Is the Changing Clock Rate in Relativity Directionally Dependent?

[JesseM]

Jesse - you can make it hard and do the analysis from any frame - but it obscures the physics - its a great mathematical exercise

Why do you think one frame's analysis is "the physics" while one is a "mathematical exercise"? You keep talking like this but you never give any actual arguments why we should agree with you. Is it simply because Einstein described the problem in the original rest frame of the two clocks? If he had instead started out by saying "suppose we have two clocks moving together inertially at 0.6c at a distance of 9.6 light seconds apart, with the front clock 7.2 seconds behind the back clock, then the front clock comes to rest while the back clock continues to move towards it at 0.6c", would you then consider this the "real physics" of the situation simply because this was the way the problem was initially described, with it being merely a "mathematical exercise" to transform this description into a frame where the two clocks were initially at rest? If not, please explain what your criteria are for deciding what frame represents the 'real physics', since it's a mystery to the rest of us.

Jersse "(see my earlier analysis, where in the second frame the accelerated clock ticked forward 16 seconds while the inertial clock only ticked forward 12.8 seconds--wouldn't you agree that in this frame it's the inertial clock that 'loses time'?)"

No - this is exactly why making measurements from moving frames distorts reality

Moving with respect to what? Is your criterion just that if the situation we are analyzing involves some objects which are initially at rest with respect to each other, their rest frame represents the "real physics" and all other frames are distortions?

 

[yogi]

OK Jesse - fair enough - The situation I have proposed is that which relates the rate of two different clocks - each moving in a different frame (I always mentally attach a frame to a clock and vice versa) So in the ECA frame we have a reference were nothing has changed physically (except you might say a temporal change has taken place as the clocks have aged during the experiment) but there is no spatial movement of any clock E,C or A. R which was originally synchronized at rest wrt to E C and A has experienced an acceleration and thereafter it runs at a uniform rate relativeto E,C and A which is different than the rate of E,C or A. What physical law operates to relate the clock rate of R to the acceleration it has experienced? Alternatively - what physical law operates to connect the velocity of R wrt C to the clock rate difference between C and R.

I suppose you will say there is nothing physical - its simply a consequence of the LT and the postulates of SR or whatever theory that yields the same results. Still, there is a curious energy relationship between the CEA frame and the R clock that corresponds to effective time dilation in a G field - so maybe physical factors are in some way at work. For me, the purpose of examining the subject is fulfilled in finding a convenient geometry - you may not find the ECA-R thought experiment of value - I consider it a useful framework

 

[Ich]

Ok yogi, I think I understand what you intend to say: R and C are at rest in equally valid inertial frames, so you don´t have to turn around as in the classical twin paradox (as Hurkyl stated), and the only thing different in both frames is that one is initially accelerated. So that must somehow be the reason for the difference in clock rates.
Assuming that I understood you correctly, I can point out the errors in your argumentation:
1. C is at rest in a global IF, but R is not. Maybe you think that the difference is negligible as you can think of the radius getting infinitely large and the inward acceleration infinitely small. But that is not true: You could set up a giant local IF but it´s extension is always confined to a region significantly smaller than the radius of the movement and a timespan significantly smaller than the time of circulation. C is necessarily always outside these bounds: the situation is not symmetric.
2. You can handle the situation in SR by dividing R´s orbit into arbitrarily many straight lines with accordingly small angles between them. The result is that R and C "see" each other go slow during the straight movement, and that R "sees" C jump ahead in time at each transition between straight lines. There is no difference to the classical twin paradox, besides that in the limit where the straight lines get infinitely small, the net effect is R´s clock going slower than C´s as "seen" in both frames.
3. The initial acceleration has nothing to do with this effect. The reason is that R is not in an inertial frame which enables him to adjust the direction of his motion in such a way that it is always perpendiculat to the distance C-R. The lorentz transformation then correctly shows C´s clock going faster.
Note that R could also move on the surface of a sphere with center C. As long as he keeps the magnitude of his velocity constant wrt C, he could accelerate and go loops and whatever ad nauseam, the result stays the same. Initial acceleration has just as little impact.

 

[JesseM]

OK Jesse - fair enough - The situation I have proposed is that which relates the rate of two different clocks - each moving in a different frame (I always mentally attach a frame to a clock and vice versa) So in the ECA frame we have a reference were nothing has changed physically (except you might say a temporal change has taken place as the clocks have aged during the experiment) but there is no spatial movement of any clock E,C or A. R which was originally synchronized at rest wrt to E C and A has experienced an acceleration and thereafter it runs at a uniform rate relativeto E,C and A which is different than the rate of E,C or A. What physical law operates to relate the clock rate of R to the acceleration it has experienced? Alternatively - what physical law operates to connect the velocity of R wrt C to the clock rate difference between C and R.

I suppose you will say there is nothing physical - its simply a consequence of the LT and the postulates of SR or whatever theory that yields the same results. Still, there is a curious energy relationship between the CEA frame and the R clock that corresponds to effective time dilation in a G field - so maybe physical factors are in some way at work. For me, the purpose of examining the subject is fulfilled in finding a convenient geometry - you may not find the ECA-R thought experiment of value - I consider it a useful framework

You didn't really answer my question--what criteria are you using to decide that the ECA frame is the "physical" one here? The fact that all clocks run at a uniform rate in this frame? The fact that E, C, and A are at rest in this frame (and that R was originally too, perhaps?) And can you also explain how the same criteria lead you to conclude that the "stationary frame" in Einstein's thought-experiment is the only physical one? Or do you not have any set of universally-applicable criteria for deciding which frame is the physical one in any situation, and it's just a sort of case-by-case, "know it when I see it" sort of thing?

 

[yogi]

Jesse - didn't mean to convey that one frame is physical - or more physical -- what I was trying to structure is a way to evaluate the underlying cause that appears as a physical difference (clocks running at intrinsically different rates) - physics is basically a study of relationships - we make experiments and from those we deduce that two charges repell each other with a certain force - but we don't have a good concept of what charge is - where it comes from etc - physics deals with relationships for the most part

So I am interested in the relationship between the situation when all clocks were at rest in the same frame and later when one has been but into motion. The ECA is not a better physical frame and it is not privileged with regard to the universe at large - but the relationship that evolves by considering the R clock to be following a circular path centered on C is useful - It is a springboard for making a prediction which you will no doubt challenge - namely, that any clock given a linear acceleration wrt to an inertial frame will run at an intrinsically lower rate at all times when compared to any clock in the inertial frame which has not been accelerated.

I await your encyclical

 

[JesseM]

Jesse - didn't mean to convey that one frame is physical - or more physical

Then what exactly did you mean when you said "you can make it hard and do the analysis from any frame - but it obscures the physics - its a great mathematical exercise"? Were you not saying that one frame's analysis is "the physics" while the other frame's analysis is a mere "mathematical exercise"?

-- what I was trying to structure is a way to evaluate the underlying cause that appears as a physical difference (clocks running at intrinsically different rates) - physics is basically a study of relationships - we make experiments and from those we deduce that two charges repell each other with a certain force - but we don't have a good concept of what charge is - where it comes from etc - physics deals with relationships for the most part

So I am interested in the relationship between the situation when all clocks were at rest in the same frame and later when one has been but into motion. The ECA is not a better physical frame and it is not privileged with regard to the universe at large - but the relationship that evolves by considering the R clock to be following a circular path centered on C is useful - It is a springboard for making a prediction which you will no doubt challenge - namely, that any clock given a linear acceleration wrt to an inertial frame will run at an intrinsically lower rate at all times when compared to any clock in the inertial frame which has not been accelerated.

I await your encyclical

How can you on the one hand say that no frame's analysis is more physical or real than any other's, and yet on the other hand say that a clock that's accelerated will always run at an "intrinsically lower rate" when there are perfectly good inertial frames where the acceleration caused the clock to lower its velocity and therefore caused its rate of ticking to speed up? How are these two statements of yours not obviously mutually contradictory?

 

[yogi]

Jesse says: "How can you on the one hand say that no frame's analysis is more physical or real than any other's, and yet on the other hand say that a clock that's accelerated will always run at an "intrinsically lower rate" when there are perfectly good inertial frames where the acceleration caused the clock to lower its velocity and therefore caused its rate of ticking to speed up? How are these two statements of yours not obviously mutually contradictory?"

That is one of the things I have been pondering - let me try this on you - mind you this idea is only in its infancy - but what if the clock rate change is somehow directionally dependent - for example - the ECA frame is taken to be an inertial frame - it would make no difference in which direction the acceleration of R proceeded as to the initial boost - any direction would have the same result - but to return - the acceleration would have to be opposite - and when it arrived back at ECA it would run at the original rate - its similar to the G potential - I raise a clock to a height above the Earth - in doing so I have done work against the G field - at the new potential it runs faster - to get back to the original rate everything is reversed. Both involve energy changes - at this point i cannot say it will provide a consistent result in every case - perhaps worth more thought -