special relativity mirror experiment

There's an experiment in special relativity that involves a light source and a mirror, both placed in a moving object. It is used to derive the time dilation equation. I'm having serious doubts about it's validity. It implies that light from the source hits the mirror in its exact center, although the mirror has moved a certain distance from the time the light source emits the wave and until it hits the mirror. If, hypothetically, the mirror had moved very fast, then light should have passed by it. But this doesn't happen in the experiment, as if light also had a velocity component in the direction of the train. But it doesn't, since that would imply that the constant speed of light postulate breaks.

• If both comoving observers agreed on the direction and path of the light, there would be no path difference and thus no time dilation or length contraction. And thus no relativity. Either that or you'd be forced to accept a variable speed of light or absolute motion, which are not supported by experiment. – Asher May 12 '16 at 6:59
• Sorry, I can't understand your answer. What do you mean by "comoving observers"? I'm not understanding what your refer to by path difference either. Remember that I've just started studying relativity. I haven't yet learned about length contraction for example. – andrei May 12 '16 at 16:58
• Sorry, relatively moving, not comoving. In any case, in one frame the light travels in one direction and in another frame it travels at an angle to that direction. This is a consequence of the consistency of the laws of physics across various frames. – Asher May 12 '16 at 18:27
• I too am confused by this experiment regarding the trajectory of light. The observer in the train should se the light go perpendicular to its motion on a straight into the mirror. Why doesn't the observer in the platform also see the light perpendicular to the movement of the train (and thus miss the mirror)? how come light has a velocity component along the train's movement? – pakman Apr 27 '17 at 21:38

Let us dive into the light clock thought experiment,

Special relativity is based on two postulates,

1. There is no such thing as absolute motion. Phrased another way, all laws of physics should be invariant under changes in inertial frame.

2. The speed of light is measured to be the same value in all inertial reference frames.

Let's say you are on the train and have light source aimed at a mirror in such a way that the light is traveling perpendicular to the motion of the train. According to postulate 1, there is no way for an observer on the train to tell that they are in motion as the train is an inertial reference frame. Thus the laws of physics should be the same for the observer on the train as it would be for an observer at rest.

From this one can conclude that the light does not miss the mirror and indeed hits it dead center as if the mirror was standing still. If this wasn't the case, then there would be a way to distinguish absolute speed and relative speed, harshly violating the first postulate.

The second postulate leads one (forces one) to the understanding that the amount of time experienced is dependent on motion. Since the speed of light must be constant in all frames of reference and the light travels between two fixed events with different lengths for the moving and stationary reference frames, we conclude that the moving and stationary references frames must have experienced different amounts of time between the two fixed events.

• I think that when the first postulate was devised, it did not take into account wave phenomena. If instead of light, the source was a ball being thrown upwards, then that ball would also have a speed component in the direction of the train and only then we could imply that it would hit the center of the mirror. If relative motion was always true, than me moving away from a standing sound source at the speed of sound would be the same as me standing still and a sound source moving away from me. In the first case, I wouldn't hear any sound. But in the second, I definitely would. – andrei May 12 '16 at 16:47