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:F1The 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.

Picture1

The relation works perfectly well for the electron. However, when applying the a = ħ/mc 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:F2What are the implications for the assumed centripetal force keeping the elementary charge in motion? The centripetal acceleration is equal to ac = vt2/a = a·ω2. 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 v = dr/dt as vx = –a·ω·sin(ωt) and vy y = –a· ω·cos(ωt) and, in the next step, the components of the (centripetal) acceleration vector ac: ax = –a·ω2·cos(ωt) and ay = –a·ω2·sin(ωt). The magnitude of this vector is then calculated as follows:

ac2 = ax2 + ay2a2·ω4·cos2(ωt) + a2·ω4·sin2(ωt) = a2·ω4ac = a·ω2 = vt2/a

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

F = mγ·ac = mγ·a·ω2

As usual, the mγ 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 Fe, we can relate it to the electron mass me as follows:F3Assuming our logic in regard to the effective mass of the zbw charge inside a proton is also valid – and using the 4E = ħω and a = ħ/4mc relations – we get the following equation for the centripetal force inside of a proton:
F4How 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 Fe and Fp as Fe = -kex and Fp = -kpx respectively. Taking the ratio of both so as to have an idea of the respective strength of both forces, we get this:F5

The ap and ae are acceleration vectors – not the radius. The equation above seems to tell us that the centripetal force inside of a proton gives the 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 ultimate electron model

A rather eminent professor in physics – who has contributed significantly to solving the so-called ‘proton radius puzzle’ – advised me to not think of the anomalous magnetic moment of the electron as an anomaly. It led to a breakthrough in my thinking of what an electron might actually be. The fine-structure constant should be part and parcel of the model, indeed. Check out my last paper ! I’d be grateful for comments !

I know the title of this post sounds really arrogant. It is what it is. Whatever brain I have has been thinking about these issues consciously and unconsciously for many years now. It looks good to me. When everything is said and done, the function of our mind is to make sense. What’s sense-making? I’d define sense-making as creating consistency between (1) the structure of our ideas and theories (which I’ll conveniently define as ‘mathematical’ here) and (2) what we think of as the structure of reality (which I’ll define as ‘physical’).

I started this blog reading Penrose (see the About page of this blog). And then I just put his books aside and started reading Feynman. I think I should start re-reading Penrose. His ‘mind-physics-math’ triangle makes a lot more sense to me now.

JL

PS: I agree the title of my post is excruciatingly arrogant but – believe me – I could have chosen an even more arrogant title. Why? Because I think my electron model actually explains mass. And it does so in a much more straightforward manner than Higgs, or Brout–Englert–Higgs, or Englert–Brout–Higgs–Guralnik–Hagen–Kibble, Anderson–Higgs, Anderson–Higgs–Kibble, Higgs–Kibble, or ABEGHHK’t (for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and ‘t Hooft) do. [I am just trying to attribute the theory here using the Wikipedia article on it.] 

Surely You’re Joking, Mr Feynman !

I think I cracked the nut. Academics always throw two nasty arguments into the discussion on any geometric or physical interpretations of the wavefunction:

  1. The superposition of wavefunctions is done in the complex space and, hence, the assumption of a real-valued envelope for the wavefunction is, therefore, not acceptable.
  2. The wavefunction for spin-1/2 particles cannot represent any real object because of its 720-degree symmetry in space. Real objects have the same spatial symmetry as space itself, which is 360 degrees. Hence, physical interpretations of the wavefunction are nonsensical.

Well… I’ve finally managed to deconstruct those arguments – using, paradoxically, Feynman’s own arguments against him. Have a look: click the link to my latest paper ! Enjoy !

Schrödinger’s equation as an energy conservation law

Post scriptum note added on 11 July 2016: This is one of the more speculative posts which led to my e-publication analyzing the wavefunction as an energy propagation. With the benefit of hindsight, I would recommend you to immediately the more recent exposé on the matter that is being presented here, which you can find by clicking on the provided link.

Original post:

In the movie about Stephen Hawking’s life, The Theory of Everything, there is talk about a single unifying equation that would explain everything in the universe. I must assume the real Stephen Hawking is familiar with Feynman’s unworldliness equation: U = 0, which – as Feynman convincingly demonstrates – effectively integrates all known equations in physics. It’s one of Feynman’s many jokes, of course, but an exceptionally clever one, as the argument convincingly shows there’s no such thing as one equation that explains all. Or, to be precise, one can, effectively, ‘hide‘ all the equations you want in a single equation, but it’s just a trick. As Feynman puts it: “When you unwrap the whole thing, you get back where you were before.”

Having said that, some equations in physics are obviously more fundamental than others. You can readily think of obvious candidates: Einstein’s mass-energy equivalence (m = E/c2); the wavefunction (ψ = ei(ω·t − k·x)) and the two de Broglie relations that come with it (ω = E/ħ and k = p/ħ); and, of course, Schrödinger’s equation, which we wrote as:

Schrodinger's equation

In my post on quantum-mechanical operators, I drew your attention to the fact that this equation is structurally similar to the heat diffusion equation. Indeed, assuming the heat per unit volume (q) is proportional to the temperature (T) – which is the case when expressing T in degrees Kelvin (K), so we can write q as q = k·T  – we can write the heat diffusion equation as:

heat diffusion 2

Moreover, I noted the similarity is not only structural. There is more to it: both equations model energy flows and/or densities. Look at it: the dimension of the left- and right-hand side of Schrödinger’s equation is the energy dimension: both quantities are expressed in joule. [Remember: a time derivative is a quantity expressed per second, and the dimension of Planck’s constant is the joule·second. You can figure out the dimension of the right-hand side yourself.] Now, the time derivative on the left-hand side is expressed in K/s. The constant in front (k) is just the (volume) heat capacity of the substance, which is expressed in J/(m3·K). So the dimension of k·(∂T/∂t) is J/(m3·s). On the right-hand side we have that Laplacian, whose dimension is K/m2, multiplied by the thermal conductivity, whose dimension is W/(m·K) = J/(m·s·K). Hence, the dimension of the product is  the same as the left-hand side: J/(m3·s).

We can present the thing in various ways: if we bring k to the other side, then we’ve got something expressed per second on the left-hand side, and something expressed per square meter on the right-hand side—but the k/κ factor makes it alright. The point is: both Schrödinger’s equation as well as the diffusion equation are actually an expression of the energy conservation law. They’re both expressions of Gauss’ flux theorem (but in differential form, rather than in integral form) which, as you know, pops up everywhere when talking energy conservation.

Huh? 

Yep. I’ll give another example. Let me first remind you that the k·(∂T/∂t) = ∂q/∂t = κ·∇2T equation can also be written as:

heat diffusion 3

The h in this equation is, obviously, not Planck’s constant, but the heat flow vector, i.e. the heat that flows through a unit area in a unit time, and h is, obviously, equal to h = −κ∇T. And, of course, you should remember your vector calculus here: ∇· is the divergence operator. In fact, we used the equation above, with ∇·h rather than ∇2T to illustrate the energy conservation principle. Now, you may or may not remember that we gave you a similar equation when talking about the energy of fields and the Poynting vector:

Poynting vector

This immediately triggers the following reflection: if there’s a ‘Poynting vector’ for heat flow (h), and for the energy of fields (S), then there must be some kind of ‘Poynting vector’ for amplitudes too! I don’t know which one, but it must exist! And it’s going to be some complex vector, no doubt! But it should be out there.

It also makes me think of a point I’ve made a couple of times already—about the similarity between the E and B vectors that characterize the traveling electromagnetic field, and the real and imaginary part of the traveling amplitude. Indeed, the similarity between the two illustrations below cannot be a coincidence. In both cases, we’ve got two oscillating magnitudes that are orthogonal to each other, always. As such, they’re not independent: one follows the other, or vice versa.

5d_euler_fFG02_06

 

 

 

 

 

The only difference is the phase shift. Euler’s formula incorporates a phase shift—remember: sinθ = cos(θ − π/2)—and so you don’t have that with the E and B vectors. But – Hey! – isn’t that why bosons and fermions are different? 🙂

[…]

This is great fun, and I’ll surely come back to it. As for now, however, I’ll let you ponder the matter for yourself. 🙂

Post scriptum: I am sure that all that the questions I raise here will be answered at the Masters’ level, most probably in some course dealing with quantum field theory, of course. 🙂 In any case, I am happy I can already anticipate such questions. 🙂

Oh – and, as for those two illustrations above, the animation below is one that should help you to think things through. It’s the electric field vector of a traveling circularly polarized electromagnetic wave, as opposed to the linearly polarized light that was illustrated above.

Animation