The End of Physics

A young researcher, Oliver Consa, managed to solve a complicated integral: he gave us an accurate calculation of the anomalous magnetic moment based on a (semi-)classical model. Here is the link to his paper, and this is the link to my first-order approach. I admit: he was first. Truth doesn’t need an author. 🙂

This is a great achievement. We now have an electron model that explains all of the mysterious ‘intrinsic’ properties of the electron. It also explains the interference of an electron with itself. Most importantly, the so-called ‘precision test of QED’ (the theoretical and experimental value of the anomalous magnetic moment) also gets a ‘common-sense’ interpretation now. Bye-bye QFT!

So now it’s time for the next step(s). If you have followed this blog, then you know I have a decent photon model too – and other researchers – most are small names but there are one or two big names as well 🙂 – are working to refine it.

The End of Physics is near. Mankind knows everything now. Sadly, this doesn’t solve any of the major issues mankind is struggling with (think of inequality and climate change here). :-/

Post scriptum: When you check the references, it would seem that Consa borrowed a lot of material from the 1990 article he mentions as a reference: David L. Bergman and J. Paul Wesley, Spinning Charged Ring Model of Electron Yielding Anomalous Magnetic Moment, Galilean Electrodynamics, Vol. 1, Sept-Oct 1990, pp. 63–67). It is strange that David Hestenes hadn’t noted this article, because it goes back to the same era during which he tried to launch the Zitterbewegung interpretation of quantum physics ! I really find it very bizarre to see how all these elements for a realist interpretation of quantum physics have been lying around for many decades now. I guess it’s got to do with what Sean Carroll suggested in his 7 Sept 2019 opinion article in the NY Times: mainstream physicists do not want to understand quantum mechanics.

A realist interpretation of quantum physics

Feyerabend was a rather famous philosopher. He was of the opinion that ‘anything goes’. We disagree. Let me know your views on my latest paper. 🙂 Let me know your views on my latest paper. 🙂 Also check out this one: https://www.academia.edu/40226046/Neutrinos_as_the_photons_of_the_strong_force.

Wikipedia censorship

I started to edit and add to the rather useless Wikipedia article on the Zitterbewegung. No mention of Hestenes or more recent electron models (e.g. Burinskii’s Kerr-Newman geometries. No mention that the model only works for electrons or leptons in general – not for non-leptonic fermions. It’s plain useless. But all the edits/changes/additions were erased by some self-appointed ‘censor’. I protested but then I got reported to the administrator ! What can I say? Don’t trust Wikipedia. Don’t trust any ‘authority’. We live in weird times. The mindset of most professional physicists seems to be governed by ego and the Bohr-Heisenberg Diktatur.

For the record, these are the changes and edits I tried to make. You can compare and judge for yourself. Needless to say, I told them I wouldn’t bother to even try to contribute any more. I published my own article on the Vixrapedia e-encyclopedia. Also, as Vixrapedia did not have an entry on realist interpretations of quantum mechanics, I created one: have a look and let me know what you think. 🙂

Zitterbewegung (“trembling” or “shaking” motion in German) – usually abbreviated as zbw – is a hypothetical rapid oscillatory motion of elementary particles that obey relativistic wave equations. The existence of such motion was first proposed by Erwin Schrödinger in 1930 as a result of his analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces what appears to be a fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of ω = 2mc2/ħ, or approximately 1.5527×1021 radians per second. Paul Dirac was initially intrigued by it, as evidenced by his rather prominent mention of it in his 1933 Nobel Prize Lecture (it may be usefully mentioned he shared this Nobel Prize with Schrödinger):

“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.”[1]

In light of Dirac’s later comments on modern quantum theory, it is rather puzzling that he did not pursue the idea of trying to understand charged particles in terms of the motion of a pointlike charge, which is what the Zitterbewegung hypothesis seems to offer. Dirac’s views on non-leptonic fermions – which were then (1950s and 1960s) being analyzed in an effort to explain the ‘particle zoo‘ in terms of decay reactions conserving newly invented or ad hoc quantum numbers such as strangeness[2] – may be summed up by quoting the last paragraph in the last edition of his Principles of Quantum Mechanics:

“Now there are other kinds of interactions, which are revealed in high-energy physics. […] These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion.”[3]

Indeed, in light of this stated preference for kinematic models, it is somewhat baffling that Dirac did not follow up on this or any of the other implications of the Zitterbewegung hypothesis, especially because it should be noted that a reexamination of Dirac theory shows that interference between positive and negative energy states is not a necessary ingredient of Zitterbewegung theories.[4] The Zitterbewegung hypothesis also seems to offer interesting shortcuts to key results of mainstream quantum theory. For example, one can show that, for the hydrogen atom, the Zitterbewegung produces the Darwin term which plays the role in the fine structure as a small correction of the energy level of the s-orbitals.[5] This is why authors such as Hestenes refers to it as a possible alternative interpretation of mainstream quantum mechanics, which may be an exaggerated claim in light of the fact that the zbw hypothesis results from the study of electron behavior only.

Zitterbewegung models have mushroomed[6] and it is, therefore, increasingly difficult to distinguish between them. The key to understanding and distinguishing the various Zitterbewegung models may well be Wheeler‘s ‘mass without mass’ idea, which implies a distinction between the idea of (i) a pointlike electric charge (i.e. the idea of a charge only, with zero rest mass) and (ii) the idea of an electron as an elementary particle whose equivalent mass is the energy of the zbw oscillation of the pointlike charge.[7] The ‘mass without mass’ concept requires a force to act on a charge – and a charge only – to explain why a force changes the state of motion of an object – its momentum p = mγ·v(with γ referring to the Lorentz factor) – in accordance with the (relativistically correct) F = dp/dt force law.

History

As mentioned above, the zbw hypothesis goes back to Schrödinger’s and Dirac’s efforts to try to explain what an electron actually is. Unfortunately, both interpreted the electron as a pointlike particle with no ‘internal structure’.David Hestenes is to be credited with reviving the Zitterbewegung hypothesis in the early 1990s. While acknowledging its origin as a (trivial) solution to Dirac’s equation for electrons, Hestenes argues the Zitterbewegung should be related to the intrinsic properties of the electron (charge, spin and magnetic moment). He argues that the Zitterbewegung hypothesis amounts to a physical interpretation of the elementary wavefunction or – more boldly – to a possible physical interpretation of all of quantum mechanics: “Spin and phase [of the wavefunction] are inseparably related — spin is not simply an add-on, but an essential feature of quantum mechanics. […] A standard observable in Dirac theory is the Dirac current, which doubles as a probability current and a charge current. However, this does not account for the magnetic moment of the electron, which many investigators conjecture is due to a circulation of charge. But what is the nature of this circulation? […] Spin and phase must be kinematical features of electron motion. The charge circulation that generates the magnetic moment can then be identified with the Zitterbewegung of Schrödinger “[8] Hestenes’ interpretation amounts to an kinematic model of an electron which can be described in terms of John Wheeler‘s mass without mass concept.[9] The rest mass of the electron is analyzed as the equivalent energy of an orbital motion of a pointlike charge. This pointlike charge has no rest mass and must, therefore, move at the speed of light (which confirms Dirac’s en Schrödinger’s remarks on the nature of the Zitterbewegung). Hestenes summarizes his interpretation as follows: “The electron is nature’s most fundamental superconducting current loop. Electron spin designates the orientation of the loop in space. The electron loop is a superconducting LC circuit. The mass of the electron is the energy in the electron’s electromagnetic field. Half of it is magnetic potential energy and half is kinetic.”[10]

Hestenes‘ articles and papers on the Zitterbewegung discuss the electron only. The interpretation of an electron as a superconducting ring of current (or as a (two-dimensional) oscillator) also works for the muon electron: its theoretical Compton radius rC = ħ/mμc ≈ 1.87 fm falls within the CODATA confidence interval for the experimentally determined charge radius.[11] Hence, the theory seems to offer a remarkably and intuitive model of leptons. However, the model cannot be generalized to non-leptonic fermions (spin-1/2 particles). Its application to protons or neutrons, for example, is problematic: when inserting the energy of a proton or a neutron into the formula for the Compton radius (the rC = ħ/mc formula follows from the kinematic model), we get a radius of the order of rC = ħ/mpc ≈ 0.21 fm, which is about 1/4 of the measured value (0.84184(67) fm to 0.897(18) fm). A radius of the order of 0.2 fm is also inconsistent with the presumed radius of the pointlike charge itself. Indeed, while the pointlike charge is supposed to be pointlike, pointlike needs to be interpreted as ‘having no internal structure’: it does not imply the pointlike charge has no (small) radius itself. The classical electron radius is a likely candidate for the radius of the pointlike charge because it emerges from low-energy (Thomson) scattering experiments (elastic scattering of photons, as opposed to inelastic Compton scattering). The assumption of a pointlike charge with radius re = α·ħ/mpc) may also offer a geometric explanation of the anomalous magnetic moment.[12]

In any case, the remarks above show that a Zitterbewegung model for non-leptonic fermions is likely to be somewhat problematic: a proton, for example, cannot be explained in terms of the Zitterbewegung of a positron (or a heavier variant of it, such as the muon- or tau-positron).[13] This is why it is generally assumed the large energy (and the small size) of nucleons is to be explained by another force – a strong force which acts on a strong charge instead of an electric charge. One should note that both color and/or flavor in the standard quarkgluon model of the strong force may be thought of as zero-mass charges in ‘mass without mass’ kinematic models and, hence, the acknowledgment of this problem does not generally lead zbw theorists to abandon the quest for an alternative realist interpretation of quantum mechanics.

While Hestenes‘ zbw interpretation (and the geometric calculus approach he developed) is elegant and attractive, he did not seem to have managed to convincingly explain an obvious question of critics of the model: what keeps the pointlike charge in the zbw electron in its circular orbit? To put it simply: one may think of the electron as a superconducting ring but there is no material ring to hold and guide the charge. Of course, one may argue that the electromotive force explains the motion but this raises the fine-tuning problem: the slightest deviation of the pointlike charge from its circular orbit would yield disequilibrium and, therefore, non-stability. [One should note the fine-tuning problem is also present in mainstream quantum mechanics. See, for example, the discussion in Feynman’s Lectures on Physics.] The lack of a convincing answer to these and other questions (e.g. on the distribution of (magnetic) energy within the superconducting ring) led several theorists working on electron models (e.g. Alexander Burinskii[14][15]) to move on and explore alternative geometric approaches, including Kerr-Newman geometries. Burinskii summarizes his model as follows: “The electron is a superconducting disk defined by an over-rotating black hole geometry. The charge emerges from the Möbius structure of the Kerr geometry.”[16] His advanced modelling of the electron also allows for a conceptual bridge with mainstream quantum mechanics, grand unification theories and string theory: “[…] Compatibility between gravity and quantum theory can be achieved without modifications of Einstein-Maxwell equations, by coupling to a supersymmetric Higgs model of symmetry breaking and forming a nonperturbative super-bag solution, which generates a gravity-free Compton zone necessary for consistent work of quantum theory. Super-bag is naturally upgraded to Wess-Zumino supersymmetric QED model, forming a bridge to perturbative formalism of conventional QED.”[17]

The various geometric approaches (Hestenes’ geometric calculus, Burinskii’s Kerr-Newman model, oscillator models) yield the same results (the intrinsic properties of the electron are derived from what may be referred to as kinematic equations or classical (but relativistically correct) equations) – except for a factor 2 or 1/2 or the inclusion (or not) of variable tuning parameters (Burinskii’s model, for example, allows for a variable geometry) – but the equivalence of the various models that may or may not explain the hypothetical Zitterbewegung still needs to be established.

The continued interest in zbw models may be explained because Zitterbewegung models – in particular Hestenes’ model and the oscillator model – are intuitive and, therefore, attractive. They are intuitive because they combine the Planck-Einstein relation (E = hf) and Einstein’s mass-energy equivalence (E = mc2): each cycle of the Zitterbewegung electron effectively packs (i) the unit of physical action (h) and (ii) the electron’s energy. This allows one to understand Planck’s quantum of action as the product of the electron’s energy and the cycle time: h = E·T = h·f·T = h·f/f = h. In addition, the idea of a centripetal force keeping some zero-mass pointlike charge in a circular orbit also offers a geometric explanation of Einstein’s mass-energy equivalence relation: this equation, therefore, is no longer a rather inexplicable consequence of special relativity theory.

The section below offers a general overview of the original discovery of Schrödinger and Dirac. It is followed by further analysis which may or may not help the reader to judge whether the Zitterbewegung hypothesis might, effectively, amount to what David Hestenes claims it actually is: an alternative interpretation of quantum mechanics.

Theory for a free fermion

[See the article: the author of this section does not seem to know – or does not mention, at least – that the Zitterbewegung hypothesis only applies to leptons (no strong charge).]

Experimental evidence

The Zitterbewegung may remain theoretical because, as Dirac notes, the frequency may be too high to be observable: it is the same frequency as that of a 0.511 MeV gamma-ray. However, some experiments may offer indirect evidence. Dirac’s reference to electron scattering experiments is also quite relevant because such experiments yield two radii: a radius for elastic scattering (the classical electron radius) and a radius for inelastic scattering (the Compton radius). Zittebewegung theorists think Compton scattering involves electron-photon interference: the energy of the high-energy photon (X- or gamma-ray photons) is briefly absorbed before the electron comes back to its equilibrium situation by emitting another (lower-energy) photon (the difference in the energy of the incoming and the outgoing photon gives the electron some extra momentum). Because of this presumed interference effect, Compton scattering is referred to as inelastic. In contrast, low-energy photons scatter elastically: they seem to bounce off some hard core inside of the electron (no interference).

Some experiments also claim they amount to a simulation of the Zitterbewegung of a free relativistic particle. First, with a trapped ion, by putting it in an environment such that the non-relativistic Schrödinger equation for the ion has the same mathematical form as the Dirac equation (although the physical situation is different).[18][19] Then, in 2013, it was simulated in a setup with Bose–Einstein condensates.[20]

The effective mass of the electric charge

The 2m factor in the formula for the zbw frequency and the interpretation of the Zitterbewegung in terms of a centripetal force acting on a pointlike charge with zero rest mass leads one to re-explore the concept of the effective mass of an electron. Indeed, if we write the effective mass of the pointlike charge as mγ = γm0 then we can derive its value from the angular momentum of the electron (L = ħ/2) using the general angular momentum formula L = r × p and equating r to the Compton radius:

This explains the 1/2 factor in the frequency formula for the Zitterbewegung. Substituting m for mγ in the ω = 2mc2/ħ yields an equivalence with the Planck-Einstein relation ω = mγc2/ħ. The electron can then be described as an oscillator (in two dimensions) whose natural frequency is given by the Planck-Einstein relation.[21]

The Emperor Has No Clothes

I am going to re-work my manuscript. I am going to restructure it, and also add the QCD analyses I did in recent posts. This is the first draft of the foreword. Let me know what you think of it. 🙂

[…] I had various working titles for this publication. I liked ‘A Bright Shining Lie’ but that title is already taken. The ‘History of a Bad Idea’ was another possibility, but my partner doesn’t like negative words. When I first talked to my new partner about my realist interpretation of quantum mechanics, she spontaneously referred to a story of that wonderful Danish storyteller, Hans Christian Andersen: The Emperor’s New Clothes. She was very surprised to hear I had actually produced a draft manuscript with the above-mentioned title (The Emperor Has No Clothes) on quantum electrodynamics which – after initially positive reactions – got turned down by two major publishers.[1] She advised me to stick to the original title and just give it another go. I might as well because the title is, obviously, also a bit of a naughty wink to one of Roger Penrose’s book.[2]

The ideas in this book are not all that easy to grasp – but they do amount to a full-blown realist interpretation of quantum mechanics, including both quantum electrodynamics (the theory of electrons and photons, and their interactions) and quantum chromodynamics – the theory of what goes on inside of a nucleus.[3] Where is gravity? And what about the weak force, and the new Higgs sector of what is commonly referred to as the Standard Model of physics? Don’t worry. We will talk about these too. Not to make any definite statements because we think science isn’t ready to make any definite statements about them. Why? Because we think it doesn’t make sense to analyze the weak force as a force. It’s just a different beast. Gravity is a different beast too: we will explore Einstein’s geometric interpretation of spacetime. As for the Higgs field, we think it is just an ugly placeholder in an equally ugly theory.

What ugly theory? Isn’t the Standard Model supposed to be beautiful? Sabine Hossenfelder[4] – writes the following about it in her latest book: “The Standard Model, despite its success, doesn’t get much love from physicists. Michio Kaku calls it “ugly and contrived,” Stephen Hawking says it’s “ugly and ad hoc,” Matt Strassler disparages it as “ugly and baroque,” Brian Greene complains that the standard model is “too flexible”, and Paul Davies thinks it “has the air of unfinished business” because “the tentative way in which it bundles together the electroweak and strong forces” is an “ugly feature.” I yet have to find someone who actually likes the standard model.”[5]

You may know Hossenfelder’s name. She recently highlighted work that doubts the rigor of the LIGO detections of gravitational waves.[6] I like it when scientists dare to question the award of a Nobel Prize. If any of what I write is true, then the Nobel Prize Committee has made a few premature awards over the past decades. Hossenfelder’s book explores the discontent with the Standard Model within the scientific community. Of course, the question is: what’s the alternative? That’s what this book is all about. You will be happy to hear that. You will be unhappy to hear that I am not to shy away from formulas and math. However, you should not worry: I am not going to pester you with gauge theory, renormalization, perturbation theory, transformations and what have you. Elementary high-school math is all you need. Reality is beautiful and complicated – but not that complicated: we can all understand it. 😊

[1] The pre-publication versions of this manuscript are date-stamped on http://vixra.org/abs/1901.0105.

[2] Roger Penrose, The Emperor’s New Mind, 1989.

[3] Physicists will note this is a rather limited definition of quantum chromodynamics. We will expand on it later.

[4] You may know her name. She recently highlighted work that doubs the rigor of the LIGO detections of gravitational waves. See: https://www.forbes.com/sites/startswithabang/2017/06/16/was-it-all-just-noise-independent-analysis-casts-doubt-on-ligos-detections. I like it when scientists dare to question a Nobel Prize. If any of what I write is true, then it’s obvious that it wouldn’t be the first time that the Nobel Prize Committee makes a premature award.

[5] Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray, 2018.

[6] See: https://www.forbes.com/sites/startswithabang/2017/06/16/was-it-all-just-noise-independent-analysis-casts-doubt-on-ligos-detections.

The virtuality of virtual particles

I’ve did what I promised to do – and that is to start posting on my other blog. On quantum chromodynamics, that is. But I think this paper deserves wider distribution. 🙂

The paper below probably sort of sums up my views on quantum field theory. I am not sure if I am going to continue to blog. I moved my papers to an academia.edu site and… Well… I think that’s about it. 🙂

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Bringing physics back to Quantum Physics: classical quantum theory

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Philosophy and Science: Dirac’s Principles

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The anomalous magnetic moment: classical calculations

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