POkay, so moving clocks run slower but there is something I don't understand when talking about relative time and proper time. Consider this example for PBS crash course relativity, it says that the train relative time is 6.66x10^-7 seconds with a velocity of 0.5c but if we calculate the proper time (the time the other person that is not moving calculates ) it results 5.77x10^-7 seconds which is less than the relative time so the time in the moving frame is higher but it should be slower (time runs slower in moving frames). In addition, the gamma factor is 1.15 so 1 second in the moving frame is 1.15 second in the proper frame so the proper time should be 1.15x6.66x10^-7 =7.6x10.7 but it actually says that the proper time is 5.77x10^-7 which brings me a lot of confusion because it is later used to calculate the length contraction from the proper time view but I can't understand why the proper time is less time. For example if the gamma factor is 4 then 1 year in a space should be 4 years in earth (proper time) and the length contraction should be done with that number. Plz explain:(
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FYI, larger value of time means that the moving clock runs slower. Try to imagine that for the clock-tick, the clock use more time (larger value of time) to make a tick in moving frame and that’s why you’d say the clock is running slower in moving frame. So you get the fact that proper time is smaller than the relative time.
