Eckhard has read and grasped my paper [link:vixra.org/abs/1812.0424]Everything's relative...[/link] and remarked above that
"Attributing gamma to energy... might be the most reasonable way out" [regardless of whether I'm correct in all other details.]
The Fizeau experiment [among others] is still not physically understood, so my details of such may or may not be correct, nevertheless the energy-time model versus the space-time model yields intuitive physical explanations of experiments without the inconsistencies of special relativity (the 'paradoxes').
Having spent almost 2 years arguing these points with excellent physicists, including two of Feynman's students, I am very aware that relativity has been pushed into countless areas of application. The application of gamma to relativistic energies is significant, but time-dilation experiments are the basis of most relativists' faith in SR.
I have become convinced that focusing on many details, while necessary, is distracting, and that it is better to focus on the root false premise - Einstein's introduction of multiple time dimensions into the problem at the 'definition-of-terms' level, and since all theoretical arguments are then framed in these terms (i.e., inertial reference frames) then the falsehood permeates every logical argument thereafter.
Einstein complemented the introduction of his false premise of multiple times with his imaginary invention of perfect, weightless clocks, that somehow magically measure time in each time dimension. With real physical clocks, based on mass and inertia, the increase in relativistic mass causes clock's inertia to increase, and since every real clock depends on inertia this provides a universal explanation of 'time dilation' in all SR experiments.
My best to all,
Edwin Eugene Klingman