Understanding Time Dilation in Einstein's Special Theory of Relativity

[cos]

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 traveled 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]

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 traveled 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]

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]

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 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

 

[cos]

.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]

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]

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]

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]

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 traveled 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]

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 traveled 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]

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]

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 traveled 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]

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]

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 traveling twin stops (after a deceleration) and performs a synchronisation with the stationary twin, the traveling (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]

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 traveling twin stops (after a deceleration) and performs a synchronisation with the stationary twin, the traveling (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]

"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 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

 

[Al68]

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.

 

[Dale]

"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".

 

[Al68]

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. :!)

 

[Dale]

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.

 

[cos]

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]

Hello cos.

You seem to be neglecting the comments of DaleSpam and Al68.

Matheinste.

 

[cos]

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 traveled 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.

 

[cos]

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."'?

 

[cos]

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]

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]

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

 

[Dale]

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".

 

[cos]

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.

 

[cos]

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.

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.

 

[cos]

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]

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]

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.

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]

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

 

[Dale]

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).

 

[jtbell]

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]

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 traveling twin turned around later than traveling twin calculated. This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin.

So if you like, both clocks really ran slow, the traveling 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]

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!

 

[Dale]

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]

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

 

[cos]

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.

 

[cos]

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.

 

[cos]

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]

cos,

I assume that you are referring 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 traveled 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 traveling 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]

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 http://de.wikibooks.org/wiki/A._Einstein:_Kommentare_und_Erl%C3%A4uterungen:_Zur_Elektrodynamik_bewegter_K%C3%B6rper:_Kinematischer_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

 

[Dale]

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]

cos,

I assume that you are referring 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 traveled 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 traveling 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 traveling 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!

 

[cos]

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]

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 traveling 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 traveling 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

 

[Ich]

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.