I just produced a first draft of the Metaphysics page of my new physics site. It does not only deal with the fundamental concepts we have been developing but – as importantly, if not more – it also offers some thoughts on all of the unanswered questions which, when trying to do science and be logical, are at least as important as the questions we do consider to be solved. Click the link or the tab. Enjoy ! 🙂 As usual, feedback is more than welcome!

# Tag: proton model

# A theory of matter-particles

**Pre-scriptum (PS)**, added on 6 March 2020: The ideas below also naturally lead to a theory about what a neutrino might actually be. As such, it’s a complete ‘alternative’ Theory of Everything. I uploaded the basics of such theory on my academia.edu site. For those who do not want to log on to academia.edu, you can also find the paper on my author’s page on Phil Gibb’s site.

**Text:**

We were rather tame in our last paper on the oscillator model of an electron. We basically took some philosophical distance from it by stating we should probably only think of it as a *mathematical equivalent *to Hestenes’ concept of the electron as a superconducting loop. However, deep inside, we feel we should *not *be invoking Maxwell’s laws of electrodynamics to explain what a proton and an electron might actually *be*. The basics of the ring current model can be summed up in one simple equation:

*c* = *a*·ω

This is the formula for the tangential velocity. Einstein’s mass-energy equivalence relation and the Planck-Einstein relation explain everything else[1], as evidenced by the fact that we can immediately derive the Compton radius of an electron from these three equations, as shown below:The reader might think we are just ‘casually connecting formulas’ here[2] but we feel we have a full-blown theory of the electron here: simple and consistent. The geometry of the model is visualized below. We think of an electron (and a proton) as consisting of a pointlike elementary charge – pointlike but *not* *dimensionless***[3]** – moving about at (*nearly*) the speed of light around the center of its motion.

The relation works perfectly well for the electron. However, when applying the *a* = *ħ*/m*c* radius formula to a proton, we get a value which is about 1/4 of the *measured *proton radius: about 0.21 fm, as opposed to the 0.83-0.84 fm charge radius which was established by Professors Pohl, Gasparan and others over the past decade.[4] In our papers on the proton radius[5], we motivated the 1/4 factor by referring to the energy equipartition theorem and assuming energy is, somehow, equally split over electromagnetic field energy and the kinetic energy in the motion of the *zbw *charge. However, the reader must have had the same feeling as we had: these assumptions are rather *ad hoc*. We, therefore, propose something more radical:

When considering systems (e.g. electron orbitals) and excited states of particles, angular momentum comes in units (nearly) equal to *ħ*, but when considering the internal structure of elementary particles, (orbital) angular momentum comes in an integer fraction of ħ. This fraction is 1/2 for the electron[6] and 1/4 for the proton.

Let us write this out for the proton radius:What are the implications for the assumed centripetal force keeping the elementary charge in motion? The centripetal acceleration is equal to *a*_{c} = *v*_{t}^{2}/*a* = *a*·ω^{2}. It is probably useful to remind ourselves how we get this result so as to make sure our calculations are relativistically correct. The position vector ** r** (which describes the position of the

*zbw*charge) has a horizontal and a vertical component:

*x*=

*a*·cos(ωt) and

*y*=

*a*·sin(ωt). We can now calculate the two components of the (tangential) velocity vector

**= d**

*v***/dt as**

*r**v*

_{x}= –

*a*·ω·sin(ωt) and

*v*

_{y}

*y*= –

*a*· ω·cos(ωt) and, in the next step, the components of the (centripetal) acceleration vector

**:**

*a*_{c}*a*

_{x}= –

*a*·ω

^{2}·cos(ωt) and

*a*

_{y}= –

*a*·ω

^{2}·sin(ωt). The magnitude of this vector is then calculated as follows:

*a*_{c}^{2} = *a _{x}*

^{2}+

*a*

_{y}^{2}=

*a*

^{2}·ω

^{4}·cos

^{2}(ωt) +

*a*

^{2}·ω

^{4}·sin

^{2}(ωt) =

*a*

^{2}·ω

^{4}⇔

*a*

_{c}=

*a*·ω

^{2}=

*v*

_{t}

^{2}/

*a*

Now, Newton’s force law tells us that the magnitude of the centripetal force will be equal to:

F = m_{γ}·*a*_{c} = m_{γ}·*a*·ω^{2}

As usual, the m_{γ} factor is, once again, the *effective mass *of the *zbw *charge as it *zitters *around the center of its motion at (nearly) the speed of light: it is *half *the electron mass.[7] If we denote the centripetal force inside the electron as F_{e}, we can relate it to the electron mass m_{e} as follows:Assuming our logic in regard to the *effective *mass of the *zbw *charge inside a proton is also valid – and using the 4E = *ħ*ω and *a *= ħ/4m*c* relations – we get the following equation for the centripetal force inside of a proton:

How should we think of this? In our oscillator model, we think of the centripetal force as a restoring force. This force depends linearly on the displacement from the center and the (linear) proportionality constant is usually written as k. Hence, we can write F_{e} and F_{p} as F_{e} = -k_{e}*x* and F_{p} = -k_{p}*x* respectively. Taking the ratio of both so as to have an idea of the respective strength of both forces, we get this:

The ** a_{p}** and

**are acceleration vectors – not the radius. The equation above seems to tell us that the centripetal force inside of a proton gives the**

*a*_{e}*zbw*charge inside – which is nothing but the elementary charge, of course – an acceleration that is

*four*times that of what might be going on inside the electron.

Nice, but how meaningful are these relations, really? If we would be thinking of the centripetal or restoring force as modeling some *elasticity *of spacetime – the *guts *intuition behind far more complicated string theories of matter – then we may think of distinguishing between a *fundamental *frequency and higher-level harmonics or overtones.[8] We will leave our reflections at that for the time being.

We should add one more note, however. We only talked about the electron and the proton here. What about other particles, such as neutrons or mesons? We do *not *consider these to be elementary because they are not stable: we think they are not stable because the Planck-Einstein relation is slightly *off*, which causes them to disintegrate into what we’ve been trying to model here: stable stuff. As for the process of their disintegration, we think the approach that was taken by Gell-Man and others[9] is not productive: inventing new quantities that are supposedly being conserved – such as strangeness – is… Well… As strange as it sounds. We, therefore, think the concept of quarks confuses rather than illuminates the search for a truthful theory of matter.

Jean Louis Van Belle, 6 March 2020

[1] In this paper, we make abstraction of the anomaly, which is related to the *zbw *charge having a (tiny) spatial dimension.

[2] We had a signed contract with the IOP and WSP scientific publishing houses for our manuscript on a realist interpretation of quantum mechanics (https://vixra.org/abs/1901.0105) which was shot down by this simple comment. We have basically stopped tried convincing mainstream academics from that point onwards.

[3] See footnote 1.

[4] See our paper on the proton radius (https://vixra.org/abs/2002.0160).

[5] See reference above.

[6] The reader may wonder why we did not present the ½ fraction is the first set of equations (calculation of the electron radius). We refer him or her to our previous paper on the effective mass of the *zbw *charge (https://vixra.org/abs/2003.0094). The 1/2 factor appears when considering *orbital *angular momentum only.

[7] The reader may not be familiar with the concept of the effective mass of an electron but it pops up very naturally in the quantum-mechanical analysis of the linear motion of electrons. Feynman, for example, gets the equation out of a quantum-mechanical analysis of how an electron could move along a line of atoms in a crystal lattice. See: Feynman’s *Lectures*, Vol. III, Chapter 16: *The Dependence of Amplitudes on Position *(https://www.feynmanlectures.caltech.edu/III_16.html). We think of the effective mass of the electron as the relativistic mass of the *zbw *charge as it whizzes about at nearly the speed of light. The rest mass of the *zbw *charge itself is close to – but also not quite equal to – zero. Indeed, based on the measured anomalous magnetic moment, we calculated the *rest *mass of the *zbw *charge as being equal to about 3.4% of the electron rest mass (https://vixra.org/abs/2002.0315).

[8] For a basic introduction, see my blog posts on *modes *or on music and physics (e.g. https://readingfeynman.org/2015/08/08/modes-and-music/).

[9] See, for example, the analysis of kaons (K-mesons) in Feynman’s *Lectures*, Vol. III, Chapter 11, section 5 (https://www.feynmanlectures.caltech.edu/III_11.html#Ch11-S5).

# The Mystery Wallahs

I’ve been working across Asia – mainly South Asia – for over 25 years now. You will google the exact meaning but my definition of a *wallah *is a someone who deals in something: it may be a street vendor, or a handyman, or anyone who brings something new. I remember I was one of the first to bring modern mountain bikes to India, and they called me a *gear wallah*—because they were absolute fascinated with the number of gears I had. [Mountain bikes are now back to a 2 by 10 or even a 1 by 11 set-up, but I still like those three *plateaux *in front on my older bikes—and, yes, my collection is becoming way too large but I just can’t do away with it.]

Any case, let me explain the title of this post. I stumbled on the work of the research group around Herman Batelaan in Nebraska. *Absolutely fascinating !* Not only did they actually do the electron double-slit experiment, but their ideas on an actual Stern-Gerlach experiment with electrons are quite interesting: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1031&context=physicsgay

I also want to look at their calculations on momentum exchange between electrons in a beam: https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012007.

Outright fascinating. Brilliant ! […]

It just makes me wonder: why is the outcome of this 100-year old battle between mainstream hocus-pocus and real physics so undecided?

I’ve come to think of mainstream physicists as peddlers in mysteries—whence the title of my post. It’s a tough conclusion. Physics is supposed to be the King of Science, right? Hence, we shouldn’t doubt it. At the same time, it is kinda comforting to know the battle between truth and lies rages everywhere—including inside of the King of Science.

JL

# 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).