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I've finished a special relativity test for high-school, and am vigorously debating the answer with friends. Here's a more detailed explanation/recollection of the situation:

A train is travelling East at a speed close to light (i.e. $0.95c$). In it, two matches: A and B are lit up at the left and right ends. An observer, Mike, stands directly between the two at the midpoint. How (from his inertial frame of reference) does he see the events happening?

From my understanding Mike would be considered the proper observer (as opposed to someone still outside of the train), as from his perspective he is stationary relative to the matches. Because he is stationary, and light travels at the same speed, will he not see the two events as taking place at the same time? The argument of my friend, is that light from B will reach him first. This is because his is travelling towards it. Please help.

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    $\begingroup$ Are the matches lit up at the same time relative to the ground or relative to the train? $\endgroup$
    – Pavlo. B.
    Apr 28 at 4:04
  • $\begingroup$ They are simultaneous relative to the observer on the ground. Sorry, I should have specified this. $\endgroup$
    – Menno
    Apr 28 at 4:47
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Because he is stationary, and light travels at the same speed, will he not see the two events as taking place at the same time? The argument of my friend, is that light from B will reach him first. This is because his is travelling towards it.

Your friend is correct.

In outside frame, the 2 events are simultaneous . But Mike is travelling towards the light coming from B and away from the light coming from A. So, the light from B will reach Mike, before the light from A.

In Mike's frame, the 2 events WOULD NOT be simultaneous. B would be lit before A. And since, the 2 are at rest and the same distance away from Mike, hence light from B would reach Mike before light from A.

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