I got the idea from a Phipps after investigating Nikolova/Zimmerman’s technical report and being referred to “Heretical Verities”* by a Princeton plasma physicist who had to validate computational models against their experiments. I believe Phipps may have gotten it from Hertz although there was probably some contribution from J. P. Wesley.
* It turns out the author of the preface was someone I knew from SLAC, who knew Phipps because they both went to UofIL HS thence to Harvard, but I didn’t know anything about that association or that book until the replication of Nikolova/Zimmerman experiments began in Urbana of all places, in 2014. Nor was the plasma physicist associated with those authors. He just had problems believing the issue of “unobservable outside of QM” had been sufficiently verified given his experience with plasma simulations.
Those experiments were initiated when a long-time friend of Carver Mead (who had a hand in encouraging Mead to complete the book “Collective Electrodynamics”) became aware of the Nikolova/Zimmerman patent – in part because of his skepticism of received wisdom regarding the vector potential’s interpretation. That’s the contact with the plasma physicist’s skepticism.
Without getting into the specifics of the current discussion - shrot on time - the Geometric Algebra (GA) / Clifford Algebra formulation of EM is the best, I believe. Essentially, it augments the algebra of vectors with higher-dimension entities such as planes of rotation (bivectors formed through the outer product of orthogonal vectors). See John Denker’s: Electromagnetism using Geometric Algebra versus Components.
I first got into GA through researching MaxEnt; David Hestenes was active in that area, but his main work was reintroducing the use of Clifford Algebras as a lingua franca for physics, for which he was awarded the Oersted Medal.
Edit: one more GA link, relevant to the original topic:" Can physics laws be derived from monogenic functions"" Jose Almeida wrote several papers that deserve more attention on the optical interpretation of relativity. “the author intends to show that GTR and Quantum Mechanics (QM) can be seen as originating from monogenic functions in the algebra of the 5-dimensional spacetime G(4,1). … Euclidean relativistic dynamics resembles Fermat’s principle extended to 4 dimensions and is thus designated as 4-Dimensional Optics (4DO).”
You appear to agree that the Lorentz force equation is no different from the other expressions that you listed above. Thus, I’m perplexed why we are having this discussion. On the other hand, you wrote:
Yet it is not unlike the Lorentz force at all; it is the same equation written in a different way. It is not like the Lorentz force and it’s the equivalent to the Lorentz force.
You seem to be in a logical cleft stick with no way out. Perhaps Bertrand Russell can help:
You belittled me over this subexpression. When I pointed out your inappropriate behavior, you doubled down by saying: “Expect some sarcasm in the meantime.”
When I pointed out that one of the most highly cited papers on the magnetic vector potential used the same subexpression to again point out your inappropriate behavior, you, instead, read me as saying that I thought that paper’s equation was the same as my original equation (despite my saying the exact opposite).
On that basis, you tripled down and then quadrupled down on your inappropriate behavior.
How much further are you willing to go before thanking me for retaining some semblance of civility?
So, I guess Mr. Russell was of no help. Better luck next time. On the other hand, Beyond the Fringe guys are always good for some laughs. Surely, you must have enjoyed that. You’re welcome.
(1) E = -∇Φ - dA/dt
(2) dA/dt = ∂A/∂t dt/dt + ∂A/∂x dx/dt + ∂A/∂y dy/dt + ∂A/∂z dz/dt
(3) dA/dt = ∂A/∂t 1 + ∂A/∂x dx/dt + ∂A/∂y dy/dt + ∂A/∂z dz/dt
(4) dA/dt = ∂A/∂t +∂A/∂x dx/dt + ∂A/∂y dy/dt + ∂A/∂z dz/dt
(5) vx = dx/dt, vy = dy/dt, vz = dz/dt
(6) dA/dt = ∂A/∂t + ∂A/∂x vx + ∂A/∂y vy + ∂A/∂z vz
(7) (v· ∇)A = ∂A/∂x vx + ∂A/∂y vy + ∂A/∂z vz
(8) dA/dt = ∂A/∂t + (v· ∇)A
(9) E = -∇Φ - ∂A/∂t - (v· ∇)A
(10) ∇(v· A) = (v· ∇)A + (A · ∇)v+ v× (∇ × A) + A × (∇ × v)
(11) ∇ × v= 0
(12) (A · ∇)v= 0
(13) ∇(v· A) = (v· ∇)A + 0 + v× (∇ × A) + A × (0)
(14) ∇(v· A) = (v· ∇)A + v× (∇ × A)
(15) (v· ∇)A + v× (∇ × A) = ∇(v· A)
(16) (v· ∇)A = - v× (∇ × A) + ∇(v· A)
(17) E = -∇Φ - ∂A/∂t + v× (∇ × A) - ∇(v· A)
(18) F = q E
(19) F = q (-∇Φ - ∂A/∂t + v× (∇ × A) - ∇(v· A))
(1) Postulate (And yes I know defining “E” this way is “wrong”.)
(2) Definition of total derivative
(3&4) Multiplicative identity
(5) Definition of velocity vector components
(6) Substitute (5) in (4)
(7) Advection identity
(8) Substitute (7) in (6)
(9) Substitute (8) in (1)
(10) Vector identity
(11) Experimental condition (direction of v not dependent on position)
(12) Experimental condition (v not dependent on position)
(13) Substitute (11 & 12) in (10)
(14) Multiplicative identity
(15) Commutativity of equality
(16) Subtract v × (∇ × A) from both sides
(17) Substitute (16) in (9)
(18) Electromotive force definition
(19) Substitute (17) in (18)
I just realized that, in addition to my being a bit too-generous in thanking Dr. Lorentz for “correcting” me for using the same expression, ∇(v ·A ), that Konopinski used, another source of misunderstanding may have been the quasi-static condition Konopinski imposed on equation (2) which makes it the equivalent of the Lorentz Force law. The quasistatic condition does render ∇(v ·A ) “unmeasurable” except in its quantum mechanical effect on the phase of the charged particle. But the reason I have, from the outset, been trying to get across to our good Dr. another interpretation of ∇(v ·A ) is that the condition is far from quasi-static within a receiving antenna consisting of relativistic plasma electrons aligned with the curl-free A region of a Hertzian dipole.
A “Heretical Verities” quote from Phipps seems quite proper:
“My message in this book, which now draws to its close, is that if you believe the experts when they tell you your native wit and critical sense are worthless then in your own case you prove them right…but if you resist their browbeating their is hope in your case for individual salvation—though Barnum be right about the public.”
These University of Illinois at Urbana physicists are nothing but trouble with their penchant for actually conducting experiments. Aside from Dr. Phipps there is this other UofIL physicst Chalmers W. Sherwin who disagreed with Phipps regarding Phipps’s refusal (to his dying day) to believe that Lorentz length contraction (as opposed to a larger time dilation than that predicted by SRT) had been observed. However, Dr. Sherwin actually ran an experiment in which he failed to find a contraction effect:
While it may be the case that there are others who have managed to poke holes in Sherwin’s experiment, I haven’t found them. And, although one shouldn’t take GPT4’s word for anything, it is generally quite willing to enforce the scientific consensus when asked questions such as the one I just did:
Just so everyone knows how great the contribution of “immigration” has been to western civilization: It terminated my authority to hire the folks I needed to pursue this:
Maybe Dr. Lorentz can explain why it is that the imperial “we” of Wolfram’s community, believes it is appropriate to drop physical dimensions in the case of a differential of a constant function with a physical dimension. Perhaps he thinks that instead of me merely committing career suicide to try to get physicists to be serious about the foundation of mathematical physics, I should have gone to the vestibule of the NSF and set myself on fire.
After wrangling Mathematica far more than should be necessary, I got it to finally behave itself and produce the simulate scope traces (composite Weber Electrodynamics Force and Rx charge velocity below it) that qualitatively matched what we saw coming from the neon indicator bulb receiving antenna with relativistic electrons with bias current qualitatively simulated by the velocity graph. The Mathematica notebook is at a repo I just created with some additional comments at the top:
I can’t tell you how frustrating it is to find myself watching the world catching up to where I was about a decade ago and being deprived of the resources to catch the wave.
I’ve been reviewing Heinlein’s early period and am particularly interested in 1951 because that is the date of another WW II veteran’s publication of a book on radical individualism that has been the single most influential book in my world view. Both were US citizens of German patrimony who obviously came out of the post war and into the McCarthy era with extreme antipathy toward communism.
So it was with some bemusement that Heinlein’s 1951, “Between Planets” , featured a character named “Phipps” as part of a kind of “invisible college” with a breakthrough in physics that is the focus of the story.
Norman Ramsey was the only Nobel Prize Laureate in physics on the DoE’s committee to review the hubbub surrounding “cold fusion” and he had to threaten to resign if they refused to include this in the preamble of its report:
…even a single short but valid cold fusion period would be revolutionary…the failure of a theory to account for cold fusion can be discounted* on the grounds that the correct explanation and theory has not been provided…The Panel recommends that the cold fusion research efforts in the area of heat production focus primarily on confirming or disproving reports of excess heat…
Of course, the exact opposite happened when Nature refused to publish an experimental protocol that reproduced excess heat early in the debacle. The reason given? The investigator provided no theory. This set the stage for people around the world losing tenure-track for so much as proposing to research the phenomena.
Then Ramsey died. 25 year later Tom Phipps died while in communication with me about the aforementioned Weber electrodynamics experiments.
* The wording of the passage about “theory” bordered on word-salad. Such is the verbal symptom of cognitive dissonance when priests are confronted with emperical evidence contrary to their theology. I seriously doubt Ramsey provided that exact wording or if he did it was in the heat his outrage at Hulzenga for being such a theocrat.
It is difficult these days to avoid the feeling that genuine science has degenerated into “SCIENCE” – “settled SCIENCE”, of course – which is showing ever more tendencies to resemble the Aristotilian-obsessed Medieval Catholic church. Worse, in a sense; while the Medieval Church was wrong about its explanations of the physical world, at least they tried to have moral standards.
Look at cosmology today. We are supposed to treat the hypothesis that 95% of the matter & energy in the Universe is invisible as incontrovertible fact, beyond the reach of controversy. And the principle of Conservation of Energy, which has served science & engineering so well, has been thrown away to allow for “Dark Energy” which appears from nowhere and pushes the galaxies apart. Perhaps that kind of hypothesis is correct, perhaps it is not. Only genuine science could ever find out.
As is evident from the treatment of Norman Ramsey and Tom Phipps, among a raft of others, the ranks of scientists has now been so whittled down in absolute numbers, not to mention relative numbers, that their positions are decreasingly secure. They are surrounded by ambitious pretenders who smell the threat they represent.
This is one of the reasons I push so hard on objective contests for model selection based on the Algorithmic Information Criterion. Even if the practical applicability of such contests is restricted, it is the kind of thing that could put people into an entirely different psychology about science, not to mention its relationship to funding sources. However the beneficiaries are now so few in number and so beleaguered that its hard to get this point across to them so as to rally a body of support that might appeal to funding sources for such a prize.
. Hop on the bus with the rest of us.