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 = 2m*c*^{2}/*ħ*, or approximately 1.5527×10^{21} 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** = m_{γ}·* v*(with γ referring to the Lorentz factor) – in accordance with the (relativistically correct)

**F**= d

**p**/dt force law.

## Contents

## 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 *r*_{C} *= ħ*/m_{μ}*c* ≈ 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 *r*_{C} *= ħ*/m*c* formula follows from the kinematic model), we get a radius of the order of *r*_{C} *= ħ*/m_{p}*c* ≈ 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 *r*_{e} *=* α·*ħ*/m_{p}*c*) 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 quark–gluon 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 = h*f*) and Einstein’s mass-energy equivalence (E = m*c*^{2}): 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 m_{γ} = γm_{0} 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 m_{γ} in the ω = 2m*c*^{2}/*ħ* yields an equivalence with the Planck-Einstein relation ω = m_{γ}*c*^{2}/*ħ*. The electron can then be described as an oscillator (in two dimensions) whose natural frequency is given by the Planck-Einstein relation.^{[21]}

# Electrons as gluons?

**Preliminary note**: Since writing the post, I developed a more comprehensive paper. You can find it on my academia.edu site (click here). It’s a bit longer – and also more technical – than the post below. Have fun ! 🙂

According to common wisdom, we need to introduce a new charge – and, therefore, a new *force *– to explain why protons will stick together. But we have neutrons too, right? Can’t they serve as *glue*? Now *that*’s an idea. About 99.999866 per cent of helium on this planet consists of two protons and two neutrons: we write this isotope as ^{4}He. The only other *stable* isotope is ^{3}He, which consists of two protons and *one* neutron. Let me *google* this… This is what Wikipedia writes: “Within the nucleus, protons and neutrons are bound together through the nuclear force. *Neutrons are required for the stability of nuclei*, with the exception of the single-proton hydrogen atom.”[1]

So now we need to examine this glue: what is it? What’s the difference between a neutron and a proton? A proton is stable. Neutrons are only stable inside of a nucleus: free neutrons *decay*. Their mean lifetime is almost 15 minutes, so that’s almost *eternity *in atomic physics. *Almost*, but not quite: free neutrons are *transient *oscillations. Why are neutrons stable in a nucleus but not in free space? We think it’s the Planck-Einstein relation: two protons, two neutrons and two electrons – a helium atom, in other words – are stable because all of the angular momenta in the *oscillation *add up to (some multiple of) Planck’s (reduced) quantum of action. The angular momentum of a neutron in free space does not, so it has to fall apart in a (stable) proton and a (stable) electron – and then a neutrino which carries the remainder of the energy. Let’s jot it down:Let’s think about energy first. The neutron’s energy is about 939,565,420 eV. The proton energy is about 938,272,088 eV. The difference is 1,293,332 eV. That’s almost 1.3 MeV.[2] The electron energy gives us close to 0.511 MeV of that difference – so that’s only 40% – but its *kinetic *energy can make up for a lot of the remainder! We then have the neutrino to provide the change—the *nickel-and-dime*, so to speak.[3]

Is this *decay *reversible? It is: a proton can *capture *an electron and, somehow, *become *a neutron. It usually happens with proton-rich nuclei absorbing an inner atomic electron, usually from the K or L electron shell, which is why the process is referred to as K- or L-electron capture:Once again, we have a neutrino providing the *nickel-and-dime* to ensure energy conservation. It is written as the anti-particle of the neutrino in the neutron decay equation. Neutrinos and anti-neutrinos are neutral, so what’s the difference? The specialists in the matter say they have no idea and that a neutrino and an anti-neutrino might well be one and the same thing.[4] Hence, for the time being, we’ll effectively assume they’re one and the same thing: we might write both as ν_{e}. No mystery here—not for me, at least. Or not here and not right now, I should say: the neutrino is just a vehicle to ensure conservation of energy and momentum (linear and/or angular).

It is tempting to think of the proton as some kind of *atomic system *itself, or a positive *ion *to which we may add an electron so as to get a neutron. You’ll say: that’s the hydrogen atom, right? No. The hydrogen atom is much larger than a neutron: the Bohr radius of a hydrogen atom is about 0.53 *pico*meter (1 pm = 1´10^{–}^{12} m). In contrast, the radius of a neutron is of the order of 0.8 *femto*meter (1 fm = 1´10^{–}^{15} m), so that’s about 660 times smaller. While a neutron is much smaller, its energy (and, therefore, its mass) is significantly higher: the energy difference between a hydrogen atom and a neutron is about 0.78 MeV. That’s about 1.5 times the energy of an electron. The table below shows these interesting numbers.A good model of what a proton and a neutron actually *are*, will also need to explain why electron-positron pair production only happens when the photon is fired into a nucleus. The mainstream interpretation of this phenomenon is that the surplus kinetic energy needs to be absorbed by some heavy particle – the nucleus itself. My guts instinct tells me something else must be going on. Electron-positron pair production does seem to involve the *creation *of an electric charge out of energy. It puzzled Dirac (and many other physicists, of course) greatly.Let us think about sizes once more. If we try the mass of a proton (or a neutron—almost the same) in the formula for the Compton radius, we get this:That’s about 1/4 of the actual radius as measured in scattering experiments. We have a good rationale for calculating the Compton radius of a proton (or a neutron). It is based on the *Zitterbewegung *model for elementary particles: a pointlike charge whizzing around at the speed of light. For the electron, the charge is electric. For the proton or the neutron, we think of some *strong *charge and we, therefore, get a very different energy and, hence, a very different Compton radius.[5] However, a factor of 1/4 is encouraging but not good enough. If anything, it may indicate that a good model of a proton (and a neutron) should, besides some strong force, also incorporate the classical electric charge. It is difficult to think about this, because we think the pointlike electric charge has a radius itself: the *Thomson *or *classical *electron radius, which is equal to:This is about 3.5 times *larger *than the proton or neutron radius. It is even larger than the measured radius of the deuteron nucleus, which consists of a proton and a neutron bound together. That radius is about 2.1 fm. As mentioned above, this ‘back-of-the-envelope’ calculation of a Compton radius is encouraging, but a good model for a proton (and for a neutron) will need to explain these 1/4 or 3.5 factors.

What happens might be something like this: we fire an enormous amount of electromagnetic energy into a nucleus (the equivalent mass of the photon has to match the mass of the electron and the positron that’s being produced) and, hence, we destabilize the stable nucleus. However, Nature is strong. The strong force is strong. Some intermediate energy state emerges but Nature throws out the spanner in the works. The end result is that all can be analyzed, once again, in terms of the Planck-Einstein relation: we have stable particles, once again. [Of course, the positron finds itself in the anti-Universe and will, therefore, quickly disappear in the reverse process: electron-positron annihilation.]

But so that’s just a story right now. We need to develop it into a proper theory.

**Post scriptum**: We’ve calculated a Compton radius for the proton. If – in analogy with the electron model – we would (also) have a current inside, then we should be able to calculate that current. Let us limit ourselves to the electric current – because we don’t have much of an idea about what a strong current would represent. The circular electric current creates a magnetic moment. We got the right value for an electron:What do we get if we do a similar calculation for a pointlike charge moving around at the speed of light but in a much smaller loop – a loop measured in *femto*meter rather than picometer? The calculation below shows we get a similar result in terms of *structure *but note the result is expressed in terms of the *nuclear *magneton (m_{N}) which uses the proton mass, as opposed to the Bohr magneton, which uses the electron (rest) mass.Unsurprisingly, the actually measured value is different, and the difference is much larger than Schwinger’s a/2p fraction. To be precise, μ_{p} » 2.8·μ_{N}, so the *measured *value of the proton’s magnetic moment is almost three times that of its theoretical value. It should be no surprise to us – because we use a radius that’s 1/4 of what might be the actual radius of the loop. In fact, the measured value of the proton’s magnetic moment suggests the *actual *radius of the loop should be 2.8 times the theoretical Compton radius:Again, these results are not exact, but they’re encouraging: they encourage us to try to describe the proton in terms of some kind of hybrid model – something that mixes the classical electric charge with some strong charge. No need for QFT or virtual particles. 🙂

[1] https://en.wikipedia.org/wiki/Neutron.

[2] CODATA data gives a standard error in the measurements that is equal to 0.46 eV. Hence, the measurements are pretty precise.

[3] When you talk money, you need big and small denominations: banknotes versus coins. However, the role of coins could be played by photons too. Gamma-ray photons – produced by radioactive decay – have energies in the MeV order of magnitude, so they should be able to play the role of whatever change we need in an energy equation, right? Yes. You’re right. So there must be more to it. We see neutrinos whenever there is radioactive decay. Hence, we should probably associate them with that, but how exactly is a bit of a mystery. Note that the decay equation conserves linear, angular (spin) momentum and (electric) charge. What about the color charge? We’re not worried about the color charge here. Should we be worried? I don’t think so, but if you’d be worried, note that this rather simple decay equation does respect color conservation – regardless of your definition of what quarks or gluons might actually *be*.

[4] See the various articles on neutrinos on Fermi National Accelerator Laboratory (FNAL), such as, for example, this one: https://neutrinos.fnal.gov/mysteries/majorana-or-dirac/. The common explanation is that neutrinos and anti-neutrinos have opposite spin but that’s nonsensical: we can very well imagine one and the same particle with two spin numbers.

[5] See: Jean Louis Van Belle, *Who Needs Yukawa’s Wave Equation?*, 24 June 2019 (http://vixra.org/abs/1906.0384).

# Mass without mass

# 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 Charge Conservation Principle and Pair Production

The creation of an electron-positron pair out of a highly energetic photon – the most common example of pair production – is often presented as an example of how energy can be converted into *matter*. Vice versa, electron-positron annihilation then amounts to the *destruction *of matter. However, if John Wheeler’s concept of ‘mass without mass’ is correct – or if Schrödinger’s trivial solution to Dirac’s equation for an electron in free space (the *Zitterbewegung *interpretation of an electron) is correct – then what might actually be happening is probably simpler—but also far more intriguing.

John Wheeler’s intuitive ‘mass without mass’ idea is that matter and energy are just two sides of the same coin. That was Einstein’s intuition too: mass is just a measure of inertia—a measure of the resistance to a change in the state of motion. Energy itself is motion: the motion of a *charge*. Some force over some distance, and we associate a force with a *charge*. Not with mass. In this interpretation of physics, an electron is nothing but a pointlike charge whizzing about some center. It’s a charge caught in an electromagnetic oscillation. The pointlike charge itself has zero rest mass, which is why it moves about at the speed of light.[1]

This electron model is easy and intuitive. Developing a similar model for a *nucleon *– a proton or a neutron – is much more complicated because nucleons are held together by another force, which we commonly refer to as the strong force.

In regard to the latter, the reader should note that I am very hesitant to take the quark-gluon model of this strong force seriously. I entirely subscribe to Dirac’s rather skeptical evaluation of it:

“Now there are other kinds of interactions, which are revealed in high-energy physics and are important for the description of atomic nuclei. These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion. Theories of them have been set up and much developed and useful results obtained from them. But in the absence of equations of motion these theories cannot be presented as a logical development of the principles set up in this book. We are effectively in the *pre-Bohr era* with regard to these other interactions.”[2]

I readily admit he wrote this in 1967 (so that’s a *very *long time ago). He was reacting, most probably, to the invention of a new conservation law (the conservation of *strangeness*, as proposed by Gell-Mann, Nishijima, Pais and others) and the introduction of many other *ad hoc* QCD quantum numbers to explain why this or that disintegration path does or does not occur. It was all part of the Great Sense-Making Exercise at the time: how to explain the particle zoo?[3] In short, I am very reluctant to take the quark-gluon model of the strong force seriously.

However, I do acknowledge the experimental discovery of the fact that pairs of matter and anti-matter particles could be created out of highly energetic photons may well be the most significant discovery in post-WW II physics. Dirac’s preface to the 4th edition of the *Principles of Quantum Mechanics* summarized this as follows:

“In present-day high-energy physics, the creation and annihilation of charged particles is a frequent occurrence. A quantum electrodynamics which demands conservation of the number of charged particles is, therefore, out of touch with physical reality. So I have replaced it by a quantum electrodynamics which includes creation and annihilation of electron-positron pairs. […] It seems that the classical concept of an electron is no longer a useful model in physics, except possibly for elementary theories that are restricted to low-energy phenomena.”

Having said this, I think it’s useful to downplay Dr. Dirac’s excitement somewhat. Our world is governed by low-energy phenomena: if our Universe was created in a Big Bang – some extremely high-energy environment – then it happened 14 billion years or so ago, and the Universe has *cooled down* since. Hence, these high-energy experiments in labs and colliders are what they are: high-energy collisions followed by disintegration processes. They emulate the conditions of what might have happened in the first second – or the first minute, perhaps (surely *not *the first day or week or so) – after Creation.[4]

I am, therefore, a bit puzzled by Dr. Dirac’s sentiment. Why would he think the classical concept of an electron is no longer useful? An electron is a permanent fixture. We can create and destroy it in our high-energy colliders, but that doesn’t mean it’s no longer useful as a concept.

Pair production only happens when the photon is fired into a nucleus, and the generalization to ‘other’ bosons ‘spontaneously’ disintegrating into a particle and an anti-particle is outright pathetic. What happens is this: we fire an enormous amount of electromagnetic energy into a nucleus (the equivalent mass of the photon has to match the mass of the electron and the positron that’s being produced) and, hence, we destabilize the stable nucleus. However, Nature is strong. The strong force is strong. Some intermediate *energy state *emerges but Nature throws out the spanner in the works. The end result is that all can be analyzed, once again, in terms of the Planck-Einstein relation: we have stable particles, once again. [Of course, the positron finds itself in the anti-Universe and will, therefore, quickly disappear in the reverse process: electron-positron annihilation.]

No magic here. And – surely – no need for strange QCD quantum numbers.

Jean Louis Van Belle, 28 July 2019

[1] Erwin Schrödinger stumbled upon the *Zitterbewegung *interpretation of an electron when he was exploring solutions to Dirac’s wave equation for free electrons. It’s worth quoting Dirac’s summary of it: “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)

[2] P. A. M. Dirac, *The Principles of Quantum Mechanics*, Oxford University Press, 4th revised edition, Chapter XII (Quantum Electrodynamics), p. 312.

[3] Feynman’s 1963 *Lecture* on K-mesons (http://www.feynmanlectures.caltech.edu/III_11.html#Ch11-S5) is an excellent summary of the *state of affairs *at the time. The new colliders had, effectively, generated a ‘particle zoo’, and it had to be explained. We think physicists should first have acknowledged that these short-lived particles should, perhaps, not be associated with the idea of a (fundamental) particle: they’re unstable. Transients, at best. Many of them are just resonances.

[4] I use the term ‘Creation’ as an absolutely non-religious concept here: it’s just a synonym of the presumed ‘Big Bang’. To be very clear on this, I am rather appalled by semi-scientific accounts of the creation of our world in terms of the biblical week.

# The oscillator model, excited states, and electron-photon interactions

# Smoking Gun Physics

### The nature of the Higgs particle

The images below visualize what is generally referred to as the first ‘evidence’ for the Higgs boson: (1) two gamma rays emerging from the CERN LHC CMS detector, and (2) the tracks of four muons in the CERN LHC ATLAS detector. These tracks result from the collision between two protons that hit each other at a velocity of 99.99999 per cent of the speed of light – which corresponds to a combined energy of about 7 to 8 TeV.[1] That’s huge. After the ‘discovery’ of the Higgs particle, the LHC was shut down for maintenance and an upgrade, and the protons in the LHC can now be accelerated to energies up to 7 TeV – which amounts to 14 TeV when they crash into each other. However, the higher energy level only produced more of the same so far.[2]

We put ‘evidence’ and ‘discovery’ between inverted commas because the Higgs particle is (and, rest assured, will *forever* remain) a *ghost* particle only: we cannot* directly* observe it. Theoretical physicists and experimentalists agree these traces are just *signatures *of the long-awaited God particle. It was long-awaited indeed: the title of the six-page ‘leaflet’ explaining the award of the 2013 Nobel Prize in Physics to François Englert and Peter Higgs is: “*Here, at last!*”[3] The long wait for it – and CERN’s excellent media team – may explain why the Nobel Physics Committee and the Royal Swedish Academy of Sciences were so eager to award a Nobel Prize for this ! So we should ask ourselves: what’s the hype, and what are the physics? And do the physics warrant the hype?

The facts are rather simple. We cannot directly observe the Higgs particle because it is just like all of the other ‘particles’ that come out of these collisions: they are too short-lived to leave a* permanent* trace. Indeed, when two protons hit each other at these incredible velocities, then all that’s left is *debris* flying around. This debris quickly disintegrates into other more debris – until we’re left with what we’re used: *real *particles, like electrons or protons. Things that don’t disintegrate.

The energy of the *debris *(the gamma rays or the muons) coming out of ‘Higgs events’ tells us the energy of the Higgs particle must be about 125 GeV. Besides its mass, it does not seem to have any other properties: no spin, no electric charge. It is, therefore, known as a *scalar *boson. In everyday language, that means it is just some (real) number. Newton had already told us that mass, as a *measure of inertia*, is just some real positive number—and Einstein taught us energy and mass are equivalent.

Interpreting the facts is tough. I am just an amateur physicists and so my opinion won’t count for much. However, I can’t help feeling Higg’s theory just confirms the obvious. For starters, we should be very hesitant to use the term ‘particle’ for the Higgs boson because its lifetime is of the order of 10^{-22} s. Think of it as the time an electron needs to go from electron orbital to another. Even at the speed of light – which an object with a rest mass of 125 GeV/*c*^{2} cannot aspire to attain – a particle with such lifetime cannot travel more than a few *tenths *of a femtometer: about 0.3´10^{-15} m, to be precise. That’s not something you would associate it with the idea of a particle: a *resonance *in particle physics has the same lifetime.

That’s why we’ll never *see *the Higgs boson—just like we’ll never *see *the W^{±} and Z bosons whose mass it’s supposed to explain. Neither will none of us ever *see *a quark or a gluon: physicists tell us the *signals *that come out of colliders such as the LHC or, in the 1970s and 1980s, that came out of the PETRA accelerator in Hamburg, the Positron-Electron Project (PEP) at the Stanford National Accelerator Laboratory (SLAC), and the Super Proton-Antiproton Synchrotron at CERN, are *consistent *with the hypothesis that the strong and weak forces are *mediated *through particles known as bosons (force carriers) but – truth be told – the whole idea of forces being *mediated *by bosons is just what it is: a weird theory.

### Are virtual particles the successor to the *aether *theory?

Maybe we should first discuss the most obvious of all bosons: the photon. Photons are real. Of course, they are. They are, effectively, the particles of light. They are, in fact, the only bosons we can effectively *observe*. In fact, we’ve got a problem here: the only bosons we can effectively *observe* – photons – do *not *have all of the theoretical properties of a boson: as a spin-1 particle, the theoretical values for its angular momentum are ± *ħ* or 0. However, photons don’t have a zero-spin state. Never. This is one of the things in mainstream quantum mechanics that has always irked me. All courses in quantum mechanics spend like two or three chapters on why bosons and fermions are different (spin-one versus spin-1/2), but when it comes to the specifics – real-life stuff – then the only boson we actually know (the photon) turns out to *not *be a typical boson because it can’t have zero spin. [Physicists will, of course, say the most important property of bosons is that they you can keep piling bosons on top of bosons, and you can do that with photons. Bosons are supposed to like to be together, because we want to keep adding to the force without limit. But… Well… I have another explanation for that. It’s got to do with the fact that bosons don’t – or shouldn’t – carry charge. But I don’t want to start another digression on that. Not here.]

So photons – the only *real-life *bosons we’ve ever observed – aren’t typical bosons. More importantly, no course in physics has ever been able to explain why we’d need photons in the role of *virtual *particles. Why would an electron in some atomic orbital continuously exchange photons with the proton that holds it in its orbit? When you ask that question to a physicist, he or she will start blubbering about quantum field theory and other mathematical wizardry—but he or she will never give you a clear answer. I’ll come back to this in the next section of this paper.

I don’t think there is a clear answer. Worse, I’ve started to think the whole idea of some particle *mediating *a force is nonsense. It’s like the 19^{th}-century *aether *theory: we don’t need it. We don’t need it in electromagnetic theory: Maxwell’s Laws – augmented with the Planck-Einstein relation – will do. We also don’t need it to model the strong force. The *quark*–*gluon *model – according to which quarks change color all of the time – does *not *come with any simplification as compared to a simpler *parton *model:

- The quark-gluon model gives us (at least) two quarks[4], two anti-quarks and nine gluons, so that adds up to 13 different objects.
- If we just combine the idea of a parton – a pointlike carrier of
*properties*– with… Well… Its properties – the possible electric charges (±2/3 and ±1/3) and the possible color charges (red, green and blue) – we’ve got 12 partons, and such ‘parton model’ explains just as much.[5]

I also don’t think we need it to model the weak force. Let me be *very *clear about my intuition/sentiment/appreciation—whatever you want to call it:

**We don’t need a Higgs theory to explain why W/Z bosons have mass because I think W/Z bosons don’t exist: they’re a figment of our imagination.**

Why do we even need the concept of a *force *to explain why things fall apart? The world of unstable particles – *transient *particles as I call them – is a different realm altogether. Physicists will cry wolf here: CERN’s Super Proton-Antiproton Synchrotron produced evidence for W^{+}, W^{–} and Z bosons back in 1983, didn’t it?

No. The evidence is just the same as the ‘evidence’ for the Higgs boson: we produce a short-lived blob of energy which disintegrates in no time (10^{-22} s or 10^{-23} s is no time, really) and, for some reason no one really understands, we think of it as a force carrier: something that’s supposed to be very different from the other blobs of energy that emerge while it disintegrates into *jets *made up of other transients and/or resonances. The end result is always the same: the various blobs of energy further dis- and reintegrate as stable particles (think of protons, electrons and neutrinos[6]). There is no good reason to introduce a bunch of weird *flavor *quantum numbers to think of how such processes might actually occur. In reality, we have a very limited number of permanent fixtures (electrons, protons and photons), hundreds of *transients *(particles that fall apart) and thousands of resonances (excited states of the transient and non-transient stuff).

You’ll ask me: so what’s the difference between them then?

Stable particles respect the E = h·*f* = ħ·ω relation—and they do so *exactly*. For non-stable particles – transients – that relation is slightly off, and so they die. They die by falling apart in more stable configurations, until we are left with stable particles only. As for resonances, they are just that: some excited state of a stable or a non-stable particle. Full stop. No magic needed.[7]

### Photons as bosons

Photons are real and, yes, they carry energy. When an electron goes from one state to another (read: from one electron orbital to another), it will absorb or emit a photon. Photons make up light: visible light, low-energy radio waves, or high-energy X- and γ-rays. These waves carry energy and – when we look real close – they are made up of photons. So, yes, it’s the photons that carry the energy.

Saying they carry electromagnetic energy is something else than saying they carry electromagnetic *force* itself. A force acts on a charge: a photon carries no charge. If photons carry no charge, then why would we think of them as carrying the force?

I wrote I’ve always been irked by the fact that photons – again, the only *real-life *bosons we’ve ever observed – don’t have all of the required properties of the theoretical force-carrying particle physicists invented: the ‘boson’. If bosons exist, then the bosons we associate with the strong and weak force should also not carry any charge: color charge or… Well… What’s the ‘weak’ charge? Flavor? *Come on guys ! *Give us something we can believe in.

That’s one reason – for me, at least – why the idea of gluons and W/Z bosons is non-sensical. Gluons carry color charge, and W/Z bosons carry electric charge (except for the Z boson – but we may think of it as carrying both positive and negative charge). They shouldn’t. Let us quickly review what I refer to as a ‘classical’ quantum theory of light.[8]

If there is one quantum-mechanical rule that no one never doubts, it is that angular momentum comes in units of *ħ*: Planck’s (reduced) constant. When analyzing the electron orbitals for the simplest of atoms (the one-proton hydrogen atom), this rule amounts to saying the electron orbitals are separated by a amount of *physical* *action *that is equal to *h* = 2π·*ħ*. Hence, when an electron jumps from one level to the next – say from the second to the first – then the atom will lose one unit of *h*. The photon that is emitted or absorbed will have to pack that somehow. It will also have to pack the related energy, which is given by the Rydberg formula:To focus our thinking, let us consider the transition from the second to the first level, for which the 1/1^{2} – 1/2^{2} is equal 0.75. Hence, the photon energy should be equal to (0.75)·E* _{R}* ≈ 10.2 eV. Now, if the total action is equal to

*h*, then the cycle time T can be calculated as:

This corresponds to a wave train with a length of (3×10

^{8}m/s)·(0.4×10

^{-15}s) = 122 nm. That is the size of a large molecule and it is, therefore, much more reasonable than the length of the wave trains we get when thinking of transients using the supposed Q of an atomic oscillator.[9] In fact, this length is the wavelength of the light (λ =

*c*/

*f*=

*c*·T = h·

*c*/E) that we would associate with this photon energy.

We should quickly insert another calculation here. If we think of an electromagnetic oscillation – as a beam or, what we are trying to do here, as some *quantum* – then its energy is going to be proportional to (a) the square of the amplitude of the oscillation – and we are *not *thinking of a quantum-mechanical amplitude here: we are talking the amplitude of a *physical* wave here – and (b) the square of the frequency. Hence, if we write the amplitude as *a* and the frequency as ω, then the energy should be equal to E = k·*a*^{2}·ω^{2}, and the k in this equation is just a proportionality factor.

However, relativity theory tells us the energy will have some equivalent mass, which is given by Einstein’s mass-equivalence relation: E = m·*c*^{2}. This equation tells us the energy of a photon is proportional to its mass, and the proportionality factor is *c*^{2}. So we have two proportionality relations now, which (should) give us the same energy. Hence, k·*a*^{2}·ω^{2} must be equal to m·*c*^{2}, *somehow*.

How should we *interpret *this? It is, obviously, very tempting to equate k and m, but we can only do this if *c*^{2} is equal to *a*^{2}·ω^{2} or – what amounts to the same – if *c *= *a*·ω. You will recognize this as a tangential velocity formula. The question is: the tangential velocity of *what*? The *a *in the E = k·*a*^{2}·ω^{2} formula that we started off with is an amplitude: why would we suddenly think of it as a radius now? Because our photon is circularly polarized. To be precise, its angular momentum is +*ħ* or –*ħ*. There is no zero-spin state. Hence, if we think of this classically, then we will associate it with circular polarization.

However, these properties do not make it a *boson* or, let me be precise, these properties do not make it a *virtual *particle. Again, I’ve haven’t seen a textbook – advanced or intermediate level – that answers this simple question: why would an electron in some *stable *atomic orbital – it does not emit or absorb any energy – continuously exchange *virtual* photons with the proton that holds it in its orbit?

How would that photon look like? It would have to have some energy, right? And it would have to pack to physical action, right? Why and how would it take that energy – or that action (I like the German *Wirkung *much better in terms of capturing that concept) – away from the electron orbital? In fact, the *idea *of an electron orbital combines the idea of the electron and the proton—and their mutual attraction. The physicists who imagine those virtual photons are making a philosophical category mistake. We think they’re making a similar mistake when advancing the *hypothesis *of gluons and W/Z bosons.

# Conclusions

We think the idea of *virtual *particles, gauge bosons and/or force-carrying particles in general is superfluous. The whole idea of bosons mediating forces resembles 19th century *aether *theory: we don’t need it. The implication is clear: if that’s the case, then we also don’t need gauge theory and/or quantum field theory.

Jean Louis Van Belle, 21 July 2019

[1] We took this from the above-mentioned leaflet. A proton has a *rest* energy of 938,272 eV, more or less. An energy equal to 4 TeV (the *tera*– prefix implies 12 zeroes) implies a Lorentz factor that is equal to γ = E/E_{0} = 4´10^{12}/938,272 » 1´10^{6}. Now, we know that 1 – β^{2} = *c*^{2}/*c*^{2} – *v*^{2}/*c*^{2} = 1/γ^{2} = 1/γ^{2} » 1´10^{-12}. The square root of that is of the order of a *millionth*, so we get the same order of magnitude.

[2] To be fair, the high-energy collisions also resulted in the production of some more short-lived ‘particles’, such as new variants of *bottomonium*: mesons that are supposed to consist of a *bottom *quark and its anti-matter counterpart.

[3] See: https://www.nobelprize.org/uploads/2018/06/popular-physicsprize2013-1.pdf. Higgs’ theory itself – on how gauge bosons can acquire non-zero masses – goes back to 1964 and was put forward by three individual research groups. See: https://en.wikipedia.org/wiki/1964_PRL_symmetry_breaking_papers.

[4] We write *at least *because we are only considering *u* and *d* quarks here: the constituents of all stable or fairly stable matter (protons and neutrons, basically).

[5] See: Jean Louis Van Belle, *A Realist Interpretation of QCD*, 16 July 2019.

[6] If we think of energy as the *currency *of the Universe, then you should think of protons and electrons as bank notes, and neutrinos as the coins: they provide the *change*.

[7] See: Jean Louis Van Belle, *Is the Weak Force a Force?*, 19 July 2019.

[8] This is a very much abbreviated summary. For a more comprehensive analysis, see: Jean Louis Van Belle, *A Classical Quantum Theory of Light*, 13 June 2019.

[9] In one of his *Lectures* (I-32-3), Feynman thinks about the Q of a sodium atom, which emits and absorbs sodium light, of course. Based on various assumptions – assumption that make sense in the context of the blackbody radiation model but *not *in the context of the Bohr model – he gets a Q of about 5×10^{7}. Now, the frequency of sodium light is about 500 THz (500×10^{12 }oscillations per second). Hence, the *decay time *of the radiation is of the order of 10^{–}^{8} seconds. So that means that, after 5×10^{7} oscillations, the amplitude will have died by a factor 1/*e* ≈ 0.37. That seems to be very short, but it still makes for 5 million oscillations and, because the wavelength of sodium light is about 600 nm (600×10^{–9 }meter), we get a wave train with a considerable length: (5×10^{6})·(600×10^{–9 }meter) = 3 meter. *Surely You’re Joking, Mr. Feynman!* A photon with a length of 3 meter – or longer? While one might argue that relativity theory saves us here (relativistic length contraction should cause this length to reduce to zero as the wave train zips by at the speed of light), this just doesn’t feel right – especially when one takes a closer look at the assumptions behind.

# Is the weak force a force?

# 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. 🙂

# Realist interpretations of QM…

One of the readers of this blog asked me what I thought of the following site: Rational Science (https://www.youtube.com/channel/UC_I_L6pPCwxTgAH7yutyxqA). I watched it – for a brief while – and I must admit I am thoroughly disappointed by it. I think it’s important enough to re-post what I posted on this YouTube channel itself:

“I do believe there is an element of irrationality in modern physics: a realist interpretation of quantum electrodynamics is possible but may not gain acceptance because religion and other factors may make scientists somewhat hesitant to accept a common-sense explanation of things. The mystery needs to be there, and it needs to be protected – somehow. Quantum mechanics may well be the only place where God can hide – in science, that is.

But – in his attempt to do away with the notion of God – Bill Gaede takes things way too far – and so I think he errs on the other side of the spectrum. Mass, energy and spacetime are essential categories of the mind (or concepts if you want) to explain the world. Mass is a measure of inertia to a change in the state of motion of an object, kinetic energy is the energy of motion, potential energy is energy because of an object’s position in spacetime, etcetera. So, yes, these are concepts – and we need these concepts to explain what we human beings refer to as ‘the World’. Space and time are categories of the mind as well – philosophical or mathematical concepts, in other words – but they are related and well-defined.

In fact, space and time define each other also because the primordial idea of motion implies both: the idea of motion implies we imagine something moving in space and in time. So that’s space-time, and it’s a useful idea. That also explains why time goes in one direction only. If we’d allow time to reverse, then we’d also an object to be in two places at the same time (if an object can go back in time, then it can also go back to some other place – and so then it’s in two places at the same time). This is just one example where math makes sense of physical realities – or where our mind meets ‘the World’.

When Bill Gaede quotes Wheeler and other physicists in an attempt to make you feel he’s on the right side of history, he quotes him very selectively. John Wheeler, for example, believed in the idea of ‘mass’ – but it was ‘mass without mass’ for him: the mass of an object was the equivalent mass of the object’s energy. The ideas of Wheeler have been taken forward by a minority of physicists, such as David Hestenes and Alexander Burinskii. They’ve developed a fully-fledged electron model that combines wave and particle characteristics. It effectively does away with all of the hocus-pocus in QED – which Bill Gaede criticizes, and rightly so.

In short, while it’s useful to criticize mainstream physics as hocus-pocus, Bill Gaede is taking it much too far and, unfortunately, gives too much ammunition to critics to think of people like us – amateur physicists or scientists who try to make sense of it all – as wackos or crackpots. Math is, effectively, descriptive but, just like anything else, we need a language to describe stuff, and math is the language in which we describe actual physics. Trying to discredit the mathematical approach to science is at least as bad – much worse, actually – than attaching too much importance to it. Yes, we need to remind ourselves constantly that we are describing something physical, but we need concepts for that – and these concepts are mathematical.

PS: Bill Gaede also has very poor credentials, but you may want to judge these for yourself: https://en.wikipedia.org/wiki/Bill_Gaede. These poor credentials do not imply that his views are automatically wrong, but it does introduce an element of insincerity. In short, watch what you’re watching and always check sources and backgrounds when googling for answers to questions, especially when you’re googling for answers to fundamental questions ! 🙂

# Moving on…

This is it, folks ! I am moving on ! It was nice camping out here. 🙂

This has been a very interesting journey for me. I wrote my first post in October 2013, so that’s almost five years ago. As mentioned in the ‘*About*‘ page, I started writing this blog because — with all those breakthroughs in science (some kind of experimental verification of what is referred to as the Higgs field in July 2012 and, more recently, the confirmation of the reality of gravitational waves in 2016 by Caltech’s LIGO Lab) — I felt I should make an honest effort to try to understand what it was all about.

Despite all of my efforts (including enrolling in MIT’s edX QM course, which I warmly recommend as an experience, especially because it’s for free), I haven’t moved much beyond quantum electrodynamics (QED). Hence, that Higgs field is a still a bit of a mystery to me. In any case, the summaries I’ve read about it say it’s just some scalar field. So that’s not very exciting: mass is some number associated with some position in spacetime. That’s nothing new, right?

In contrast, I am very enthusiastic about the LIGO Lab discovery. Why? Because it confirms Einstein was right all along.

If you have read any of my posts, you will know I actually disagree with Feynman. I have to thank him for his *Lectures *— and I would, once again, like to thank Michael Gottlieb and Rudolf Pfeiffer, who have worked for decades to get those *Lectures online* — but my explorations did confirm that guts feeling I had deep inside when starting this journey: the complexity in the quantum-mechanical framework does not match the intuition that, if the theory 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. And the interference of a photon with itself in the Mach-Zehnder interference experiment has a classical explanation too. The ‘zero state’ of a photon – or its zero *states* (plural), I should say – are the linear components of the circular polarization. In fact, I really wish someone would have gently told me that an actual beam splitter changes the polarization of light. I could have solved the Mach-Zehnder puzzle with that information like a year ago.]

This will probably sound like Chinese to you, so let me translate it: there is no mystery. Not in the QED sector of the Standard Model, at least. All can be explained by simple geometry and the idea of a naked charge: something that has no other property but its electric charge and – importantly – some tiny radius, which is given by the fine-structure constant (the ratio becomes a distance if we think of the electron’s Compton radius as a natural (distance) unit). So the meaning of God’s Number is clear now: there is nothing miraculous about it either. Maxwell’s equations combined with the Planck-Einstein Law (E = h·*f*) are all we need to explain the whole QED sector. No hocus-pocus needed. The elementary wavefunction exp(±*i*·θ) = exp(±ω·t) = exp[±(E/ħ)·t] represents an equally elementary oscillation. Physicists should just think some more about the sign convention and, more generally, think some more about Occam’s Razor Principle when modeling their problems. 🙂

Am I a crackpot? Maybe. I must be one, because I think the academics have a problem, not me. So… Well… That’s the definition of a crackpot, isn’t it? 🙂 It feels weird. Almost all physicists I got in touch with – spare two or three (I won’t mention their names because they too don’t quite know what to do with me) – are all stuck in their *Copenhagen *interpretation of quantum mechanics: reality is some kind of black box and we’ll never understand it the way we would want to understand it. Almost none of them is willing to think outside of the box. I blame vested interests (we’re talking Nobel Prize stuff, unfortunately) and Ivory Tower culture.

In any case, I found the answers to the questions I started out with, and I don’t think the academics I crossed (s)words with have found that peace of mind yet. So if I am a crackpot, then I am a happy one. 😊

The Grand Conclusion is that the Emperor is not wearing any clothes. Not in the QED sector, at least. In fact, I think the situation is a lot worse. The Copenhagen interpretation of quantum mechanics feels like a Bright Shining Lie. [Yes, I know that’s an ugly reference.] But… Yes. Just mathematical gimmicks to entertain students – and academics ! Of course, I can appreciate the fact that Nobel Prizes have been awarded and that academic reputations have to be upheld — posthumously or… I would want to write ‘humously’ here but that word doesn’t exist so I should replace it by ‘humorously’. 🙂 […] OK. Poor joke. 🙂

Frankly, it is a sad situation. Physics has become the domain of hype and canonical nonsense. To the few readers who have been faithful followers (this blog attracted about 154,034 visitors so far which is — of course — close to nothing), I’d say: think for yourself. Honor Boltzman’s spirit: “*Bring forward what is true. Write it so that it is clear. Defend it to your last breath.*” I actually like another quote of him too: “If you are out to describe the truth, leave elegance to the tailor.” But that’s *too *rough, isn’t it? And then I am also not sure he really said that. 🙂

Of course, QCD is another matter altogether — because of the non-linearity of the force(s) involved, and the multiplication of ‘colors’ **— **but my research over the past five years (longer than that, actually) have taught me that there is no ‘deep mystery’ in the QED sector. All is logical – including the meaning of the fine-structure constant: that’s just the radius of the naked charge expressed in natural units. All the rest can be derived. And 99% of what you’ll read or *google* about quantum mechanics is about QED: perturbation theory, propagators, the quantized field, etcetera to talk about photons and electrons, and their interactions. If you have a good idea about what an electron and a photon actually *are*, then you do *not* need *anything *of that to understand QED.

In short, quantum electrodynamics – as a theory, and in its current shape and form – is 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*. All of the weirdness of Nature is, therefore, in this weird description of the fields: gauge theories, Feynman diagrams, quantum field theory, etcetera. And the common-sense is right there: right in front of us. It’s easy and elegant: a plain common-sense interpretation of quantum mechanics — which, I should remind the reader, is based on Erwin Schrödinger’s trivial solution for Dirac’s wave equation for an electron in free space.

So is no one picking this up? Let’s see. Truth cannot be hidden, right? Having said that, I must admit I have been very surprised by the rigidity of thought of academics (which I know all too well from my experience as a PhD student in economics) in this domain. If math is the queen of science, then physics is the king, right? Well… Maybe not. The brightest minds seem to have abandoned the field.

But I will stop my rant here. I want to examine the QCD sector now. What theories do we have for the non-linear force(s) that keep(s) protons together? What explains electron capture by a proton—turning it into a neutron in the process? What’s the *nature *of neutrinos? How should we think of all these intermediary particles—which are probably just temporary *resonances* rather than permanent fixtures?

My new readingeinstein.blog will be devoted to that. I think I’ll need some time to post my first posts (pun intended)—but… Well… We’ve started this adventure and so I want to get to the next destination. It’s a mind thing, right? 🙂

# Bringing physics back to Quantum Physics: classical quantum theory

# God’s Number explained

My posts on the fine-structure constant – God’s Number as it is often referred to – have always attracted a fair amount of views. I think that’s because I have always tried to clarify this or that relation by showing *how and why exactly *it pops us in this or that formula (e.g. Rydberg’s energy formula, the ratio of the various radii of an electron (Thomson, Compton and Bohr radius), the coupling constant, the anomalous magnetic moment, etcetera), as opposed to what most seem to try to do, and that is to further mystify it. You will probably not want to search through all of my writing so I will just refer you to my summary of these efforts on the viXra.org site: “*Layered Motions: the Meaning* *of the Fine-Structure Constant.*”

However, I must admit that – till now – I wasn’t quite able to answer this very simple question: what *is* that fine-structure constant? Why *exactly *does it appear as a scaling constant or a coupling constant in almost any equation you can think of but *not *in, say, Einstein’s mass-energy equivalence relation, or the *de Broglie *relations?

I finally have a final answer (pun intended) to the question, and it’s surprisingly easy: it is the radius of the naked charge in the electron expressed in terms of the natural distance unit that comes out of our realist interpretation of what an electron actually is. [For those who haven’t read me before, this realist interpretation is based on Schrödinger’s discovery of the *Zitterbewegung *of an electron.] That natural distance unit is the *Compton *radius of the electron: it is the effective radius of an electron as measured in inelastic collisions between high-energy photons and the electron. I like to think of it as a quantum of space in which interference happens but you will want to think that through for yourself.* *

The point is: that’s it. That’s all. All the other calculations follow from it. Why? It would take me a while to explain that but, if you carefully look at the logic in my classical calculations of the anomalous magnetic moment, then you should be able to understand why these calculations are somewhat more fundamental than the others and why we can, therefore, get everything else out of them. 🙂

**Post scriptum**: I quickly checked the downloads of my papers on Phil Gibbs’ site, and I am extremely surprised my very first paper (the quantum-mechanical wavefunction as a gravitational wave) of mine still gets downloads. To whomever is interested in this paper, I would say: the realist interpretation we have been pursuing – based on the Zitterbewegung model of an electron – is based on the idea of a naked charge (with zero rest mass) orbiting around some center. The energy in its motion – a perpetual current ring, really – gives the electron its (equivalent) mass. That’s just Wheeler’s idea of ‘mass without mass’. But the force is *definitely not* gravitational. It cannot be. The force has to grab onto something, and all it can grab onto here is that naked charge. The force is, therefore, electromagnetic. It must be. I now look at my very first paper as a first immature essay. It did help me to develop some basic intuitive ideas on what any realist interpretation of QM should look like, but the quantum-mechanical wavefunction has nothing to do with gravity. Quantum mechanics is electromagnetics: we just add the quantum. The idea of an elementary cycle. Gravity is dealt with by general relativity theory: energy – or its equivalent mass – bends spacetime. That’s very significant, but it doesn’t help you when analyzing the QED sector of physics. I should probably pull this paper of the site – but I won’t. Because I think it shows where I come from: very humble origins. 🙂

# Philosophy and Science: Dirac’s Principles

# Philosophy and Physics

# The anomalous magnetic moment: classical calculations

# The electron as a harmonic electromagnetic oscillator

# Interpreting quantum mechanics

My book is moving forward. I just produced a very first promotional video. Have a look and let me know what you think of it ! 🙂