Variable Speed of Light Theories

Sorry for the late reply, but part of answer your question in a respectable manner entailed me having to review my own understanding of the matter from first principles. The following derivation was my reconstruction of a homework assignment in my first day of class in grad school 12 years ago that relates Special Relativity with the even the more elementary theory of electro magnetism.

A calculus teach pointed out a few typo-mistakes in my derivation, but otherwise liked it as a potential pedagogical tool:

Reviewing Special Relativity and Lorentz Trasformations, Relevance to Alternate Cosmologies - #25 by stcordova

You act as if experiments done on Earth indicate some sort of absolute frame

We’re probably close to the absolute zero velocity, and that claim is experimentally testable.

However, I don’t see how you can determine which frame is the frame without any movement.

Correct!!! We need movement to find out if our absolute speed relative to space is close to zero. It centers around this formula of Special Relativity (by Lorentz):

\large t' = \gamma \Delta t

where
\LARGE \gamma = \frac {1}{\sqrt {1 - \frac{v^2}{c^2} }}

the present point of contention is the meaning of “V” in the above Lorentz factor \gamma

The way I interpret the meaning of V is not the same as how others here might interpret V.

I want to diagram the experiment that will show that V is best interpreted in relation to the absolute zero V_{ref} = 0 other wise this leads to absurdities.

Absolute zero V_{ref} implies velocity relative to vacuum space which is really “something”, not nothing, and this something has properties like \mu_0 and \epsilon_0, and I speculate it may be possible that even these “constants” may not be constant after all.

The speed of light depends on these “constants”, but most, if not all variable speed of light theories would entail variability of these “constants” which may be argued are even more fundamental than light itself.