I am no experimentalist, but doesn't Cockroft-Walton voltage multiplier use diodes, which were possible only after quantum mechanics, which depended on deBroglie's hypothesis of the wave nature of the electron, which he borrowed from Einstein's relativistic formula for the energy of the photon?
You are again making a mistake---there is a difference between "what physics topics are fully understood" and "what technologies are available to experimentalists". The "rectifier" effect of certain crystals were discovered in the 1870s, and heavily studied after that. Cockroft and Walton built their accelerator in 1932, using diodes that had been available long before Felix Bloch explained bandgaps or conduction at all, and the p-n junction that actually makes diodes work was not explained until 1938.
I have been able to find references to the use of the Van de Graaff for accelerating ions and protons, but not electrons. In all the cases that I have been able to find, the velocity is too small (max of 40 MeV for the kinetic energy of the proton). If you know of an actual experiment in which ELECTRONS were accelerated by a Van de Graaff, please share it with us. Maybe there is some kind of theoretical barrier for the electrons.
Electrostatic accelerators work at fixed energies, not fixed velocities. If you can charge the terminal to 20 MV, you can get 20 MeV protons (which are slow) or 20 MeV xenon ions (which are very slow) or 20 MeV electrons (which are very, very fast).
There are currently-active electron Van de Graaffs at Chalk River, TU Delft, UC Santa Barbara; the Notre Dame van de Graaff used to have an electron mode, but that capability (probably a terminal-mounted filament and an alternative corona needle) was removed in the 70s. I would virtually guarantee that the Van de Graaffs of the 1930s and 40s would have been considered as all-purpose electron/ion machines.
Nowadays, if you need a 10-30 MeV electron beam, you can build or buy a linac, which is compact and inexpensive. That's why Van de Graaffs are so rare for this purpose nowadays. But there is no engineering or physics barrier.
Why do you seem so certain that this is wrong?
I don't question this at all. What I find it difficult to accept is spotting a deviation and coming up with the full relativity theory, which brings me back to my intention of posting my original article.
"Spotting a deviation, exploring it in every way you can, and coming up with a theory that makes it make sense" is
what physicists do. Yes, it's difficult, but ... this sort of thinking is the whole point of being a physicist. That is the particular sort of hard problem that the Golden Age physicists were so incredibly good at.
The "deviation" is not some tiny subtlety---"if you have the spectrometer tune juuuusst right and the moon is full and the barometer is falling". The deviation is a large, reproducible effect, seen in quantities (energy, momentum, velocity) for which we've had excellent and reliable measuring instruments for a long time. The "deviation", plotted on simple graphs---a plot of v vs E or v vs. p for example---has a big obvious feature, an asymptote, pointing towards v=c, which provides a big hint in the right direction.
If it was possible for Einstein to come up with the whole SR theory---a connection between E&M (where C comes from) and kinematics (v/p/E relations) that includes a speed limit---
without strong prodding from experiments; indeed, was probably one of only of a handful of people worrying about the foundations of E&M at all. In an alternate universe where
experimentalists report discovery of a particle speed limit at c, and publish curves of v-vs-p and v-vs-E and such, I would bet on multiple independent theorists coming up with the full Einstein solution.