Ambiguity in time dilation due to relative velocity

[davidf32]

JessieM, Unfortunately you are doing exactly what I hoped would not happen: You are variously wrong in your statements and bringing in irrelevancies. Here are my responses:

QUOTE Do you mean "simultaneously" in the third party's frame? Or do you mean they are the same age when the signal reaches them? Or both? And after they wake up, what are their velocities in the third party's frame? END OF QUOTE.

ANSWER: Since the velocity of light is the same for all observers, and the third party is midway between the twins, and RF energy travels spherically from an omnidirectional anetenna, it is clear that, from the point of view of the third party, the signal arrives SIMULTANIOUSLY at each ship. Hence, from the third parties point of view, the subsequent accelerated motions of the two ships are identical both as to timing and magnitude. It is irrelevant as to the relative velocities of the twins ships and also irrelevant as to the twins ages in their own inertial reference systems. What they can and do know is that they are both accelerating towards one another and eventually meet (again at rest) at some point in space that is adjacent to the third party. They do not know if that is the place they started from. END OF ANSWER

QUOTE Just as in the twin paradox, the question of who accelerated initially is basically irrelevant to who will have aged less when they reunite (completely irrelevant if we assume an instantaneous acceleration that immediately takes one up to the outbound "cruising speed") END OF QUOTE

Answer: Oh, Really? Do you really believe in the so-called twin paradox that if there is assymmetry in their initial acceleration that when they get back together they will still have aged the same amount? I cannot believe you really believe that. It's wrong. PROOF: If one twin stays at home and the other accelerates out and then returns, the traveling twin will have aged less. Symmetry is important QED! END OF ANSWER

QUOTE it's the accelerations that happen when they are a significant distance apart that matter. END OF QUOTE

ANSWER; Yes, that is true. If that acceleration is symmetric in both timing and magnitude (relative to the third parties reference frame) than it will cancel out for the final answer. If it is not symmetric, it will result in an offset one way or other. In my example I made it symmetric both for the third party and each of the twins EVEN IF the twins don't know it. END OF ANSWER

The remainder of your coments are irrelevant to the point of my thought experiment: The point of the thought experiment was that the twins could not know apriori if their ages would be the same or different when the came back together BECAUSE they didn't know what happened while they were asleep. In other words, without some historical knowledge of the model. Since the ouside observers (us) did know that history, we COULD properly predict the outcome.
Peace davidf32

To find their ages upon reuniting in this scenario you just need to know, at some time after they have woken up, what their ages and velocities and separation are in some inertial frame (perhaps the third party's frame), and at what time the signal to turn around reaches each one in this frame, and what their new velocities after turning around are (again assuming an instantaneous change in velocity to make the problem simpler). With this information you can calculate their ages upon reuniting without any knowledge of what happened when they were asleep.

 

[JesseM]

JessieM, Unfortunately you are doing exactly what I hoped would not happen: You are variously wrong in your statements and bringing in irrelevancies. Here are my responses:

QUOTE Do you mean "simultaneously" in the third party's frame? Or do you mean they are the same age when the signal reaches them? Or both? And after they wake up, what are their velocities in the third party's frame? END OF QUOTE.

ANSWER: Since the velocity of light is the same for all observers, and the third party is midway between the twins, and RF energy travels spherically from an omnidirectional anetenna, it is clear that, from the point of view of the third party, the signal arrives SIMULTANIOUSLY at each ship.

OK, that's all I was asking, I don't know why you denigrate this as an "irrelevancy". You never specified that the velocities of the two ships were equal and opposite in the frame of the third party, if they weren't then the signals wouldn't reach the ships simultaneously in the third party's frame.

Hence, from the third parties point of view, the subsequent accelerated motions of the two ships are identical both as to timing and magnitude. It is irrelevant as to the relative velocities of the twins ships and also irrelevant as to the twins ages in their own inertial reference systems.

I didn't ask about their ages in any particular frame, I just mean you needed to specify their ages some way or another. For example, you could specify their ages in the third party's frame at the moment he sends the signals, or you could specify their ages at the moment they receive the signals. Obviously this is relevant to the final answer--if one is 20 and the other 80 at the moment they receive the signals, and their subsequent motions are "identical both as to timing and magnitude" in the third party's frame, then one will still be 60 years older when they reunite. On the other hand if they are both the same age when they receive the signals, they'll be the same age when they reunite. Without specifying something about their ages (again, it needn't be in their frame) the question doesn't provide enough information for a definite answer about whether they'll be the same age on reuniting.

QUOTE Just as in the twin paradox, the question of who accelerated initially is basically irrelevant to who will have aged less when they reunite (completely irrelevant if we assume an instantaneous acceleration that immediately takes one up to the outbound "cruising speed") END OF QUOTE

Answer: Oh, Really? Do you really believe in the so-called twin paradox that if there is assymmetry in their initial acceleration that when they get back together they will still have aged the same amount?

Huh? In the twin paradox they have not aged the same amount upon return, because one accelerated midway through the journey while the other didn't (did you miss that I was talking specifically about who "accelerated initially" in the quote above, which I contrasted with the very relevant issue of which one accelerates "when they are a significant distance"?) If their initial difference in velocity is caused by A instantaneously accelerating away from B, and then after they have moved apart for X years B instantaneously accelerates in the direction of A and then cruises until catching up with A, we'll find that B has aged less than A when they reunite, because B was the one who accelerated midway through the journey. A's initial acceleration is totally irrelevant here, in fact if you changed this scenario so that B was the one who initially accelerated instantaneously to create the initial velocity difference between them, but kept all the other aspects of the problem the same, then when they reunited B's age would be behind A's age by exactly the same amount as in the first scenario. I can give a numerical example illustrating this if you're familiar with how to solve problems in SR using inertial coordinate systems and the time dilation equation.

I cannot believe you really believe that. It's wrong. PROOF: If one twin stays at home and the other accelerates out and then returns, the traveling twin will have aged less. Symmetry is important QED! END OF ANSWER

But here again you are talking about an acceleration midway through the journey. I said that the initial acceleration, when they were starting at the same location, was irrelevant (it would make a slight difference to the total aging if it occurred over an extended period of time, but usually in these problems we treat accelerations as instantaneous, in this case the question of who accelerated initially is 100% irrelevant to all questions about aging)

QUOTE it's the accelerations that happen when they are a significant distance apart that matter. END OF QUOTE

ANSWER; Yes, that is true. If that acceleration is symmetric in both timing and magnitude (relative to the third parties reference frame) than it will cancel out for the final answer. If it is not symmetric, it will result in an offset one way or other. In my example I made it symmetric both for the third party and each of the twins EVEN IF the twins don't know it. END OF ANSWER

Yes, but you didn't answer the question of whether their ages were also identical in the frame of the third party to begin with, that's important to answering the question of whether they'll be the same age when they reunite.

The remainder of your coments are irrelevant to the point of my thought experiment: The point of the thought experiment was that the twins could not know apriori if their ages would be the same or different when the came back together BECAUSE they didn't know what happened while they were asleep. In other words, without some historical knowledge of the model. Since the ouside observers (us) did know that history, we COULD properly predict the outcome.

But we don't need to know the history either, if we knew their ages on receiving the signals (or at any specific time in the frame of the third party after they wake up), that would suffice to allow us to predict their ages when they reunite, without knowing anything else about the prior history.

 

[davidf32]

Everybody, You all win up to a point. I agree that for the last example I gave the issue is symmetry and neither the beginning acceleration nor the later acceleration matter by themselves. There are an infinite number of ways to have symmetric situations and the test of it ultimately occurs when the two twins get back together. If they have aged to the same degree the situation was symmetric: If they have aged differently, the situation was not symmetric. "SYMMETRY" can be obtained by varying the accelerations, the lengths of time each twin is coasting and so on. Although this is close to being a tautology, the definition of symmetry I am using is simply this--if the twins have aged the same when they meet, they both have traversed space-time in such manners to arrive back at some place (not necessarily where they started from) having aged to the same degree. Are all of you satisfied that you have convinced me of something?
1 for the gang and 0 for david32.

The next part of this, my original thesis, that there is an ambiguity in the time dilation concept, I am not yet ready to concede and I have to think a bit more about it. if you guys (and gals if there are any) want to go on about this, so do I.
david32-who at least in part has been wrong in much he has said.

 

[harrylin]

Everybody, You all win up to a point.

This wasn't about winning but about giving you "some comments on this observation that appears to lead to an ambiguity", in the hope to clarify matters for you...

[..] "SYMMETRY" can be obtained by varying the accelerations, the lengths of time each twin is coasting and so on. [..]

Tinkering isn't symmetry... I gave you an example of symmetry in my last message.

[..] The next part of this, my original thesis, that there is an ambiguity in the time dilation concept, I am not yet ready to concede and I have to think a bit more about it. if you guys (and gals if there are any) want to go on about this, so do I.
david32-who at least in part has been wrong in much he has said.

I take that to mean that some of our comments were helpful.

Harald

 

[davidf32]

Harald, yes you all have been most helpful and I appreciate it greatly. So far as my comment about "winning and losing", that was meant as a joke and the joke was on me. As I commented earlier in this discussion I am new to this mode of communication: This is the first time I have ever used a chat site. I find the experience a bit strange--a like learning a new language. Some of the nuance in face to face gets lost. I will be more careful in the future. So far as the next stuff I want to present---I;m working on it now and trying to do an expansion on the time dilation equation using gamma. I'm a bit uneasy about using this expression because of the comments from Bcrowell re: that expression and what is meant by scalar. That issue, however, will come out in the wash.
In the meantime--again thinks. davidf32-the dolt! (lol)

 

[davidf32]

To all, I am wrong about the ambiguity. I was assuming that time dilation between two inertial frames was proportional to v^2 (energy). That of course is incorrect. However, this discussion was very useful to me in that I learned a lot about a number of things (including me). So I thank you all.
davidf32