Let’s assume I measure time t in my rest frame - thus in a moving frame I have t’ corrected according to the Lorentz factor.
I have a moving primed frame such that t’= 0.5t for example.
I measure 1 second in my rest frame, which is observed as 0.5 second in my primed frame.
If I now consider my primed frame to be the rest frame, and my previous rest frame to now be my “primed” frame, and measure 0.5 seconds in my now rest frame, I get 0.25 seconds in my now moving frame. How does that work out? Shouldn’t I get my whole 1 second back?
It is safe to assume I could consider any possible frame of reference, so what detail is it that I’m missing?
Edit*: I have 2 pairs of frames:
Rest1: Let time be t Motion1: moving observer relative to Rest1 such that t’=.5t
Rest2: chosen such that Rest2 is at same speed as Motion1. Let time be T Motion2: chosen such that Motion2 is at same speed as Rest1. T’ = 0.5T
If t = 1, then t’=0.5 Since Rest2 and Motion 1 are at the same speed, then T = t’ = 0.5 Therefore T’ = 0.5*0.5 = 0.25
Motion2 and Rest1 are at the same speed, thus T’ = t, 1=0.25!?