I assume most people are familiar with the thought experiment for gravitational time dilation. First the time dilation effect is demonstrated for two observers in an accelerating rocket, one at the top and one at the bottom. The one at the bottom sends light signals to the one at the top. Since the observer at the top is accelerating away from the light signals, he receives them at a slower rate than than they are emitted. It is then argued that time runs at different rates at the top and bottom of the rocket, and the equivalence principle is invoked to extend the argument to a gravitational field.
My question is this: consider the same experiment, but analysed entirely using Newtonian physics with absolute space and time. I know that there should be no time dilation effect predicted. Where exactly in the above argument is the absolute space and time of Newtonian physics rejected?
Short question: Why can't we argue (using the standard thought experiment) in Newtonian physics that clocks at different ends of an accelerating rocket tick at different rates?