Understanding Time Dilation in Einstein's Special Theory of Relativity

[Al68]

"...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."

In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.

No, that's not why they're no longer in synch.

Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.

No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than Earth's clock in Earth's frame.

When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than Earth's clock, he knew all along that the ship's clock ran slower than Earth's clock in Earth's frame.

The idea (during the astronaut's period of acceleration following turn around) that the stationary clock incurs time contraction (i.e. 'is' ticking over at a faster rate than it was before he accelerated) was, for Einstein, an anathema and it it is his depictions to which I refer not interpretations arrived at by anybody else.

The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with Earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.

It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.

 

[Dale]

My references are to reality and I am of the opinion that fictitious forces do not come under that category.

That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.

The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.

This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.

It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.

No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.

 

[Al68]

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.

What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not. The reason that the ship's clock readings coincide with the end result of elapsed time is because the ship's clock is local to every relevant event and therefore represents the proper elapsed time for the ship for every event in every frame. That is not true of Earth's clock. Earth's clock is local to the departure and return only, so only those readings represent proper time for the Earth twin in a different frame. For events not local to earth, the Earth clock represents proper time in Earth's frame only. Clocks in relative motion only read proper time locally, not at a distance. So an Earth clock reading in the ship's frame does not represent the proper time in Earth's frame for any event not local to earth, like the ship's turnaround.

If that's what you mean by not being "reality", then just say so and I think everyone would agree.

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math

He got no erroneous answer. All of his math gave correct answers. And it's not contradictory because he didn't confuse reciprocal time dilation between the twins' clocks with the non-symmetrical elapsed time of the clocks.

 

[Al68]

You would probably be better off if you search for one of his papers or essays written after 1929.

Hi, neopolitan,

I think Einstein's best work was prior to 1929, despite not being perfect.

His 1918 paper on the twins paradox is nothing like the way cos is interpreting it. The only difference between it and standard resolutions is that instead of using an instantaneous turnaround with Earth's clock "jumping" ahead suddenly, he uses a realistic acceleration turnaround with Earth's clock "running fast" in the ship's frame during the turnaround. It's essentially the same as the standard resolutions, at least as far as this topic is concerned.

 

[cos]

I think cos is moving towards something like this:

"if the slowing down of clocks is supposed to real or physical, then something is amiss, and if results (like the twin paradox) suggest that only one clock ran slow, then the mathematics should be suspected, rather than the reality or physical results"

cos,

I am not saying categorically that that is your contention, it is merely what I think you are saying.

However, I should point out that you have to take into account everything in a situation like the twin's paradox. Specifically, you need to consider simultaneity (I say this even though this is not my favoured approach). Both twins will calculate that the other twin's clock ran slow during the inertial phases. What the twins will not agree on is how long those inertial phases lasted.

(I missed this posting; perhaps because it was a response to jtbell.)

I assume that you are here referring to an astronaut's out-and-return journey. You wrote "...during the inertial phases." There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.

So the results will be (time on a slow clock running for a longer time) and (time on a slow clock running for a shorter time). The change in direction was an event that was colocal with the acelerated twin, but not colocal with the twin who was inertial throughout, which means that - taking into account simultaneity - the stationary twin will calculate that the 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.

"This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin." that's what I'm saying!

So if you like, both clocks really ran slow, the 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.

"...both clocks really ran slow..." In his 1918 article Einstein attempted to overcome the paradox that 'both clocks run slow' suggesting that it is only the clock that experiences a force of acceleration that incurs time dilation not the stationary clock ergo, according to that article which, in my opinion, directly complies with his 1905 depiction of A moving in a polygonal path to B's location, both clocks do NOT 'run slow'.

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

 

[cos]

You are quite welcome, but you should be aware that I am open-minded on the subject of the meaning of the word "physical". I am willing to take either position for the sake of communication. Also, I suspect (again just guessing) that Einstein's opinion changed after Minkowski.

I would really appreciate it if we could limit the discussion to facts rather than suppositions.

However, since your opinion appears to be firm that frame-dependent quantities can be considered "physical", then it should come as no surprise that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation. The same thing happens with all other frame-variant "physical" quantities like energy, momentum, speed, etc. (e.g. clock A can "physically" have more speed than clock B in one frame and vice versa in another frame).

The idea "that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation.." Is I believe the 'paradox' that Einstein attempted to solve in his 1918 article wherein he presented that it is only the clock that experiences forces of acceleration that ticks over at the slower rate not the clock that has remained inertial thus that, according to that article (which I believe was merely an extension of his section 4 comments), Einstein effectively pointed out that clock B does not tick over at a slower rate than A.

Perhaps you could show me where, in your opinion, Einstein's shows in section 4 STR or his 1918 article that the inertial clock, B, ticks over at a slower rate than A. Prior to section 4 STR he does show that clock A ticks over at a slower rate than clock B in one frame whilst clock B ticks over at a slower rate than clock A in another frame however it is specifically his section 4 depiction to which I refer.

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

 

[Mentz114]

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

You've repeated this a number of times.

So what ? I'm not in the least perturbed. When I look in a mirror left and right are reversed, if I look through a telescope things look nearer. Nothing to lose sleep over.

 

[cos]

Then why don't you help C with his predictions? Let the movement be sinusoidal, and let the "clock rate" be adjusted by -1/2 v². Sometimes a decent calculation saves many lines of philosophical debate.

Why should I 'help C with his predictions'?

Why should I let his movement be in the nature of a curve having the form of a sine wave? Why can't he, as most sensible astronaut's would, travel in a direct route to C's location?

Sometimes a 'decent calculation' can create obfuscation.

 

[matheinste]

Cos

To observers in relative inertial motion each will see the others clock running slow due to the effects time dilation. This is fundamental to Einstein and SR. In the example you give, Enstein's clock moving in a closed path is non inertial and so factors other than time dilation must be taken into account. The non-inertial clock will show less accumulated time on its return. That is fact. Beacuse it shows a reading which lags behind that of the inertial clock you could perhaps say either that it has ticked slower for the same amount of time or that it has ticked at the same rate for a shorter length of time. I am unsure of your interpretation but I suspect the former would be what you describe as a physical change. Perhaps that is what your question boils down to i.e ticking slower for the same time as the inertial clock or ticking at the same rate as the inertial clock for less time than the inertial clock.

There is no scenario in which two clocks can separate and reunite with both having remained in inertial motion throughout. So the scenario Einstein descibes is not a denial of reciprocal time dilation.

Matheinste.

 

[JesseM]

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

As long as you stick to inertial frames, all frames will always agree about what two clocks read when they meet each other (and therefore whose time is behind), in spite of the fact that they may disagree about which clock was ticking slower at a given moment. Are you suggesting otherwise?

 

[neopolitan]

There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.

I was perhaps unclear about what I meant about "inertial phase", there are four or five inertial phases and I was only referring to two, the inertial phases in which the twins are not at rest with respect to each other. There are two or three more inertial phases: at rest together before, at rest with respect to each other in the middle and at rest together after. The other phases are when one twin accelerates (first in one direction and then in the other direction ,possibly in two stages, and finally in the first direction again to decelerate). The other twin remains inertial throughout.

"This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin." that's what I'm saying!

But my comment was directly after a passage in which I said that during inertial phases (as defined above) both twins' clocks run slow with respect to the other. That is not what you seem to be agreeing to.

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

I am going to make a huge assumption here. You are monolingual.

If you were fluently bilingual, or multilingual, you could not possibly believe that a paper could be translated from German into English without being interpreted. A word for word transliteration would be nigh on impossible to read and impossible to understand. What would be easy to comprehend when transliterated from German to English would be the mathematics, which I find rather amusing.

Perhaps I am wrong and you are fluent in German, in which case, you may be better off working directly from the German rather than the 1922 translation by W. Perrett and G.B. Jeffery, which I took to be your source (and this is why I posted words from it earlier, because there are apparently other translations). But so long as you quote English words and claim Einstein wrote them, you are just making yourself look silly.

cheers,

neopolitan

 

[jtbell]

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

Physics is not like literature or history, in which "original sources" have primary importance.

With all due respect to Einstein, one should not attach any more weight to his writings about relativity than to those of the many physicists who have refined, tested, and extended his ideas during the past century. His papers are not the last word about SR, and not the "bible" of SR. I consider them to be mainly of historical interest today.

Similarly, we don't consider Newton's "Principia Mathematica" as having precedence over all other works on classical mechanics, nor do we consider Maxwell's works as uniquely defining for classical electrodynamics.

 

[cos]

When the clocks are not colocated it takes time for the information from one clock to reach the other.

Nothing that I have written (nor, in my opinion, to which Einstein referred in his section 4 depiction) says anything about the time that it takes for the information from one clock to reach the other!

If the moving clock "looked" back at the stationary clock (as per Einstein's scenario), just before stopping...

To which of Einstein's scenario are you now referring? I can only assume that you are referring to an astronaut who has traveled out into space who, 'just before stopping' (i.e. just before coming to a stop at the end of his outward bound journey) 'looks back' at his twin's clock yet I see nothing in Einstein's section 4 depictio where he refers to that scenario.

In Einstein's initial polygonal line trip the traveler looks ahead to the stationary clock however I am of the opinion that his 'determination' (that B is, as has been claimed, ticking over at a slower rate than his own clock) is based on his calculations not on his perception of what clock B appears to be doing.

it would see only the time on the stationary clock that happened, in the moving clock's frame, x'/c ago (where x' is the separation that the moving clock thinks that it has from the stationary clock based on the traveling time). There will be more information still in transit.

You are, here, apparently referring to light travel time which I thought we had agreed the astronaut allows for!

Given that we can't agree as to whether you are saying Einstein's maths was erroneous or not, or that what he said matches with his maths, I don't feel this is going anywhere.

If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.

My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!

If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.[/QUOTE]

On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.

 

[JesseM]

My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!

No, the fact that one clock lags behind is not proof that it was ticking more slowly--you're forgetting to take into account the relativity of simultaneity. In some frames clock B may be ticking slower than clock A and yet clock A will still be behind when they meet, because A and B did not start out in sync in the first place in these frames. Consider Einstein's example in section 4 of the 1905 paper:

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.

Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.

 

[neopolitan]

If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.

On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.

Don't you love language?

I agree with Jtbell, at least in part. This is not a physics discussion.

I disagree with Jtbell, at least in part. This is not a philosophy discussion.

Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind - an example, totally not about physics but toally unhinged is http://www.geocities.com/Baja/5692/". Your increasing use of bold, and underline, concerns me.

No matter what emphasis you place on an inherently incorrect statement, it will remain an inherently incorrect statement.

If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.

So, I put it to you again, try the maths. The maths worked for Einstein...

Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.

According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?

 

[cos]

[cos] "...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."

In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.

[A168]No, that's not why they're no longer in synch.

I did NOT refer to WHY they're no longer in synch but pointed out that according to Einstein they ARE no longer in synch.

In his 1918 article (which, in my opinion, was effectively an extension of his 1905 section 4 depiction) Einstein points out that the clocks are 'no longer in synch' because one of them (clock A in his section 4 depiction) has undergone acceleration!

You may have your own interpretation of why those clocks ar no longer in synch however I'm referring to Einstein's explanation.

[cos]Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.

No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than Earth's clock in Earth's frame.

I find it particularly galling that some people take phenomenon out of context.

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than Earth's clock,

Having come to a stop (analagous to Einstein's section 4 clock A moving to B's location) his clock will, according to Einstein, lag behind the previously synchronous Earth clock.

He allows for light travel time whereupon he eventually notices that the Earth clock is ahead of his own clock (although now ticking over at the same rate as his own clock).

He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.

Alternatively, there could be a clock located at the point where he comes to a stop that is synchronous with the Earth clock (it's mechanism compensates for it's location in a much weaker gravitational tidal area) whereupon he finds that his clock lags behind that clock. He can either assume that this clock physically ticked over at faster rate than it did before he started moving toward it (in total contradiction of what his calculations 'showed' him is taking place) OR that, as Einstein suggested, his clock was 'going more slowly' than it was before he left the planet ergo is ticking over at a slower rate than this clock.

he knew all along that the ship's clock ran slower than Earth's clock in Earth's frame.

Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.

The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with Earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.

The relative rate may well be 'frame-dependent' on the basis of the calculations made by observers in those frames however the physical rate of clocks is not frame-dependant. All clocks will tick over at their own rate regardless of the opinions expressed, or determinations arrived at, by other frames.

Nothing changed with Earth clock during the turn-around nor when the astronaut previously accelerates away from the planet nor when he was moving away at uniform vleocity nor when he slows down nor when he turns his ship around nor when he accelerates back to the planet nor when he moves with uniform velocity nor when he decelerates prior to landing!

Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!

It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.

That's precisely what I'm saying!

That clock's rate of operation does not change!

Ergo when a traveler 'determines' that the inertial clock 'is' running slower or faster than his own clock he is deluding himself if he believes that the inertial clock's rate of operation has physically changed in lieu of accepting that it is his clock's rate of operation that has changed.

When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.

 

[JesseM]

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

He is obviously not saying that the accelerated clock is ticking more slowly at every instant, since at any given instant you can pick an inertial frame where the accelerated clock has a smaller velocity and thus is ticking faster. Presumably in section 4 he's talking about something like the average rate of ticking of the accelerated clock, either between the time it departs from and returns to a non-accelerating clock, or over the course of a complete orbit in the case of the clock which is accelerating because it's at the equator of a rotating sphere. All inertial frames will agree in these cases that the average rate of ticking of the accelerated clock is slower, even though in a given inertial frame there may be periods of time where it is ticking faster.

 

[cos]

[cos]My references are to reality and I am of the opinion that fictitious forces do not come under that category.

That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.

Does your comment "That is fine by me." mean that you agree with me that fictitious forces do not come under the heading of reality?

[cos]The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.

This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.

In my opinion this means that unless I accept the 'reality' of purely hypothetical, non-existent, fictitious forces I cannot, in a non-inertial frame, do any analysis.

[cos]It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.

No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.

What 'second leg of the trip'?

A accelerates toward and comes to a stop alongside B. There is only one leg of that trip unless of course you are referring to periods of acceleration as being 'legs' of that trip.

A does not, from C's point of view 'travel at a faster speed than B'.

In C's frame A decelerates and comes to a stop alongside C whilst B keeps moving at it's original speed ergo B is moving whilst A has 'come to a stop'.

On the basis that A has come to a stop alongside C it cannot, from C's point of view, be experiencing any time dilation! A is then ticking over at the same rate as C!

 

[cos]

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.

A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?

Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!

What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not.

According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!

According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.

According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.

 

[cos]

Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind -

In my case it is a result of sheer frustration.

Correspondence terminated.

 

[neopolitan]

In my case it is a result of sheer frustration.

Correspondence terminated.

Desperation perhaps.

My final advice to you may sound familiar: try working through the maths.

Final comment: the (applied) mathematics does actually reflect the reality. The reality and the mathematics underlying the physics involved are not separate such that one can be ignored in favor of the other, irrespective of what anyone may say, be it Einstein, Gandhi, Queen Elizabeth, Jesus, Mohammed, Buddha or, believe it or not, you.

cheers,

neopolitan

 

[JesseM]

According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!

According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.

Again, on average only. At any given instant, there is no objective truth about which clock is ticking slower, it's obvious Einstein would not disagree with this since the basic postulate of relativity is that the laws of physics are the same in all frames, and basic calculations show that all inertial frames will agree about average rates of ticking between two points where clocks meet, while disagreeing about instantaneous rates of ticking.

 

[cos]

He is obviously not saying that the accelerated clock is ticking more slowly at every instant, since at any given instant you can pick an inertial frame where the accelerated clock has a smaller velocity and thus is ticking faster. Presumably in section 4 he's talking about something like the average rate of ticking of the accelerated clock, either between the time it departs from and returns to a non-accelerating clock, or over the course of a complete orbit in the case of the clock which is accelerating because it's at the equator of a rotating sphere. All inertial frames will agree in these cases that the average rate of ticking of the accelerated clock is slower, even though in a given inertial frame there may be periods of time where it is ticking faster.

Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving.

Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.

His observations would not negate Einstein's comment that, whilst it is moving, clock A will 'go more slowly' than it did before it started moving.

 

[matheinste]

Cos.

As nothing anyone says seems to be of any help, perhaps the only way forward is for you to undertake an even deeper study of the subject of relativity and then you may be able to answer your own question.

Matheinste.

 

[Dale]

In my opinion this means that unless I accept the 'reality' of purely hypothetical, non-existent, fictitious forces I cannot, in a non-inertial frame, do any analysis.

That is correct. If you want to use a non-inertial frame then you must also use fictitious forces, they go together. The fictitious forces are every bit as "real" and "physical" as their corresponding non-inertial frames. Therefore, if you object to fictitious forces then you cannot use non-inertial frames.

What 'second leg of the trip'?

Isn't A the traveling twin and B the home twin of a standard twins scenario? If so, then A clearly has two legs of his trip, the outbound and the inbound leg. If this is not a standard twins scenario then what is the scenario? There are too many A and B scenarios in Einstein's paper for me to be sure which one you mean.

 

[JesseM]

Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving.

As Einstein makes clear in sections 1 and 2 of the 1905 paper, in order to talk about any inertial frame you must at least hypothetically be able to imagine a network of rulers and clocks at rest in that frame which can be used to assign coordinates to events. Of course, once we accept relativity we can use other types of observations to figure out what such a network would measure even if we haven't actually physically constructed it.

Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.

Sure it does, it gives you the correct predictions about what the clocks read when they meet, given that frame's definition of simultaneity which tells you their initial times at the moment before clock A is accelerated towards clock B. There is no "objective" sense in which they both read the same time at the moment before A was accelerated, that is only true in one particular frame, the frame where they were both initially at rest before the acceleration. In other frames, A and B were initially out-of-sync, and thus B could be ahead of A when they meet even though B was the one ticking more slowly after A accelerated.

His observations would not negate Einstein's comment that, whilst it is moving, clock A will 'go more slowly' than it did before it started moving.

Einstein was only saying A goes more slowly in one particular frame, the "stationary frame" K. The observations in another frame certainly negate your idea (not Einstein's) that A will "go more slowly" in some objective sense, since they show that it is equally valid to say that A ticks more quickly after it accelerates (and in this frame, it stops moving when it accelerates). If both frames make exactly the same physical predictions about what A and B will read when they meet, what possible basis could there be for considering one frame's perspective more valid than any other's? If you think Einstein would ever consider one frame more valid than another, you need to re-read section 2 of the paper, the whole point of the first postulate is that all inertial frames are equally valid (you might also re-read section 1 which shows there can be no objective truth about whether the two clocks are synchronized prior to A's acceleration).

 

[Al68]

I did NOT refer to WHY they're no longer in synch but pointed out that according to Einstein they ARE no longer in synch.

That's right.

In his 1918 article (which, in my opinion, was effectively an extension of his 1905 section 4 depiction) Einstein points out that the clocks are 'no longer in synch' because one of them (clock A in his section 4 depiction) has undergone acceleration!

That's right.

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

That's right except that it's not a matter of opinion that "the other clock 'is' ticking over at a slower rate than his own clock".

Having come to a stop (analagous to Einstein's section 4 clock A moving to B's location) his clock will, according to Einstein, lag behind the previously synchronous Earth clock.

That's right.

He allows for light travel time whereupon he eventually notices that the Earth clock is ahead of his own clock (although now ticking over at the same rate as his own clock).

That's right.

He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.

Or he can realize that the Earth clock was ticking slower than his in the ship's frame, and that after he comes to rest at the turnaround point his clock reads less time than earth's.

Alternatively, there could be a clock located at the point where he comes to a stop that is synchronous with the Earth clock (it's mechanism compensates for it's location in a much weaker gravitational tidal area) whereupon he finds that his clock lags behind that clock. He can either assume that this clock physically ticked over at faster rate than it did before he started moving toward it (in total contradiction of what his calculations 'showed' him is taking place) OR that, as Einstein suggested, his clock was 'going more slowly' than it was before he left the planet ergo is ticking over at a slower rate than this clock.

Or he can correctly conclude that the clock at the turnaround point represents proper time in Earth's frame, and that the Earth clock cannot read the same as the clock at the turnaround point in the ship frame because they read the same in Earth's frame.

Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.

That's not what Einstein said. The clock goes the same speed it always did in its own rest frame.

Nothing changed with Earth clock during the turn-around nor when the astronaut previously accelerates away from the planet nor when he was moving away at uniform vleocity nor when he slows down nor when he turns his ship around nor when he accelerates back to the planet nor when he moves with uniform velocity nor when he decelerates prior to landing!

Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!

That's correct. The same can be said of the ship's clock. Nothing physically happened to either clock.

When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.

Earth's clock did tick faster than the ship's clock in Earth's frame, but not because anything physically happened to either clock.

A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?

It will be slower than the ship's clock in the ship's frame all the way up until the ship accelerates. After the ship comes to a stop, the Earth clock will read more than the ship's. In Einstein's 1918 paper, the Earth clock runs very fast in the ship's frame during the turnaround, enough so that it starts out reading less than the ship clock, and ends up reading more than the ship clock.

Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!

Reality, but he doesn't confuse that with the greater lapse in proper time by the Earth clock.

According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!

I misspoke. I should have said reciprocal.

According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.

This is true in Earth's frame, which is the frame both twins end up in.

According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.

That is only true if you're referring specifically to Earth's frame. Which is a reasonable thing to do, since that's the frame in which the twins will reunite and compare clocks.

Another thing to remember is that in STR, two clocks separated by a distance that are synchronized in one frame (like an Earth clock and one at the turnaround point at rest with earth) are not in synch in any other frame. So the two clocks would have different readings in the ship frame. It is the clock local to the ship that reads the proper time of the event in Earth's frame. The Earth clock reading in the ship's frame does not represent the proper time of the turnaround event in Earth's frame. The math is not erroneous, unless it's misapplied to suggest that the time on a non-local clock in relative motion represents proper time for any event in the frame of that clock.

It seems that perhaps you are using the word "reality" to mean clock readings that represent the proper time in each frame, and "illusion" to mean clock readings that do not represent proper time. If that's the case, then what you're calling reality is called proper time in SR, and what you're calling illusion is called coordinate time. It's coordinate time that is frame dependent and reciprocal, not the proper time elapsed between events. Proper time is not frame dependent.

 

[Dale]

It seems that perhaps you are using the word "reality" to mean clock readings that represent the proper time in each frame, and "illusion" to mean clock readings that do not represent proper time. If that's the case, then what you're calling reality is called proper time in SR, and what you're calling illusion is called coordinate time. It's coordinate time that is frame dependent and reciprocal, not the proper time elapsed between events. Proper time is not frame dependent.

I think you are correct in this. It is difficult to know since cos has not been completely explicit, but I believe that he most commonly uses the word "reality" to refer to frame-invariant measurements whereas the word "physical" applies to frame-variant measurements in inertial frames and "illusion" refers to frame-variant measures in non-inertial frames. I think that is reasonable usage since those terms are not well-defined.

cos, can you confirm that usage or would you prefer to amend it?

 

[cos]

Again, on average only. At any given instant, there is no objective truth about which clock is ticking slower, it's obvious Einstein would not disagree with this since the basic postulate of relativity is that the laws of physics are the same in all frames, and basic calculations show that all inertial frames will agree about average rates of ticking between two points where clocks meet, while disagreeing about instantaneous rates of ticking.

"At any given instant" neither of the clocks are ticking. I agree wholeheartedly.

When Einstein wrote that the accelerated clock 'must go more slowly' than the at rest clock to what was he referring?

I assume that he was talking about the slower average rate of the accelerated clock as compared to the average rate of the stationary clock.

 

[cos]

That is correct. If you want to use a non-inertial frame then you must also use fictitious forces, they go together. The fictitious forces are every bit as "real" and "physical" as their corresponding non-inertial frames. Therefore, if you object to fictitious forces then you cannot use non-inertial frames.

In special theory Einstein points out that because we cannot determine any form of absolute rest ("...the phenomena of electrodynamics as well as of mechanics possesses no properies corresponding to the idea of [same]") hence "...an absolutely sttionary space..." can be ignored with respect to ".. the view here to be developed."

Some authors point out that because we cannot detect an 'edge' to the universe then there is no 'edge' in accordance with the special theory-quantum physics basis that 'observation creates reality'.

Other than it's 'effect' on other objects this fictitious force cannot be detected

What is that creates this 'fictitious force' that cannot be detected - a fictitious force generator that, itself, cannot be detected?

What fuels this fictitious force generator? Ex nihilo gas?

In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.

Isn't A the traveling twin and B the home twin of a standard twins scenario? If so, then A clearly has two legs of his trip, the outbound and the inbound leg. If this is not a standard twins scenario then what is the scenario? There are too many A and B scenarios in Einstein's paper for me to be sure which one you mean.

That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.

In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.

 

[JesseM]

"At any given instant" neither of the clocks are ticking. I agree wholeheartedly.

You can certainly talk about instantaneous rate of ticking, just like you can talk about instantaneous velocity; by considering average rate of ticking/average speed over some finite time interval, and then considering the limit as the size of the time interval approaches zero.

In any case, we don't have to worry about instantaneous quantities if we just consider segments of the non-inertial clock's worldline in which it is traveling at constant velocity, like a single "leg" of the non-inertial twin's journey in the twin paradox, or the time interval where clock A is moving at constant velocity towards clock B after having been accelerated in section 4 of Einstein's 1905 paper. Would you dispute that for any such segment, there is no objective truth about whether the clock that was accelerated is ticking faster or slower than the clock that wasn't?

When Einstein wrote that the accelerated clock 'must go more slowly' than the at rest clock to what was he referring?

I assume that he was talking about the slower average rate of the accelerated clock as compared to the average rate of the stationary clock.

Well, if you're just talking about average rate of ticking for a non-inertial clock between the times it departs from and returns to an inertial clock, then you aren't saying anything controversial if you say that the non-inertial clock has a slower average rate of ticking between these events, since this is true in all frames. I thought you were saying something more, that the clock A in his example in section 4 was objectively ticking slower than clock B during the after it was accelerated to the time it met clock B; that would be incorrect, but if you didn't mean to suggest this, please clarify.

 

[cos]

[cos]Although, from the alternative point of view of a 'given inertial frame', the clock could appear to be ticking faster during certain periods of time that observer's point of view has absolutely no physical effect whatsoever on that clock's rate of operation.

Sure it does, it gives you the correct predictions about what the clocks read when they meet, given that frame's definition of simultaneity which tells you their initial times at the moment before clock A is accelerated towards clock B.

Although the frame to which you refer may be able to determine 'correct predictions' I refuse to accept that his observations will have any physical affect whatsoever on clock A's rate of operation! His observations only provide him with an appearance of what that clock seems to be doing. His observations do not make that clock physically tick over at a faster or slower rate.

There is no "objective" sense in which they both read the same time at the moment before A was accelerated, that is only true in one particular frame, the frame where they were both initially at rest before the acceleration. In other frames, A and B were initially out-of-sync, and thus B could be ahead of A when they meet even though B was the one ticking more slowly after A accelerated.

I wrote -

"Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving."

Apart from observers A and B there are no other observers who can determine that A and B are 'initially out-of-synch'.

It is observer A's point of view (determinations) whilst he is moving to which my posting refers not to any other observer's points of view!

Einstein was only saying A goes more slowly in one particular frame, the "stationary frame" K.

On the basis that A arrives at Bs location to find that his clock lags behind B he is fully entitled to be of the opinion that this was due to the fact that, as Einstein pointed out, his clock 'went more slowly' (i.e. ticked over at a slower rate) than B.

His alternative is to assume that clock B physically ticked over at a faster rate than it did before he started moving however on the basis that, in my opinion, his actions can have absolutely no physical affect whatsoever on the rate of operation of that clock A can only conclude that his assumption is erroneous!

The observations in another frame certainly negate your idea (not Einstein's) that A will "go more slowly" in some objective sense, since they show that it is equally valid to say that A ticks more quickly after it accelerates (and in this frame, it stops moving when it accelerates). If both frames make exactly the same physical predictions about what A and B will read when they meet, what possible basis could there be for considering one frame's perspective more valid than any other's? If you think Einstein would ever consider one frame more valid than another, you need to re-read section 2 of the paper, the whole point of the first postulate is that all inertial frames are equally valid (you might also re-read section 1 which shows there can be no objective truth about whether the two clocks are synchronized prior to A's acceleration).

There are, in this otherwise empty universe, no observers in any other frame however even if there were then their observations do NOT negate my idea in the same way that my observations have no affect whatsoever on their 'ideas' or determinations!

On the basis that "...the whole point of the first postulate is that all inertial frames are equally valid." then that other observer should be able to accept that my observations are just as valid as his observations ergo that his observations do not negate mine!

In section 4 Einstein stipulates that the two clocks are synchronised prior to A's acceleration.

Having read, and fully accepted, special theory your observer could realize that whilst in his opinion A and B are seemingly not synchronized he should be able to apply special theory thus determine that in their reference frame they are synchronized thus that it is only his relative rate of travel to that system which has made them appear not to be synchronized.

He therefore cannot believe that his relative rate of travel has physically caused them to not be synchronous in their own reference frame!

 

[AEM]

I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/

I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.

 

[AEM]

I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/

I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.

In my browser it appears that the url in my post is not coming through properly. the missing word is "Articles"

 

[JesseM]

Although the frame to which you refer may be able to determine 'correct predictions' I refuse to accept that his observations will have any physical affect whatsoever on clock A's rate of operation! His observations only provide him with an appearance of what that clock seems to be doing. His observations do not make that clock physically tick over at a faster or slower rate.

The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking, if "physical" is taken to mean something objective that doesn't depend on an arbitrary choice of coordinate system (which is how physicists usually use the word 'physical'). Similarly, there is no "physical" truth about which of two objects has a greater x-coordinate; it depends on what coordinate system you use, where you place the origin and how you orient the x-axis of that system. Perhaps you are just using a different definition of "physical"? Would you say that a "physical" truth need not be frame-invariant, but can be relative to one's choice of coordinate system. If so, I would certainly agree that in the frame where A and B were initially at rest, it is a physical truth that A ticked more slowly after accelerating. But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.

I wrote -

"Let us assume, for the purpose of the exercise, that the systems Einstein depicted are in an SR otherwise-empty universe in which there are no other observers and nothing relative to which the system itself could be moving."

Apart from observers A and B there are no other observers who can determine that A and B are 'initially out-of-synch'.

It is observer A's point of view (determinations) whilst he is moving to which my posting refers not to any other observer's points of view!

Of course, an "observer" is just a shorthand for talking about a certain coordinate system; in reality, an intelligent observer is perfectly capable of determining the coordinates of events in a system other than his own rest frame. However, if you are only talking about what's true in the frame where A and B were initially at rest, I agree that in this frame A was ticking more slowly after accelerating.

On the basis that A arrives at Bs location to find that his clock lags behind B he is fully entitled to be of the opinion that this was due to the fact that, as Einstein pointed out, his clock 'went more slowly' (i.e. ticked over at a slower rate) than B.

Only if he acknowledges that this "fact" is specific to a particular (arbitrary) choice of coordinate system, just like the "fact" that A's velocity increased rather than decreased after accelerating, or the "fact" that A may have had a greater x-coordinate than B before accelerating due to a particular choice of how to orient the x-axis of whatever coordinate system he chose.

His alternative is to assume that clock B physically ticked over at a faster rate than it did before he started moving

There is no inertial frame where B was ticking faster than A before A accelerated, so this has nothing to do with what I was arguing.

There are, in this otherwise empty universe, no observers in any other frame however even if there were then their observations do NOT negate my idea in the same way that my observations have no affect whatsoever on their 'ideas' or determinations!

On the basis that "...the whole point of the first postulate is that all inertial frames are equally valid." then that other observer should be able to accept that my observations are just as valid as his observations ergo that his observations do not negate mine!

Again, these are not physical "observations" as most physicists would define the term; you're not talking about what the observer sees with their eyes (i.e. local facts about when light from various events reaches their position), but about the coordinates they assign to events using certain calculations. For example, if when my clock reads 20 seconds I see the light from an explosion, that is a local physical fact which all frames agree occurred. Likewise, if the explosion happened next to the 5 light-second mark on my ruler, and I am next to the 0 light-second mark on my ruler, those are also local physical facts. On the other hand, if I say that the light from the explosion must have taken 5 seconds to reach me and therefore must have been simultaneous with the event of my clock reading 15 seconds even though I didn't see it until later, that is a calculation based on certain assumptions about the coordinate system I want to use, I could equally well use some different assumptions and calculate the explosion happened simultaneously with my clock reading 14 seconds or 16 seconds.

But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower, or which events were simultaneous, or which event had a greater x-coordinate. If that's all you're saying then I would agree.

In section 4 Einstein stipulates that the two clocks are synchronised prior to A's acceleration.

He specifically stated that this was only true relative to one particular choice of coordinate system: "If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous"

Having read, and fully accepted, special theory your observer could realize that whilst in his opinion A and B are seemingly not synchronized he should be able to apply special theory thus determine that in their reference frame they are synchronized thus that it is only his relative rate of travel to that system which has made them appear not to be synchronized.

He therefore cannot believe that his relative rate of travel has physically caused them to not be synchronous in their own reference frame!

Of course I was never arguing that they were not synchronized in their own reference frame, just that this is not an objective "physical" truth. According to the usual way of speaking, there is no physical truth about whether they were synchronized or not, because simultaneity is a coordinate-dependent quantity. But as I said, maybe you are using a different definition of "physical truth" from the usual one in which there can be "physical truths" about coordinate-dependent notions like which of two objects has a greater x-coordinate.

 

[Dale]

In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.

That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.

That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.

In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.

Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.

 

[cos]

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

That's right except that it's not a matter of opinion that "the other clock 'is' ticking over at a slower rate than his own clock".

Semantics! The astronaut makes his calculations as a result of which he is of the opinion (or 'accepts' or 'believes') that this is taking place. His opinion is that it is taking place. He is entitled to be of that opinion!

He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.

Or he can correctly conclude that the clock at the turnaround point represents proper time in Earth's frame, and that the Earth clock cannot read the same as the clock at the turnaround point in the ship frame because they read the same in Earth's frame.

Having arrived at the turnaround point thus having obviously come to a stop alongside a clock (B') at that location (which he knows to be synchronous with the Earth clock) he finds that his clock lags behind that clock.

It makes no difference whatsoever if, during that trip, he is of the opinion that B and B' are no longer synchronized on the basis that, having learned STR he ca determine that in their reference frame they are synchronized.

During that trip he determines that B' is ticking over at a slower rate than his clock whereupon he predicts that B' will resultantly lag behind his own clock yet he arrives at that location to find that B' does not lag behind his clock but that his clock lags behind B'.

Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.

That's not what Einstein said. The clock goes the same speed it always did in its own rest frame.

The clock appears to be ticking over at the same rate as it always has and this determination is based on the fact that there is no evidence - no internal dynamic experiment that he can conduct - that indicates otherwise however having arrived at the location of B' and found that his clock lags behind that clock he can conclude that this is due to the fact that, as Einstein stated, his clock 'went more slowly' than it did before he left the planet.

In his 1918 article (which I believe was merely an extension of his section 4 STR depictions) Einstein pointed out that it is ONLY the clock that experiences forces of acceleration (i.e. his section 4 clock A) that incurs a variation in it's rate of operation (a slower tick rate) NOT the unaccelerated inertial reference frame clock (i.e. his section 4 clock B).

He would, I believe, have been appalled if anyone had suggested (as do some people) that the accelerated clock does not incur time contraction but that the unaccelerated clock incurred time contraction!

Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!

That's correct. The same can be said of the ship's clock. Nothing physically happened to either clock.

The ship's clock accelerated; the Earth clock did not! According to Einstein's 1918 extension of his section 4 depiction - the accelerated clock ticks over at a slower rate than the unaccelerated clock and it is for that reason, according to Einstein, that the unaccelerated clock ticks over at a slower rate than it did before it started accelerating and at a slower rate than the unaccelerated clock.

When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.

Earth's clock did tick faster than the ship's clock in Earth's frame, but not because anything physically happened to either clock.

This is, of course reciprocal. The ship's clock can tick slower than the Earth clock in the ship's frame. The ship's clock has. as Einstein pointed out, accelerated thus it is, according to Einstein, the accelerated ship's clock that incurs time dilation - the Earth clock does not incur time contraction.

A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?

It will be slower than the ship's clock in the ship's frame all the way up until the ship accelerates. After the ship comes to a stop, the Earth clock will read more than the ship's.

(In an attempt to overcome confusion on my behalf I assume that when you say that the ship accelerates it is incurring negative acceleration i.e. it is slowing down.)

I've seen and heard of some fantastic claims but this one is a beauty.

The astronaut is moving at a velocity that generates a gamma factor of 400 000. He 'sees' or 'determines' that his clock is ticking over at the rate of 400 000 seconds for each of clock B' seconds (i.e. B is ticking over at a slower rate than his clock) but at the very moment that he puts his foot on the gas pedal to power up his retrorockets clock B stops
ticking over at that slower rate and instantaneously starts ticking over the faster rate of 400 000 seconds for each of his seconds. is it not possible that he would believe that such an enormous rate of instantaneous reversal would have some affect on that clock's mechanism?

That clock instantaneously reverses its rate of operation from being 400 000 times slower than his clock to being 400 000 times faster?

If you believe that I've got a bridge you might be interested in buying.

Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!

Reality, but he doesn't confuse that with the greater lapse in proper time by the Earth clock.

If you know somebody who believes that is reality please let him know that I've got other bridges for sale.

According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.

This is true in Earth's frame, which is the frame both twins end up in.

I don't care in which frame the observations are made. In my opinion nothing that any frame 'observes' can physically affect the rate of operation of any clock!

The astronaut comes to a stop alongside clock B' and is then 'in the Earth's frame'. He sees that his clock lags behind B' and on the assumption that he does not believe that B' was ticking over at the rate of 1 second for each of his own 400 000 seconds and that it instantaneously reverts to 400 000 seconds for each of his seconds I do not believe that any sensible person would believe that what they 'determined' was reality!

According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.

That is only true if you're referring specifically to Earth's frame. Which is a reasonable thing to do, since that's the frame in which the twins will reunite and compare clocks.

See above.

Another thing to remember is that in STR, two clocks separated by a distance that are synchronized in one frame (like an Earth clock and one at the turnaround point at rest with earth) are not in synch in any other frame.

This has been covered above.

It seems that perhaps you are using the word "reality" to mean...

I am using the word 'reality' in the same way as did Einstein in section 4 wherein he wrote that a clock at the equator "...must go more slowly..." than a clock at one of the poles. I don't care which frame makes the observation or determination; none of their findings will have any affect whatsoever on the tick rate of that clock.

 

[cos]

I think you are correct in this. It is difficult to know since cos has not been completely explicit, but I believe that he most commonly uses the word "reality" to refer to frame-invariant measurements whereas the word "physical" applies to frame-variant measurements in inertial frames and "illusion" refers to frame-variant measures in non-inertial frames. I think that is reasonable usage since those terms are not well-defined.

cos, can you confirm that usage or would you prefer to amend it?

I am saying that because, according to Einstein in section 4 STR, a clock at the equator 'must go more slowly' than a clock at one of the poles then a person located at the equator could be of the opinion that Einstein may have ben right; that his clock is ticking over at a slower rate than a polar clock.

I am further saying that because of Einstein's analogy to a clock (A) that has been made to travel in a polygonal line to another clock's location (B) then A will also 'go more slowly' than that 'at rest' clock.

Translate those comments into your own 'frame'. I fail to see that they are overly complicated for you.

 

[JesseM]

In his 1918 article (which I believe was merely an extension of his section 4 STR depictions) Einstein pointed out that it is ONLY the clock that experiences forces of acceleration (i.e. his section 4 clock A) that incurs a variation in it's rate of operation (a slower tick rate) NOT the unaccelerated inertial reference frame clock (i.e. his section 4 clock B).

He would, I believe, have been appalled if anyone had suggested (as do some people) that the accelerated clock does not incur time contraction but that the unaccelerated clock incurred time contraction!

No one has suggested that that the unaccelerated "inertial reference frame clock" experiences a variation in its rate of ticking, at least not in any inertial reference frame (if we consider non-inertial coordinate systems, virtually anything can be true about the rate of ticking of any clock). The point is just that although the accelerated clock does change its rate of ticking in almost every inertial frame (except the frame where its direction changes but its speed stays the same), there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after. Do you disagree with this?

 

[Dale]

cos, Einstein never used the word "physical" to refer to time dilation and he never used the word "real" or "illusion" at all. So the question remains, what do you mean by those words? I have suggested what I think you mean (although you are not consistent in your usage), but you haven't even had the courtesy to say yes or no to it. I don't care how you use those words, but just define them and use them consistently so that we can communicate.

 

[cos]

I have come to this thread long after it began and have not gone through every posting from the beginning to the end, so some one may have mentioned this already, if so I apologize for the duplication. Special relativistic effects on time measurements and general relativistic effects on time measurements are reaffirmed continuously everyday in the Global Positioning Satellite system. If these effects were not taken into account, then the GPS system would fail within about 30 minutes. Those who were discussing math vs reality might want to read this paper: http://relativity.livingreviews.org/Articles/lrr-2003-1/

I suspect that a great deal of discussion could be dispensed with by examining the details discussed in the above paper and realizing that, yes, relativity works.

Your contribution to the discussion may have been unneccesary if you had gone through previous postings wherein I made no suggestion that relativity does not work.

 

[phyti]

cos post;

In my previous thread ‘Time dilation’ dated Mar22-09 I wrote -
In section 4 STR Einstein wrote -

"If one of two synchronous clocks at A is moved in a closed curve
with constant velocity until it returns to A, the journey lasting
t seconds, then by the clock which has remained at rest the
travelled clock on its arrival at A will be a .5tv^2/c^2 second
slow. Thence we conclude that a balance-clock at the equator must
go more slowly, by a very small amount, than a precisely similar
clock situated at one of the poles under otherwise identical
conditions."

What do people think he meant by the phrase "...must go more
slowly..."?
Does anyone agree that he meant that the moving clock will tick
over at a slower rate than (i.e. incur time dilation relatively
to) the other clock?

********************

On the (probably erroneous) basis that some people may agree that
he did I follow that up with the question - On the basis of his
depiction of a clock that is made to move in a closed curve around
another clock is it correct for me to assume that Einstein meant
that the clock that is moving in a closed curve will “go more
lowly”(i.e. tick over at a slower rate) than the clock “which has
remained at rest.”?

The A clock must accelerate to leave the B clock, move at a
constant speed for most of the path, then decelerate to reunite
with the B clock. Since A initiated the trip, and traveled a
greater distance than B, in the same amount of elapsed B time, A
would have an average speed greater than B. Time dilation is a
functon of speed, therefore the A clock experiences more time
dilation than B. When reunited, A clock is lagging behind B clock.
This is not about perception of clocks, but the physics of clock
function according to light propagation. Each will
observe/perceive the others clock to be running faster or slower,
depending on direction of motion.

This is a repeat of my reply for the your first thread.

Here is a quote from the Max Born book, page 257, which you have (A and B swapped).

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

Because A & B are synchronized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

I can only add, time dilation is a real factor affecting particle accelerators and gps systems.

 

[cos]

The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking...

So when Einstein wrote that clock A 'must go more slowly' than clock B he was not describing a 'physical' fact (or truth)?

But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.

By the comment "... A ticked more rapidly after accelerating." I take it that you mean that A ticked more rapidly whilst it was moving with uniform velocity (i.e. after accelerating)?

By "ticked more rapidly" did you mean that A ticks over at a faster rate than it did before it accelerated (or whilst it is accelerating) or that because A, applying the Lorentz transformations, 'determines' that B is ticking over at a slower rate than itself?

The idea of time contraction was, I believe, an unacceptable concept as far as Einstein was concerned.

You wrote, below, "...I agree that in this frame A was ticking more slowly after accelerating." It was 'this frame' to which I have consistently been referring.

Of course, an "observer" is just a shorthand for talking about a certain coordinate system; in reality, an intelligent observer is perfectly capable of determining the coordinates of events in a system other than his own rest frame. However, if you are only talking about what's true in the frame where A and B were initially at rest, I agree that in this frame A was ticking more slowly after accelerating.

"After accelerating"? I am of the opinion that the v in Einstein's equation .5tv^2/c^2 can be his instantaneous velocity whilst accelerating.

The slower rate of operation of clock A is not affected by the fact that he takes his foot off the gas pedal at any given instant.

But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower...

So A, having arrived at B's location, is, apparently, entitled to be of the opinion that his clock lags behind B due to the fact that whilst he was moving his clock was 'going more slowly' (i.e. ticking over at a slower rate) than B?

 

[cos]

In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.

That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.

They apparently not only assumed that I understood Newtonian mechanics but that the potentially millions of other people who were to read those books and articles also understood Newtonian mechanics!

Somewhat presumptuous of them wouldn't you agree?

You state that fictitious forces are not 'Einstein'. Do you mean that they are not special theory?

If they are incorporated in STR perhaps you would be so kind as to point out where in STR Einstein refers, or alludes to, fictitious forces?

That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.

In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.

Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.

There is NO observer C in Einstein's section 4 STR depiction and the introduction of same is nothing more than a deliberate obfuscation!

Determinations made by a hypothetical observer C can have no effect whatsoever on what is taking place as far as A or B are concerned nor on the rates of operation of their clocks!

 

[cos]

In the 26 years that I have been researching Einstein's special theory I have read at least 100 popularization books and possibly thousands of articles on the subject however none of those authors have referred to a 'fictitious force'.

That is probably because all of those authors assumed that you understood Newtonian mechanics. Fictitious forces are a product of Newton, not Einstein.

They apparently not only assumed that I understood Newtonian mechanics but that the potentially millions of other people who were to read those books and articles also understood Newtonian mechanics!

On the basis that a majority of those items were popularization works this attitude would be somewhat presumptuous of those authors wouldn't you agree?

You state that fictitious forces are not 'Einstein'. Do you mean that they are not special theory?

If they are incorporated in STR perhaps you would be so kind as to point out where in STR Einstein refers, or alludes to, fictitious forces?

That's my point, the scenario to which I was referring was not an out and return trip but was Einstein's initial (section 4) depiction of one clock that is made to travel to another clock's location.

In an out-and-return trip Einstein's depiction could be applied to a twin's return journey whereupon, according to Einstein, his clock will 'go more slowly' than it did before he started moving.

Ah, ok. So A and B are initially synchronized in B's rest frame and at different locations. Then A is moved with a velocity v (in B's frame) to B and is found to lag B. The calculation in B's frame shows that A and B started synchronized, A "went more slowly", and thus A was found to lag. C is an inertial observer in a frame where A is at rest after beginning to move. The calculation in C's frame shows that B started out ahead (relativity of simultaneity, see section 2), B "went more slowly", but A didn't catch up, and thus A was found to lag. In both cases the calculations show that A lags B by the same amount so there is no conflict between either calculation or the measured outcome.

There is NO observer C in Einstein's section 4 STR depiction and the introduction of same is nothing more than a deliberate obfuscation!

Determinations made by a hypothetical observer C can have no effect whatsoever on what is taking place as far as A or B are concerned nor on the rates of operation of their clocks!

 

[cos]

No one has suggested that that the unaccelerated "inertial reference frame clock" experiences a variation in its rate of ticking, at least not in any inertial reference frame (if we consider non-inertial coordinate systems, virtually anything can be true about the rate of ticking of any clock). The point is just that although the accelerated clock does change its rate of ticking in almost every inertial frame (except the frame where its direction changes but its speed stays the same), there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after. Do you disagree with this?

Some people insist that after A accelerates (and is then moving with uniform velocity toward B) observer A 'determines', in accordance with the Lorentz transformations, that B is ticking over at a slower rate than it was before A started moving.

I wholeheartedly agree that "...there are some frames which say it ticks slower after the acceleration than it was ticking before the acceleration, and other frames which say it ticked slower before the acceleration than it did after." The point that I'm trying to make is that irrespective of what those frames 'say' or 'determine' their observations have absolutely no affect whatsoever on clocks A or B!

As I have also pointed out, the systems that Einstein depicted could be contained in an otherwise empty universe in which there are obviously no other frames!

 

[cos]

cos, Einstein never used the word "physical" to refer to time dilation and he never used the word "real" or "illusion" at all. So the question remains, what do you mean by those words? I have suggested what I think you mean (although you are not consistent in your usage), but you haven't even had the courtesy to say yes or no to it. I don't care how you use those words, but just define them and use them consistently so that we can communicate.

It is not important what I think about the words 'physical' or 'real' but what Einstein meant by the words 'must go more slowly'!

I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowly (i.e. ticks over at a slower rate) than a clock at one of the poles or, analogously, than a clock around which it has moved in a closed curve or, analogously, relative to which it has moved in any polygonal line including it's original trip to B's location.

What do you believe he meant by the words 'must go more slowly'?

 

[JesseM]

So when Einstein wrote that clock A 'must go more slowly' than clock B he was not describing a 'physical' fact (or truth)?

Not if "physical truth" is defined to mean something that is true regardless of your choice of conventions about coordinate systems, and as I said before, this is how most physicists nowadays use the word "physical". If you want to use a different definition that's fine, it's just semantics, but I would ask that you spell out what you mean by physical. That's what DaleSpam asked you in post #90 above, and I also asked you about this in post #85 which you were responding to here:

The whole point is that in relativity there is no "physical" truth about the rate a clock is ticking, if "physical" is taken to mean something objective that doesn't depend on an arbitrary choice of coordinate system (which is how physicists usually use the word 'physical'). Similarly, there is no "physical" truth about which of two objects has a greater x-coordinate; it depends on what coordinate system you use, where you place the origin and how you orient the x-axis of that system. Perhaps you are just using a different definition of "physical"? Would you say that a "physical" truth need not be frame-invariant, but can be relative to one's choice of coordinate system? If so, I would certainly agree that in the frame where A and B were initially at rest, it is a physical truth that A ticked more slowly after accelerating. But if you're defining "physical truth" in this way, then you'd have to agree that in the frame where A and B were initially in motion and then A came to rest after accelerating, it's a physical truth that A ticked more rapidly after accelerating.

Could you please answer these questions? Specifically, do you want to define "physical" differently from how most physicists define it, so that it no longer implies coordinate-invariance? If so, do you acknowledge that under such a nonstandard definition, there could also be a "physical truth" about which of two objects has a greater x-coordinate, even though this truth can obviously only be decided relative to a particular (arbitrary) choice of how to orient our coordinate axes?

By the comment "... A ticked more rapidly after accelerating." I take it that you mean that A ticked more rapidly whilst it was moving with uniform velocity (i.e. after accelerating)?

Yes, in the frame where it came to rest after accelerating.

By "ticked more rapidly" did you mean that A ticks over at a faster rate than it did before it accelerated (or whilst it is accelerating) or that because A, applying the Lorentz transformations, 'determines' that B is ticking over at a slower rate than itself?

Since A accelerated, A does not have a single rest frame, so the meaning of "applying the Lorentz transformations" is ambiguous--what frame would you have A use, the frame where A was at rest before the acceleration, or the frame where A was at rest after the acceleration? I was thinking of the inertial frame where A was at rest after acceleration, and in this frame both of your above statements are true; in this frame A ticks faster after acceleration than before acceleration, and in this frame B ticks more slowly than A after A has accelerated.

The idea of time contraction was, I believe, an unacceptable concept as far as Einstein was concerned.

I don't understand what you mean by "time contraction", can you explain this? No clocks rate of ticking is faster than the rate coordinate time is passing in any inertial frame, if that's what you mean; it can only be ticking at the same rate as coordinate time (if it's at rest in the chosen frame), or slower than coordinate time (if it's moving in this frame).

"After accelerating"? I am of the opinion that the v in Einstein's equation .5tv^2/c^2 can be his instantaneous velocity whilst accelerating.

Please note that Einstein's equation above is an amount of time, not an instantaneous rate of ticking, and certainly not an instantaneous velocity. It's meant to tell you how much a moving clock will lag behind a non-moving clock in a given frame after some time t has passed in that frame. Also, it is only an approximation; the non-approximate equation would be t*(1 - \sqrt{1 - v^2/c^2}). For example, if clock A is moving at 0.6c and clock B is at rest in a certain frame, and they start off showing the same time, then after t=10 seconds of coordinate time have passed in that frame, clock A will lag behind clock B by 10*(1 - \sqrt{1 - 0.6^2}) = 10*(1 - 0.8) = 2 seconds. If you use Einstein's approximation you predict that clock A lags behind clock B by 0.5*10*0.6^2 = 1.8 seconds, which is close to the correct value of 2 seconds although a little off.

The slower rate of operation of clock A is not affected by the fact that he takes his foot off the gas pedal at any given instant.

It's true that if you accept the notion of "instantaneous rate of ticking" (which you objected to earlier), then the instantaneous rate of ticking in a given frame depends solely on the instantaneous velocity in that frame, it doesn't depend on whether the clock is accelerating or moving at constant speed. In any case, in most thought-experiments in SR we just assume the accelerations are instantaneous.

But yes, relative to a particular choice of coordinate system there can be definite truths about which clock was ticking slower...

So A, having arrived at B's location, is, apparently, entitled to be of the opinion that his clock lags behind B due to the fact that whilst he was moving his clock was 'going more slowly' (i.e. ticking over at a slower rate) than B?

It is meaningless to state an "opinion" about clock rates without specifying what coordinate system you want to use, and of course A is "entitled" to use absolutely any frame he wants, even one where neither he nor B have been at rest at any point during the experiment. If A wishes to calculate things relative to the inertial frame where B is at rest, then in this frame it is certainly true that A lagged behind because A ticked more slowly after accelerating. But again, you always have to specify a choice of frame you use when talking about rates of ticking, to do otherwise would be like saying "it's my opinion that Earth has a greater x-coordinate than the Sun" without specifying where you want the origin of your coordinate system to be and which direction the x-axis is pointing relative to this origin.

 

[JesseM]

I am of the opinion that he meant that clock A 'physically' or 'really' or 'actually' goes more slowly (i.e. ticks over at a slower rate) than a clock at one of the poles

But you're still haven't defined what you mean by words like "physically", "really", or "actually"! It is true that relative to a particular choice of coordinate system A ticks more slowly, but we understand that this choice is an arbitrary one and the universe doesn't care which coordinate system we use, nothing in the laws of physics justifies the idea that one coordinate system's point of view is somehow more correct than another's. Similarly, if you pick a coordinate system where the origin is at the center of the Sun and the positive x-direction is pointed towards the Earth, it's true in this coordinate system that the Earth has a greater x-coordinate than the Sun...but would you say that the Earth "physically" or "really" or "actually" has a greater x-coordinate than the Sun, in spite of the fact that we are obviously free to use a coordinate system where the origin is at a different position? Please answer this question about whether you would use words like "physical" to describe statements about which of two objects has a greater x-coordinate, and it will help me to understand what you mean by the word "physical" when you talk about clock rates.

 

[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
travelled clock on its arrival at A will be a .5tv^2/c^2 second
slow. Thence we conclude that a balance-clock at the equator must
go more slowly, by a very small amount, than a precisely similar
clock situated at one of the poles under otherwise identical
conditions."

What do people think he meant by the phrase "...must go more
slowly..."?
Does anyone agree that he meant that the moving clock will tick
over at a slower rate than (i.e. incur time dilation relatively
to) the other clock?

********************

On the (probably erroneous) basis that some people may agree that
he did - I follow that up with the question - On the basis of his
depiction of a clock that is made to move in a closed curve around
another clock is it correct for me to assume that Einstein meant
that the clock that is moving in a closed curve will “go more
slowly” (i.e. tick over at a slower rate) than the clock “which has
remained at rest.”?

The A clock must accelerate to leave the B clock, move at a
constant speed for most of the path, then decelerate to reunite
with the B clock. Since A initiated the trip, and traveled a
greater distance than B, in the same amount of elapsed B time, A
would have an average speed greater than B. Time dilation is a
function of speed, therefore the A clock experiences more time
dilation than B. When reunited, A clock is lagging behind B clock.
This is not about perception of clocks, but the physics of clock
function according to light propagation. Each will
observe/perceive the others clock to be running faster or slower,
depending on direction of motion.

In Einstein's section 4 depiction of an equatorial clock which 'must go more slowly' than a polar clock there is no relationship to "...the physics of clock function according to light propagation."

"The physics of clock function according to light propagation." is solely in relation to Doppler shift and light travel time which, I believe, has absolutely no physical effect whatsoever on any clocks physical rate of operation.

As you point out, above, "...Time dilation is a function of speed." It is not a function of Doppler shift or light travel time which, although bought about by relative speed, only create an illusion of time variations.

You wrote "...Since A initiated the trip, and traveled a greater distance than B..." Clock B travels no distance! It has, according to Einstein, remained at rest!

You wrote "..therefore the A clock experiences more time dilation than B." Clock B, in Einstein's depiction "...has remained at rest..." ergo it incurs no time dilation!

This is a repeat of my reply for the your first thread.

Here is a quote from the Max Born book, page 257, which you have (A and B swapped).

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

My interpretation of that comment is that every internal process in A's system (including the rate of operation of his clocks) must take place more slowly (i.e. his clocks must 'go more slowly') than the same process (i.e. the rate of operation of the clocks) in system B.

Because A & B are synchronized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

I wholeheartedly agree - the time effect (i.e. the slower rate of operation of A's clock compared to it's rate of operation before he started moving) is, according to Einstein, caused by the motion and as you point out above "Time dilation is a function of speed, therefore the A clock experiences [sic. more] time dilation."

I can only add, time dilation is a real factor affecting particle accelerators and gps systems.

Irrelevant, I made no suggestion whatsoever that time dilation (as depicted by Einstein's section 4 STR comments) is not 'a real factor'!