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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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: A Manifesto for the Revolution?

Dear All – Thanks for the bilateral exchanges. Perhaps it is time to bring all spacetime rebels together here. 😊

I think we are all agreed on the fact that the Big Ship is not moving anymore. It feels like there has been a sort of academic brain freeze ever since Heisenberg imposed his Diktatur on how we should think about quantum mechanics. Orthodox quantum mechanics is broken beyond repair. Hence, we need to build our own spaceship to venture out to the New Universe. It should be small and nimble. The Seeds of the Revolution 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 QM 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 Schroedinger’s wave equation. In fact, I would dare to say that, for the first time, we will actually have a (geometric) interpretation of Schroedinger’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 site for rebels – yes, sorry, I don’t bother to even try to get stuff published) – 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).

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

Enter the void…

I woke up this morning with an inspiring idea. I wrote it on my Facebook page. It is this:

Turbulence… This animation (https://www.youtube.com/watch?v=C680Zz7MyP) has been made by another passenger on this spaceship. We’re traveling into a new Universe. We’re not re-writing the laws of physics. We’re re-writing the way they are written. We have a new language. It’s been a very lonely trip. We’re just a small band of travelers, and the big guns out there don’t like us. All those professors who tell us our ideas look good but that we should not try to challenge the current academic brain freeze… We have only one answer to the skepticism: our ship is small, but it moves. Your ships are big – but they’ve been frozen in time ever since the imposition of the Heisenberg Diktatur. Onwards ! I have a set of papers on the Los Alamos safe haven for rebels that encompasses virtually everything that needs to be explained: the anomalous magnetic moment, Mach-Zehnder interference, Einstein’s E = mc2 equation itself, the spin form factor,… The seeds of the Revolution have been sown.  

Because this site has become very crowded with posts and pages, I will use my other site to relaunch. The other site was supposed to be a site on Einstein – but I hope He is with us in Spirit. 🙂 

Jean Louis Van Belle, 20 December 2018

PS: For some reason, WordPress blocks the YouTube link. Just cut and paste the address in your browser. It’s worth it. 🙂

The not-so-anomalous magnetic moment of an electron

Note: Check the revised paper on this topic. The substance is the same, but it is a more coherent development. 

Jean Louis Van Belle, 23 December 2018

Original post:

I am going to expose a bright shining lie in (quantum) physics in this post: what is referred to as the electron’s anomalous magnetic moment is actually not a magnetic moment, and it is not anomalous. Let’s start with the first remark. The anomalous magnetic moment is not a magnetic moment. It is just some (real) number: it’s a ratio, to be precise. It does not have any physical dimension. If it would be an actual magnetic moment then we would measure it as we usually do in the context of quantum mechanics, and that is in terms of the Bohr magneton, which is equal to: μB = qeħ/2m ≈ 9.274×10−24 joule per tesla.[1]

So what is the electron’s anomalous magnetic moment – denoted by ae – then? It is defined as the (half-)difference between (1) some supposedly real gyromagnetic ratio (ge) and (2) Dirac’s theoretical value for the gyromagnetic ratio of a spin-only electron (g = 2)[2]:F1This immediately triggers an obvious question: why would we use the g-factor of a spin-only electron. This is a very weird thing to do, because the electron in the cyclotron (a Penning trap) is actually not a spin-only electron: it follows an orbital motion – as we will explain shortly.

So… Well… It is also routinely said (and written) that its measured value is equal to 0.00115965218085(76). The 76 (between brackets) is the uncertainty – which looks pretty certain, because it is equal to 0.00000000000076. Hence, the precision here is equivalent to 76 parts per trillion (ppt). It is measured as a standard deviation.[3] However, the problem is that these experiments actually do not directly measure ae. What is being measured in the so-called Penning traps that are used in these experiments (think of them as a sort of cyclotron) are two slightly different frequencies – an orbital frequency and a precession frequency, to be precise – and ae is then calculated as the fractional difference between the two:F2Let us go through the motions here – literally. The orbital frequency fc is the cyclotron frequency: a charged particle in a Penning trap will move in a circular orbit whose frequency depends on the charge, its mass and the strength of the magnetic field only. Let us give you the formula (we will derive it for you in an instant):F3The subscript c stands for cyclotron – or circular, if you want. We should not think of the speed of light here! In fact, the orbital velocity is a (relatively small) fraction of the speed of light and we can, therefore, use non-relativistic formulas. The derivation of the formula is quite straightforward – but we find it useful to recap it. It is based on a simple analysis of the Lorentz force, which is just the magnetic force here[4]: F = v(q×B). Note that the frequency does not depend on the velocity or the radius of the circular motion. This is actually the whole idea of the trap: the electron can be inserted into the trap with a precise kinetic energy and will follow a circular trajectory if the frequency of the alternating voltage is kept constant. This is why we italicized only when writing that the orbital frequency depends on the charge, the mass and the strength of the magnetic field only. So what is the derivation? The Lorentz force is equal to the centripetal force here. We can therefore write:F4The v2/r factor is the centripetal acceleration. Hence, the F = m·v2/r does effectively represent Newton’s force law. The equation above yields the following formula for v and the v/r ratio:vNow, the cyclotron frequency fc will respect the following equation:F7Re-arranging and substituting v for q·r·b/m yields:F8The associated current will be equal to:F9Hence, the magnetic moment is equal to:F10The angular momentum – which we will denote by – is equal to[5]:F11Hence, we can write the g-factor as:F12It is what we would expect it to be: it is the gyromagnetic ratio for the orbital moment of the electron. It is one, not 2. Because gc is 1, we can write something very obvious:F13We should also note another equality here:F14Let us now look at the other frequency fs. It is the Larmor or precession frequency. It is (also) a classical thing: if we think of the electron as a tiny magnet with a magnetic moment that is proportional to its angular momentum, then it should, effectively, precess in a magnetic field. The analysis of precession is quite straightforward. The geometry of the situation is shown below and we may refer to (almost) any standard physics textbook for the derivation.[6]

precession frequency

pIt is tempting to use the equality above and write this as:F16However, we should not do this. The precession causes the electron to wobble: its plane of rotation – and, hence, the axis of the angular momentum (and the magnetic moment) – is no longer fixed. This wobbling motion changes the orbital and, therefore, we can no longer trust the values we have used in our formulas for the angular momentum and the magnetic moment. There is, therefore, nothing anomalous about the anomalous magnetic moment. In fact, we should not wonder why it is not zero, but – as we will argue – we should wonder why it is so nearly zero.

Let us continue our analysis. It is, in fact, a bit weird to associate a gyromagnetic ratio with this motion, but that is what the physicists doing these experiments do. We will denote this g-factor by gp:F17Hence, we can write the following tautology:F18You can verify that this is nothing but a tautology by writing it all out:F19We can, of course, measure the frequency in cycles per second (as opposed to radians per second):F20Hence, we get the following expression for the so-called anomalous magnetic moment of an electron ae:F21Hence, the so-called anomalous magnetic moment of an electron is nothing but the ratio of two mathematical factors – definitions, basically – which we can express in terms of actual frequencies:F22Our formula for ae now becomes:F23Of course, if we use the μ/J = 2m/q equality, then the fp/fc ratio will be equal to 1/2, and ae will not be zero but −1/2:F24However, as mentioned above, we should not do that. The precession causes the magnetic moment and the angular momentum to wobble. Hence, there is nothing anomalous about the anomalous magnetic moment. We should not wonder why its value is not zero. We should wonder why it is so nearly zero.

[1] Needless to say, the tesla is the SI unit for the magnitude of a magnetic field. We can also write it as [B] = N/(m∙A), using the SI unit for current, i.e. the ampere (A). Now, 1 C = 1 A∙s and, hence, 1 N/(m∙A) = 1 (N/C)/(m/s). Hence, the physical dimension of the magnetic field is the physical dimension of the electric field (N/C) divided by m/s. We like the [E] = [B]·m/s expression because it reflects the geometry of the electric and magnetic field vectors.

[2] See: Physics Today, 1 August 2006, p. 15 (https://physicstoday.scitation.org/doi/10.1063/1.2349714). The article also explains the methodology of the experiment in terms of the frequency measurements, which we explain above.

[3] See: G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, New Determination of the Fine Structure Constant from the Electron g Value and QED, Phys. Rev. Lett. 97, 030802 (2006). More recent theory and experiments may have come up with an even more precise number.

[4] Our derivation is based on the following reference: https://www.didaktik.physik.uni-muenchen.de/elektronenbahnen/en/b-feld/anwendung/zyklotron2.php.

[5] J is the symbol which Feynman uses. In many articles and textbooks, one will read L instead of J. Note that the symbols may be confusing: I is a current, but I is the moment of inertia. It is equal to m·r2 for a rotating mass.

[6] We like the intuitive – but precise – explanation in Feynman’s Lectures (II-34-3), from which we also copied the illustration.