On the PoundRebka results
Just a short blog post demonstrating the consistency between the proposed model of relativistic spatial dilation and the results found by Pound and Rebka.
Let's take a closer look at the results found by Pound and Rebka1 back in 1959. Recall that they conducted their experiment in a manner which allowed relative motion to precisely offset the gravitational Doppler shift over a height,
They found a result of
which follows with the equivalence principle preciously. If instead of accepting that light gains or loses energy depending upon it's path through a gravitational field, what if the light actually is unaffected, but it is space that is in motion?
In the context of relativistic spatial dilation
Let's now consider this result on the context of the relativistic model that inspired the development of ULLD. Recall that the equivalence principle in this model is attributed to the dilation of space, integrated over the radial vector
The integral to achieve the equivalence principle is simply the derivative of
In this case however, we want to find the integral over
This means that for every tiny shift in time,
This leaves the energry state of light unchanged by gravity, creating a Doppler shift and shift in
Footnotes

Due to my current living conditions I'm currently working offline, without access to the internet, and I don't have a copy of the paper on my computer. I can't recall if it was the emitter that was placed at
, or the receiver, but the principle remains. If I'm wrong, just stick a factor of in here somewhere. ↩