from a distant event. The rate you see a clock ticking is in general different from the rate you calculate it to be ticking in the frame where you're at rest--for example, as A is approaching B, B will see A's clock ticking faster than his own, even though in B's rest frame A's clock is really ticking slower than his own. In order to determine when things happen in a given frame, you have to take the times you saw events and do some abstract calculations in order to determine when the events "really" happened in that frame, and it's just as easy to do the calculations using a frame where you are not at rest as it is to do the calculations for the frame where you are at rest.
If when you said An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time" you did not mean to talk about how fast the distant clock appeared to be ticking visually but rather about how fast it was calculated to be ticking in the observer's frame, then perhaps you should clarify. As I said, in the thought-experiment where A and B are initially at rest with respect to each other and then A moves to meet with B, B will see A's clock ticking faster than his own due to the Doppler effect, in spite of the fact that in B's rest frame A's clock was "really" ticking more slowly than his own as it moved.
As far as I am concerned it makes no difference whatsoever if I 'look' at this event from a frame dependent point of view or a frame independent point of view I take Einstein's word for it that my clock is ticking over at a slower rate than clock B.
In fact I do not 'look' at this event from a frame dependent point of view or a frame independent point of view but sit back serenely, confidently, of the opinion that Einstein was right; that my clock is ticking over at a slower rate than it was before I started moving.
This shows that you still don't understand or accept the basic point everyone on the thread has been making: namely, that any statement about which clock is "ticking at a slower rate" at a given time is by definition frame-dependent (unless you're talking about visual appearances, but in that case you should accept that B sees A's clock ticking faster than his own, not slower). Unless there was a miscommunication and you actually don't disagree with this (in which case please say so), my opinion is that this thread should probably be shut down, since many people have told you that this is the standard view that would be accepted by any physicist (including Einstein, who specifically referred to the fact that he was talking about the 'stationary system' K, and never suggested anything about one clock ticking slower than another in a frame-independent sense), and it's against the rules to intentionally use this forum as a platform to argue for contrarian ideas about physics.
As far as i am concerned there is no distinction between my interpretations.
I am of the opinion that you have, using the word 'cunningly', deliberately disparaged my comments.
No, "cunningly" is a compliment. However, it seems that you have been more cunning than you realise! Whether or not I have actually done my calculations correctly as to what special relativity predicts for each of your interpretations, there is certainly a great, and fundamental, difference between your interpretations. Read JesseM's post #221, or study the distinction between "sees" and "computes" drawn here: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html.
DaleSpam
Apr14-09, 12:16 PM
Einstein clearly understood that a clock's rate was frame dependent. Hence his derivations in the first few sections and his repeated specification of the reference frame, including in section 4.
Huh? Typo or total contradiction of Einstein's section 4? I'll assume that you meant to write that clock A ticks slower than clock B in both B's inertial frame and the rotating frame.OOps, that was a typo on my part.In A's non-inertial frame clock B is faster than his own clock (A) not slower!Another typo on my part. Sorry about that, I know the last thing this thread needs are those kind of mistakes.
Einstein 'said' that clock A would tick slower than clock B (which I take it corrects your typo above) because A is made to move relative to clock B!Yes, that does correct my typo. Clock A ticks slower than clock B in B's inertial frame (the frame in which A is in motion). Clock A also ticks slower than clock B in the rotating frame, although the equation in section 4 is not valid for that frame, since both clocks are at rest in the rotating frame, using that equation would give a contradictory result in that frame (ie that the clocks run at the same rate).
According to your comment, he was not only referring to B's inertial frame but also to A's non-inertial frame.No, he was referring to B's inertial frame, I was referring to both. He never made the calculation from A's non-inertial frame in section 4.
When he refers to the difference in the elapsed proper time of different clocks between events (ie departure and arrival of a clock moved in a closed curve), he is not referring to any particular frame, since proper time is not frame dependent.
So SR 'predicts' (or can be shown to) that a clock can instantaneously revert from being 400 000 times slow to being 400 000 times fast and we are expected to believe that because SR says this that it can take place in reality?
"As far as the propositions of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."Wow, I was going to use that same exact quote to answer you. The above (not those exact numbers) happens in the accelerated frame of the ship in Einstein's 1918 paper, whether or not you consider that reality is up to you. Lots of funny things happen in accelerated frames, even in classical physics. Light does not travel at c, it doesn't even take a straight path relative to accelerated frames. Force does not equal mass times acceleration. The trajectory of an object moving in a straight line relative to an inertial frames takes a curved path relative to an accelerated frame.
I read that as indicating that Einstein may have been of the opinion that whilst the fully internally balanced, self-sufficient, mathematical propositions of SR can be shown to indicate that this will take place without totally destroying that clock in reality the clock will be destroyed!No, he was showing what would happen if the clock is not destroyed. He made no claim as to whether a clock would or wouldn't be destroyed.If he determines that, in it's own reference frame, the Earth clock is not ticking over at a rate of 400 000 seconds for each of his own seconds (or at the rate of one second for each of his own 400 0000 seconds depending on his direction of travel and location of his foot relative to the gas pedal) why would he be of the opinion that it is ticking over at a faster (or slower) rate than his own clock?
In Einstein's 1918 paper, the earth clock is ticking many times faster than the ship clock in the ship's accelerating reference frame, not in earth's frame.
For example, I am driving in my car in the city, I am driving in a straight line at a constant velocity, are you suggesting that the frame of reference that I occupy is physically applying energy to the people on the street, the people in their buildings, the objects all around me, all the objects in the buildings, and depending on how far this energy can influence other things, could I include planes in the sky, boats on the ocean and other more distant things and people as those things that are influenced or having energy applied to them by my frame of reference?I am saying that, in your example, kinetic energy equals 0.5 times mass times relative velocity squared in classical physics, so the kinetic energy of any of those people/objects depends on reference frame, since relative velocity depends on reference frame. In your example, a person standing in the street would have kinetic energy in the rest frame of the car equal to 0.5 times their mass times the relative velocity squared. Obviously the kinetic energy of any object is frame dependent, since relative velocity is frame dependent.
Really, I am not aware of this notion that energy is frame dependent. If my example is incorrect then could you please give an example, or refer me to something that gives an example. I am familiar with Einstein’s book on relativity, if there is an example in there could you please give me the chapter.
One last thing just to be clear. Do you think that this notion of frame dependent energy is a real physical phenomenon that actually occurs in this universe on a daily basis?
If so, man I would really like you to tell me what type of energy this is or where I can research it more.Well, if you're referring to kinetic energy, any classical physics textbook will do.
No, "cunningly" is a compliment.
I am of the opinion that whether the word 'cunning' is meant as a disparagement or a compliment depends on who is using the word and to whom they are referring.
Websters - 'cunning': characterized by wiliness and trickery.
You wrote "I think you have cunningly shown...." whereas you could have written "I think you have shown..."
However, it seems that you have been more cunning than you realise! Whether or not I have actually done my calculations correctly as to what special relativity predicts for each of your interpretations, there is certainly a great, and fundamental, difference between your interpretations.
When my observer looks at a distant clock as in my comment viz -
"An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"."
he is aware of and deletes any Doppler effect as I have pointed out in previous messages.
Would be so kind as to point out to me the "great and fundamental difference" between my comments -
"An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time"."
and
"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"
Thank you for your input. I do not want to be picky here, but not all energy is transferred at the speed of light. If I drop a ball the potential energy is converted to kinetic energy and that kinetic energy is transferred to the ground at whatever the velocity of the ball was when it contacted the ground. But that is a minor point.
I am much more interested in what you said about time. You said time is not a thing, I agree. So in this whole theory of time dilation, what do you think is actually being dilated? If time is not a thing, then what is being dilated do you think? Or are you of the mindset, like me, that time dilation is not a real physical occurrence?
Transfer of energy via photons was referring to the atomic level, but I wasn't specific about that.
Time is a measurement process, and not exclusive to science. People used the monthly cycles for agricultural purposes and the daily cycles for most other human affairs. The clock is a sequence of standard events, and events in the world are matched to the current clock event. It's the same as measuring a dimension with a ruler. In both cases, the results are recorded for future purposes, such as ordering, comparisons, and predictions. It is a human conceptual tool. The light clock is the simplest way to demonstrate how motion affects the physical clock function. Then the subjective nature of time is apparent, because the effect applies to all material objects, which includes the observer, i.e. altered perception.
As an example, if a drawing contains a scale of 1 unit = 1', and the object is dra