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jrlogan1

**[SOLVED] A twist on the twin paradox, help me figure this out!**

Relativity question:

A twist on the twin paradox (that again??) Yes, that again.

First, it took me a while to accept that the acceleration breaks the symmetry of special relativity and accounts for the difference in aging of the twins when one returns to the other. But finally, I am able to see that their frames of reference are in fact different due to this acceleration, and grudgingly accept it, because it is still hard for me to understand. I don’t know any relativity math, but I’m sure ole Einstein came up with a formula that explains this perfectly. Now let me propose a thought experiment that I still don’t understand.

Two people living on two ‘planets’, surrounded by a vacuum. Both planets have equal net negative charges, so that they can be equally acted upon by a magnetic force. Starting with both planets at rest and their perfect wrist watches are in sync. They are in the same frame of reference with respect to motion.

Now, let’s turn on a large negative magnetic field that is directly in between the two planets, and acts to uniformly accelerate the two planets directly away from each other. Both people feel equal forces, of course. Continue this until they are almost at the speed of light and then turn the field off and let them coast. (Note: the magnetic field stuff has nothing to do with the physics question here, I am just using a plausible method of doing my experiment to avoid confusion.)

Questions:

1. When accelerating, what are their clocks doing relative to each other. My logic tells me that they must still be in sync, because if you were to immediately reverse the field and bring them back together they would have both taken the exact same journey, acceleration and all, and so one can’t have aged more than the other. If one were to be older, which one would it be?

2. Now we’re coasting, so each person can argue they are at rest and the other is moving. Now, each person could look at the others watch with an amazing telescope (oh yeah, their planet is equipped with one of those too!), and see the other’s watch going slower than their own. This is basic special relativity, is it not? Is this correct?

If so, then the next part of the experiment really baffles me. If not, then please explain, but let me finish the experiment.

According to what I understand of SR, now that they’ve coasted a bit, their watches will no longer be in sync. Now, let’s reverse the magnetic field (which is quite strong and can reach the planets without any problem at all, just a wee bit bigger than a typical refrigerator magnet… ). Now the planets are accelerating, or decelerating relative to each other and come to a relative halt and then accelerate toward each other. All the same concepts apply, we let them coast back together (further increasing the difference in their watches, not resolving it, because time dilation has nothing do do with the direction of the motion, just the motion itself) and then stop them again where they started. All logic tells me that their watches must, must, MUST be the same, but what I know of SR, during both coasting periods, their watches weren’t in sync. In fact, each would have measured the others as going slower than their own, equally. Both can’t be right, because for all practical purposes they are equal. How would you distinguish which would go faster or slower?

I think my logic is correct, and their watches will be the same, however I don’t understand why under the laws of relativity. Will someone please explain this in layman’s terms, as I don’t know the math formulas, nor do I care to!

Thanks!