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).

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.