Einstein's resolution of the clock paradox

[Al68]

I just read what you said again. It seems to me that your definition of SR has led you to some strange ideas about what the problem is and what its resolution is. (Those ideas are strange to me, but they are perfectly consistent with your definition of SR, so it seems to me that it's your definition of SR that has made you miss the point of the twin paradox). This seems to be what you're thinking:

[Incorrect][/color] Problem: From the ship's point of view the other twin is younger.
[Incorrect][/color] Resolution: The "ship's point of view" is undefined in SR.

As I pointed out in my previous post, the most natural definition of SR includes all coordinate systems, and if you use one (of many possible) coordinate systems that we can think of as representing the ship's point of view, you will definitely find that the twin on the ship is younger when they meet again. This is a perfectly valid resolution of the "paradox".

If you instead choose to define SR such that non-inertial frames aren't included in the model, then I agree that the problem, as you have interpreted it, doesn't need to be resolved within SR. It is by definition not a problem in SR. It's a problem in some other theory (that I call SR and you call GR). Of course that means that we still have to find the resolution of the problem in that theory. (I described one way to do it in the preceding paragraph, and I will describe one more way to do it below).

This is how I would describe the problem and its resolution:

Problem: The time dilation formula says that both twins are right when they claim that the other twin is aging slower, both when the ship's moving away from Earth and when it's on its way back. (Note that this illusion of a paradox is present even in the kind of "SR" that you have in mind).

Resolution: The twins are both right, but the fact that the twin on the ship can conclude correctly that the other twin is aging slower during both parts of the trip doesn't imply that the other twin will be younger when the ship gets back to Earth. You will only think that it does if you forget to take into account that the simultaneity lines get tilted in the opposite direction when the rocket turns around. (See my spacetime diagram. You will find if you follow the link in my previous post).

My statements here have been about Einstein's papers on the twins paradox and SR, not my own views. I was asking what others thought of his view, not mine.

And it seems strange to me that the way Einstein viewed the issue would be indicative of "strange ideas about what the problem is and what its resolution is", "missing the point of the twin paradox", since he is the one who had the point to make initially (though a different point than most here consider important).

You do make a very good point about defining SR, as Einstein's "GR resolution" of the twins paradox is based on the equivalence principle and gravitational time dilation, which predate GR. It has been called the "GR resolution" by others (and me) perhaps incorrectly.

 

[Al68]

Al68,
OK. you should put 'paradox' in quotes, in that case.



The thing is, the ageing is given by the proper length of the worldlines, and this is agreed on by all inertial observers ( IOW, invariant under LT) and I don't see how E thinks this is a defect. It works even if both travellers have accelerated world-lines.

Anyhow, I'm pretty bored with this subject so if you don't mind I'll bow out for now.

M

Thanks for all your responses,

Al

 

[Dale]

I always prefer the spacetime geometric resolution. It works in both SR and GR contexts, with gravity or without, for inertial or non-inertial observers, for arbitrary paths, and for more complicated "paradox" scenarios. Plus, it is, IMO, useful for pedagogy as well, and gives quantitative answers.