Special Relativity - cloocks on two trains

[Mike_bb]

Hello, PF!

Example: Two trains are moving in opposite directions with constant velocity $V$. Clocks in the trains are synchronized at start point. Clocks on the platform are synchronized too. Left clock and right clock on the platform read 4sec. Due to time dilation clocks in the trains read 2sec.

Observer in the left train see the clock (1) in the left train and read the clock (2) in the right train and conclude that clock (2) is slowed.
Observer in the right train see the clock (2) in the right train and read the clock (1) in the left train and conclud that clock (1) is slowed.

My question: Is it possible that differences in time are the same (due to given conditions and relativity of simultaneity)?
For example, for observer in the left train: clock (1) = 2sec; clock(2)=1.5sec and for observer in the right train: clock (2) = 2sec; clock(1) = 1.5sec.
The difference in time for observer in the left train = 2sec-1.5sec=0.5sec.
The difference in time for observer in the right train = 2sec-1.5sec=0.5sec.

Thanks!

 

[FactChecker]

I'm not completely clear on the scenario (probably my fault), but you are correct that the time dilation is the same regardless of the direction of the relative velocity.

 

[Dale]

Is it possible that differences in time are the same (due to given conditions and relativity of simultaneity)?

If I correctly understood your setup then, yes. Not only is it possible, it is required. Otherwise one inertial frame would be distinguished from the other. That would violate the principle of relativity.

 

[Mike_bb]

If I correctly understood your setup then, yes. Not only is it possible, it is required. Otherwise one inertial frame would be distinguished from the other. That would violate the principle of relativity.

I meant following: for the left train: clock(1)=2sec; clock(2)=1.5sec and for the right train: clock(2)=2sec; clock(1)=1.5sec. The difference in time is 0.5sec (relativity of simulteneity).
Right?