Events in different reference frames

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I am having trouble with measuring coordinate time in different inertial reference frames. For example:
Say a car is driving around a circular track (at constant v) and passes a stationary observer. I'll call this event A. Then the car makes another lap and passes the observer again (Event B). Say there are also two observers on a train that passes the track (also at constant v); one of these observers is present at event A and the other is present at event B. The observers on the train have synchronized clocks and calculate the time between A and B.

Do the observers on the train observe a different time than the stationary observer? If they do, how do you calculate the time they observe if you only know the speed of the train and the time observed by the stationary observer?

Thanks
 

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  • #2
JesseM
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Is this a homework problem? Anyway, translating position and time in one frame to position and time in another is what the Lorentz transformation is for, are you familiar with how to use it?
 
  • #3
ghwellsjr
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Yes, the observers on the train observe a different time than the stationary observer. Their measurement of the same time interval will be smaller. The faster they are traveling, the smaller it will be.

The car on the circular track is irrelevant to the question you asked. All you need to say is that there are two events separated by some time interval according to the stationary observer. Then you apply the time dilation formula (look it up in wikipedia) based on the speed of the train to get the gamma factor. Then you divide the stationary observer's measurement of the time interval by the gamma factor and you will get what the moving observers measure for the same time interval.

By the way, you don't need a second observer on the train nor a second synchronized clock, one observer with one clock on the train can make the same measurement.
 

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