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 4He. The only other stable isotope is 3He, 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:F A1Let’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:F A2Once 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 νe. 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 picometer (1 pm = 1´1012 m). In contrast, the radius of a neutron is of the order of 0.8 femtometer (1 fm = 1´1015 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.tableA 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:F1That’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:F2This 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:FE1What 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 femtometer 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 (mN) which uses the  proton mass, as opposed to the Bohr magneton, which uses the electron (rest) mass.FE 2Unsurprisingly, the actually measured value is different, and the difference is much larger than Schwinger’s a/2p fraction. To be precise, μp » 2.8·μN, 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:F E3Again, 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).

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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.

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/c2 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 19th-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 quarkgluon model – according to which quarks change color all of the time – does not come with any simplification as compared to a simpler parton model:

  1. 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.
  2. 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:Formula 1To focus our thinking, let us consider the transition from the second to the first level, for which the 1/12 – 1/22 is equal 0.75. Hence, the photon energy should be equal to (0.75)·ER ≈ 10.2 eV. Now, if the total action is equal to h, then the cycle time T can be calculated as:
Formula 2This corresponds to a wave train with a length of (3×108 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·a2·ω2, 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·c2. This equation tells us the energy of a photon is proportional to its mass, and the proportionality factor is c2. So we have two proportionality relations now, which (should) give us the same energy. Hence, k·a2·ω2 must be equal to m·c2, somehow.

How should we interpret this? It is, obviously, very tempting to equate k and m, but we can only do this if c2 is equal to a2·ω2 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·a2·ω2 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/E0 = 4´1012/938,272 » 1´106. Now, we know that 1 – β2 = c2/c2v2/c2 = 1/γ2 = 1/γ2 » 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 5×107. Now, the frequency of sodium light is about 500 THz (500×1012 oscillations per second). Hence, the decay time of the radiation is of the order of 108 seconds. So that means that, after 5×107 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: (5×106)·(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.