The Time Dilation Equation (TDE) of Special Relativity

Have you tried to calculate what the speed of light would be if he uses her clocks and measuring rods instead of his own? Hint: it does not violate SR because it is still c. The apparatus of SR is designed to ensure that the speed of light measures c in both reference frames. So your claim that he cannot use her clocks and rods due to it violating constancy of the speed of light is false.

 

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He knows that that would be a phony calculation for him to make, because her clocks aren't synchronized (according to him). As long as he isn't stationary in her frame, he isn't interested in using her clocks for anything, but he knows that it's appropriate for HER to use her clocks (and for her to ignore HIS clocks and his conclusions therefrom). It's weird for them to BOTH be right, but that's just the way Special Relativity IS.

 

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To put it in context:
Suppose when the traveling twin is 10 years old he wants to know what his sister's age would be if he jumped off the train he's riding, and became stationary with respect to her. He doesn't actually have to jump off the train, he can look over at the nearest clock in her synchronous array of clocks and see that it displays t=20 and he would then know she would be 20 years old if he were to jump off then. There could also be a mile marker there that says x=17.32 light years, and he would know that is how far away from her he would be if he jumped off the train. That is an example of him using the reference frame in which she is stationary for his own measurements, and they are not "phony" unless the context of "what if he were to jump off the train" is not specified.

Using the the reference frame in which he is stationary, he would say she is 5 years old and a distance of 8.66 light years away. That doesn't help him to know what he wants to know, which pertains to the "what if he were to jump off the train" question. He could also just want to know what she would say the situation is, regardless of whether he jumps off the train or not. That is what I meant by putting himself in her place. As long as it is specified that he is doing that, I don't see anything wrong with it. But if you do, then I guess you just can't do that!

 

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Special Relativity is just STRANGE! If I'm unaccelerated (for some period of time), I'm stationary in some inertial frame during that time. And I KNOW that the clocks stationary in that frame all run at the same rate, and have been synchronized so that they all show exactly the same reading at the same instant in my life. And I know that all of that follows from the fundamental assumption of Special Relativity: that any light pulse moving in my inertial frame travels at 186,000 miles per second. I also know that the clocks that are stationary wrt my home twin are NOT synchronized, according to my (correct) measurements of them. But I ALSO realize that my home twin will correctly say that it is HER clocks that are synchronized, and it is MINE that are unsynchronized. That is just WEIRD! But that's just the way Special Relativity IS, and there is NOTHING we can do about it.