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Suppose that we have two platforms: A and B. Each of them has a special photon detector on them. Detectors are constructed in such a way so that only photons falling on them with 90 degrees incidence angle will be detected.

Now at $t_A=t_B=0$, the two platforms are parallel to each other with sensors facing one another(as shown on the sketch) with platform A not moving in the lab's reference frame and platfrom B has velocity of magnitude $v$ towards $+x$ direction. enter image description here

At $t_A = 0$, a flash of spherical light is ejected from the point situated between sensors and equidistant to them.

My question is, what which sensor is going to detect light on them? Sensor A? Sensor B? Both of them? It seems natural to me that only sensor A detects light, however doesn't a photon reach sensor B perpendicularly in B's reference frame as well?

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    $\begingroup$ A flash means lots of light so both detectors will get light. But since B is moving and depending on the tube length, it will get less. $\endgroup$ – PhysicsDave Jul 8 at 2:55
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The problem is completely symmetric in terms of what A and B see, except obviously A will see B as moving right and B will see A as moving left. According to both A and B, the flash occurs halfway between the detectors, when the detectors are facing each other. This means that according to A, the detector on A receives the light at a right angle; and according to B, the detector on B receives the light at a right angle.

What is interesting is that according to A, the detector on B will not receive the light at a right angle, and vice versa, since the detector on B will have moved by the time the light reaches it. The perceived angle of incidence will be $\sin^{-1}(v/c)$. This indicates that the angle of incidence is observer-dependent. In terms of detection, however, what would be relevant is the angle of incidence in the detector's frame of reference, so both detectors would receive the light.

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  • $\begingroup$ That's correct, just a small note that B will see redshifted light (due to transverse Doppler effect in B's frame) $\endgroup$ – Albert Jul 11 at 6:27
  • $\begingroup$ Albert: Yes, good point. This is of course assuming that the flash is emitted by a source that is at rest with respect to A. Otherwise we need to know how the source is moving for a complete description of how the detectors will see the light. $\endgroup$ – Puk Jul 12 at 7:08

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