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On a train there are two light sources, one at the front, and one at the rear. In the middle of the train is a mirror angled upwards 45° in relation to the front light source. The mirror has a light activated switch on its back, which, when activated, instantly flips it to face 45° downwards in relation to the front light source. The light beam at the rear of the train is activated a fraction of a second before the one at the front, so it reaches the mirror first and activates the switch. The light beam from the front of the train then hits the downward facing mirror and is reflected downwards.

However, the train is moving at a significant percentage of light speed towards a stationary observer, so that from the observer's perspective the light from the front of the train reaches the mirror first. My question then is: What will the stationary observer see at this moment? As far as I can think there are four options:

  1. When the front light strikes the mirror the mirror still faces upwards so the light is reflected upwards. This seems impossible because in the reference frame of the light source the light must be reflected downwards.

  2. When the front light reaches the mirror the mirror still faces up, but the light is reflected downwards. This seems impossible because in the reference frame of the observer the mirror is facing up so the light must be reflected upwards.

  3. When the front light reaches the mirror the mirror faces downwards and the light is reflected downwards. This seems impossible because in the reference frame of the observer the rear light has not yet reached the switch in order to flip the mirror.

  4. I've got something fundamentally wrong. This seems entirely possible.

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  • $\begingroup$ this is why simultaneity must be relative in a world where $c$ is not. $\endgroup$ – JEB Feb 28 '20 at 2:42
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The solution to the paradox is that what is simultaneous for the observer at the train (the two lights being turned on) is not simultaneous for the observer at the station. For this observer the light from the rear of the train leaves first, so it will reach the mirror first too.

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