Explaining the proton mass and radius

Our alternative realist interpretation of quantum physics is pretty complete but one thing that has been puzzling us is the mass density of a proton: why is it so massive as compared to an electron? We simplified things by adding a factor in the Planck-Einstein relation. To be precise, we wrote it as E = 4·h·f. This allowed us to derive the proton radius from the ring current model:

proton radius This felt a bit artificial. Writing the Planck-Einstein relation using an integer multiple of h or ħ (E = n·h·f = n·ħ·ω) is not uncommon. You should have encountered this relation when studying the black-body problem, for example, and it is also commonly used in the context of Bohr orbitals of electrons. But why is n equal to 4 here? Why not 2, or 3, or 5 or some other integer? We do not know: all we know is that the proton is very different. A proton is, effectively, not the antimatter counterpart of an electron—a positron. While the proton is much smaller – 459 times smaller, to be precise – its mass is 1,836 times that of the electron. Note that we have the same 1/4 factor here because the mass and Compton radius are inversely proportional:

ratii

This doesn’t look all that bad but it feels artificial. In addition, our reasoning involved a unexplained difference – a mysterious but exact SQRT(2) factor, to be precise – between the theoretical and experimentally measured magnetic moment of a proton. In short, we assumed some form factor must explain both the extraordinary mass density as well as this SQRT(2) factor but we were not quite able to pin it down, exactly. A remark on a video on our YouTube channel inspired us to think some more – thank you for that, Andy! – and we think we may have the answer now.

We now think the mass – or energy – of a proton combines two oscillations: one is the Zitterbewegung oscillation of the pointlike charge (which is a circular oscillation in a plane) while the other is the oscillation of the plane itself. The illustration below is a bit horrendous (I am not so good at drawings) but might help you to get the point. The plane of the Zitterbewegung (the plane of the proton ring current, in other words) may oscillate itself between +90 and −90 degrees. If so, the effective magnetic moment will differ from the theoretical magnetic moment we calculated, and it will differ by that SQRT(2) factor.

Proton oscillation

Hence, we should rewrite our paper, but the logic remains the same: we just have a much better explanation now of why we should apply the energy equipartition theorem.

Mystery solved! 🙂

Post scriptum (9 August 2020): The solution is not as simple as you may imagine. When combining the idea of some other motion to the ring current, we must remember that the speed of light –  the presumed tangential speed of our pointlike charge – cannot change. Hence, the radius must become smaller. We also need to think about distinguishing two different frequencies, and things quickly become quite complicated.

Do we only see what we want to see?

I had a short but interesting exchange with a student in physics—one of the very few who actually reads (some of) the stuff on this and my other blog (the latter is more technical than this one).

It was an exchange on the double-slit experiment with electrons—one of these experiments which is supposed to prove that classical concepts and electromagnetic theory fail when analyzing the smallest of small things and that only an analysis in terms of those weird probability amplitudes can explain what might or might not be going on.

Plain rubbish, of course. I asked him to carefully look at the pattern of blobs when only one of the slits is open, which are shown in the top and bottom illustrations below respectively (the inset (top-left) shows how the mask moves over the slits—covering both, one or none of the two slits respectively).

Interference 1

Of course, you see interference when both slits are open (all of the stuff in the middle above). However, I find it much more interesting to see there is interference too (or diffraction—my preferred term for an interference pattern when there is only one slit or one hole) even if only one of the slits is open. In fact, the interference pattern when two slits are open, is just the pattern one gets from the superposition of the diffraction pattern for the two slits respectively. Hence, an analysis in terms of probability amplitudes associated with this or that path—the usual thing: add the amplitudes and then take the absolute square to get the probabilities—is pretty nonsensical. The tough question physicists need to answer is not how interference can be explained, but this: how do we explain the diffraction pattern when electrons go through one slit only?

[…]

I realize you may be as brainwashed as the bright young student who contacted me: he did not see it at first! You should, therefore, probably have another look at the illustrations above too: there are brighter and darker spots when one slit is open too, especially on the sides—a bit further away from the center.

[Just do it before you read on: look, once more, at the illustration above before you look at the next.]

[…]

The diffraction pattern (when only one slit is open) resembles that of light going through a circular aperture (think of light going through a simple pinhole), which is shown below: it is known as the Airy disk or the Airy pattern. [I should, of course, mention the source of my illustrations: the one above (on electron interference) comes from the article on the 2012 Nebraska-Lincoln experiment, while the ones below come from the articles on the Airy disk and the (angular) resolution of a microscope in Wikipedia respectively. I no longer refer to Feynman’s Lectures or related material because of an attack by the dark force.]

Beugungsscheibchen

When we combine two pinholes and move them further or closer to each other, we get what is shown below: a superposition of the two diffraction patterns. The patterns in that double-slit experiment with electrons look what you would get using slits instead of pinholes.

airy_disk_spacing_near_rayleigh_criterion

It obviously led to a bit of an Aha-Erlebnis for the student who bothered to write and ask. I told him a mathematical analysis using classical wave equations would not be easy, but that it should be possible. Unfortunately, mainstream physicists − academic teachers and professors, in particular – seem to prefer the nonsensical but easier analysis in terms of probability amplitudes. I guess they only see what they want to see. :-/

Note: For those who would want to dig a bit further, I could refer to them to a September 20, 2014 post as well as a successor post to that on diffraction and interference of EM waves (plain ‘light’, in other words). The dark force did some damage to both, but they are still very readable. In fact, the fact that one or two illustrations and formulas have been removed there will force you to think for yourself, so it is all good. 🙂

Uncertainty, quantum math, and A(Y)MS

This morning, one of my readers wrote me to say I should refrain from criticizing mainstream theory or – if I do – in friendlier or more constructive terms. He is right, of course: my blog on Feynman’s Lectures proves I suffer from Angry Young Man Syndrome (AYMS), which does not befit a 50-year old. It is also true I will probably not be able to convince those whom I have not convinced yet.

What to do? I should probably find easier metaphors and bridge apparent contradictions—and write friendlier posts and articles, of course! 🙂

In my last paper, for example, I make a rather harsh distinction between discrete physical states and continuous logical states in mainstream theory. We may illustrate this using Schrödinger’s thought experiment with the cat: we know the cat is either dead or alive—depending on whether or not the poison was released. However, as long as we do not check, we may describe it by some logical state that mixes the ideas of a dead and a live cat. This logical state is defined in probabilistic terms: as time goes by, the likelihood of the cat being dead increases. The actual physical state does not have such ambiguity: the cat is either dead or alive.

The point that I want to make here is that the uncertainty is not physical. It is in our mind only: we have no knowledge of the physical state because we cannot (or do not want to) measure it, or because measurement is not possible because it would interfere (or possibly even destroy) the system: we are usually probing the smallest of stuff with the smallest of stuff in these experiments—which is why Heisenberg himself originally referred to uncertainty as Ungenauigkeit instead of Unbestimmtheit.

So, yes, as long as we do not look inside of the box – by opening or, preferably, through some window on the side (the cat could scratch you or jump out when opening it) – we may think of Schrödinger’s cat-in-the-box experiment as a simple quantum-mechanical two-state system. However, it is a rather special one: the poison is likely to be released after some time only (it depend on a probabilistic process itself) and we should, therefore, model this time as a random variable which will be distributed – usually more or less normally – around some mean. The (cumulative) probability distribution function for the cat being dead will, therefore, resemble something like the curves below, whose shapes depend not only on the mean but also on the standard deviation from the mean.

1920px-Normal_Distribution_CDF

Schrödinger’s cat-in-the-box experiment involves a transition from an alive to a dead state: it is sure and irreversible. Most real-life quantum-mechanical two-state systems will look very different: they will not involve some dead-or-alive situation but two very different states—position states, or energy states, for example—and the probability of the system being in this or that physical state will, therefore, slosh back and forth between the two, as illustrated below.

Probabilities desmos

I took this illustration from the mentioned paper, which deals with amplitude math, so I should refer you there for an explanation of the rather particular cycle time (π) and measurement units (ħ/A). The important thing here – in the context of this blog post, that is – is not the nitty-gritty but the basic idea of a quantum-mechanical two-state system. That basic idea is needed because the point that I want to make here is this: thinking that some system can be in two (discrete) physical states only may often be a bit of an idealization too. The system or whatever is that we are trying to describe might be in-between two states while oscillating between the two states, for example—or we may, perhaps, not be able to define the position of whatever it is that we are tracking—say, an atom or a nucleus in a molecule—because the idea of an atom or a nucleus might itself be quite fuzzy.

To explain what fuzziness might be in the context of physics, I often use the metaphor below: the propeller of the little plane is always somewhere, obviously—but the question is: where exactly? When the frequency of going from one place to another becomes quite high, the concept of an exact position becomes quite fuzzy. The metaphor of a rapidly rotating propeller may also illustrate the fuzziness of the concept of mass or even energy: if we think of the propeller being pretty much everywhere, then it is also more useful to think in terms of some dynamically defined mass or energy density concept in the space it is, somehow, filling.

propeller This, then, should take some of the perceived harshness of my analyses away: I should not say the mainstream interpretation of quantum physics is all wrong and that states are either physical or logical: our models may inevitably have to mix a bit of the two! So, yes, I should be much more polite and say the mainstream interpretation prefers to leave things vague or unsaid, and that physicists should, therefore, be more precise and avoid hyping up stuff that can easily be explained in terms of common-sense physical interpretations.

Having said that, I think that only sounds slightly less polite, and I also continue to think some Nobel Prize awards did exactly that: they rewarded the invention of hyped-up concepts rather than true science, and so now we are stuck with these things. To be precise, I think the award of the 1933 Nobel Prize to Werner Heisenberg is a very significant example of this, and it was followed by others. I am not shy or ashamed when writing this because I know I am in rather good company thinking that. Unfortunately, not enough people dare to say what they really think, and that is that the Emperor may have no clothes.

That is sad, because there are effectively a lot of enthusiastic and rather smart people who try to understand physics but become disillusioned when they enroll in online or real physics courses: when asking too many questions, they are effectively told to just shut up and calculate. I also think John Baez’ Crackpot Index is, all too often, abused to defend mainstream mediocrity and Ivory Tower theorizing. At the same time, I promise my friendly critic I will think some more about my Angry 50-Year-Old Syndrome.

Perhaps I should take a break from quantum mechanics and study, say, chaos theory, or fluid dynamics—something else, some new math. I should probably also train to go up Mont Blanc again this year: I gained a fair amount of physical weight while doing all this mental exercise over the past few years, and I do intend to climb again—50-year-old or not. Let’s just call it AMS. 🙂 And, yes, I should also focus on my day job, of course! 🙂

However, I probably won’t get rid of the quantum physics virus any time soon. In fact, I just started exploring the QCD sector, and I am documenting this new journey in a new blog: Reading Einstein. Go have a look. 🙂

Post scriptum: The probability distribution for the cat’s death sentence is, technically, speaking a Poisson distribution (the name is easy to remember because it does not differ too much from the poison that is used). However, because we are modeling probabilities here, its parameters k and λ should be thought of as being very large. It, therefore, approaches a normal distribution. Quantum-mechanical amplitude math implicitly assumes we can use normal distributions to model state transitions (see my paper on Feynman’s Time Machine).