For some details, see the "Hertzian Electromagnetism" Chapter 4 of "Heretical Verities: Mathematical Themes in Physical Description" (1986) by Thomas E. Phipps.
I read 'Heretical Verities' by Thomas E. Phipps, Jr., about 15 years ago. Although I haven't read it since, it made a lasting impression on me. I remember it well.
What I concluded is that Thomas E. Phipps, Jr. is both a mathematical and illiterate and a very toxic phony. He does not understand the subjects that he claims to rewrite. He tries to intimidate the reader with ad hominem attacks without correctly representing their point of view.
This genius wanna-be has made grand claims based on false hypotheses on basic science.
Most of his experiments required a lock-in amplifier. Phipps does not understand how a lock-in amplifier works. He explains the operation of a lock-in amplifier using an invalid analogy with the harmonic oscillator. There is no such things as 'velocity-like component' and 'translation-like component'. One reason that he doesn't understand lock-in amplifiers is that he doesn't believe in the Fourier transform. He says the Fourier transform (FT) is too 'theoretical'. Maybe that is why he he doesn't use it to analyze the lock-in amplifier.
He has this strange model where the 'velocity-like components' are ninety degrees out of phase with the 'translation components'. So he looks for the velocity components at 90 degrees phase difference to the tuning fork vibration. However, he is using a square wave as a reference. He doesn't seem to realize that the square wave has second harmonics! So in all likelihood, he is picking up the second harmonic of the square wave then any components of the vibration.
I know because I have use lock-in amplifiers in my experiments. I am an optical physicist. I know the limits of a lock-in amplifier. If I was trying to knock down the foundations of physics in my garage, I would provide the lock-in amplifier with a sinusoidal reference. He also seems unaware that nonlinear effects in the optics table can generate second harmonic signals. Thus, his experiments who conclusion 'debunk relativity' are bogus.
He doesn't try to verify that there are no significant vibrations from outside. I know physicists who do supersensitive measurements in quantum mechanics.They take great pains to isolate the system. They measure the background for days. If the background signal peaks at rush hour, they assume that it is caused by cars. They then take extra precautions. I met a physicist who detached the room from the rest of the building to eliminate outside vibration! Phipps feels that his 'soft materials' totally block vibration. He doesn't even try to check where the materials really block vibration.
Phipps relies on his own theory that soft materials don't carry vibration. He doesn't know about dispersive relations in waves. He doesn't know that the optical tables has its own resonant frequencies, even when loaded. He doesn't even try to check. So he claims that no one else has tried such experiments.
Apparently, he doesn't even believe the manufacturers manual on his equipment! BTW: He doesn't tell us what equipment he is using. So I can't give exact numbers for most of this stuff. However, the second harmonic amplitude of a square wave is about 30% the fundamental amplitude of the square wave. So obviously his 'velocity component' has to be an artifact.
Phipps doesn't understand the properties of elastic materials in any context. Half his experiments with a lock-in amplifier can be compromised by vibration. They probably were. However, he placed a metal frame made of invar on his lock-in amplifier. He then claimed that the invar blocks vibrations. In fact, invar transmits vibrations fine. The reason scents like to use invar alloys is that invar at room temperatures has a very small thermal expansion coefficient. So his invar frame does nothing to stop vibration.
He also tries to disprove the small angle approximation using a calculator. He claims that he prefers this approach because it is experimental. You see the calculator is a machine. Calculus is only a theory. Hence, if the small angle approximation fails in a calculator then obvious it has been experimentally disproved. Thus, he shows that he is unaware of truncation error.
That is one of his main failings in experimental science. Lets go into his theoretical science.
He knows nothing about elastic properties of materials. He doesn't understand that so called rigid bodies are really elastic up to their plastic limit of amplitude. So he often makes the assumption that there are no internal forces in a material that is effectively rigid. He effectively makes the assumption that the speed of sound in a solid is much greater than the speed of light in a vacuum. I think he says that explicitly at one point! He doesn't understand that energy is carried in strain fields. In his view, a mechanical impulse travels through a steel rod instantly.
Anyone who has worked with real materials knows how wrong this assumption is. Mechanical impulse travel through a material at the sped of sound, which is much less than the speed of light. Hence, his claims about instantaneous transmission are garbage. He claims he is analyzing the propagation of electromagnetic signals. In actual fact, there is a delay due to the propagation of compressive waves.
The compressive waves carry both energy and momentum even according to classical theory. Phipps does not consider the energy and momentum carried by a compressive wave. Since the wave carries energy, , relativity says they contain mass. He ignores the mass carried by the wave. So he misrepresents relativistic theory. He claims that he has found inconsistencies with Einsteinian theory, when he doesn't even have the Galilean theory correct!
I have followed the cult that has grown around Thomas E. Phipps, Jr. I am fascinated with it. So I would be glad to discuss Vereties with you. One condition:
Please don't deflect by bringing up the 'failings' of Einstein. I have full respect for real scientists trying to challenge the theories of Einstein and Lorentz. I don't want to talk about the 'cult of Einstein'.
I want to talk about the 'cult of Phipps'. Phipps is a phony. He is a sociopath. He is a conman. I can demonstrate that he doesn't know a thing about actual physics or engineering.
Phipps fails in the little stuff. He doesn't know how a lock-in amplifier works. He has severe problems with the concept of mathematical limit. He doesn't know the more formal aspects of calculus. He does know acoustics. He hides his ignorance with his hostility. Phipps claims to be ignored by a scared scientific establishment. So lets talk about Phipps!!!!