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One way time dilation is derived is as follows. A light source inside a train sends photons vertically to a mirror on the ceiling of the train. Observer A is inside the train and observer B is outside. The train is moving with speed $v$. B sees the photons hit the mirror with an angle greater than 0 with respect to a vertical line to the floor, as the light reflects its path forms a non-zero angle which is what i don't understand, why does B see the light travel in a different trajectory than the one A sees?

paradox
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For observer B, the light source and the detector lie either side of a normal to the mirror at the point where the light is reflected.

Spherical wavefronts (or at least wavefronts that are parts of spheres) leave the source. Different parts of these wavefronts hit the mirror all over, travelling a variety of angles depending on where they hit. Observer B's detector receives waves travelling such that angle of incidence = angle of reflection. The same is the case for observer A, only both angles are zero.

Recommendation: draw a few wavefronts – or just consider a 'fan' of 'rays' sent out by the source. A gets back the ray reflected normally, B gets a ray that's bounced off the mirror at an equal angle to the normal on the other side of the normal. Not very physically instructive but gets you there.

Philip Wood
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    Surely considering spherical wavefronts is an unnecessary complication. You could imagine just a single photon that both observers perceive differently due to the relative motion... – lemon Jun 11 '18 at 09:57
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    Depends on questioner's background knowledge. But with the benefit of your comment there's now a choice... – Philip Wood Jun 11 '18 at 09:58