Sure I could go read a book
That would be a very good idea. You should also try to do the exercises, and then you could find out if you
really understand relativity.
Look: I already pointed out that your interpretation of what he said is stupid. Or do you have an answer to "is six feet equal to thirty miles per hour"? Either I'm a competent physicist and Greene is a competent physicist and you should listen to my clarifications of what's basically a decent video let down by a little laziness, or we're both idiots and you should ignore us. You can't have it both ways.
So your question was a rhetorical game of guess what number am I thinking.
Not really. I've read your posts before and I can see the way you treat Neddy Bate and Q-reeus, both of whom appear to understand this a whole lot better than you do. Your problem is that you want someone competent to talk to but you also want them to agree that you're right and you understand relativity better than anyone else. So I already know you're going to ignore everything I have to say. I only asked who were the other 2.5 people to see if perhaps you'd actually taken on board some of what I've said before, in which case it might be worth trying again. Apparently not. Apparently I'm going to try anyway.
My guess is you're Queerus' sock puppet
Um... no.
Since the mirrors are moving from the stationary perspective, the light has to leave one plate at an angle to meet up with the other one. Sure but how does this principle enact this physically?
You don't need to care at this point. All Greene is developing is relativistic kinematics. Basic sanity requires that the light come off the mirror at an angle in the moving frame. Greene just works out the implications of this, assuming that the speed of light is $$c$$ in all frames. The result is time dilation.
The detailed mechanism requires Maxwell's equations, but in short the light induces currents in the surface of the mirror and the electric and magnetic field of those currents is the reflected light. Roughly speaking. In the stationary frame the electrons move back and forth, but in the moving frame they move in a zigzag because as they move back and forth they move sideways along with the mirror. Back and forth currents induce vertical radiation, zigzag currents induce diagonal radiation.
Greene suggests the photon acts like a ping pong ball when he knows that the speed of light can't be altered by the speed of the source like a ping pong ball being hit sideways by a racket
The speed of light is not altered. Its direction is different in the two frames - aberration, as Neddy Bate already told you.
He never mentions any length contraction in his derivation and he proves time dilation by assuming time dilation.
He does not. He derives time dilation assuming consistency between the frames (what I called basic sanity above) and the invariance of the speed of light.
My math showed where theta came from but you probably didn't read that either
How are you drawing Minkowski diagrams without assuming the Lorentz transforms and all that goes with them, including the relativistic aberration phenomenon you claim to be deriving?
It doesn't bounce at an angle off the plate. Do you not realize the frame is moving? The ball of light in the moving frame is always directly above the center of the plate, it is not moving at an angle to either plate. This is pretty basic to the whole analysis.
It does bounce at an angle in the moving frame, exactly the angle necessary so that the horizontal component of its velocity is equal to the velocity of the mirror and it remains between the mirrors. That angle is Greene's $$\theta$$, and obviously it must satisfy $$c\cos\theta=v$$ (the bit ralfcis thinks means that lengths are velocities).