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Take two objects, A and B. A is stationary, and B is in motion with velocity v in the positive x direction. Initial conditions are t

_{A}=t

_{B}=x

_{A}=x

_{B}=0.

From the way special relativity has been described to me, it is allowable to take a reference frame that is stationary with object A, or a reference frame that is moving with velocity v along with object B.

If the reference frame is instead set to move at [itex]\frac{1}{2}[/itex]v, this would cause the equation for time dilation to be t'=[itex]\gamma[/itex]t for object B, with velocity [itex]\frac{1}{2}[/itex]v. The same equation would apply for object A, but with velocity -[itex]\frac{1}{2}[/itex]v.

Setting these two equations equal, you show that time passes equally for objects A and B. I posed this problem to my professor, who told me to read about the twin paradox in my book. I did so, and it failed to answer any questions in a mathematical way, or even definitively in a logical way. Further research hasn't clarified this for me (it's given me more questions!) The closest I've come to an answer to this question was "The short answer is yes, you are correct, and the long answer is general relativity."

I'm one of those learners who has issue with accepting canon and learning half-truths, but I think GR is still a bit above me at this point. Any elucidation would be greatly appreciated!

Carl