Relativity -- The Path Not Taken

The great challenge facing physics today is the inability to combine Quantum Theory (which applies to the very small) with General Relativity (which applies to the very large). The search for a combined Theory of Everything has been a decades-long failure. Is it possible that this failure may be due to an inadequacy in General Relativity, despite its many successes?

Einstein developed General Relativity in 1915, making the prediction that light would be bent when passing massive objects – gravitational lensing, as it is called today. Einstein hypothesized that space and time (two obviously very different things) were united mathematically into a 4-dimensional space-time which became distorted in the presence of mass – thus light travelling at constant speed would be bent when passing the Sun. This prediction was confirmed in 1919 by Eddington’s observations of star positions during a total eclipse – and General Relativity became accepted wisdom.

However, gadfly physicist Alexander Unzicker points out that Einstein had four years earlier in 1911 proposed a different, much simpler hypothesis which led to a similar prediction. Einstein’s 1911 hypothesis was that the speed of light in a vacuum is not constant, but drops in the presence of a gravitational field.

The oft-stated concept that the speed of light is constant for all observers applies only in a vacuum. The reason rays of light bend when passing through a lens is that light slows down in glass. Analogously, if light slows down in the presence of a gravitational field, it would change direction slightly, similar to the more complex theory of General Relativity.

Unzicker adopts the reasonable approach that simpler explanations in physics should generally be preferred to complex ones, and wonders why Einstein’s simpler 1911 hypothesis has been forgotten. The story turns out to have some complexities, such as an oversight in Einstein’s 1911 paper. In 1957, Robert Dicke – the physicist who predicted Cosmic Microwave Background radiation but was overlooked for the associated Nobel prize – picked up Einstein’s 1911 idea and fixed the oversight; but there the matter has languished.

Would it matter if the complex 4-Dimensional General Relativity theory were replaced by a simpler hypothesis? Well, the assumed size of the Universe would change, and much of the steam would go out of the Dark Matter/Dark Energy hypothesis. However, Unzicker sees that herd behavior places immense barriers to the open evaluation of competing ideas in modern science, as is obvious from the ClimateScam and the CovidScam.

Unzicker has some You-Tube videos on this, but personally I do not find him to be a clear exponent of the theory. He has written a more comprehensible (but still not entirely clear) book on the topic: “Einstein’s Lost Key: How We Overlooked the Best Idea of the 20th Century”, ISBN 978-1519473431, 235 pages (2022). A translation of Einstein’s 1911 paper is available on-line from Princeton, “On the Influence of Gravitation on the Propagation of Light”:
Volume 3: The Swiss Years: Writings 1909-1911 (English translation supplement) Page 379 (393 of 452) (


The key issue to address is, does this alternative theory also predict other observed phenomena besides the bending of light in a gravitational field. General Relativity explained the precession of the perihelion of Mercury. It also made predictions such as the gravitational redshift (observed in the Pound-Rebka experiment) and gravitational radiation, which was observed first in the decay of the orbit of two pulsars by Taylor and Hulse and later directly observed by LIGO.

General Relativity also solved a philosophical problem with Newtonian gravitation, i.e., action at a distance. Relativity solves the causality problem by having gravitational forces propagate at a finite speed (c) instead of being instantaneous.

The trouble with these theories from left field is that they often fail to account for all of the phenomena already observed. They also often fail to make predictions that would distinguish them from other theories. Occam’s Razor is not enough, in and of itself, to prefer one theory over another. Does this alternative theory do all these things? If not, it’s not worthy of further consideration.

I’d add that if Einstein abandoned that earlier approach, it was probably for good reason, He was no dummy.


That is a fair point. How do we find out where the simpler explanation falls short of General Relativity and where (possibly) it might do better? Obviously, by working on that simpler theory!

Why has that not happened? When we look at the disgrace of Climate “Science”, the answer is clearly that Big Science has fallen into the trap outlined by President Eisenhower in his Farewell Address – dependency on politically-driven government funding. Some things get funded, many other things don’t.

If we want to break with the herd, we should consciously try to be open-minded about everything and skeptical about conventional wisdom. Remember – there is never such a thing as “settled science”.


Uh… regarding your comment on “Occam’s Razor”: No and Damn NO.

There, I fixed that for you.

Please try to avoid joining Professor Jonathan Haidt in marching with the moronic lemmings into the new dark ages.

“These things” are sometimes called “parameters” in the field of information criteria for model selection. Count the parameters… all of them. Sadly, people who think they know something about complexity and model selection forget that the number of “parameters” come in two forms: Data and Information. They aren’t the same thing and, no, you can’t fall back on Shannon’s statistical notion of information to avoid the fact that dynamics are necessary in any field presuming to make predictions, such as natural science, since predictions immediately get you into time where the time coordinate implies contradiction from one moment to the next since these things, uh, change. You have to be lossless in terms of data (observations at the phenomenological level) when you extract the information in the form of the bits in the binary executable model that expands into the totality of your data.


As for “Lorentz”, my dear Dr., might I suggest clicking the above screenshot of Phipps’s email and scrolling down to “15.5.3 Meaning of the Velocity According to Lorentz”.


I don’t find General Relativity to be particularly complicated. It is, in fact, a simple and elegant extension of Special Relativity to include gravitation. It’s a matter of taste, I suppose.

Space-time were already viewed as four dimensional in Special Relativity. That notion of including time as a dimension is hardly a radical idea, which, by the way, is mostly due to Minkowski, who died before General Relativity was conceived. Furthermore, non-Euclidean geometry such GR uses was widely accepted in the 19th century.

This facile comparison to climate science is not valid. With one relatively recent exception (LIGO), there’s never been any big money in General Relativity. In fact, it was long considered a backwater where careers went to die. Long after Ike gave that speech, very few people worked on relativity or cosmology. High-energy physics is another matter but that’s not the topic of this thread.


Rarely have I encountered such a cogent, well-reasoned argument. Bravo!


The accusation made in the section you referenced (“To our knowledge he never performed a single experiment to arrive at his expression.”) is probably as nonsensical as the rest of this 500-plus page screed. Hendrick Lorentz was a theorist, not an experimentalist. The expression in question (see below) has been verified countless times by others over the last century-plus. It is an integral part of Maxwell’s classical electrodynamics, which theory happens to be in conformity with Special Relativity (Lorentz covariant, in the technical parlance).

Classical electrodynamics is, in some sense, the first modern physical theory because it does not include acausal action at a distance. Of course, electrodynamics and relativity are still both classical theories, as distinguished from quantum mechanics.

The dread expression in question:


That might be missing the point. Fewer people worked on relativity or cosmology than other areas because the funding was not there. The bureaucrats were happy with General Relativity – no need to spend money which might end up rocking the boat.

I always loved that sick joke among the scientific staff at some of the National Laboratories. The A students joined the National Labs so they could work on cutting edge research. The C students became DC Swamp bureaucrats and decided what the A students would be allowed to research.

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Consider the Aharonov Bohm effect’s dependence not on the velocity’s cross product with the curl of the vector potential A but on the velocity’s dot product with the vector potential A itself. While this is considered a pure QM effect (ie: only the “phase” of the electron velocity field is affected) I was involved in experiments that tested the hypothesis that in the “null” of a dipole antenna, one could detect the dot product of relativistic electrons with the vector potential A in the voltage of the aligned electron field.

The relativistic electrons were generated by a simple Ne indicator bulb (plasma) with a bias current across it which could be reversed as well as turned off and on. Forward and reverse velocity fields resulted in constructive and destructive effects not observed in the dipole antenna’s Poynting vector maximum (90 degrees off of the antenna null axis).

If one defines:
F = q (-∇Φ - dA/dt)
ie: the total derivative of A, one gets a dot product term:
F = q (-∇Φ - ∂A/∂t + v × (∇ × A) - ∇(v · A))
and our scope traces matched,
unlike the Lorentz force:
F = q (-∇Φ - ∂A/∂t + v × (∇ × A)
That’s what got me interested in Weber electrodynamics – screed or no screed.

And, yes, I know that this violates all kinds of constraints on theory, not the least of which is special relativity and/or gauge independence and/or locality, etc. Recall, if you will, my prior screen shot of an ancient paper involving Bell and Phipps.

And then there is this recent paper trying to come to grips with some of the apparent paradoxes:

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As you noted, the Aharonov-Bohm effect is a strictly quantum mechanical effect on the phase of the wavefunction. To my knowledge, there are no classical effects. Thus, forces on classical particles, which is the subject of the Lorentz force equation, are not affected by such phase changes. Also there are no directly obsevable effects of the vector potential in classical electrodynamics, which is why the Aharonov-Bohm effect was such a surprise.

I find this term in your equation perplexing:
∇(v·A )
Perhaps I’m missing something here. The velocity vector v is not a vector field, unlike A. The clue is the q in the formula, which represents the charge of a discrete particle with velocity v. One can compute v·A (a scalar) but it is only defined at one point at a given time. Thus, it is not possible to compute its gradient, which is a strictly spatial derivative. Gradients of scalar fields, such as Φ, can be computed but not gradients of scalar functions valid only at one point at a time.

I don’t understand what this experiment was. However, if your observable was on the Poynting vector (a strictly classical quantity), it’s not clear how an effect on the wavefunction phase could be manifest there. Is there a publication on this experiment so I could understand it better?

Finally, the paper you linked on the Aharonov-Bohm Effect raises the same issues that have been around forever. Please note this quotation from the abstract: “…in quantum mechanics A is in some sense more ‘fundamental’ than B in spite of the former being gauge dependent, and thus unobservable.” [emphasis added] This is what I learned in school. There is no implication that the Lorentz force equation, mentioned in the abstract, is not valid or complete. Instead, the authors raise the usual problem of nonlocality in quantum mechanics, which problem arises repeatedly as in Bell’s inequality and the Aharonov-Bohm Effect.

Far from being ignored or suppressed, these two issues have been the subject of lively discussion since I was a graduate student (and probably before then). The 2022 Nobel Prize in physics was awarded for precisely the topic of nonlocality. It is a complicated topic about which there’s no broad consensus about its philosophical interpretation. But there’s no controversy about the empirical predictions of either classical electrodynamics or quantum electrodynamics. Outside of the quantum domain, the classical theory has proven quite satisfactory for the 150 or so years they’ve been around.


If one views ‘q’ as comprising a charge distribution then it is a scalar field and an expression like qv = Jq makes sense as a charge current configuration where J is a current (vector). For example one can use charge current configurations in calculating radiationless sources:

This kind of charge current distribution is also relevant in the Lorentz force equation’s occurrence of v and is used in antenna design for example.

Probably the best reference would be the patent US8165531.

An earlier experiment at McMaster is documented in “Detection of the Time-dependent Electromagnetic Potential at 1.3 GHz”.

Prof. Nikolova is not responsible for any errors in my presentation nor for my interest in Weber electrodynamics screeds.

As regards your emphasis on unobservable and that there has been lively discussion of the AB effect and its interpretations for a long time – yes, of course, that’s reiterating what I called “constraints on theory” that are apparently violated by interpreting the experiment in terms of the scalar potential dot product term v·A, the gradient of which gives rise to a motional electric field, ∇(v·A ) by virtue of which it becomes commensurable (same physical dimensions) therefore subject to addition (superposition) with the other term of the motional electric field v × (∇ × A ) that is added to the definition of the non-motional (conventional) electric field E = -∇Φ - ∂A /∂t.

We could get into discussions of fringe physics which, almost by definition, violate “constraints on theory”, but I suspect we’d just end up going round in circles with you suggesting that I reexamine the experimental conditions for flaws.

BTW: The idea of “reexamining the experimental conditions for flaws” is, in the context of Occam’s Razor (as opposed to Massacre), one of the reasons I’m so insistent on the application of Algorithmic Information as the model selection criterion going clear back to the phenomenology of the observations. Emphasizing that something or other is unobservable gets into issues of operational definitions which gets into modeling one’s experimental apparatus, which I fucking had to do.

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This is incorrect. If it were a charge distribution, one would need terms for the mutual interactions among the charge elements. The Lorentz force equation is explicitly for a point charge. A charge density distribution ρ would behave very differently. Specifically, the charges would repel, resulting in a time varying ρ, whereas point charges do not repel themselves.

In short, if you don’t mean q, don’t write q.


This equation is dimensionally nonsensical. I’ve noticed that this is a feature of fringe theorists: they can’t seem to do dimensional analysis. What are the units of J? What are the units of q? What are the untis of v? Does the equation still hold if the units are furlongs and fortnights?


I stand corrected: I should have used the ρ rather than q.

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See if replacing q with rho sustains your sarcasm. In particular, pay attention to (6.29) above.

It is rather ironic that you’d sarcastically accuse me of being incapable of doing dimensional analysis as opposed to merely using the wrong expression of a physical quantity. The substance of the discourse remains unaddressed. The sarcasm is particularly misplaced when I’ve been for decades complaining that the foundation of mathematics fails at the outset to deal with dimensioned quantities and this has crippled computer programming languages – and cost untold damage to civilization. This is the kind of thing that should be automated, as much of it is in Calchemy.


Thanks. I’ll have a look at that over the next few days.

Equation 6.29 is not really about the Lorentz force. You have yet to write the correct expression for F or whatever is on the LHS of your equation for force when q is replaced by ρ, if that is the replacement you intend. If the velocity vector is replaced by a vector field, will it be a three-dimensional delta function as in Eq. 6.29? If so, you will find it rather awkward inasmuch as the gradient is divergent, resulting in a singularity in the RHS of the equation.

It should be possible for you to write the correct equation and give the solution for the simple case of a particle in circular motion in a uniform magnetic field, in which v and A are parallel (viz. Fig. 14-1). This particular motion is well-studied and well-understood; we know what the answer should look like.

It is not enough to replace q with ρ. Please take the time and effort to write the correct equation. Expect some sarcasm in the meantime.


From a widely cited paper by Konopinski: “What the electromagnetic vector potential describes” we find this equation:


And although it was about a decade ago, I do recall puzzling over this exact equation, but not because he used q rather than ρ in the gradient expression.

The point is that even in the original form with ‘q’, a reasonable peer review would point out that in order for there to be a voltage derivable from a force, on the electrode, a charge force per area must obtain which implies certain conditions on v (ie: uniformity) and on the charge ρ in motion (ie: uniformity) within the neutral plasma current. This isn’t that complicated.

While its nice to have things like spell checkers and dimensionality checkers, and I do thank you for your service, they don’t generally resort to sarcasm when correcting the hapless human:

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I hope you realize that this is just a re-written version of the Lorentz force law (Eq. 2 of that same paper) without any weird extra terms. Equations 2 and 3 are mathematically equivalent, as the author states that the latter is a “reexpression” of the former. Re-casting the equation in terms of the potentials does not change anything whatsoever. Whether you use Eq. 2 or Eq. 3, the same result obtains. Consequently, there is no different prediction of any experimental result.

The A-B Effect is a result different from what would obtain if one did not account for the vector potential. However, this result is a creature of quantum mechanics, i.e., it only affects the wavefunction the system. There are no wavefunctions in classical electrodynamics. The force on a charged particle, the subject of the Lorentz force equation, is a classical quantity and not a wavefunction.

Quantum mechanics does not give a different answer than the Lorentz equation for the motion of charged particles. For quantum effects to manifest, there must be coherent interference of the wavefunction. If that coherence is destroyed or doesn’t exist in the first place, there’s no interference, no A-B Effect. Classical theory is simply wrong in treating such interference effects. That’s why quantum mechanics is a better theory. However, when it comes to the motion of a charged particle in a magnetic field, the two theories are in agreement.

In short, just because you can express any classical formula in terms of A doesn’t mean there’s any new effect that didn’t exist before. Equations 2 and 3 give the same answers.

What the author does point out just before Eq. 15 is that something interesting happens when the solenoid current is interrupted. This is a variant of Feynman’s disk paradox (sec. 17-4). I’m so thrilled that you brought this up since I happen to have a paper in the same journal (Am. J. Phys.) a few years after the paper you cited. In that paper (Am. J. Phys. 51, 213–214), I treat the problem of the effect without needing to resort to vector potentials at all. You know, it’s not often that I have an excuse to bring up one of my old papers, so thanks! It’s not my most cited publication but it’s probably the most fun one.