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Time dilation ll

by cos
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cos
#1
Mar25-09, 01:47 AM
P: 212
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.
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neopolitan
#2
Mar25-09, 02:33 AM
P: 645
Quote Quote by cos View 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 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

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
cos
#3
Mar25-09, 08:03 PM
P: 212
Quote Quote by neopolitan View Post
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

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
#4
Mar25-09, 09:08 PM
P: 645
Time dilation ll

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 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
cos
#5
Mar26-09, 02:25 AM
P: 212
Quote Quote by neopolitan View Post
.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
#6
Mar26-09, 02:50 AM
P: 645
Quote Quote by cos View Post
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.
cos
#7
Mar26-09, 07:53 PM
P: 212
Quote Quote by neopolitan View Post
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
#8
Mar26-09, 08:32 PM
P: 645
Quote Quote by cos View Post
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.

Quote Quote by cos View Post
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
#9
Mar26-09, 09:24 PM
P: 1,060
Quote Quote by cos View 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 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.
cos
#10
Mar26-09, 11:31 PM
P: 212
Quote Quote by neopolitan View Post
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?

Quote Quote by neopolitan View Post
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!

Quote Quote by neopolitan View Post
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?
cos
#11
Mar26-09, 11:47 PM
P: 212
Quote Quote by matheinste View Post
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
#12
Mar27-09, 12:03 AM
P: 645
Quote Quote by cos View Post
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.

Quote Quote by cos View Post
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.

Quote Quote by cos View Post
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
cos
#13
Mar27-09, 01:46 AM
P: 212
Quote Quote by neopolitan View Post
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.

Quote Quote by neopolitan View Post
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
#14
Mar27-09, 06:58 AM
P: 645
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
cos
#15
Mar27-09, 05:50 PM
P: 212
Quote Quote by neopolitan View Post
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)?

Quote Quote by neopolitan View Post
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.

Quote Quote by neopolitan View Post
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.

Quote Quote by neopolitan View Post
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
#16
Mar27-09, 09:06 PM
P: 645
Quote Quote by cos View Post
"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 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
Al68
#17
Mar27-09, 10:27 PM
P: 801
Quote Quote by cos View Post
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
#18
Mar28-09, 12:47 AM
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Quote Quote by cos View Post
"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".


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