Chapter I

As mentioned in my previous post, I am going to publish a book. The Emperor has No Clothes. This is the introduction. I am probably going to release the various chapters one by one for my readers here. Thanks for being there ! The working title of the book is still the same:

The Emperor has No Clothes

A classical interpretation of quantum mechanics

I. Introduction, history and acknowledgments

This book is the result of a long search for understanding. The journey started about thirty-five years ago when – I was a teenager then – I started reading popular physics books. Gribbin’s In Search of Schrödinger’s Cat is just one of the many that left me unsatisfied in my quest for knowledge.

However, my dad never pushed me and so I went the easy route: humanities, and economics – plus some philosophy and a research degree afterwards. Those rather awkward qualifications (for an author on physics, that is) have served me well – not only because I had a great career abroad, but also because I now realize that physics, as a science, is in a rather sorry state: the academic search for understanding has become a race to get the next non-sensical but conformist theory published.

Why do we want to understand? What is understanding? I am not sure, but my search was fueled by a discontent with the orthodox view that we will never be able to understand quantum mechanics “the way we would like to understand it”, as Richard Feynman puts it. Talking Feynman, I must admit his meandering Lectures are the foundation of my current knowledge, and the reference point from where I started to think for myself. I had been studying them on and off – an original print edition that I had found in a bookshop in Old Delhi – but it was really the 2012 Higgs-Englert experiments in CERN’s LHC accelerator, and the award of the Nobel prize to these two scientists, that made me accelerate my studies. It coincided with my return from Afghanistan – where I had served for five years – and, hence, I could afford to reorient myself. I had married a wonderful woman, Maria, who gave me the emotional and physical space to pursue this intellectual adventure.

I started a blog ( as I started struggling through it all – and that helped me greatly. I fondly recall that, back in 2015, Dr. Lloyd N. Trefethen from the Oxford Math Institute reacted to a post in which I had pointed out a flaw in one of Richard Feynman’s arguments. It was on a topic that had nothing to do with quantum mechanics – the rather mundane topic of electromagnetic 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.” This resulted in a firm determination to not take any formula for granted – even if they have been written by Richard Feynman! With the benefit of hindsight, I might say this episode provided me with the guts to question orthodox quantum theory.

The informed reader will now wonder: what do I mean with orthodox quantum theory? I should be precise here, and I will. It is the modern theory of quantum electrodynamics (QED) as established by Dyson, Schwinger, Feynman, Tomonaga and other post-World War II physicists. It’s the explanation of the behavior of electrons and photons – and their interactions – in terms of Feynman diagrams and propagators. I instinctively felt their theory might be incomplete because it lacks a good description of what electrons and photons actually are. Hence, all of the weirdness of quantum mechanics is now in this weird description of the fields – as reflected in the path integral formulation of quantum mechanics. Whatever an electron or a photon might be, we cannot really believe that it sort of travels along an infinite number of possible spacetime trajectories all over space simultaneously, can we?

I also found what Brian Hayes refers to as “the tennis match between experiment and theory” – the measurement (experiment) or calculation (theory) of the so-called anomalous magnetic moment – a rather weird business: the complexity in the mathematical framework just doesn’t match the intuition that, if the theory of QED has a simple circle group structure, 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. There must be some form factor coming out of a decent electron model that can explain it, right?

Of course, all of the above sounds very arrogant, and it is. However, I always felt I was in good company, because I realized that not only Einstein but the whole first generation of quantum physicists (Schrödinger, Dirac, Pauli and Heisenberg) had become skeptical about the theory they had created – if only because perturbation theory yielded those weird diverging higher-order terms. With the benefit of hindsight, we may say that the likes of Dyson, Schwinger, Feynman – the whole younger generation of mainly American scientists who dominated the discourse at the time – lacked a true general: they just kept soldiering on by inventing renormalization and other mathematical techniques to ensure those weird divergences cancel out, but they had no direction.

However, I should not get ahead of myself here. This is just an introduction, after all. Before getting to the meat of the matter, I should just make some remarks and acknowledge all the people who supported me in this rather lonely search. First, whom am I writing for? I am writing for people like me: amateur physicists. Not-so-dummies, that is. People who don’t shy away from calculations. People who understand a differential equation, some complex algebra and classical electromagnetism – all of which are, indeed, necessary, to understand anything at all in this field. I have good news for these people: I have come to the conclusion that we do not need to understand anything about gauges or propagators or Feynman diagrams to understand quantum electrodynamics.

Indeed, rather than “using his renormalized QED to calculate the one loop electron vertex function in an external magnetic field”, Schwinger should, perhaps, have listened to Oppenheimer’s predecessor on the Manhattan project, Gregory Breit, who wrote a number of letters to both fellow scientists as well as the editors of the Physical Review journal suggesting that the origin of the so-called discrepancy might be due to an ”intrinsic magnetic moment of the electron of the order of αµB.” In other words, I do not think Breit was acting schizophrenic when complaining about the attitude of Kusch and Lamb when they got the 1955 Nobel Prize for Physics for their work on the anomalous magnetic moment. I think he was just making a very sensible suggestion – and that is that one should probably first try investing in a good theory of the electron before embarking on mindless quantum field calculations.

My search naturally led me to the Zitterbewegung hypothesis. Zitter is German for shaking or trembling. It refers to a presumed local oscillatory motion – which I now believe to be true, whatever that means. Erwin Schrödinger found this Zitterbewegung as he was exploring solutions to Dirac’s wave equation for free electrons. In 1933, he shared the Nobel Prize for Physics with Paul Dirac for “the discovery of new productive forms of atomic theory”, and it is worth quoting Dirac’s summary of Schrödinger’s discovery:

“The variables give rise to some rather unexpected phenomena concerning the motion of the electron. These have been fully worked out by Schrödinger. It is found that an electron which seems to us to be moving slowly, must actually have a very high frequency oscillatory motion of small amplitude superposed on the regular motion which appears to us. As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light. This is a prediction which cannot be directly verified by experiment, since the frequency of the oscillatory motion is so high and its amplitude is so small. But one must believe in this consequence of the theory, since other consequences of the theory which are inseparably bound up with this one, such as the law of scattering of light by an electron, are confirmed by experiment.” (Paul A.M. Dirac, Theory of Electrons and Positrons, Nobel Lecture, December 12, 1933)

Dirac obviously refers to the phenomenon of Compton scattering of light by an electron. Indeed, as we shall see, the Zitterbewegung model naturally yields the Compton radius of an electron and – as such – effectively provides some geometric explanation of what might be happening. It took me a while to figure out that some non-mainstream physicists had actually continued to further explore this concept, and the writings of David Hestenes from the Arizona State University of Arizona who – back in 1990 – proposed a whole new interpretation of quantum mechanics based on the Zitterbewegung concept (Hestenes, 1990, The Zitterbewegung Interpretation of Quantum Mechanics) made me realize there was sort of a parallel universe of research out there – but it is not being promoted by the likes of MIT, Caltech or Harvard University – and, even more importantly, their friends who review and select articles for scientific journals.

I reached out to Hestenes, but he is 85 by now – and I don’t have his private email, so I never got any reply to the one or two emails I sent him on his ASU address. In contrast, Giorgio Vassallo – one of the researchers of an Italian group centered around Francesco Celani – who followed up on the Schrödinger-Hestenes zbw model of an electron – politely directed me towards Dr. Alex Burinskii (I should have put a Prof. and/or Dr. title in front of every name mentioned above, because they all are professors and/or doctors in science). Both have been invaluable – not because they would want to be associated with any of our ideas – but because they gave me the benefit of the doubt in their occasional but consistent communications. Hence, I would like to thank them here for reacting and encouraging me for at least trying to understand.

I think Mr. Burinskii deserves a Nobel Price, but he will probably never get one – because it would question not one but two previously awarded Nobel Prizes (1955 and 1965). I feel validated because, in his latest communication, Dr. Burinskii wrote he takes my 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. [He is working on an article right now, and I am sure it is going to take a lot of people out of their comfort zone – which is always a good thing.]

It is now time to start the book. However, before we do so, I should wrap up the acknowledgments section, so let us do that here. I have also been in touch with Prof. Dr. John P. Ralston, who wrote one of a very rare number of texts that, at the very least, tries to address some of the honest questions of amateur physicists and philosophers upfront. I was not convinced by his interpretation of quantum mechanics, but I loved 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.” We exchanged some messages, but then concluded that our respective interpretations of the wavefunction are very different and, hence, that we should not “waste any electrons” (his expression) on trying to convince each other. In the same vein, I should mention some other seemingly random exchanges – such as those with the staff and fellow students when going through the MIT’s edX course on quantum mechanics which – I admit – I did not fully complete because, while I don’t mind calculations in general, I do mind mindless calculations.

I am also very grateful to my brother, Prof. 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 discussions actually provided the inspiration for the earlier draft title of this book: The Emperor has no clothes: the sorry state of Quantum Physics. We will 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. Her independent research is very similar to ours. She has, therefore, provided much-needed moral support and external validation. We also warmly thank Jason Hise, whose wonderful animations of 720-degree symmetries did not convince me that electrons – as spin-1/2 particles – 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 of my friends (my university friends, in particular (loyal as ever), and I will also single out Soumaya Hasni, who has provided me with a whole new fan club here here in Brussels) and, of course, 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 grow into the person I am right now.

So, now we should really start the book. Its structure is simple. In the first chapters, I’ll just introduce the most basic math – Euler’s function, basically – and then we’ll take it from there. I will regularly refer to a series of papers I published on what I refer to as the Los Alamos Site for Spacetime Rebels: The site is managed by Phil Gibbs. I would like to acknowledge and thank him here for providing a space for independent thinkers. You can find my papers on They are numbered, and I will often refer to those papers by mentioning their number between square brackets. In fact, this very first version of this book follows the structure of paper [17]. Click, have a look, and you’ll understand. 😊

Or so I hope. This brings me to the final point in my introduction. This is just the first version of this book. It is rather short – cryptic, I’d say. As such, you might give up after a few pages and say: this may be a classical interpretation but it is not an easy one. You are right. But let me say two things to you:

  1. It may not be easy, but it is definitely easier than whatever else you’ll read when exploring the more serious stuff.
  2. To get my degree in philsophy, I had to study Wittgenstein’s Tractatus Logico-Philosophicus. I hated that booklet – not because it is dense but because it is nonsense. Wittgenstein wasn’t even aware of the scientific revolution that was taking place while he was writing it. Still, it became a bestseller. Why? Because it was so abstruse it made people think for themselves.

The first version of this book is going to be dense but – hopefully – you will find it is full of sense. If so (I’ll find out from the number of copies sold), I might go through the trouble of unpacking it in the second edition. 🙂

Jean Louis Van Belle,  7 January 2019





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