Question

Bob and 2 students of his drift by Dave at velocity vH in the x-direction. He then synchronizes all the clocks in his reference frame, using the perfect Einstein Convention.

Bob has a flashlight. Dave is some distance away from Bob, observing.

Consider two students, with t-shirts reading l and -l, along the x-axis of Bob, one in front, and one behind Bob.

When Bob fires his light flash, which student receives the light flash first, as observed by Dave? Dave is in the positive x-direction. Out in front of the direction that Bob is traveling.

A. The student behind Bob (T-Shirt “–l”)

B. The student ahead of Bob (T-Shirt “l”)

C. They receive the flash simultaneously

D. One or the other never receives the flash at all

E. Something else happens

Answer 1

Before answering the question, let us first look at the what special theory of relativity says:

1) time dilates for moving clock.

2) Length contracts while moving at high speed(close to c).

3) The two events that occurs simultaneously in one frame of reference does not occur simultaneous in another frame of reference moving if the two events takes place in different location.

So using point number 3 we will understand the answer to this question.

Let there be two frame of reference , Bob's frame and Dave's frame. In Bob's frame, both students I and -I will receive the light at the same time which implies that the two events in simultaneous in Bob's frame. However since student I and -I are at different location therefore, in Dave's frame, the event will not be simultaneous i.e they will not receive the light simultaneously when observed from Dave's frame. Now Dave is in +x direction and Bob's frame is travelling towards Dave's frame which makes Dave closer to student I and far from student -I . Thus Dave observes that flash light reaches student I who is ahead of Bob (who is closer to Dave) earlier.

Answer : B