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Suppose we are in an IF(inertial frame) and a fast air plane flying overhead constitutes a second IF; let it be the top plane in Fig. 2.3(a). Suppose that a flash bulb goes off in the exact middle of it's cabin. Then the passengers at the front and back of the cabin will see the flash at the same time, say when their clocks or watches read '3'. But now consider the progress of this same flash in our IF. Here, too the light travels with equal speed fore and aft. Here, too, the flash occured exactly half-way between the front and back of the plane (..). But now,the rear passenger who travel into the signal will receive it before the front passenger who travel away from the signal. The top of Fig. 2.3(a) is a snapshot of that plane in our IF when the signal hits the back of the cabin. We know that the rear clock reads 3. But since the signal has not reached the front, the front clock will read less than 3 , say 1. ...

Picture : enter image description here

In the moving frame, we measure 3 second for signal to hit either side that I understand. My issue is with seeing the event in static frame.

If passenger at back receives the signal quicker than one at the right, shouldn't the time for the beam to reach them be less than three seconds? I think the right side passenger must take longer contrary to the final claim because the light has travel longer to reach them.

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You are overlooking the relativity of simultaneity. In the plane, the passengers at the front and the back see the flash at the same time. In the stationary frame, the passenger at the back sees the flash before the passenger at the front. In other words, two events that are simultaneous in the plane are not simultaneous in the frame of an observer on the ground (and vice versa).

To expand on my answer, suppose the flash goes off at a point in spacetime in which it is exactly 12:00:00 on both the plane and in the ground frame. If the plane is six light seconds long, then on the plane it will be 12:00:03 when the light reaches the passenger at the front and the same time, 12:00:03 when the light reaches the passenger at the back. In the ground frame, however, the flash will reach the rear passenger before it reaches the front passenger. Let's suppose the speed of the plane is such that in the ground frame the flash reaches the rear passenger at 12:00:02 and the front passenger at 12:00:04.

What that means is that 12:00:03 in the rear of the plane is the same time as 12:00:02 in the ground frame, while 12:00:03 in the front of the plane is the same time as 12:00:04 in the ground frame.

So when you ask, how long doe it take for the light to reach one of the passengers, the answer is that it depends on which of the two frames you measure it in.

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  • $\begingroup$ I feel like you didn't really read my question or have misunderstood it. I edited it again. Could you check please? $\endgroup$ May 20 at 14:50
  • $\begingroup$ I have not misunderstood your question, but I have clearly not given an answer you understand! I will add a further explanation to my answer in a minute or two. $\endgroup$ May 20 at 15:15
  • $\begingroup$ Oh I think I am understanding more now. The clocks in the last section are all in the inertial frames. $\endgroup$ May 20 at 17:15
  • $\begingroup$ ahaha I can't believe it was this simple! $\endgroup$ May 20 at 17:16

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