special relativity - Why light moves sideways?

Greatings! I'm trying to understand special relativity and have one question bugging me.

In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.

So the question is this: When a light source on the MOVING light clock emits a photon of light the path of the photon is triangular.

How this can be?

I thought since light speed is constant in every reference frame the movment of the "emmiter" can't affect the movment of the light so light should shoot right up (from the point of stationary observer) and thus move backward and up from the point of moving observer.

So you see my logic is: light speed is invariant => you can't make it move UP & FORWARD only UP. i.e. you can't change it's direction once it's emited in UP direction. Why the hell light moves sideways then?

And I'm puzzeled. There is flaw in the logic but I don't see it.

Thanks for help.

Answer

There are actually more than one ways to look at this problem. I am going to explain why the light must not go straight upward in the ground frame if the light clock is moving horizontally wrt ground frame.

The fundamental postulates of relativity is:

Laws of physics are invariant in all inertial frames.

Suppose the in the ground frame, the mid-point of the lower plate of the light clock is at (0,0) at time $t=0$. The upper plate of the light clock is at ($l$,0) at the same time. The clock is moving with constant speed $v$ in wrt the ground frame. A photon leaves the lower plate at $t=0$ (in ground's clock) in such a way that it is going straight upwards in the light clock frame. Now suppose there is a switch of some bomb attached with the midpoint of the upper-plate which if hit by a photon blows the light clock. Since the photon is going straight upwards in the light clock frame it will surely hit the upper plate and blow the light clock itself. Now if the photon moves straight upward even in the ground frame then it can never hit the upper plate as the light clock is moving and the upper plate must have travelled forward and thus the light clock actually survives in the ground frame. Which just can't happen because otherwise it indicates that laws of physics are different in the light clock frame and in the ground frame which just can't be the case in accordance with the first postulate of special relativity. Further, in order to be consistent with the first postulate of relativity, light has to go precisely in the direction so that it can hit the upper plate. So rather than contradicting with the relativity, the different direction of light is a necessity for the principle of relativity to hold.

Another thing: It is not dictated by the maxwell equations that the direction of light must be the same for all the inertial frame. If it would be the case it would actually break the directional symmetry of space. Because it would define a particular direction with a preference - the direction in which the light goes. Maxwell's equations just dictate that speed of light is same in all frames where Maxwell's equations are valid. i.e. at least all inertial frames.