The book !

I just pre-published a very first draft on the usual site for independent thinkers. It still requires a lot of work – but I need to get back to my day job in the coming weeks and months, so don’t expect a second draft any time soon. 🙂 We’ll keep you updated on progress ! It’s sure not going to be a book like the others. Its working title is still the same: The Emperor has No Clothes: A Classical Explanation of Quantum Physics.

The whole idea is that a good electron and photon model can take all of the weirdness out of the QED sector of the Standard Model. What we’ve written so far, looks promising. Let’s see where it all goes ! 🙂

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Introductions…

As mentioned in my previous post, I thought it might be a good idea to release bits and pieces of my book on the go. It gives me the feeling I get something done, at least. 🙂

Introduction

If you are reading this book, then you are like me. You want to understand. Something inside of you tells you that the idea that we will never be able to understand quantum mechanics “the way we would like to understand it” does not make any sense. The quote is from Richard Feynman – probably the most eminent of all post-World War II physicists – and, yes, this is an aggressive opening. But you are right: our mind is flexible. We can imagine weird shapes and hybrid models. Hence, we should be able to understand quantum physics in some kind of intuitive way.

But what is intuitive? A lot of the formulas in this book feel intuitive to me, but that is only because I have been working with them for quite a while now. They may not feel very intuitive to you. However, I have confidence you will also sort of understand what they represent – intuitively, that is – because all of the formulas I use represent something we can imagine in space and in time – and I mean 3D space here: our Universe. Not the Universe of strings and hidden dimensions. An intuitive understanding of things means an understanding in terms of their geometry and their physicality.

You bought the right book. No hocus-pocus here. All physicists – and popular writers on physics – will tell you it is not possible. You see, the wavefunction of a particle – say, an electron – has this weird 720-degree symmetry, which we cannot really imagine. Of course, we have these professors doing the Dirac belt trick on YouTube – and wonderful animations (Jason Hise – whom I’ve been in touch with – makes the best ones) but, still, these visualizations all assume some weird relation between the object and the subject. In short, we cannot really imagine an object with a 720-degree symmetry.

The good news is: you don’t have to. The early theorists made a small mistake: they did not fully exploit the power of Euler’s ubiquitous a·eiθ function. The mistake is illustrated below – but don’t worry if this looks like you won’t understand: we’ll come back to it. It is a very subtle thing. Quantum physicists will tell you they don’t really think of the elementary wavefunction as representing anything real but, in fact, they do. And they will tell you, rather reluctantly because they are not so sure about what is what, that it might represent some theoretical spin-zero particle. Now, we all know spin-zero particles do not exist. All real particles – electrons, photons, anything – have spin, and spin (a shorthand for angular momentum) is always in one direction or the other: it is just the magnitude of the spin that differs. So it’s completely odd that the plus (+) or the minus (-) sign of the imaginary unit (i) in the a·e±iθ function is not being used to include the spin direction in the mathematical description.

clock

Figure 1: The meaning of +i and –i

Indeed, most introductory courses in quantum mechanics will show that both a·ei·θ = a·ei·(wtkx) and a·e+i·θ = a·e+i·(wtkx) are acceptable waveforms for a particle that is propagating in a given direction (as opposed to, say, some real-valued sinusoid). We would think physicists would then proceed to provide some argument showing why one would be better than the other, or some discussion on why they might be different, but that is not the case. The professors usually conclude that “the choice is a matter of convention” and, that “happily, most physicists use the same convention.” In case you wonder, this is a quote from the MIT’s edX course on quantum mechanics (8.01.1x).

That leads to the false argument that the wavefunction of spin-½ particles have a 720-degree symmetry. Again, you should not worry if you don’t get anything of what I write here – because I will come back to it – but the gist of the matter is the following: because they think the elementary wavefunction describes some theoretical zero-spin particle, physicists treat -1 as a common phase factor: they think we can just multiply a set of amplitudes – let’s say two amplitudes, to focus our mind (think of a beam splitter or alternative paths here) – with -1 and we’re going to get the same states. We find it rather obvious that that is not necessarily the case: -1 is not necessarily a common phase factor. We should think of -1 as a complex number itself: the phase factor may be +π or, alternatively, -π. To put it simply, when going from +1 to -1, it matters how you get there – and vice versa – as illustrated below.

rotation

Figure 2: e+iπ ¹ eiπ

I know this sounds like a bad start for a book that promises to be easy – but I just thought it would be good to be upfront about why this book is very different than anything you’ve ever read about quantum physics. If we exploit the full descriptive power of Euler’s function, then all weird symmetries disappear – and we just talk standard 360-degree symmetries in space. Also, weird mathematical conditions – such as the Hermiticity of quantum-mechanical operators – can easily be explained as embodying some common-sense physical law. In this particular case (Hermitian operators), we are talking physical reversibility: when we see something happening at the elementary particle level, then we need to be able to play the movie backwards. Physicists refer to it as CPT-symmetry, but that’s what it is really: physical reversibility.

The argument above involved geometry, and this brings me to a second mistake of the early quantum physicists: a total neglect of what I refer to as the form factor in physics. Why would an electron be some perfect sphere, or some perfect disk? In fact, we will argue it is not. It is a regular geometric shape – the Dirac-Kerr-Newman model suggests it’s an oblate spheroid – but so that’s not a perfect sphere. Once you acknowledge that, the so-called anomalous magnetic moment is not-so-anomalous anymore.

The mistake is actually more general than what I wrote above. We are thinking of the key constants in Nature as some number. Most notably, we think of Planck’s quantum of action (h ≈ 6.626×10−34 N·m·s) as some (scalar) number. Why would it be? It is – obviously – some vector quantity or – let me be precise – some matrix quantity: h is the product of a force (some vector in three-dimensional space), a distance (another three-dimensional concept) and time (one direction only). Somehow, those dimensions disappeared in the analysis. Vector equations became flat: vector quantities became magnitudes. Schrödinger’s equation should be rewritten as a vector or matrix equation. We do think of Planck’s quantum of action as some vector. We, therefore, think that the uncertainty – or the probabilistic nature of Nature, so to speak[1] – is not in its magnitude: it’s in its direction. But we are getting ahead of ourselves here – as usual. We should go step by step. Let us first acknowledge where we came from.

Before doing so, I would like to make yet another remark – one that is actually not so relevant for what we are going to try to do this in this book – and that is to understand the QED sector of the Standard Model geometrically – or physically, I should say. The innate nature of man to generalize did not contribute to greater clarity – in my humble opinion, that is. Feynman’s weird Lecture (Volume III, Chapter 4) on the key difference between bosons and fermions does not have any practical value: it just confuses the picture.

Likewise, it makes perfect sense to me to think that each sector of the Standard Model requires its own mathematical approach. I will briefly summarize this idea in totally non-scientific language. We may say that mass comes in one ‘color’ only: it is just some scalar number. Hence, Einstein’s geometric approach to gravity makes total sense. In contrast, the electromagnetic force is based on the idea of an electric charge, which can come in two ‘colors’ (+ or -), so to speak. Maxwell’s equation seemed to cover it all until it was discovered the nature of Nature – sorry for the wordplay – might be discrete and probabilistic. However, that’s fine. We should be able to modify the classical theory to take that into account. There is no need to invent an entirely new mathematical framework (I am talking quantum field and gauge theories here). Now, the strong force comes in three colors, and the rules for mixing them, so to speak, are very particular. It is, therefore, only natural that its analysis requires a wholly different approach. Hence, I would think the new mathematical framework should be reserved for that sector. I don’t like the reference of Aitchison and Hey to gauge theories as ‘the electron-figure’. The electron figure is a pretty classical idea to me. Hence, I do hope one day some alien will show us that the application of the Dyson-Feynman-Schwinger-Tomonaga ‘electron-figure’ to what goes on inside of the nucleus of an atom was, perhaps, not all that useful. A simple exponential series should not be explained by calculating a zillion integrals over 891 Feynman diagrams. It should be explained by a simple set of equations. If I have not lost you by now, please follow me to the acknowledgments section.

[1] A fair amount of so-called thought experiments in quantum mechanics – and we are not (only) talking the more popular accounts on what quantum mechanics is supposed to be all about – do not model the uncertainty in Nature, but on our uncertainty on what might actually be going on. Einstein was not worried about the conclusion that Nature was probabilistic (he fully agreed we cannot know everything): a quick analysis of the full transcriptions of his oft-quoted remarks reveal that he just wanted to see a theory that explains the probabilities. A theory that just describes them didn’t satisfy him.

PS: The book might take a while – as I am probably going to co-publish with another author (it’s perhaps a bit too big for me alone). In the meanwhile, you can just read the articles that are going to make up its contents.

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 nonsensical 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 (readingfeynman.org) 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). We 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: vixra.org. 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 http://vixra.org/author/jean_louis_van_belle. 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 on the link above, 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

[START OF THE BOOK]

[FIRST CHAPTERS: EXPLAIN EULER’S FORMULA AND BASIC THEORY.]

[OTHER CHAPTERS: SEE VIXRA.ORG]

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 a working title for the 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.

The Emperor has no clothes…

Hi guys (and ladies) – I should copy the paper into this post but… Well… That’s rather tedious. :-/ The topic is one that is of interest of you. You’re looking for a classical explanation of the anomalous magnetic moment, right? Well… We don’t have one – but we’re pretty sure this paper has all the right ingredients for one. We also designed a test for it. Also check out my other paper on the fine-structure constant. It explains everything.

Everything? Well… Almost everything. 🙂 The Revolution has started. The (quantum-mechanical) Emperor seems to have no clothes. 🙂

I am damn serious. This is what I wrote on my FB page today:

The only thing I can be proud of this year is a series of papers on quantum math. I will probably turn them into a popular book on physics. Its working title is “The Emperor Has No Clothes !” Indeed – if anything – these papers show that a lot of the highbrow stuff is just unnecessary complexity or deliberate hyping up of models that can be simplified significantly.

Worse, through my interactions with some physicists, I found some serious research into the nature of matter and energy is being neglected or ignored just because it challenges the Copenhagen interpretation of quantum physics. Most papers of Alexander Burinskii, for example, a brilliant physicist who developed a very plausible model of an electron, have been re-classified from ‘quantum physics’ to ‘general physics’ – which means no one will read them. Worse, he has had trouble just getting stuff published over the last four years! It’s plain censorship! 

I now summarize the Copenhagen interpretation as: “Calculate, don’t think !”  It’s a Diktatur, really! And I now also understand why the founding fathers of quantum mechanics (Dirac, Heisenberg, Pauli, Schroedinger,…) thought the theory they helped to create didn’t quite make the cut. It’s going to be a sad story to tell. In fact, I think Burinskii is in trouble because his model may show that a lot of the research on the anomalous magnetic moment is plain humbug – but so that got some people a Nobel Prize in 1955 and it’s popularly referred to as the ‘high-precision test’ of QED, so… Well… I looked at it too, and for quite a long time, and I’ve come to the conclusion that it’s plain nonsense – but so that cannot be said.

Hmm… If the state of physics is so poor, then we should not be surprised that we are constantly being misled in other fields as well. Let us remember Boltzmann:

“Bring forth what is true. Write it so it it’s clear. Defend it to your last breath.”

Oh – and I have a sort of classical explanation for what happens in the one-photon Mach-Zehnder experiment too. Check it out here. Quantum mechanics is not a mystery. Mr. Bell has got it all wrong. 🙂

Kind regards – JL

Call to Arms

Sent: Thursday, December 20, 2018 12:59 PM
To: All Rebels
Subject: The Manifesto for the Revolution

Dear All – Thanks for the bilateral exchanges. It is time to bring all spacetime rebels together in this Quest. The Mother Ship is not moving anymore. Orthodox quantum mechanics is broken beyond repair. We know why: it is because of the academic brain freeze – the Heisenberg Diktatur on how we should think about quantum mechanics. We need to build our own spacecraft to venture out to the New Universe. It should be small and nimble.

The Seeds of the Revolution have started to grow. They are the following:

1. The + or – sign in front of the argument of the wavefunction has a meaning. It’s a degree of freedom in the mathematical description that has not been exploited by physicists. If we want to give it a meaning, then it’s probably the spin direction. It is plain weird that we need the concept of spin in all of our discussions and models on quantum physics but that the Founding Fathers of Quantum Mechanics chose to limit the power of Euler’s function to describe a spin-zero particle only.

Once we acknowledge that, all these weird symmetries (720-degree symmetry for spin-1/2) disappear, so there is no ‘excuse’ anymore to not think about a geometric/physical interpretation of the wavefunction. That should trigger a new burst of creative thinking. For starters, we’ll have a different interpretation of Schrödinger’s wave equation. In fact, I would dare to say that, for the first time, we will actually have a (geometric) interpretation of Schrödinger’s wave equation (and its solutions – the orbitals – of course).

2. The difference between the g-factor for spin versus orbital momentum (2 versus 1) can easily be explained by a form factor. If we think of the (free) electron as some disk-like structure (a two-dimensional oscillation, that is), then we’ll have a ½ factor in the formula for its angular momentum and the ‘mystery’ is solved. The anomalous magnetic moment is then not anomalous anymore: it’s just a coupling between the spin and orbital angular momentum that occurs because of the Larmor precession.

Schwinger’s α/2π factor says it all here: if the fine-structure constant is just a dimensional scaling factor explaining the disk-like shape of the (free) electron, then we would expect to see it pop up in some form in the final equations for the motion of real-life electron, which combines orbital motion, Larmor precession (just the effect of magnetism) and spin. I’ve re-written my paper on the anomalous magnetic moment in this sense (it’s on the Los Alamos pre-publishing site for rebels) – but I need to do so more work on it. These motions are complicated and to get the coupling factor, we can – unfortunately – not just superpose motions: there is only one value for the magnetic field vector and the magnetic moment/angular momentum of the whole thing (i.e. the real-life (disk-like) electron moving in this complicated orbital). So, yes, the result is beautiful but it is going to be tough to go through the motions – literally. 🙂

3. Interference and diffraction – stuff like the Mach-Zehner experiment – should be explained the way one would usually explain diffraction and interference: if we are going to force a wave through a slit or an aperture, the wave shape is going to change. We need to distinguish between linear and circular polarization ‘states’ – which become real states here! And we should think about how plane waves become spherical waves when they go through an aperture. I think a photon is a circularly polarized wave, but when it goes through the beam splitter, it might be broken up in two linearly polarized waves – each going in a different direction (to the top or, alternatively, to the bottom mirror). If one of them finds its way blocked, it will – somehow – rejoin the other direction (it might just bounce back, right?). Weak measurement shows there is something there. Weak measurement shows the idea of an amplitude is real. It’s not just a mathematical thing. We just need to do some hard thinking on wave shapes and form factors.

We’re not challenging any basic results of quantum mechanics here. We’re just challenging the standard Copenhagen interpretation, which is – basically – that we should not even try to understand what’s going on.

I have a lot of crazy followers on my physics blog (https://readingfeynman.org/). I am going to re-direct them another site – which I really wanted to reserve for the truly crazy ideas (https://readingeinstein.blog/).

On-on ! Let’s honor the Spirit of Ludwig Boltzmann: “Bring forth what is true. Write it so it’s clear. Defend it to your last breath.”

I would add: Please enjoy while doing so! 😊

Dōgen

Mass as a two-dimensional oscillation (2)

This post basically further develops my speculative thoughts about the real meaning of the E = m·c2 formula. However, I’ll use the relativistically correct formulas for the calculations this time, so it may look somewhat more complicated. However, I think you should be able to digest it relatively easily, as none of the math is exceedingly difficult.

My previous post explored the similarity between the formula for the energy of a harmonic oscillator and the E = m·c2 formula. Now, there is another formula that sort of resembles it: the E = m·v2/2 formula for the kinetic energy. Could we relate them somehow and – in the process – gain a better understanding of Einstein’s famous formula? I think we can, and I want to show you how. In fact, in this post, I will try to relate all three.

We should first note that the E = m·v2/2 is a non-relativistic formula. It is only correct if we assume the mass – defined as a measure of inertia, remember? – to be constant, which we know isn’t true. As an object accelerates and gains kinetic energy, its effective mass will increase. In fact, the relativistically correct formula for the kinetic energy just calculates it as the difference between (1) the total energy (which is given by the E = m·c2 formula, always) and (2) its rest energy, so we write:

K.E. = E − E0 = mv·c2 − m0·c2 = m0·γ·c2 − m0·c2 = m0·c2·(γ − 1)

The γ in this formula is, of course, the ubiquitous Lorentz factor. Hence, the correct formula for the kinetic energy is m0·c2·(γ − 1). We shouldn’t use that m·v2/2 formula. Still, the two formulas are remarkably similar: there is a squared velocity (v2 and c2) and some factor (1/2 versus γ − 1). Why the squared velocity? That’s child play, right? Yep, I effectively wrote a post on that for my kids. We have a force that acts on some object over some time and over some distance, and so that force is going to do some work. While it’s child play, we’re calculating a path or line integral here:

KEChild play? Perhaps, but many kids don’t know what a vector dot product is (the F·dx), and they also don’t realize we can only solve this because we assume the mass m to be constant (i.e. not a function of the velocity v). So… Well… In our flywheel model of an electron, we’ve been using a non-relativistic formula, but we’ve calculated the tangential speed as being equal to c. A recipe for disaster, right? 🙂 Can we re-do the calculations? We can. You can google a zillion publications on relativistic harmonic oscillators but I took the derivation below from a fairly simple one I’d recommend. The only correction we’ll do here is to use the relativistically correct expression of Newton’s force law: the force equals the time rate of change of the (relativistic) momentum p = mvv = γm0v. So we write:

F = dp/dt = F = –kx with p = mvv = γm0v

Multiplying both sides with = dx/dt yields the following expression: relativistic spring energyNow, when we combine two oscillators – think of the metaphor of a frictionless V-twin engine, as illustrated below 🙂 – then we know that – because of the 90° angle between the two cylinders, the motion of one piston will be equal to x = a∙cos(ω∙t), while the
motion of the other is given by y = a∙cos(ω∙t–π/2) = a∙sin(ω∙t).V-2 engineNow how do we calculate the total energy in this system? Should we distinguish the x– and y– components of the total momentum p? We can easily do that. Look at the animation below, and you’ll immediately understand that we can easily calculate the velocities in the x– and a y-direction: vx = dx/dt = −a·ω·sin(ω∙t) and vy = dy/dta·ω·cos(ω∙t). The sum of the square of both then gives us the tangential velocity vv2 a2∙ω2∙sin2(ω∙t) + a2∙ω2∙cos2(ω∙t) = a2∙ω2 ⇔ va∙ω.  Circle_cos_sinBut how do we add energies here? It’s a tricky question: we have potential energy in one oscillator, and then in the other, and these energies are being transferred from one to another through the flywheel, so to speak. So there is kinetic energy there. Can we just add it all? Let us think about our perpetuum mobile once more, noting that the equilibrium position for the piston is at the center of each cylinder. When it goes past that position, extra pressure will build up and eventually push the piston back. When it is below that position, pressure is below equilibrium and will, therefore, also want to pull the piston back. The dynamics are as follows:

  • When θ is zero, the air in cylinder 1 is fully compressed, and the piston will return to the equilibrium position (x = 0) as θ goes to 90°. The flywheel will transfer energy to cylinder 2, where the piston goes from the equilibrium position to full compression. Cylinder 2 borrows energy, and will want to return to its equilibrium position.
  • When θ is 90°, the air in cylinder 2 is fully compressed, and the piston will return to the equilibrium position (y = 0) as θ goes to 180°. The flywheel will transfer energy back to cylinder 1, where the piston goes past the equilibrium position to create a vacuum. The piston in cylinder 1 borrows energy, and will want to return to its equilibrium position.
  • When θ is 180°, the piston in cylinder 1 is fully extended, and will want to return to equilibrium because the pressure is lower than when in equilibrium. As θ goes from 180° to 270°, the piston in cylinder 1 does effectively return to equilibrium and, through the flywheel, pushes the piston in cylinder 2 past the equilibrium to create vacuum. The piston in cylinder 2 borrows energy, and will want to return to equilibrium.
  • Finally, between 270° and 360°, the piston in cylinder 2 returns to equilibrium and, through the flywheel, causes the piston in cylinder 1 to compress air. The piston in cylinder 2 borrows energy, and will want to return to equilibrium.

It is a funny thing. Where is the energy in this system? Energy is not supposed to be thought as being directional but, here, direction clearly matters! We need to think about averages here (kinetic energy is a non-directional (scalar) quantity but it’s a function of velocity, and velocity is directional. If we have two directions only (x and y), then we can write: 〈vx2〉 = 〈vy2〉 = [〈vx2〉 + 〈vy2〉]/2 = 〈v2〉/2. So this gives us a clue, but we won’t make things to complicated here. Think of it like this. While transferring energy from one piston to the other, the crankshaft will rotate with a constant angular velocity: linear motion becomes circular motion, and vice versa. So what is the total energy in the system? What if we would want to use it? What can we take from it? You’d agree we would have to take it from the flywheel, right? The usable energy is in the flywheel. Let’s have a look at that energy conservation law we derived above: conservation lawThe usable energy in the flywheel is the E = m·c2 term. This, and my previous post, suggests we may interpret the mass of an electron as a two-dimensional oscillation. In fact, I think my previous post is an easier read because I use the classical (non-relativistic) formulas there. This post, hopefully, demonstrates that a relativistically correct mathematical treatment doesn’t alter the picture that I’ve been trying to offer. 🙂

Of course, the more difficult thing is to go beyond this metaphor and explain how exactly this motion from borrowing and returning energy to space would actually work. 🙂 So that would be a proper ‘ring theory’ of matter. 🙂