The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in an accelerating spaceship.
The books seem to say this implies time dilation, but I don't completely see why. Could it not just be like any other doppler effect? If I send a sound wave towards you and you are moving towards me, the frequency you observe will be greater than what I send out, but that doesn't mean your clock ticks slower (assume his speed is non-relativistic). Why does it necessarily imply time dilation?
In the derivation used to derive this redshift, from the light beam on a spaceship, special relativity doesn't even seem to come into play, just newtonian physics is used. Anyway if the physics on the ground is indistinguishable from the physics in the spaceship, would that not mean that at the back of the spaceship a clock ticks slower, rather than just appearing to click slower, relative to someone at the front? Otherwise it would seem to me that the EEP would just say that we can't do any experiment to distinguish the physics between the rocket and the gravitational field, though the physics wouldn't really seem to be the same.