A cart of length 2L with one marker at each end is moving at constant speed v along a straight rail. On board is Observer A. Right in the middle is a light source. On the ground is Observer B. Both observers are able to measure the time instantly wheneve a light pulse(you can treat it as a small ball of light) hits a marker.
a) THe light source sent out two light pulses simultaneously, one to the left and one to the right. The pulses eventually hit the markers. The time for the right pulse to travel from the source to the right marker is Tr, and the time for the left pulse to travel from the source to hte left marker is Tl. Find Tr and Tl in terms of c, L and v if necessary, as recorded by Observer A. According to her, did the two pulses hit their markers simultaneously?
b) Find Tr and Tl as recorded by observer B. According to him did the two pulses hit their markers simultaneously?
c) Along the same way of thinking as (a) and (b), design an experiment to demonstrate that it is possible for Observer A to see a pulse hits the right marker(let us call it event-1) before another pulse hits the left marker(event-2), while accroding to Observer B the same pulse hits the right marker (event-1) after the other pulse hits the left marker (event 2)
d) What has been shown in (c) is that the sequence of two events can be reversed, ie, according to Observer A event-1 took place before event-2, while to Observer B event -2 took place before event-1. However, reversing the sequence of two events is not always possible. Use the results in (c), prove that the two events are reversible if the distance bewteen the two events in larger than |c[del]t|, where [del] t = Tl-Tr is the difference in time between event-1 and event-2. THe max value of v is c.
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