My new book project

Dear readers of this blog – As you may or may not know, I had already published two or three books on amazon.com with some of the ideas on the geometric of physical interpretation of the wavefunction that I have been promoting on this blog. These books sold some copies but – all in all – were not a huge success. That’s fine – because I just wanted to try things out.

I will soon come up with an entirely new book. Its working title is what is mentioned in the current draft of the acknowledgments – copied below. The e-book will be published in a few weeks from now. It may – by some magic 🙂 – coincide with the publication of a convincing classical explanation of the anomalous magnetic moment of an electron – not written by me, of course, but by one of the foremost experts on quantum gravity (and QED in general). 🙂 It would upset the orthodox/mainstream/Copenhagen interpretation of quantum electrodynamics, and that will be a good thing: it will bring more reality to the interpretation (read: just a much easier way to truly understand everything).

If so, my book should sell – if only because it will document a history of scientific discovery. 🙂

The Emperor has no clothes:

The sorry state of Quantum Physics.

Acknowledgements

Although Dr. Alex Burinskii, Dr. Giorgio Vassallo and Dr. Christoph Schiller would probably prefer not to be associated with anything we write, they gave us the benefit of the doubt in their occasional, terse, but consistent communications and, hence, we would like to thank them here – not for believing in anything we write but for encouraging us for at least trying to understand.

More importantly, they made me realize that QED, as a theory, is probably incomplete: it is all about electrons and photons, and the interactions between the two – but the theory lacks a good description of what electrons and photons actually are. Hence, all of the weirdness of Nature is now, somehow, in this weird description of the fields: perturbation theory, gauge theories, Feynman diagrams, quantum field theory, etcetera. This complexity in the mathematical framework does not match the intuition that, if the theory has a simple circle group structure[1], one should not be calculating a zillion integrals all over space over 891 4-loop Feynman diagrams to explain the magnetic moment of an electron in a Penning trap.[2] We feel validated because, in his latest communication, Dr. Burinskii wrote he takes our idea of trying to corroborate his Dirac-Kerr-Newman electron model by inserting it into models that involve some kind of slow orbital motion of the electron – as it does in the Penning trap – seriously.[3]

There are some more professors who may or may not want to be mentioned but who have, somehow, been responsive and, therefore, encouraging. I fondly recall that, back in 2015, Dr. Lloyd N. Trefethen from the Oxford Math Institute reacted to a blog article on mine[4] – in which I pointed out a potential flaw in one of Richard Feynman’s arguments. It was on a totally unrelated topic – the rather mundane topic of shielding, to be precise – but his acknowledgement that Feynman’s argument was, effectively, flawed and that he and his colleagues had solved the issue in 2014 only (Chapman, Hewett and Trefethen, The Mathematics of the Faraday Cage) was an eye-opener for me. Trefethen concluded his email as follows: “Most texts on physics and electromagnetism, weirdly, don’t treat shielding at all, neither correctly nor incorrectly. This seems a real oddity of history given how important shielding is to technology.” When I read this, it made me think: how is it possible that engineers, technicians, physicists just took these equations for granted? How is it possible that scientists, for almost 200 years,[5], worked with a correct formula based on the wrong argument? This, too, resulted in a firm determination to not take any formula for granted but re-visit its origin instead.[6]

We have also been in touch with Dr. John P. Ralston, who wrote one of a very rare number of texts that address the honest questions of amateur physicists and philosophers upfront. I love the self-criticism of the profession: “Quantum mechanics is the only subject in physics where teachers traditionally present haywire axioms they don’t really believe, and regularly violate in research.”[7] We both concluded that our respective interpretations of the wavefunction are very different and, hence, that we should not  waste any electrons on trying to convince each other. However, the discussions were interesting.

I am grateful to my brother, Dr. Jean Paul Van Belle, for totally unrelated discussions on his key topic of research (which is information systems and artificial intelligence), which included discussions on Roger Penrose’s books – mainly The Emperor’s New Mind and The Road to Reality. These books made me think of the working title for this book: The Emperor has no clothes: the sorry state of Quantum Physics. We should go for another mountainbike or mountain-climbing adventure when this project is over.

Among other academics, I would like to single out Dr. Ines Urdaneta who – benefiting from more academic freedom than other researchers, perhaps – has just been plain sympathetic and, as such, provided great moral support. I also warmly thank Jason Hise, whose wonderful animations of 720-degree symmetries did not convince me that electrons (or spin-1/2 particles in general) actually have such symmetries – but whose communications stimulated my thinking on the subject-object relation in quantum mechanics.

Finally, I would like to thank all my friends and my family for keeping me sane. I would like to thank, in particular, my children – Hannah and Vincent – and my wife, Maria, for having given me the emotional, intellectual and financial space to pursue this intellectual adventure.

[1] QED is an Abelian gauge theory with the symmetry group U(1). This sounds extremely complicated – and it is. However, it can be translated as: its mathematical structure is basically the same as that of classical electromagnetics.

[2] We refer to the latest theoretical explanation of the anomalous magnetic moment here: Stefano Laporta, High-precision calculation of the 4-loop contribution to the electron g-2 in QED, 10 July 2017, https://arxiv.org/abs/1704.06996.

[3] Prof. Dr. Burinskii, email communication, 29 December 2018 2.13 pm (Brussels time). To be precise, he just wrote me to say he is ‘working on the magnetic moment’. I interpret this as saying he is looking at his model again to calculate the magnetic moment of the Dirac-Kerr-Newman electron so we will be in a position to show how the Kerr-Newman geometry – which I refer to as the (neglected) form factor in QED – might affect it. To be fully transparent, Dr. Burinskii made it clear his terse reactions do not amount to any endorsement or association of the ideas expressed in this and other papers. It only amounts to an admission our logic may have flaws but no fatal errors – not at first reading, at least.

[4] Jean Louis Van Belle, The field from a grid, 31 August 2015, https://readingfeynman.org/2015/08/.

[5] We should not be misunderstood here: the formulas – the conclusions – are fully correct, but the argument behind was, somehow, misconstrued. As Faraday performed his experiment with a metal mesh (instead of a metal shell) in 1836, we may say it took mankind 2014 – 1836 = 178 years to figure this out. In fact, the original experiments on Faraday’s cage were done by Benjamin Franklin – back in 1755, so that is 263 years ago!

[6] We reached out to Dr. Trefethen and some of his colleagues again to solicit comments on our more recent papers, but we received no reply. Only Dr. André Weideman wrote us back saying that this was completely out of his field and that he would, therefore, not invest in it.

[7] John P. Ralston, How to understand quantum mechanics (2017), p. 1-10.

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Freewheeling once more…

You remember the elementary wavefunction Ψ(x, t) = Ψ(θ), with θ = ω·t−k∙x = (E/ħ)·t − (p/ħ)∙x = (E·t−p∙x)/ħ. Now, we can re-scale θ and define a new argument, which we’ll write as:

φ = θ/ħ = E·t−p∙x

The Ψ(θ) function can now be written as:

Ψ(x, t) = Ψ(θ) = [ei·(θ/ħ)]ħ = Φ(φ) = [ei·φ]ħ with φ = E·t−p∙x

This doesn’t change the fundamentals: we’re just re-scaling E and p here, by measuring them in units of ħ. 

You’ll wonder: can we do that? We’re talking physics here, so our variables represent something real. Not all we can do in math, should be done in physics, right? So what does it mean? We need to look at the dimensions of our variables. Does it affect our time and distance units, i.e. the second and the meter? Well… I’d say it’s OK.

Energy is expressed in joule: 1 J = 1 N·m. [In SI base units, we write: J = N·m = (kg·m/s2)·m = kg·(m/s)2.] So if we divide it by ħ, whose dimension is joule-second (J·s), we get some value expressed per second, i.e. a (temporal) frequency. That’s what we want, as we’re multiplying it with t in the argument of our wavefunction!

Momentum is expressed in newton-second (N·s). Now, 1 J = 1 N·m, so 1 N = 1 J/m. Hence, if we divide the momentum value by ħ, we get some value expressed per meter: N·s/J·s = N/J = N/N·m = 1/m. So we get a spatial frequency here. That’s what we want, as we’re multiplying it with x!

So the answer is yes: we can re-scale energy and momentum and we get a temporal and spatial frequency respectively, which we can multiply with t and x respectively: we do not need to change our time and distance units when re-scaling E and p by dividing by ħ!

The next question is: if we express energy and momentum as temporal and spatial frequencies, do our E = m·cand p = m·formulas still apply? They should: both and v are expressed in meter per second (m/s) and, as mentioned above, the re-scaling does not affect our time and distance units. Hence, the energy-mass equivalence relation, and the definition of p (p = m·v), imply that we can re-write the argument (φ) of our ‘new’ wavefunction – i.e. Φ(φ) – as:

φ = E·t−p∙x = m·c2∙t − m∙v·x = m·c2[t – (v/c)∙(x/c)] = m·c2[t – (v/c)∙(x/c)]

In effect, when re-scaling our energy and momentum values, we’ve also re-scaled our unit of inertia, i.e. the unit in which we measure the mass m, which is directly related to both energy as well as momentum. To be precise, from a math point of view, m is nothing but a proportionality constant in both the E = m·cand p = m·formulas.

The next step is to fiddle with the time and distance units. If we

  1. measure x and t in equivalent units (so c = 1);
  2. denote v/c by β; and
  3. re-use the x symbol to denote x/c (that’s just to simplify by saving symbols);

we get:

φ = m·(t–β∙x)

This argument is the product of two factors: (1) m and (2) t–β∙x.

  1. The first factor – i.e. the mass m – is an inherent property of the particle that we’re looking at: it measures its inertia, i.e. the key variable in any dynamical model (i.e. any model – classical or quantum-mechanical – representing the motion of the particle).
  2. The second factor – i.e. t–v∙x – reminds one of the argument of the wavefunction that’s used in classical mechanics, i.e. x–vt, with v the velocity of the wave. Of course, we should note two major differences between the t–β∙x and x–vt expressions:
  1. β is a relative velocity (i.e. a ratio between 0 and 1), while v is an absolute velocity (i.e. a number between 0 and ≈ 299,792,458 m/s).
  2. The t–β∙x expression switches the time and distance variables as compared to the x–vt expression, and vice versa.

Both differences are important, but let’s focus on the second one. From a math point of view, the t–β∙x and x–vt expressions are equivalent. However, time is time, and distance is distance—in physics, that is. So what can we conclude here? To answer that question, let’s re-analyze the x–vt expression. Remember its origin: if we have some wave function F(x–vt), and we add some time Δt to its argument – so we’re looking at F[x−v(t+Δt)] now, instead of F(x−vt) – then we can restore it to its former value by also adding some distance Δx = v∙Δt to the argument: indeed, if we do so, we get F[x+Δx−v(t+Δt)] = F(x+vΔt–vt−vΔt) = F(x–vt). Of course, we can do the same analysis the other way around, so we add some Δx and then… Well… You get the idea.

Can we do that for for the F(t–β∙x) expression too? Sure. If we add some Δt to its argument, then we can restore it to its former value by also adding some distance Δx = Δt/β. Just check it: F[(t+Δt)–β(x+Δx)] = F(t+Δt–βx−βΔx) = F(t+Δt–βx−βΔt/β) = F(t–β∙x).

So the mathematical equivalence between the t–β∙x and x–vt expressions is surely meaningful. The F(x–vt) function uniquely determines the waveform and, as part of that determination (or definition, if you want), it also defines its velocity v. Likewise, we can say that the Φ(φ) = Φ[m·(t–β∙x)] function defines the (relative) velocity (β) of the particle that we’re looking at—quantum-mechanically, that is.

You’ll say: we’ve got two variables here: m and β. Well… Yes and no. We can look at m as an independent variable here. In fact, if you want, we could define yet another variable –χ = φ/m = t–β∙x – and, hence, yet another wavefunction here:

Ψ(θ) = [ei·(θ/ħ)]ħ = [ei·φ]ħ = Φ(φ) = Χ(χ) = [ei·φ/m]ħ·m = [ei·χ]ħ·m = [ei·θ/(ħ·m)]ħ·m

Does that make sense? Maybe. Think of it: the spatial dimension of the wave pulse F(x–vt) – if you don’t know what I am talking about: just think of its ‘position’ – is defined by its velocity v = x/t, which – from a math point of view – is equivalent to stating: x – v∙t = 0. Likewise, if we look at our wavefunction as some pulse in space, then its spatial dimension would also be defined by its (relative) velocity, which corresponds to the classical (relative) velocity of the particle we’re looking at. So… Well… As I said, I’ll let you think of all this.

Post Scriptum:

  1. You may wonder what that ħ·m factor in that Χ(χ) = [ei·χ]ħ·m = [ei·(t–β∙x)/(ħ·m)]ħ·m function actually stands for. Well… If we measure time and distance in equivalent units (so = 1 and, therefore, E = m), and if we measure energy in units of ħ, then ħ·m corresponds to our old energy unit, i.e. E measured in joule, rather than in terms of ħ. So… Well… I don’t think we can say much more about it.
  2. Another thing you may want to think about is the relativistic transformation of the wavefunction. You know that we should correct Newton’s Law of Motion for velocities approaching c. We do so by integrating the Lorentz factor. In light of the fact that we’re using the relative velocity (β) in our wave function, do you think we still need to apply such corrections for the wavefunction? What’s your guess? 🙂