When reading this blog and/or my papers on ResearchGate, you may wonder what kind of mathematical framework you need to appreciate the finer details. We ourselves were asked by fellow proponents of the kind of local and realist interpretation of QM that we are pursuing to look at Clifford or space-time algebra (STA). Well… We looked at it as part of our farewell to this weird pastime of ours, and we documented our response in our very last RG paper on physics, math and (a)symmetries in Nature. If you struggle with the question above, then our answer will probably make you happy: there is no need to learn fancy math to understand easy physics. 🙂
Post scriptum (10 November 2024): As for the “farewell” part of this – I swear – very last paper on all of this weird stuff, it is probably a bit too harsh – but then it is what it is. Let me say a few things about it for the benefit of the would-be student or the starting amateur physicist. Should you study modern physics? I do not think so now, but then I also know that one cannot help oneself when it comes to satisfying some curiosity on fundamental questions. So it probably does not really matter what I advise you to do or not do. I can only say what I write below.
When I started this intellectual journey – what’s this quantum stuff all about? – decades ago, and especially when I got serious about it back in 2013, I had never expected that what happened would happen. No. I’ve always been a good student, and so I expected to sail smoothly through the required math and the intricacies of relativistic mechanics and all of the subtleties of electromagnetic theory – which sort of happened – and, then, to sail through the wonderful world of quantum electrodynamics, quantum field theory and – ultimately – quantum chromodynamics (or let’s call it high-energy physics now) in pretty much the same way.
The latter part did not happen. At each and every page of Feynman’s third volume of Lectures – the ones I was most interested in: on quantum mechanics – I found myself jotting down lots of questions. Questions which took me days, weeks or even years to solve, or not. Most of these questions led me to conclude that a lot of what is there in these Lectures are nothing but sophisms: clever but false arguments aimed at proving the many ad hoc hypotheses that make up the Standard Model. I started to realize the Standard Model is anything but standard: it is just a weird collection of mini-theories that are loosely connected to one another – if connected at all! I started buying more modern textbooks – like Aitchison’s and Hey’s Gauge Theories, which is apparently the standard for grad students in physics – but that did not help. I got stuck in the first chapter already: this Yukawa potential – or the concept of a non-conservative nuclear force itself – did not make sense to me. Not only in an intuitive way: the logic and the math of it does not make sense, either!
Fortunately, I reached out and wrote to non-mainstream researchers whose ideas resonated with me. For example, I will be eternally grateful to Dr. Vassallo for his suggestion to read Paolo Di Sia’s paper on the nuclear force, in which he provides heuristic but good arguments showing the nuclear force might just be a dynamic electromagnetic dipole field. So then I found myself in the business of deconstructing the idea of a strong force. A deeper historical analysis of all these new strange quantum numbers and new quantum conservation laws led to the same: I started looking at sensible suggestions to explain what happens or not in terms of electromagnetic disequilibrium states – developing my own fair share of such suggestions – rather than irrationally or uncritically swallowing the idea of hypothetical sub-nuclear particles on which you then load all kinds of equally hypothetical properties.
While I thought I was doing well in terms of pointing out both the good as well as the bad things in Feynman’s Lectures, I suffered from the weirdest thing ever: censorship on the Internet. Some strange caretaker of Feynman’s intellectual heritage apparently used the weight of his MIT-connection to take down substantial parts of many of my blog posts, accusing me of “unfair use” of this 1963 textbook. Unfair use? Over-use, perhaps, but unfair? All was nicely referenced: when you want to talk about quantum physics, you need some reference textbook, right? And Feynman’s Lectures are – or were, I would say now – the reference then. It was ridiculous. Even more so when he went as far as asking YouTube to strike a video of mine. YouTube complied. I laughed: it took me ten minutes or so to re-edit the video – a chance to finally use all that video editing software I have on my laptop 🙂 – and then put it back online. End of problem.
Case closed? I am not sure. I am a pretty cheerful guy, but I am also quite stubborn when I think something isn’t right. So I just carried on and shrugged it all off thinking this would only boost my readership. It probably did, so: Thank You, Mr. Gottlieb! 🙂 But things like that are hurtful. In any case, that doesn’t matter much. What matters is that things like that do reinforce the rather depressing and very poor perception of academic physics that a Sabine Hossenfelder now (very) loudly talks or – should I say: rants? – about: the King of Science is in deep trouble, and there is no easy way out.
So, what is my conclusion then? I am happy I found the answers I was looking for: there is a logical explanation for everything, and that explanation has been there for about 100 years now: Max Planck, Albert Einstein, H.A. Lorentz, Louis de Broglie, Erwin Schrödinger, Arthur Compton and then some more geniuses of those times have probably said all one can say about it all. And it makes sense. In contrast, I feel the past fifty years of mainstream research were probably nothing more than a huge waste of human intellect. Am I right? Am I wrong? Only the future can tell. To be frank, I am not too worried about it.
I may add one anecdote, perhaps. I did talk to my own son six or seven years ago about what he’d like to study. He was most interested in engineering, but we did talk about the more fundamental study of physics. I told him to surely not study that. In his first year of his Master’s degree, he had to do one course in quantum physics. We walked through it together, and he passed with flying colors. However, he also told me then he now fully understood why I had told him to surely not go for theoretical studies in physics: it just does not make all that much sense. If you would happen to be very young and you want to study something useful, then go for applied science: chemistry, biology or – when you are really smart – engineering or medicine. Something like that. If you want to do physics, go join CERN or something: they probably value engineers or technicians more than theorists there, too! 🙂
Personal note: As for myself, I wanted to study philosophy when I was about 15 years old (so that’s 40 years ago now). I did that eventually, but in evening classes, and only after I did what my good old dad (he died from old age about twenty years ago) then told me to do: study something useful first. I was not all that good with math, so I chose economics. I did not regret that. I even caught up with the math because the math – including statistical modeling! – that you need to understand physics is pretty much what you need in econometric modeling too. So I’ll conclude with a wise saying: all’s well that ends well. 🙂
Today I made a major step towards a very different Zitterbewegung model of a proton. With different, I mean different from the usual toroidal or helical model(s). I had a first version of this paper but the hyperlink gives you the updated paper. The update is small but very important: I checked all the formulas with ChatGPT and, hence, consider that as confirmation that I am on the right track. To my surprise, ChatGPT first fed me the wrong formula for an orbital frequency formula. Because I thought it could not be wrong on such simple matters, I asked it to check and double-check. It came with rather convincing geometrical explanations but I finally found an error in its reasoning, and the old formula from an online engineering textbook turned out to be correct.
In any case, I now have a sparring partner – ChatGPT o1 – to further develop the model that we finally settled on. That is a major breakthrough in this realistic interpretation of quantum theory and particle models that I have been trying to develop: the electron model is fine, and so now all that is left is this proton model. And then, of course, a model for a neutron or the deuteron nucleus. That will probably be a retirement project, or something for my next life. 🙂
Post scriptum: I followed up. “A theory’s value lies in its utility and ability to explain phenomena, regardless of whether it’s mainstream or not.” That’s ChatGPT’s conclusion after various explorations and chats with it over the past few weeks: https://lnkd.in/ekAAbvwc. I think I tried to push its limits when discussing problems in physics, leading it to make a rather remarkable distinction between “it’s” perspective and mine (see point 6 of Annex I of https://lnkd.in/eFVAyHn8), but – frankly – it may have no limits. As far as I can see, ChatGPT-o1 is truly amazing: sheer logic. 🙂 hashtag#AIhashtag#ChatGPThashtag#theoryofreality
Pre-scriptum (3 October 2024): I came back from holiday and, because this week-long up and down became quite convoluted, I did what I like to do in a case like that, and that is to take my Bamboo notebook and talk about it all in a video which I added to my Real Quantum Physics channel on YouTube. I also updated my paper on RG: as usual, it went through a few versions, but this one – with a summary co-authored by ChatGTP-4 (and ChatGPT-o1) – should be the final one: enjoy!
Indeed, instead of listening to the international news on the war with Russia and on what is happening in the Middle East (all very depressing), you may want to listen to this and read the latest theory. Perhaps you will be inspired by it to develop your own pet realist theory of what an electron might actually be. I can assure you that it is more fun than trying to understand Feynman diagrams and how QED calculations work. 🙂 But don’t think you will win a Nobel Prize if you do not have the right connections and pedigree and all of that: see this analysis of what makes Nobel Prize winners Nobel Prize winners. 🙂
Original post:
I asked some questions to ChatGPT about my geometric explanation of the anomaly in the electron’s magnetic moment. Here is the chat: https://chatgpt.com/share/66f91760-68b8-8004-8cb2-7d2d3624e0aa. To me, it confirms the ‘explanation’ of mainstream QED makes no sense. We can take Schwinger’s factor and build a series of converging terms using that factor. We can also take my first rough cut at a first-order correction (π(alpha)2/8, see my very early 2019 paper on a classical explanation of the amm), and use that.
You may wonder: why not ask ChatGPT about the best first-order factor to be used here considering the geometry of the situation? The fact is: I did, but the geometry is not all that easy. It first came up with the formula for a spherical cap, but that one does not do the trick. See the latter part of the conversation (link above).
I am on holiday now, and so I will switch off a while but I am thinking AI will do what two generations of ‘new’ quantum physicists did not do: come up with a model that is based on real physics and is easy to understand intuitively. 🙂
PS: Of course, I did another rapid-fire paper on ResearchGate to document it all (the logic step-by-step, so to speak). As the chat is public, feel free to continue the conversation. Note that I used the newest ChatGPT o1 version, now in preview but part of a subscription (which you may not have). Yet again a different beast! The older versions of ChatGPT may not be so smart. This conversation is totally worth the US$20/month I pay for my subscription. 🙂
PS 2: Now that I had it open, I also quickly queried it on my wildest hypothesis: a ‘mirror’ electromagnetic force explaining dark matter and dark energy. While it is totally wild (read: nuts), I entertain it because it does away with the need for an explanation in terms of some cosmological constant. Here is the conversation: https://chatgpt.com/share/66f92c7f-82a0-8004-a226-bde65085f18d. I like it that ChatGPT warns me a bit about privacy. It does look wild. However, it is nice to see how gentle ChatGPT is in pointing out what work needs to be done on a theory in order to make it look somewhat less wild. 🙂
PS 3 (yes, ChatGPT is addictive): I also queried it on the rather puzzling 8π/3 factor in the CODATA formula for the Thomson photon-electron scattering cross-section. See its response to our question in the updated chat: https://chatgpt.com/share/66f91760-68b8-8004-8cb2-7d2d3624e0aa. Just scroll down to the bottom. It took 31 seconds to generate the reply: I would be curious to know if that is just courtesy from ChatGPT (we all like to think our questions are complicated, don’t we?), or if this was effectively the time it needed to go through its knowledge base. Whatever the case might be, we think it is brilliant. 🙂 It is nothing to be afraid of, although I did feel a bit like: what’s left to learn to it but for asking intelligent questions. What if it starts really learning by asking intelligent questions itself to us? I am all ready for it. 🙂
As an amateur physicist, I get a regular stream of email updates from Science, Nature and Phys.org on new discoveries and new theories in quantum physics. I usually have no idea what to do with them. However, I want to single out two recent updates on the state of affairs of research which these channels report on. The first one is reflected in the title of this post. It’s on a very rare decay mode of kaons: see https://phys.org/news/2024-09-ultra-rare-particle-decay-uncover.html.
Something inside of me says this may lead to a review of all these newly invented conservation laws – combined with new ideas on symmetry breaking too – and/or new ‘quantum numbers’ that are associated with the quark hypothesis: I think everyone has already forgotten about ‘baryon conservation’, so other simplifications based on, yes, simpler Zitterbewegung models of particles may be possible.
The historical background to this is well described by Richard Feynman in his discussion of how these new quantum numbers – strangeness, specifically – were invented to deal with the observation that certain decay reactions were not being observed (see: Feynman’s Lectures, III-11-5, the (neutral) K-meson). So now it turns that certain decay reactions are being observed! Shouldn’t that lead to (future) scientists revisiting the quark/gluon hypothesis itself?
Of course, that would call into question several Nobel Prize awards, so we think it won’t happen any time soon. 🙂 This brings me to the second update from the field. Indeed, a more recent Nobel Prize in Physics which should, perhaps, be questioned in light of more recent measurements questioning old(er) ones (and the theories that are based on them) is the Nobel Prize in 2011 for work on the cosmological constant. Why? Because… Well… New measurements on the rate of expansion of the Universe as reported by Phys.org last month question the measurements which led to that 2011 Prize. Is anyone bothered by that? No. Except me, perhaps, because I am old-fashioned and wonder what is going on.
I get asked about gravity, and some people push particle theories to me talking about gravity. I am, quite simply, not interested. This ‘coming and going’ of the “cosmological constant hypothesis” over the past decades – or, should we say, the past 80 years or so – makes me stay away from GUTs and anything that is related to it. If scientists cannot even agree on these measurements, it is of not much use to invent new modified gravity theories fitting into ever-expanding grand unification schemes based on mathematical frameworks that can only be understood by the conoscienti, isn’t it?
It is tough: I am not the only one (and definitely not the best placed one) to see a lot of researchers – both amateur as well as professional – “getting lost in math” (cf. the title of Hossenfelder’s best-seller). Will there be an end to this, one day?
I am optimistic and so I think: yes. One of the recurring principles that guides some of the critical physicists I greatly admire is Occam’sRazor Principle: keep it simple! Make sure the degrees of freedom in your mathematical scheme match those of the physics you are trying to describe. That requires a lot of rigor in the use of concepts: perhaps we should add concepts to those that, say, Schrödinger and Einstein used 100 years ago. However, my own pet theories and recycling of their ideas do not suggest that. And so I really just can’t get myself to read up on Clifford algebras and other mathematical constructs I am told to study – simply because this or that person tells me I should think in terms of spinors rather than in terms of currents (to just give one specific example here).
I can only hope that more and more academics will come to see this, and that the Nobel Prize committee may think some more about rewarding more conservative approaches rather than the next cargo cult science idea.
OK. I should stop rambling. The musings above do not answer the question we all have: what about gravity, then? My take on that is this: I am fine with Einstein’s idea of gravity just being a reflection of the distribution of energy/mass in the Universe. Whether or not the Universe expands at an ever-faster-accelerating pace must, first, be firmly established by measurements and then, secondly, even then there may be no need for invoking a cosmological constant or other elements of a new “aetherial” theory of space and time.
Indeed, Einstein thought that his first hypothesis on a possible cosmological constant was “his biggest blunder ever.” While I know nothing of the nitty-gritty, I think it is important to listen to “good ol’ Einstein” – especially when he talked about what he ‘trusted’ or not in terms of physical explanations. Einstein’s rejection of the idea of a cosmological constant – after first coming up with it himself and, therefore, having probably having the best grasp of its implications – suggests the cosmological constant is just yet another non-justifiable metaphysical construct in physics and astronomy.
So, let us wrap up this post: is or is there not a need for ‘modified gravity’ theories? I will let you think about that. I am fine with Einstein’s ‘geometric’ explanation of it.
Post scriptum: While I think quite a few of these new quantum numbers related to quarks and – most probably – the quark hypothesis itself will be forgotten in, say, 50 or 100 years from now, the idea of some ‘triadic’ structure to explain the three generations of particles and strange decay modes, is – essentially – sound. Some kind of ‘color’ scheme (I call, rather jokingly, an “RGB scheme” – referring to the color scheme used in video/image processing) should be very useful: an electron annihilates a positron but an electron combines with a proton to form an atom, so there’s something different about these two charges. Likewise, if we think of a neutron as neutral neutronic current, the two charges “inside” must be very different… See pp. 7 ff. on this in my recent paper on multi-charge zbw models.
I was sceptical before – and I am still not a believer in the quark hypothesis – but I do think physicists – or, more likely, future generations of physicists – should get a better “grip” on these three different ‘types’ of electric charge as part of a more realist explanation of what second- or third-generation “versions” of elementary particles might actually be. Such explanation will then probably also explain these “unstable states” (not quite respecting the Planck-Einstein relation) or “exotic” particles. Indeed, I do not see much of a distinction between stable and unstable particle states in current physics. But that’s a remark that’s probably not essential to the discussion here… 🙂
One final remark, perhaps: my first instinct when looking at particle physics, was actually very much inspired by the idea that the quantum-mechanical wavefunction might be something else than just an EM oscillation. When I first calculated force fields in a Zitter electron, and then in the muon-electron and proton, I was rather shocked (see pp. 16 ff. of one of my early papers) and thought: wow! Are we modelling tiny black holes here? But then I quickly came to terms with it. Small massive things must come with such huge field strengths, and all particle radius formulas have mass (or energy) in the denominator: so more mass/energy means smaller scale, indeed! And I also quickly calculated the Schwarzschild radius for these elementary particles, and that is A WHOLE LOT smaller than the radius I get from my simple electromagnetic equations and the Planck-Einstein relation. So I see absolutely no reason whatsoever to think gravitational effects might take over from plain EM fields when you look at things at the smallest of scales.
But, then, who am I? I like to think I am not inventing anything new. I just enjoy playing with old ideas to see if something new comes out of it. I think I am fortunate because I do see a lot of new things coming out of the old ideas, even if there is little or nothing we can add to them: the old Masters have already written it all out. So, now I should stop chewing on these old ideas as well and conclude: if you want to read something, don’t read me or anything contemporary. Just read the classics! Many modern minds – often great mathematicians – tried or try to be smarter than Einstein, Lorentz, de Broglie or Schrödinger (I am deliberately not mentioning other great names): I think the more recent discoveries in physics and cosmology show they are not. 🙂
Just after finishing a rather sober and, probably, overly pessimistic reflection on where the Zitterbewegung interpretation of quantum theory stands, I am excited to see a superbly written article by Dr. Kovacs and Dr. Vassallo on what I now think of as the ultimate electron model: Rethinking electron statistics rules (10 September 2024). I think it is great because it addresses several points in my rather depressing description of the state of zbw theory:
Multiple Zitterbewegung interpretations of what an electron actually is, currently coexist. Indeed, both mainstream and non-mainstream physicists have now been going back and forth for about 100 years on this or that electron model: the referenced Kovacs/Vassallo article effectively appeared in a special journal issue titled: “100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie.” 100+ years of discussion have basically led us back to Parson’s 1915 ring current model, which Joseph Larmor presented so well at the 1921 Solvay Conference. We do not think that is a good situation: it looks a bit like 100 years of re-inventing the wheel – or, perhaps, I should say: wheels within wheels. 🙂 I could write more about this but I am happy to see the discussion on – just one example of differing views here – whether or not there should be a 1/2 factor in the electron’s frequency may be considered to be finally solved: de Broglie’s matter-wave frequency is just the same as the Planck-Einstein frequency in this paper. This factor 2 or 1/2 pops up when considering ideas such as the effective mass of the zbw charge or – in the context of Schrödinger’s equation – because we’re modeling the motion of electron pairs rather than electrons (see the annexes to my paper on de Broglie’s matter-wave concept). In short: great! Now we can, finally, leave those 100+ years of discussions behind us. 🙂
Dr. Kovacs and Dr. Vassallo also explore the nature of superconductivity and Bose-Einstein statistics, and not only does their analysis away with the rather mystical explanation in Feynman’s last and final chapter of his lectures on quantum mechanics but it also offers a very fine treatment of n-electron systems. Their comments on ‘bosonic’ and ‘fermionic’ properties of matter-particles also tie in with my early assessment that the boson-fermion dichotomy has no ontological basis.
The hundreds of downloads of their article since it was published just two weeks ago also shows new and old ways of thinking and modelling apparently come nicely together in this article: if your articles get hundreds of reads as soon as published, then you are definitely not non-mainstream any more: both Dr. Kovacs and Dr. Vassallo have an extraordinary talent for rephrasing old questions in the new “language” of modern quantum theory. That is to be lauded. Hopefully, work on a proton and a neutron model will now complement what I think of as the ultimate electron model based on a local and realist interpretation of what de Broglie’s matter-wave actually is. Indeed, critics of modern quantum theory often quote the following line from Philip Pearle’s Classical Electron Models[1]:
“The state of the classical electron theory reminds one of a house under construction that was abandoned by its workmen upon receiving news of an approaching plague. The plague in this case, of course, was quantum theory. As a result, classical electron theory stands with many interesting unsolved or partially solved problems.”
I think Dr. Kovacs and Dr. Vassallo may have managed to finish this “abandoned construction” – albeit with an approach which differs significantly from that of Pearle: that is good because I think there were good reasons for the “workmen” to leave the construction site (see footnote [1]). 🙂 So, yes, I hope they will be able – a few years from now – to also solve the questions related to a Zitterbewegung proton and neutron model.
In fact, they already have a consistent proton model (see: the proton and Occam’s Razor, May 2023), but something inside of me says that they should also explore different topologies, such as this Lissajous-like trajectory which intrigues me more than helical/toroidal approaches – but then who am I? I am the first to recognize my limitations as an amateur and it is, therefore, great to see professionals such as Dr. Kovacs and Dr. Vassallo applying their formidable skills and intuition to the problem. 🙂
[1] Pearle’s paper is the seventh in a volume of eight chapters. The book’s title is, quite simply, titled Electromagnetism (1982), and it was put together and edited by Doris Teplitz (1982). Few who quote this famous line, bother to read the Philip Pearle paper itself. This paper effectively presents what Pearle refers to as classical electron models: all of them are based on “rigid or flexible shell surfaces” of charge, which is why we think they did not “cut it” for the many “workmen” (read: the mainstream scientists who thought the Bohr-Heisenberg amplitude math and the probability theory that comes with it) who left the then unfinished construction.
We think the approach taken by Dr. Kovacs and Dr. Vassallo is more productive when it comes to bringing mainstream and Zitterbewegung theorists together around a productive mathematical framework in which the probabibilities are explained based on a plain interpretation of Schrödinger’s ‘discovery’ – which is that the elementary wavefunction represents a real equation of motion of a pointlike but not infinitesimally charge inside of an electron.
As for trying out different topologies, we understand Dr. Kovacs and Dr. Vassallo are working very hard on that, so all we can do is to wish them the best of luck. Godspeed! 🙂
John Duffield’s comment on my post on a (possible) 3D Lissajous trajectory for the proton zbw charge – as opposed to a helical/toroidial/solenoidal model – makes me think and, therefore, deserves some better answer than my quick reply to it. So, that “better answer” is what I am putting down here. [I am writing from a beach apartment in Castelldefels (Spain), so I will be brief.]
He may disagree, of course, but I see two very different aspects in his question/remark/criticism:
Why a Lissajous-like trajectory as opposed to, say, a trajectory like that of a trefoil knot or – more generally – a torus knot ?
What about the spin of the zbw charge itself?
I must answer the first question by explaining what sets me apart from mainstream Zitterbewegung models of elementary particles: any toroidial/helical/solenoidal model comes with two different frequencies and, therefore, two oscillatory modes: toroidal and poloidal (the link is to the Wikipedia article from which I also copy the illustration below).
That does not appeal to me. Try to create the trajectories below with Desmos 3D grapher: you will also end up using two or three different frequencies – even if the below trajectories were created using the same base frequency: we have t, 2t, and 3t in the sine and cosine functions here. The Lissajous curve has only one frequency, and it is the one that comes out of the Planck-Einstein relation. So I feel good about that.
The second remark (what about spin of the zbw charge itself?) is more important, and makes me think much more. Would we have a twist in the loop because the zbw charge spins around its own axis? Maybe. However, we must note this:
The zbw charge is not like some car in a Ferris wheel: there is no force keeping it in the same orientation and it likely rotates around its own axis at the same frequency of the 2D ring current (electron) or 3D Lissajous trajectory (proton). The only thing you need to justify this hypothesis is the idea of inertia to a change in the state of motion of the zbw charge. Indeed, we can think of the zbw charge being symmetrical and acquiring an effective mass as it zips around, and so it will rotate around its own axis as it zips around some center.
However, should we, perhaps, be even more creative and also consider an extra twist – on top of that rotation of the zbw charge that is due to the inertia from its effective mass (half of the energy of the elementary particle is in its kinetic energy, and the other half in the EM field that causes it to go around in a 2D or 3D ring current)? That would give rise to John Duffield’s Möbiusstripconcept for modeling elementary particles.
For the time being, I see no need to make such assumption, but he sure got me thinking! The extra spin would probably help to explain the second- or third-order terms in the anomaly of the magnetic moment of an electron (as for now, I only have an approximative theory based on the effective radius (Lorentz or classical electron radius) of the zbw charge).
[…]
I would like to wrap up these musings by acknowledging Dennis P. Whiterell. He is an amateur physicist – just like me – and he sent me a manuscript which, among other interesting things, also talks about the “Ferris wheel analogy”. His arguments are very subtle but fail to convince me: I do not think the “Ferris wheel analogy” is useful in the context of elementary ring currents. Again, that is just for the time being, of course. I will leave it at that, and think some more over the comings weeks or months. 🙂
I added a very last paper to my list on ResearchGate. Its title is: what about multi-charge Zitterbewegung models? Indeed, if this local and realist interpretation of quantum mechanics is to break through, then it is logical to wonder about a generalization of a model involving only one charge: think of an electron (e.g., Consa, 2018) or proton model (e.g., Vassallo & Kovacs, 2023) here. With a generalization, we do not mean some unique general solution for all motion, but just what would result from combining 1-charge models into structures with two or more charges. [Just to be sure, we are not talking about electron orbitals here: Schrödinger’s equation models these sufficiently well. No. We are talking about the possible equations of motion of the charges in a neutron, the deuteron nucleus, and a helium-3 or helium-4 nucleus.]
So our question in this paper is this: how do we build the real world from elementary electron and proton particle models? We speculate about that using our own simplified models, which boil down to two geometrical elements: (i) the planar or 2D ring current of the zbw electron, and (ii) the three-dimensional Lissajous trajectory on a sphere which we think might make sense when modeling the orbital of the zbw charge in a proton. Both have the advantage they involve only one frequency rather than the two frequencies (or two modes of oscillation) one sees in helical or toroidal models. Why do we prefer to stick to the idea of one frequency only, even if we readily admit helical or toroidal models are far more precise in terms of generating the experimentally measured value of the magnetic moment of electrons and protons, respectively? The answer is simple: I am just an amateur and so I like to roll with very simple things when trying to tackle something difficult. 🙂
So, go and have a look at our reflections on multi-charge Zitterbewegung models – if only because we also started writing about the history of the Zitterbewegung interpretation and a few other things. To sum it up:
The paper offers a new brief history of how interpretations of the new quantum physics evolved, and why I am with Schrödinger’s Zitterbewegung hypothesis: it just explains the (possible) structure of elementary particles so well.
It speculates about how positive and negative charge may combine in a neutron, and then also about how a deuteron nucleus might look like.
We did not get to specific suggestions for helium-3 and helium-4 nuclei because these depend on how you think about the neutron and the deuteron nucleus. However, I do spell out why and how about I think of a neutron playing the role I think it plays in a nucleus: the glue that holds protons together (so there is no need for quark-gluon theory, I think, even if I do acknowledge the value of some triadic color scheme on top of the classical quantum numbers).
Indeed, despite my aversion of the new metaphysics that crept into physics in the 1970s, I explain why the idea of some color typing (not a color charge but just an extra triadic classification of charge) might still be useful. [I secretly hope this may help me to understand why this color scheme was introduced in the 1970s, because I do not see it as anything more than mathematical factoring of matrix equations describing disequilibrium states – which may be impossible to solve.]
Have a look, even if it is only to appreciate some of the 3D images of what I think as elementary equations of motion (I copy some below). I should do more with these images. Some art, perhaps, using OpenAI’s DALL·E image generator. Who knows: perhaps AI may, one day, solve the n-body problems I write about and, thereby, come up with the ultimate interpretation of quantum mechanics?
That sounds crazy but, from one or two conversations (with real people), it looks like I am not alone with that idea. 🙂 There are good reasons why CERN turned to AI a few years ago: for the time being, they use it to detect anomalies in the jets that come out of high-energy collissions, but – who knows? – perhaps a more advanced AI Logic Theorist programme could simplify the rather messy quark-gluon hypothesis some day?
Because I am disengaging from this field (it is mentally exhausting, and one gets stuck rather quickly), I surely hope so.
For this kind of thinking or problem solving, I guess I am still better than ChatGPT-4. 🙂 ChatGPT-4 did pass ‘my’ Turing test on intelligence, however. And that is quite something. I write about the ouch!factor in my recent LinkedIn article on AI. Yesterday, I definitely had such ouch! feeling (gentle – just in the sense that I thought ChatGPT-4 was smarter than me on this too), but so it’s OK now. 🙂 I win. A nice thing about this simple calculation is that this SQRT(2) factor pops up: it must be the same SQRT(2) factor that is related to the magnetic moment of a proton in my proton radius derivation, although I am not yet sure why and how exactly.
I did a quick video on it on YouTube: https://www.youtube.com/watch?v=-HnaLG8bY6o. Unfortunately, I cannot extract a transcript from it for ChatGPT-4. However, I had a quick conversation with it on what remains to be done, and that is to calculate the magnetic moment of this 3D Lissajous loop (it will depend on the orientation but we just need it in one direction: where it is strongest because that is how it will line up in a Penning trap of whatever device that is/was used to determine its value). I asked ChatGPT how it could possibly help with these calculations, mentioning the Biot-Savart law and the 3D integrals this would imply. This was ChatGPT’s answer:
“Regarding the Biot-Savart law and calculating the magnetic moment for such a complex 3D current loop, you’re correct that this involves intricate 3D integrals. I can certainly help set up or guide through parts of the calculation, especially in formulating the integral and explaining how to approach the problem. If you share the specifics of your current loop’s geometry and the required variables, we can work through how to structure the integrals needed for the magnetic moment calculation. Feel free to provide details if you want to give this a try!”
AI is, clearly, not was it was even just a year ago: it is much better now. As for me, I will let the problem rest now. 🙂
Pre-scriptum 2 (18 September): Please do check out the comment from the ‘Physics Detective’ to this post (and the Physics Detective site itself, of course): a Möbius ring for the electron and – who knows – a 3D trefoil loop for the proton might do the trick in 2D/3D as well. It would be nice if it did because it would bring helical/toroidal/solenoid-like spin of the charge itself into the model, possibly unifying the math behind these models. Thank you for noting this, John ! 🙂
Original post (9/10):
End of last year, I started to play with ChatGPT-4. Only a few times, really, because, for ordinary questions or web searches, it is not much better than your Google AI assistant or Microsoft’s CoPilot: it just comes with a very pleasant style of conversation (yes). I counted and, so far, I only five conversations with it. However, I do admit I have a habit of continuing an old conversation (ChatGPT now uses your old conversations anyway). Also, these five conversations were good and long. It helped me, for example, greatly to get a quick overview and understanding of IT product offerings in the cloud: it made/makes great comparisons between the offerings of Google Cloud, Azure and AWS, not only for infrastructure but also in the area of modern AI applications. I also asked questions on other technical things, like object-oriented programming, and in this field also it really excels at giving you very precise and relevant answers. In fact, I now understand why many programmers turn to it to write code. 🙂
However, I was mainly interested in ChatGPT-4 because it knows how to parse (read: it can read) documents now. So it does a lot more than just scraping things on products and services from websites. To be precise, it does not just parse text only: it actually ‘understands’ complex mathematical formulas and advanced symbols (think of differential operators here), and so that’s what I wanted to use it for. Indeed, I asked it to read my papers on ResearchGate and, because I do think I should rewrite and restructure them (too many of them cover more or less the same topic), I asked it to rewrite some of them. However, I was very dissatisfied with the result, and so the versions on RG are still the versions that I wrote: no change by AI whatsoever. Just in case you wonder. 🙂
The point is this: I am not ashamed to (a) admit I did that and (b) to share the link of the conversation here, which shows you that I got a bit impatient and why and how I left that conversation last year. I simply thought ChatGPT-4 did not have a clue about what I was writing about. So… It did not pass my Turing test on this particular topic, and that was that. Again: this was about a year ago. So what happened now?
I have a bit of time on my hands currently, and so I revisited some of my research in this very weird field. In fact, I was thinking about one problem about my Zitterbewegung proton model which I can’t solve. It bothers me. It is this: I am happy with my proton model – which is an exceedingly simple 3D elementary particle model, but I want the equations of motion for it. Yes. It is simple. It is what Dirac said: if you don’t have the equations of motion, you have nothing. That’s physics, and the problem with modern or mainstream quantum mechanics (the Bohr-Heisenberg interpretation, basically: the idea that probabilities cannot be further explained) is because it forgets about that. It dissatisfies not only me but anyone with common sense, I think. 😉 So I want these equations of motion. I have them for an electron (simple ring current), and now I hope to see them – one day, at least – for the proton also. [I am actually not too worried about it because others have developed such equations of motion already. However, such models (e.g., Vassallo and Kovacs, 2023) are, usually, toroidal and, therefore, involve two frequencies rather than just one. They are also not what I’d refer to as pure mass-without-mass models. Hence, they do not look so nice – geometrically speaking – to me as my own spherical model.
But so I do not have equations of motion for my model. This very particular problem should be rather straightforward but it is not: 3D motion is far more complex than 2D motion. Calculating a magnetic moment for (i) a simple ring current or for (ii) a very complex motion of charge in three dimensions are two very different things. The first is easy. The second is incredibly complicated. So, I am happy that my paper on my primitive efforts to find something better (I call it the “proton yarnball puzzle”) attracted almost no readers, because it is an awful paper, indeed! It rambles about me trying this or that, and it is full of quick-and-dirty screenshots from the free online Desmos 3D graphing calculator – which I find great to quickly get a visual on something that moves around in two or in three dimensions. But so whatever I try, it explains, basically, nothing: my only real result is nothing more than a Lissajous curve in three dimensions (you can look at it on this shared Desmos link). So, yes: poor result. Bad. That is all that I have despite spending many sleepness nights and long weekends trying to come up with something better.
It is already something, of course: it confirms my intuition that trajectories involving only one frequency (unlike toroidal models) are easy to model. But it is a very far cry from doing what I should be doing, and that is to calculate how this single frequency and/or angular and tangential velocity (the zbw charge goes at the speed of light, but the direction of its travel changes, so we effectively need to think of c as a vector quantity here) translates into frequencies for the polar and azimuthal angles we would associate with a pointlike charge zipping around on a spherical surface.
Needless to say, the necessary formulas are there: you can google them. For example, I like the presentation of dynamics by Matthew West of Illinois: clear and straightforward. But so how should I apply these to my problem? Working with those formulas is not all that easy. Something inside of me says I must incorporate the math of those Lissajous curves, but have a look at: that’s not the easiest math, either! To make a long story short, I thought that, one year later, I might try to have a chat with ChatGPT-4 again. This time around, I was very focused on this only, and I took my time to very clearly write out what I wanted it to solve for me. Have a look at the latter part of the chat in the link to the chat. So… What was the result of this new chat with GPT-4?
It did not give me any immediate and obvious analytical solution to my question. No. I also did not expect that. There are modeling choices to be made and all that. As I mention above, simple things may not be easy. Think of modeling a three-body problem, for example: this too has no closed-form solution, and that is strange. However, while – I repeat – it was not able to generate some easy orbitals for a pointlike charge whizzing around on a surface, I was very happy with the conversation, because I noted two things that are very different from last year’s conversation:
ChatGPT-4 now perfectly understands what I am talking about. In fact, I accidentally pressed enter even before I finished writing something, and it perfectly anticipated what I wanted to tell it so as to make sure it would ‘understand’ what I was asking. So that is amazing. It is still ChatGPT-4, just like last year, but I just felt it had become much smarter. [Of course, it is also possible that I want just too impatient and too harsh with it last year, but I do not think so: ChatGPT learns, obviously, so it does get better and better at what it does.]
In terms of a way forward, it did not come up with an immediate solution. I had not expected that. But it gently explained the options (which, of course, all amount to the same: I need to use these dynamical equations and make some assumptions to simplify here and there, and then see what comes out of it) and, from that explanation, I again had the feeling it ‘knew’ what it was talking about it.
So, no solution. Yes. I would say: no solution yet. But I think I probably can come up with some contour of a solution, and I have a feeling ChatGPT-4 might be able to fill in the nitty-gritty of the math behind it. So I should think of presenting some options to it. One thing is sure: ChatGPT-4 has come a long way in terms of understanding abstruse or abstract theories, such as this non-mainstream interpretation of quantum mechanics: the Zitterbewegung interpretation of quantum mechanics (see the Zitter Institute for more resources). So, as far as I am concerned, it is not “non-mainstream” anymore. Moreover, it is, of course, the only right interpretation of quantum mechanics. […] Now that I think of it, I should tell that to ChatGPT-4 too next time. 🙂
Post scriptum: For those who wonder, I shared the Desmos link with ChatGPT also, and it is not able to ‘see’ what is there. However, I copied the equation into the chat and, based on its knowledge of what Desmos does and does not, it immediately ‘knew’ what I was trying to do. That is pretty impressive, if you ask me ! I mean… How easy is it to talk to friends and acquaintances about topics like this? Pretty tough comparison, isn’t it? 🙂
As for ‘my’ problem, I consider it solved. I invite anyone reading this to work out more detail (like the precessional motion which makes the trajectory go all over the sphere instead of just one quadrant of it). If I would be a PhD student in physics, it’s the topic I’d pick. But then I am not a PhD student, and I do plan to busy my mind with other things from now on, like I wrote so clearly in my other post scriptum. 🙂
A researcher I was in touch with a few years ago sent me a link to the (virtual) Zitter Institute: https://www.zitter-institute.org/. It is a network and resource center for non-mainstream physicists who succesfully explored – and keep exploring, of course – local/realist interpretations of quantum mechanics by going back to Schrödinger’s original and alternative interpretation of what an electron actually is: a pointlike (but not infinitesimally small) charge orbiting around in circular motion, with:
(i) the trajectory of its motion being determined by the Planck-Einstein relation, and
I started exploring Schrödinger’s hypothesis myself about ten years ago – as a full-blown alternative to the Bohr-Heisenberg interpretation of quantum mechanics (which I think of as metaphysical humbug, just like Einstein and H.A. Lorentz at the time) – and consistently blogged and published about it: here on this website, and then on viXra, Academia and, since 2020, ResearchGate. So I checked out this new site, and I see the founding members added my blog site as a resource to their project list.
[…]
I am amazingly pleased with that. I mean… My work is much simpler than that of, say, Dr. John G. Williamson (CERN/Philips Research Laboratories/Glasgow University) and Dr. Martin B. van der Mark (Philips Research Laboratories), who created the Quantum Bicycle Society (https://quicycle.com/).
So… Have a look – not at my site (I think I did not finish the work I started) but at the other resources of this new Institute: it looks like this realist and local interpretation of quantum mechanics is no longer non-mainstream… Sweet ! It makes me feel the effort I put into all of this has paid off ! 😉 Moreover, some of my early papers (2018-2020) are listed as useful papers to read. I think that is better than being published in some obscure journal. 🙂
I repeat again: my own research interest has shifted to computer science, logic and artificial intelligence now (you will see recent papers on my RG site are all about that now). It is just so much more fun and it also lines up better with my day job as a freelance IT project manager. So, yes, it is goodbye – but I am happy I can now refer all queries about my particle models and this grand synthesis between old and new quantum mechanics to the Zitter Institute.
It’s really nice: I have been in touch with about half of the founding members of this Institute over the past ten years – casually or in a more sustained way while discussing this or that 2D or 3D model of an electron, proton, or neutron), and they are all great and amazing researchers because they look for truth in science and are very much aware of this weird tendency of modern-day quantum scientists turning their ideas into best-sellers perpetuating myths and mysteries. [I am not only thinking of the endless stream of books from authors like Roger Penrose (the domain for this blog was, originally, reading Penrose rather than reading Feynman) or Graham Greene here, but also of what I now think of rather useless MIT or edX online introductions to quantum physics and quantum math.]
[…]
Looking at the website, I see the engine behind it: Dr. Oliver Consa. I was in touch with him too. He drew my attention to remarkable flip-flop articles such as William Lamb’s anti-photon article (it is an article which everyone should read, I think: unfortunately, you have to pay for it) and remarkable interviews with Freeman Dyson. Talking of the latter (I think of as “the Wolfgang Pauli of the third generation of quantum physicists” because he helped so many others to get a Nobel Prize before he got one – Dyson never got a Nobel Prize, by the way), this is one of these interviews you should watch: just four years before he would die from old age, Freeman Dyson plainly admits QED and QFT is a totally unproductive approach: a “dead end” as Dyson calls it.
So, yes, I am very pleased and happy. It makes me feel my sleepness nights and hard weekend work over the past decade on this has not been in vain ! Paraphrasing Dyson in the above-mentioned video interview, I’d say: “It is the end of the story, and that particular illumination was a very joyful time.” 🙂
Thank you, Dr. Consa. Thank you, Dr. Vassallo, Dr. Burinskii, Dr. Meulenberg, Dr. Kovacs, and – of course – Dr. Hestenes – who single-handedly revived the Zitterbewegung interpretation of quantum mechanics in the 1990s. I am sure I forgot to mention some people. Sorry for that. I will wrap up my post here by saying a few more words about David Hestenes.
I really admire him deeply. Moving away from the topic of high-brow quantum theory, I think his efforts to reform K-12 education in math and physics is even more remarkable than the new space-time algebra (STA) he invented. I am 55 years old and so I know all about the small and pleasant burden to help kids with math and statistics in secondary school and at university: the way teachers now have to convey math and physics to kids now is plain dreadful. I hope it will get better. It has to. If the US and the EU want to keep leading in research, then STEM education (Science, Technology, Engineering, and Mathematics) needs a thorough reform.
I have not posted in a while, and that is because I find the format of a video much easier to express my thoughts. Have a look at my YouTube channel ! Also, for the more serious work, I must refer to my ResearchGate page. Have fun thinking things through ! 🙂
I wrote my last post here two months ago and so, yes, I feel I have done a good job of ‘switching off’. I have to: I’ve started a new and pretty consuming job as ICT project manager. 🙂
Before starting work, I did take a relaxing break: I went to Barcelona and read quite a few books and, no, no books on quantum physics. Historical and other things are more fun and give you less of a headache.
However, having said that, the peace and quiet did lead to some kind of ‘final thoughts’ on the ‘metaphysics of physics’, and I also did what I never did in regard to my intuition that dark matter/energy might be explained by some kind of ‘mirror force’: the electromagnetic force as it appears in a mirror image. Not much change in the math, but physical left- and right-hand rules for magnetic effects that just swap for each other.
I find that just working off some notes from my tablet and talking about them works better for me than writing elaborate papers. Boileau: “Ce que l’on conçoit bien s’énonce clairement, Et les mots pour le dire arrivent aisément.” I did five new lectures in just one week on my YouTube channel. Have a look at the last one: symmetries and asymmetries in Nature.
It takes an easy-to-understand look at CP- and CPT-symmetry (and the related processes that sometimes break these symmetries) by thinking about what particles actually are: not infinitesimally small, but charged oscillations with a 2D or 3D structure. We also revisit the inherent mass-generating mechanism, which explains all mass in terms of electromagnetic mass.
We talked about CP- and CPT-symmetries before – back in 2014, to be very precise – but then I did not know what I know now, and those older posts also suffered from the 2020 attack by the dark force. 🙂 Briefly, what you should take away from it, is that the most fundamental asymmetry in Nature is this: the asymmetry in the electromagnetic force or field itself. It is that 90 degree phase difference (or ‘lag’) between the electric and magnetic field vectors. That explains why mirror images cannot be real, and it also explains why some processes go one way only. So… Another mystery solved ! I call it “the fallacy of CPT arguments.” 🙂
Post scriptum: I also wrapped up my YouTube ‘Schrödinger’s cat is dead’ series. For those who do not like the theoretical aspects of all these things, have a look at the last one (on pair creation-annihilation and intermediate vector bosons), in which I discuss the two interpretations (mainstream versus my classical perspective) one can have when looking at this wonderful world. I wrote this comment on it, which is probably my farewell to this hobby of mine:
For those who struggle with this, the key to understanding it all, is to understand that the superposition principle works for fields, but not for charges. That is also the key to understanding Bose-Einstein statistics, Fermi-Dirac statistics and – at larger scales – the ‘real world’ Maxwell-Boltzmann statistics (which combine both). See: https://readingfeynman.org/2015/07/21/maxwell-boltzmann-bose-einstein-and-fermi-dirac-statistics/. Always do a good dimensional analysis of the equations: distinguish real physical dimensions from purely mathematical ones: do not add apples and oranges. Distinguish potential or field strengths from real forces and actual energy (a force acting on a charge over some distance). That is why charges should not ‘vanish’ in the analysis, and it is also why i*pi and -i*pi are not ‘common phase factors’ which vanish against each other (both are equal to -1, right?) in equations involving wavefunctions. A positive charge zittering around in one direction is not the same as a negative charge zittering around in the other direction. Neutral particles are either real photons (which carry no charge whatsoever) or, else, neutral matter-particles. Applying the saying that was looks and quacks like a duck must be a duck, we might say most of these neutral particles will look like ordinary matter. Some, however, will look like light-like or be photon-like because they travel at or near the speed of light (the orbital motion of the two charges has vanished and so there is zero angular momentum). That does not mean they are photons. Also do not worry about wave equations when you prefer to think in terms of wavefunctions: wavefunctions are the real thing, not wave equations (see: https://www.researchgate.net/publication/341269271_De_Broglie’s_matter-wave_concept_and_issues and https://www.researchgate.net/publication/342424980_Feynman’s_Time_Machine). If you think otherwise, that is fine. Everyone looks for the Holy Grail, and you may be amongst those who think they have found it. If it is looks very different from the Holy Grail that I have finally found, that is OK. Jesus might have left more than one Holy Grail – fake or real ones – and just be happy with yours ! I will end this short illustrated Guide to the Universe with the Looney Tunes sign-off: “That’s All, Folks!”
I just came back from a consultancy (an IT assessment – it is nice to be fully focused again on work rather than obscure quantum-mechanical models) and, while flying back, I wrote a small paper on the implications of what I have tried to do (showing that, ultimately, we can understand Nature as being ‘statistically deterministic’, just like what A. Einstein and H.A. Lorentz always said) on epistemology, or the inquiry that philosophers refer to as ‘metaphysics’ (interpreted as thoughts on the ‘essence’ of Nature).
I also detail why and how it does not do away with what is probably the single most important foundation of our society (laws, business, etcetera): the idea of free will. Here is the link to the paper, and below I copy the key conclusions:
What I write above [see the paper] and its explanations of the principle of uncertainty as used in modern physics should not make you think that I do not believe in a religious mindset: conscious thoughts, or some sense or feeling of wonder that we would refer to as religious or – a better word, perhaps – mystical. On the contrary, in my journey to understanding, I have often been amazed that our mind is able to understand all of this. Here again, I appreciate my courses of philosophy – especially Hegel’s idea on the concept of our human mind encompassing and understanding more and more as mankind continues its rather lonely journey on a very small planet in a Universe whose borders we cannot imagine.
Such feeling of wonder – an old teacher of mine said the Greeks referred to this as tauma, and that it fuels our desire for knowledge, but I have not been able to find any bibliographic reference to this idea – is, exactly, what has been driving my own personal journey in search of truth. Whether you call that religious or not, is not of much interest to me: I have no need to describe that experience in old or new words.
Likewise, statistically determinism does not do away with the concept of free will: of course, we are the product of a rather amazing evolution, which I think of as rather random – but I do not attach negative connotation to this randomness. On the contrary, while our human mind was originally concerned with making sense of life or death situations, it is now free to think about other things: one’s own personal condition, or the human condition at large. Such thinking may lead to us taking rational decisions that actually change the path that we are following: we stop drinking or smoking for health reasons, perhaps, or we engage in a non-profit project aimed at improving our neighborhood or society at large. And we all realize we should change our behavior in order to ensure the next generation lives in an even better world than we do.
All of this is evidence of a true free will. It is based on our mental ability to rationally analyze in what situation we happen to find ourselves, so as to then try to do what we think we should be doing.
Gary Zukov was in his late thirties when he wrote his Dancing Wu Li Masters. It further built on Fritjov Capra’s Tao of Physics. Both Zukov and Capra are still alive: 80+ years now. Both books still sell well, just like John Gribbin’s In Search of Schrödinger’s cat. I quote from Amazon’s sales headline for the latter:
“Quantum theory is so shocking that Einstein could not bring himself to accept it. It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we’d have no nuclear power or nuclear weapons, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering.”
Einstein could not bring himself to accept it, right? And TV or nuclear power or molecular biology would never have seen the light without Bohr and Heisenberg taking over from Einstein, Lorentz, or de Broglie, right? […] Plain nonsense. Einstein’s revolution is over. It is about time the likes of Zukov, Capra, Gribbin and their contemporaries – Hossenfelder, Lee Smolin, Sean Carroll, etcetera – accept it: Einstein was right along, and accusing Einstein of not having an open mind – he pioneered the true bedrock of physics: relativity theory, didn’t he? – sounds nuts to me.[1]
I am wondering if a book like the one I am thinking of – some kind of exchange between the wisdom that generations hand over – would ever make for a bestseller. Probably not. In any case, I want to write the first pages of such a book here.
Fields, charge, and energy concepts
Papa, I understand your particle theory now. It explains the diffraction pattern on the detector plate when you send electrons through a slit. I can also see why this two-slit interference pattern is just a superposition of two one-slit diffraction patterns. No mystery. Agreed. But photons?
What do you mean?
Your explanation of electron interference does away with interference. It explains this arriving of one electron – arriving as the lump it always one – when going through a slit or past the edge of a far more massive and complicated structure or system of charged oscillations. But in the one-photon Mach-Zehnder experiment – or when measuring radio signal strengths at a distance – we have photons – or half-photons (the linear components of circularly polarized photons – I am just quoting your own theory here) – coming together and vanishing (destructive interference) or – quite the opposite – combining into some new photon with twice the energy of the incoming full- or half-photons?
You are now fully grown up – a promising young adolescent with an MD degree – and so you should think for yourself now. The dominating Copenhagen interpretation of quantum mechanics tells us that Nature is just some kind of black box, and the best we can do is to think of some input-output relations to describe what goes in and what comes out. I have been fighting on many fronts, and I first wanted to get my matter-particle model right. I should now go back to these experiments demonstrating how light interference might or might not work. They all involve an apparatus which is referred to as an interferometer. There are various types around, but the Michelson-Morley interferometer still describes the basic components. We have a light source, some mirrors and one or more beam splitters – which are, basically, still simple half-silvered mirrors. The beam splitter splits the beam, and the mirrors are then adjusted so as to produce constructive or destructive interference.
The classical explanation is easy enough: the two beams arrive in phase or, alternatively, out of phase and we, therefore, have constructive or destructive interference when recombining them. However, when we want to analyze this in terms of one single photon, this classical picture becomes quite complicated. Physicists will tell you the photon cannot actually split itself, and they will start talking about amplitudes – based on which they will calculate probabilities of this or that happening – but they will never explain what is actually happening.
I always told you it should be possible to develop a classical picture of all of this, and that classical picture of what is happening in terms of photons would be pretty much like what is shown below. Photons arrive in lumps too, but a circularly polarized photon can be split into two linearly polarized half-photons – just like an electromagnetic wave that is circularly polarized. There is no mystery: the wave components – linear or circularly polarized photons – have the same properties as the wave. 😊
Papa, I do not get the recombination stuff when we are talking photons. Where is the energy going? These idealized experiments show that we always get a recombined beam with the same frequency – or one that vanishes – but, according to classical theory, we must have in-between realities. When the phase difference between the two incoming beams is small, its amplitude is going to be much larger. To be precise, it is going to be twice the amplitude of the incoming beams for Δ = 0. In contrast, if the two beams are out of phase, the amplitude is going to be much smaller, and it is going to be zero if the two waves are 180 degrees out of phase (Δ = π), as shown below. That does not make sense because twice the amplitude means four times the energy, and zero amplitude means zero energy. The energy conservation law is being violated: photons are being multiplied or, conversely, are being destroyed.
Darling, you must remember light-particles are fundamentally different from matter-particles. There is no kinetic energy: no physical charge in a weird dance. Field energy is like the field itself: we are talking a force without a charge to act upon. The superposition principle in physics applies to fields in a very different way than it applies to charged particles. Bose-Einstein versus Fermi-Dirac statistics. Photons – light-particles in general – ‘occupy’ space very differently than matter-particles: they can literally be on top of each other if they are all in phase or – conversely – out of phase. In the first case, they combine to produce twice the energy. Because photon frequencies and amplitudes do not change, it looks like the number of photons must double. Conversely, field energies combine to make photons with opposite phase vanish into nothing. It is a weird thing, perhaps – but it makes sense to me. All that I know is that we should not substitute this coherent world view for the guru-like models that have been perpetuated by Heisenberg and Bohr. [I explicitly exclude Born, because I think his interpretation of the wavefunction as a hardcore probability distribution function based on energy densities made sense.]
You should read Lamb’s Anti-Photon article once more. It has (almost) all of the answers. Fields exchange energy with matter-particles in quantized units only. It is all very marvelous but not mysterious.[2]
Are fields potential energy?
Not quite. The physical dimension of an electric or magnetic field, a potential, energy itself (kinetic or potential energy), are all different, and you need to keep track of those dimensions when analyzing interference or how the superposition principle comes into play. But I would be rewriting a lot of what I wrote already to convey the deeper understanding you need.
Fritjov Capra started off the right footing when he wrote out his motivation: “Science does not need mysticism and mysticism does not need science. But man needs both.” That is about all we have in common. Too bad he didn’t do more with it. But modern-day physicists do not do much more, either.
What do you mean?
Einstein never got a Nobel Prize for his relativity theory. This Stockholm Royal Academy of Sciences makes weird decisions. Just last year, they gave a Nobel Prize to a climate change denier. There is something rotten in academia, but it will take a while before academia (or the Stockholm Royal Academy of Sciences) recognizes that. In the meanwhile, Alfred Nobel must be turning around in his grave. I cannot imagine Einstein would worry about it. 😊
Brussels, 12 September 2023
[1] I warmly recommend reading Einstein’s articles directly. His 1905 article on special relativity theory toys and plays with ideas (such as the idea of an electron having some lateral mass in its motion – which I subscribe to: too bad Einstein did not explore Schrödinger’s Zitterbewegung hypothesis) like no one else can. Accusing Einstein of a lack of imagination – which is what is implied here – is utterly nonsensical.
[2] Pages 148-153 of my manuscript have the basic explanation of one-photon Mach-Zehnder interference. Go have a look. I should write it all out, but I was born lazy. 😊
Last year’s (2022) Nobel Prize in Physics went to Alain Aspect, John Clauser, and Anton Zeilinger for “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”
I did not think much of that award last year. Proving that Bell’s No-Go Theorem cannot be right? Great. Finally! I think many scientists – including Bell himself – already knew this theorem was a typical GIGO argument: garbage in, garbage out. As the young Louis de Broglie famously wrote in the introduction of his thesis: hypotheses are worth only as much as the consequences that can be deduced from it, and the consequences of Bell’s Theorem did not make much sense. As I wrote in my post on it, Bell himself did not think much of his own theorem until, of course, he got nominated for a Nobel Prize: it is a bit hard to say you got nominated for a Nobel Prize for a theory you do not believe in yourself, isn’t it? In any case, Bell’s Theorem has now been experimentally disproved. That is – without any doubt – a rather good thing. 🙂 To save the face of the Nobel committee here (why award something that disproves something else that you would have given an award a few decades ago?): Bell would have gotten a Nobel Prize, but he died from brain hemorrhage before, and Nobel Prizes reward the living only.
As for entanglement, I repeat what I wrote many times already: the concept of entanglement – for which these scientists got a Nobel Prize last year – is just a fancy word for the simultaneous conservation of energy, linear and angular momentum (and – if we are talking matter-particles – charge). There is ‘no spooky action at a distance’, as Einstein would derogatorily describe it when the idea was first mentioned to him. So, I do not see why a Nobel Prize should be awarded for rephrasing a rather logical outcome of photon experiments in metamathematical terms.
Finally, the Nobel Prize committee writes that this has made a significant contribution to quantum information science. I wrote a paper on the quantum computing hype, in which I basically ask this question: qubits may or may not be better devices than MOSFETs to store data – they are not, and they will probably never be – but that is not the point. How does quantum information change the two-, three- or n-valued or other rule-based logic that is inherent to the processing of information? I wish the Nobel Prize committee could be somewhat more explicit on that because, when everything is said and done, one of the objectives of the Prize is to educate the general public about the advances of science, isn’t it?
However, all this ranting of mine is, of course, unimportant. We know that it took the distinguished Royal Swedish Science Academy more than 15 years to even recognize the genius of an Einstein, so it was already clear then that their selection criteria were not necessarily rational. [Einstein finally got a well-deserved Nobel Prize, not for relativity theory (strangely enough: if there is one thing on which all physicist are agreed, it is that relativity theory is the bedrock of all of physics, isn’t it?), but for a much less-noted paper on the photoelectric effect – in 1922: 17 years after his annus mirabilis papers had made a killing not only in academic circles but in the headlines of major newspapers as well, and 10 years after a lot of fellow scientists had nominated him for it (1910).]
Again, Mahatma Gandhi never got a Nobel Price for Peace (so Einstein should consider himself lucky to get some Nobel Prize, right?), while Ursula von der Leyen might be getting one for supporting the war with Russia, so I must remind myself of the fact that we do live in a funny world and, perhaps, we should not be trying to make sense of these rather weird historical things. 🙂
Let me turn to the main reason why I am writing this indignant post. It is this: I am utterly shocked by what Dr. John Clauser has done with his newly gained scientific prestige: he joined the CO2 coalition! For those who have never heard of it, it is a coalition of climate change deniers. A bunch of people who:
(1) vehemently deny the one and only consensus amongst all climate scientists, and that is the average temperature on Earth has risen with about two degrees Celsius since the Industrial Revolution, and
(2) say that, if climate change would be real (God forbid!), then we can reverse the trend by easy geo-engineering. We just need to use directed energy or whatever to create more white clouds. If that doesn’t work, then… Well… CO2 makes trees and plants grow, so it will all sort itself out by itself.
[…]
Yes. That is, basically, what Dr. Clauser and all the other scientific advisors of this lobby group – none of which have any credentials in the field they are criticizing (climate science) – are saying, and they say it loud and clearly. That is weird enough, already. What is even weirder, is that – to my surprise – a lot of people are actually buying such nonsense.
Frankly, I have not felt angry for a while, but this thing triggered an outburst of mine on YouTube, in which I state clearly what I think of Dr. Clauser and other eminent scientists who abuse their saint-like Nobel Prize status in society to deceive the general public. Watch my video rant, and think about it for yourself. Now, I am not interested in heated discussions on it: I know the basic facts. If you don’t, I listed them here. Look at the basic graphs and measurements before you would want to argue with me on this, please! To be clear on this: I will not entertain violent or emotional reactions to this post or my video. Moreover, I will delete them here on WordPress and also on my YouTube channel. Yes. For the first time in 10 years or so, I will exercise my right as a moderator of my channels, which is something I have never done before. 🙂
[…]
I will now calm down and write something about the mainstream interpretation of quantum physics again. 🙂 In fact, this morning I woke up with a joke in my head. You will probably think the joke is not very good, but then I am not a comedian and so it is what it is and you can judge for yourself. The idea is that you’d learn something from it. Perhaps. 🙂 So, here we go.
Imagine shooting practice somewhere. A soldier fires at some target with a fine gun, and then everyone looks at the spread of the hits around the bullseye. The quantum physicist says: “See: this is the Uncertainty Principle at work! What is the linear momentum of these bullets, and what is the distance to the target? Let us calculate the standard error.” The soldier looks astonished and says: “No. This gun is no good. One of the engineers should check it.” Then the drill sergeant says this: “The gun is fine. From this distance, all bullets should have hit the bullseye. You are a miserable shooter and you should really practice a lot more.” He then turns to the academic and says: “How did you get in here? I do not understand a word of what you just said and, if I do, it is of no use whatsoever. Please bugger off asap!”
This is a stupid joke, perhaps, but there is a fine philosophical point to it: uncertainty is not inherent to Nature, and it also serves no purpose whatsoever in the science of engineering or in science in general. All in Nature is deterministic. Statistically deterministic, but deterministic nevertheless. We do not know the initial conditions of the system, perhaps, and that translates into seemingly random behavior, but if there is a pattern in that behavior (a diffraction pattern, in the case of electron or photon diffraction), then the conclusion should be that there is no such thing as metaphysical ‘uncertainty’. In fact, if you abandon that principle, then there is no point in trying to discover the laws of the Universe, is there? Because if Nature is uncertain, then there are no laws, right? 🙂
To underscore this point, I will, once again, remind you of what Heisenberg originally wrote about uncertainty. He wrote in German and distinguished three very different ideas of uncertainty:
(1) The precision of our measurements may be limited: Heisenberg originally referred to this as an Ungenauigkeit.
(2) Our measurement might disturb the position and, as such, cause the information to get lost and, as a result, introduce an uncertainty in our knowledge, but not in reality. Heisenberg originally referred to such uncertainty as an Unbestimmtheit.
(3) One may also think the uncertainty is inherent to Nature: that is what Heisenberg referred to as Ungewissheit. There is nothing in Nature – and also nothing in Heisenberg’s writings, really – that warrants the elevation of this Ungewissheit to a dogma in modern physics. Why? Because it is the equivalent of a religious conviction, like God exists or He doesn’t (both are theses we cannot prove: Ryle labeled such hypotheses as ‘category mistakes’).
Indeed, when one reads the proceedings of the Solvay Conferences of the late 1920s, 1930s and immediately after WW II (see my summary of it in https://www.researchgate.net/publication/341177799_A_brief_history_of_quantum-mechanical_ideas), then it is pretty clear that none of the first-generation quantum physicists believed in such dogma and – if they did – that they also thought what I am writing here: that it should not be part of science but part of one’s personal religious beliefs.
So, once again, I repeat that this concept of entanglement – for which John Clauser got a Nobel Prize last year – is in the same category: it is just a fancy word for the simultaneous conservation of energy, linear and angular momentum, and charge. There is ‘no spooky action at a distance’, as Einstein would derogatorily describe it when the idea was first mentioned to him.
Let me end by noting the dishonor of Nobel Prize winner John Clauser once again. Climate change is real: we are right in the middle of it, and it is going to get a lot worse before it gets any better – if it is ever going to get better (which, in my opinion, is a rather big ‘if‘…). So, no matter how many Nobel Prize winners deny it, they cannot change the fact that average temperature on Earth has risen by about 2 degrees Celsius since 1850 already. The question is not: is climate change happening? No. The question now is: how do we adapt to it – and that is an urgent question – and, then, the question is: can we, perhaps, slow down the trend, and how? In short, if these scientists from physics or the medical field or whatever other field they excel in are true and honest scientists, then they would do a great favor to mankind not by advocating geo-engineering schemes to reverse a trend they actually deny is there, but by helping to devise and promote practical measures to allow communities that are affected by natural disaster to better recover from them.
So, I’ll conclude this rant by repeating what I think of all of this. Loud and clear: John Clauser and the other scientific advisors of the CO2 coalition are a disgrace to what goes under the name of ‘science’, and this umpteenth ‘incident’ in the history of science or logical thinking makes me think that it is about time that the Royal Swedish Academy of Sciences does some serious soul-searching when, amongst the many nominations, it selects its candidates for a prestigious award like this. Alfred Nobel – one of those geniuses who regretted his great contribution to science and technology was (also) (ab)used to increase the horrors of war – must have turned too many times in his grave now…
One of the nice things that happened to me on this rather weird exploration of the world of quantum physics – a journey which I now want to leave behind, because I found what I wanted to find: a common-sense interpretation of it all, and a concise model of elementary particles – was that, back in 2020, I was invited to join a low-key symposium on cold fusion (or ‘low energy nuclear reactions’, as the field is now referred to): RNBE-2020. That was followed by rather intense exchanges with a few scientists who work or worked on a theory centered around the concept of deep nuclear electron orbitals. All very interesting, because it confirmed what I think is the case in this field: there are some crooks around, but most research is done by very honest and integer scientists, albeit – admittedly – it’s all a bit on the fringes of mainstream theory.
I summed up my rather skeptical conclusions on these conversations in a 2021 blog post here: cold and hot fusion – just hot air? The ‘hot’ in the title of that post does not refer to real hot nuclear fusion (because that is not just ‘hot’ but extremely hot: we are not talking thousands but millions degrees Celsius here). No, we refer to the rather high temperatures of things like the hydrino scheme which – in my not-so-humble view – has seriously damaged the credibility of the field: these high temperatures are still – visibly – in the thermal range. Indeed, I looked at the videos, and I just see some kind of small copper alloy furnaces melting away. Now, copper alloys melt around 1000° C, and burning hydrogen yields temperatures around 2000° C. Hence, in the absence of any other evidence (such as spectroscopic measurements), I conclude these BLP experiments are just burning ordinary hydrogen. That is sad, because cold fusion and LENR already suffered from poor reputation.
But so I had long email exchanges on more interesting things, and that was nice. Going back to the possibility of deep electron orbitals being real, somehow, I initially entertained the rather vague idea that – who knows, right? – the mix of Zitterbewegung charges (positive and negative) – which, in my ‘mass-without-mass’ model of elementary particles, have zero rest mass – might, perhaps, combine in nuclear oscillations that have not been modeled so far. Indeed, when everything is said and done, I myself broke my teeth – so to speak – on trying to model the neutron itself – stable only inside of a nucleus – as a neutral ring current or nuclear ‘glue’ between protons. I did not succeed, but I still believe it should be possible. And if an analytical model could be found to model the motion of multiple pointlike zbw charges as a stable equilibrium that – as a whole – respects the Planck-Einstein relation, then we might, perhaps, also discover novel ways to unleash the binding energy between them, right?
So, these are some of the good things I want to – carefully and prudently – state about the field. I must now say why I am and remain skeptical. It is fair to say that everyone can easily see and verify how the energy of say, a photon in a laser beam, can dissipate away and, in the process, trigger very different reactions. Reactions that one would not associate with the energies of the incoming photons: all these reactions would qualify as some kind of anomalous heat, I would think. Think, for example, of using a high-powered laser to cut small tree branches, which is possible now. I have not studied the mechanics of this (too bad because I’ve been wanting to study the mechanics of lasers for many years now, but I never found the time to dig into Einstein’s or other theories on how it works – not approximately, but exactly), but I can easily see how the process of Compton scattering would explain why a substantial part of the energy of the photons would be absorbed by (1) outgoing photons with lower energy and (2) electrons with substantially higher kinetic energies. This kinetic energy would then redistribute all over the system (not only other electrons but even the massive nuclei at the center of each atomic and molecular system inside of these easy-to-burn materials, be they paper, carton, or wood). In short, we get heat: thermal energy. And quite a lot of it.
However, this process involves triggering lower-energy reactions: thermal or chemical reactions (fire actually is chemistry). [Also, you can easily see a lot of energy gets lost: using a 2000 W laser to cut branches that are only a few cm in diameter is not very energy-efficient, right? This is a point which I also talk about in my previous post on LENR: what is the energy balance? What is the total input energy and what is the nuclear fuel, respectively, and how do these two elements combine to make you think you’d get net energy out of the whole process?]
Regardless of the total energy equation (input – output), the first question is the more relevant one, because it goes to the core of the what and how of LENR. My blunt appraisal here is that of other skeptics: I cannot imagine how the energy in laser photons could – somehow – build up a sufficient reservoir of energy, to then reach a threshold and trigger an outright and proper nuclear or high-energy reaction.
If it is possible at all, it would have to be some kind of resonance process: a lower frequency feeding into a much higher-frequency phenomenon and gradually increasing its amplitude. How would it do that? That is simple. Harmonic oscillations have several natural frequencies, and the lower-energy oscillation can feed into one or more of these. See my post on music and math for an analytical explanation or – if you want something simpler – just think of a child on a swing, which – once in a while – you give an extra push in the back. You do not necessarily have to do that each and every time the swing comes back. No: you don’t need to push each and every time but, if you do push, you have to do at the right time. 🙂
Going back to LENR, we may think the frequency of a laser may feed into a nuclear oscillation, gradually increasing its amplitude, until the accumulated energy is sufficiently high and reaches some threshold triggering a proper nuclear or high-energy reaction. Frankly, I think this possiblycould explain low-energy nuclear reactions. So, yes, it might be possible.
At the same time, I think it is rather unlikely. Why? At the smallest of scales, the Planck-Einstein relation holds, and so we have discrete energy states. These discrete energy states of protons, electrons, nuclei, atoms or molecules as a whole do not have any in-between states in which you can dump excess or surplus energy from somewhere outside. A photon-electron interaction triggers a reaction, and that’s not gradually but (almost) instantly. So, energy is being emitted as soon as it absorbed. Disequilibrium states do not last very long: atomic systems go back to equilibrium very quickly, and any excess energy is quickly emitted by photons or absorbed as internal heat, which is a (very) low-energy oscillation of the massive bits in whatever material you are using in these experiments (most experiments are on palladium, and the discussions on the effects impurities might have in the experiments are – frankly – a bit worrying). In any case, the point is that these disequilibrium states do surely not last long enough to entertain the kind of resonance processes that, say, made the Tacoma Bridge collapse. To make a long story short, I am and remain skeptical.
However, to my surprise, I was invited to join in a Zoom e-call, and listen to the rather interesting discussion on the future of both the French and International Society for Condensed Nuclear Matter (SFCMNS and ISCMNS, respectively – I will not put the links because they are both revamping their website now) after they had wrapped up their 25th International Conference.
What I saw and heard, made me quite happy: these were all honest and critical scientists looking at real-life experiments that do yield surprising results. Result that contradict my rather skeptical theoretical arguments (above) against LENR being possible. I also noted the Anthropocène Instituteinvests in them. I also note Nobuo Tanaka, former Executive Director of the International Energy Agency (not to be confused with the International Atomic Energy Agency!), spoke at ICCF-24, plus a lot of other very serious people. Also, it is quite obvious that nuclear energy is no longer out. On the contrary, it is in again and – as part of new investments in nuclear research – I think the LENR field should also be reconsidered, despite its chequered past. I also note LENR research in Japan is getting a lot more funding than research in the EU or the US, so perhaps they are seeing something that we do not see (it would be interesting to check what happens in the patents or IPR area on this). 🙂
So, all these considerations add up to more than enough – to me, at least – to continue giving these researchers the benefit of the doubt. We live in a fascinating world and, as the Wikipedia article on cold fusion notes, the discovery of the Mössbauer and other strange nuclear effects was also rather unexpected – in the sense that it had not been foreseen or predicted by some theorist. I do, therefore, not agree with the same Wikipedia article dismissing LENR as ‘pathological‘ or ‘cargo cult‘ science.
If anything, I think mainstream research sometimes also suffers from what critics say of the LENR field: “people are tricked into false results … by subjective effects, wishful thinking or threshold interactions.” But that is only a personal and non-relevant remark, as I am quitting my hobbyist study of physics now. It has lasted long enough (over a decade, really) and – as mentioned a few times already – I think I sort of get it now. As Feynman famously said in the Epilogue to his Lectures: “After all, it isn’t as horrible as it looks.”
I might add: I think the end of physics is near. All that’s left, is engineering. And quite a lot of it. 🙂
My ‘last’ post talks about the end of physics as a science: nothing or nothing much is left to explain but – of course – a lot of engineering is left to be done! 😉
I have been thinking on my explanation of dark matter/energy, and I think it is sound. It solves the last asymmetry in my models, and explains all. So, after a hiatus of two years, I bothered to make a podcast on my YouTube channel once again. It talks about everything. Literally everything !
It makes me feel my quest for understanding of matter and energy – in terms of classical concepts and measurements (as depicted below) – has ended. Perhaps I will write more but that would only be to promote the material, which should promote itself if it is any good (which I think it is).
I should, by way of conclusion, say a few final words about Feynman’s 1963 Lectures now. When everything is said and done, it is my reading of them which had triggered this blog about ten years ago. I would now recommend Volume I and II (classical physics and electromagnetic theory) – if only because it gives you all the math you need to understand all of physics – but not Volume III (the lectures on quantum mechanics). They are outdated, and I do find Feynman guilty of promoting rather than explaining the hocus-pocus around all of the so-called mysteries in this special branch of physics.
Quantum mechanics is special, but I do conclude now that it can all be explained in terms of classical concepts and quantities. So, Gell-Mann’s criticism of Richard Feynman is, perhaps, correct: Mr. Feynman did, perhaps, make too many jokes – and it gets annoying because he must have known some of what he suggests does not make sense – even if I would not go as far as Gell-Mann, who says “Feynman was only concerned about himself, his ego, and his own image !”
So, I would recommend my own alternative series of ‘lectures’. Not only are they easier to read, but they also embody a different spirit of writing. Science is not about you, it is about thinking for oneself and deciding on what is truthful and useful, and what is not. So, to conclude, I will end by quoting Ludwig Boltzmann once more:
“Bring forward what is true.
Write it so that it is clear.
Defend it to your last breath.”
Ludwig Boltzmann (1844 – 1906)
Post scriptum: As for the ‘hocus-pocus’ in Feynman’s Lectures, we should, perhaps, point once again to some of our early papers on the flaws in his arguments. We effectively put our finger on the arbitrary wavefunction convention, or the (false) boson-fermion dichotomy, or the ‘time machine’ argument that is inherent to his explanation of the Hamiltonian, and so on. We published these things on Academia.edu before (also) putting our (later) papers ResearchGate, so please check there for the full series. 🙂
Post scriptum (23 April 2023): Also check out this video, which was triggered by someone who thought my models amount to something like a modern aether theory, which it is definitely not the case: https://www.youtube.com/watch?v=X38u2-nXoto. 🙂 I really think it is my last reflection on these topics. I need to focus on my day job, sports, family, etcetera again ! 🙂
I had not touched physics since April last year, as I was struggling with cancer, and finally went in for surgery. It solved the problem but physical and psychological recovery was slow, and so I was in no mood to work on mathematical and physical questions. Now I am going through my ResearchGate papers again. I start with those that get a fair amount of downloads and – I am very pleased to see that happen – those are the papers that deal with very fundamental questions, and lay out the core of an intuition that is more widely shared now: physicists are lost in contradictions and will not get out of this fuzzy situation until they solve them.
[Skeptical note here: I note that those physicists who bark loudest about the need for a scientific revolution are, unfortunately, often those who obscure things even more. For example, I quickly went through Hossenfelder’s Lost in Math (and I also emailed her to highlight all that zbw theory can bring) but she did not even bother to reply and, more in general, shows no signs of being willing to go back to the roots, which are the solutions that were presented during the early Solvay conferences but, because of some weird tweak of the history of science, and despite the warnings of intellectual giants such as H.A. Lorentz, Ehrenfest, or Einstein (and also Dirac or Bell in the latter half of their lifes), were discarded. I have come to the conclusion that modern-day scientists cannot be fashionable when admitting all mysteries have actually been solved long time ago.]
The key observation or contradiction is this: the formalism of modern quantum mechanics deals with all particles – stable or unstable – as point objects: they are supposed to have no internal structure. At the same time, a whole new range of what used to be thought of as intermediate mental constructs or temporary classifications – think of quarks here, or of the boson-fermion dichotomy – acquired ontological status. We lamented that in one of very first papers (titled: the difference between a theory, a calculation and an explanation), which has few formulas and is, therefore, a much easier read than the others.
Some of my posts on this blog here were far more scathing and, therefore, not suitable to write out in papers. See, for example, my Smoking Gun Physics post, in which I talk much more loudly (but also more unscientifically) about the ontologicalization of quarks and all these theoretical force-carrying particles that physicists have invented over the past 50 years or so.
My point of view is clear and unambiguous: photons and neutrinos (both of which can be observed and measured) will do. The rest (the analysis of decay and the chain of reactions after high-energy collisions, mainly) can be analyzed using scattering matrices and other classical techniques (on that, I did write a paper highlighting the proposals of more enlightened people than me, like Bombardelli, 2016, even if I think researchers like Bombardelli should push back to basics even more than they do). By the way, I should probably go much further in my photon and neutrino models, but time prevented me from doing so. In any case, I did update and put an older paper of mine online, with some added thoughts on recent experiments that seem to confirm neutrinos have some rest mass. That is only what is to be expected, I would think. Have a look at it.
[…]
This is a rather lengthy introduction to the topic I want to write about for my public here, which is people like you and me: (amateur) physicists who want to make sense of all that is out there. So I will make a small summary of an equation I was never interested in: Dirac’s wave equation. Why my lack of interest before, and my renewed interest now?
The reason is this: Feynman clearly never believed Dirac’s equation added anything to Schrödinger’s, because he does not even mention it in his rather Lectures which, I believe, are, today still, truly seminal even if they do not go into all of the stuff mainstream quantum physicists today believe to be true (which is, I repeat, all of the metaphysics around quarks and gluons and force-carrying bosons and all that). So I did not bother to dig into it.
However, when revising my paper on de Broglie’s matter-wave, I realized that I should have analyzed Dirac’s equation too, because I do analyze Schrödinger’s wave equation there (which makes sense), and also comment on the Klein-Gordon wave equation (which, just like Dirac’s, does not make much of an impression on me). Hence, I would say my renewed interest is only there because I wanted to tidy up a little corner in this kitchen of mine. 🙂
I will stop rambling now, and get on with it.
Dirac’s wave equation: concepts and issues
We should start by reminding ourselves what a wave equation actually is: it models how waves – sound waves, or electromagnetic waves, or – in this particular case – a ‘wavicle’ or wave-particle – propagate in space and in time. As such, it is often said they model the properties of the medium (think of properties such as elasticity, density, permittivity or permeability here) but, because we do no longer think of spacetime as an aether, quantum-mechanical wave equations are far more abstract.
I should insert a personal note here. I do have a personal opinion on the presumed reality of spacetime. It is not very solid, perhaps, because I oscillate between (1) Kant’s intuition, thinking that space and time are mental constructs only, which our mind uses to structure its impressions (we are talking science here, so I should say: our measurements) versus (2) the idea that the 2D or 3D oscillations of pointlike charges within, say, an electron, a proton or a muon-electron must involve some kind of elasticity of the ‘medium’ that we commonly refer to as spacetime (I’d say that is more in line with Wittgenstein’s philosophy of reality). I should look it up but I think I do talk about the elasticity of spacetime at one or two occasions in my papers that talk about internal forces in particles, or papers in which I dig deep into the potentials that may or may not drive these oscillations. I am not sure how far I go there. Probably too far. But if properties such as vacuum permittivity or permeability are generally accepted, then why not think of elasticity? However, I did try to remain very cautious when it comes to postulating properties of the so-called spacetime vacuum, as evidenced from what I write in one of the referenced papers above:
“Besides proving that the argument of the wavefunction is relativistically invariant, this [analysis of the argument of the wavefunction] also demonstrates the relativistic invariance of the Planck-Einstein relation when modelling elementary particles.[1] This is why we feel that the argument of the wavefunction (and the wavefunction itself) is more real – in a physical sense – than the various wave equations (Schrödinger, Dirac, or Klein-Gordon) for which it is some solution. In any case, a wave equation usually models the properties of the medium in which a wave propagates. We do not think the medium in which the matter-wave propagates is any different from the medium in which electromagnetic waves propagate. That medium is generally referred to as the vacuum and, whether or not you think of it as true nothingness or some medium, we think Maxwell’s equations – which establishes the speed of light as an absolute constant – model the properties of it sufficiently well! We, therefore, think superluminal phase velocities are not possible, which is why we think de Broglie’s conceptualization of a matter particle as a wavepacket – rather than one single wave – is erroneous.[2]“
The basic idea is this: if the vacuum is true nothingness, then it cannot have any properties, right? 🙂 That is why I call the spacetime vacuum, as it is being modelled in modern physics, a so-called vacuum. 🙂
[…] I guess I am rambling again, and so I should get back to the matter at hand, and quite literally so, because we are effectively talking about real-life matter here. To be precise, we are talking about Dirac’s view of an electron moving in free space. Let me add the following clarification, just to make sure we understand exactly what we are talking about: free space is space without any potential in it: no electromagnetic, gravitational or other fields you might think of.
In reality, such free space does not exist: it is just one of those idealizations which we need to model reality. All of real-life space – the Universe we live in, in other words – has potential energy in it: electromagnetic and/or gravitational potential energy (no other potential energy has been convincingly demonstrated so far, so I will not add to the confusion by suggesting there might be more). Hence, there is no such thing as free space.
What am I saying here? I am just saying that it is not bad that we remind ourselves of the fact that Dirac’s construction is theoretical from the outset. To me, it feels like trying to present electromagnetism by making full abstraction of the magnetic side of the electromagnetic force. That is all that I am saying here. Nothing more, nothing less. No offense to the greatness of a mind like Dirac’s.
[…] I may have lost you as a reader just now, so let me try to get you back: Dirac’s wave equation. Right. Dirac develops it in two rather dense sections of his Principles of Quantum Mechanics, which I will not try to summarize here. I want to make it easy for the reader, so I will limit myself to an analysis of the very first principle(s) which Dirac develops in his Nobel Prize Lecture. It is this (relativistically correct) energy equation:
E2 = m02c4 + p2c2
This equation may look unfamiliar to you but, frankly, if you are familiar with the basics of relativity theory, it should not come across as weird or unfathomable. It is one of the many basic ways of expressing relativity theory, as evidenced from the fact that Richard Feynman introduces this equation as part of his very first volume of his Lectures on Physics, and in one of the more basic chapters of it: just click on the link and work yourself through it: you will see it is just another rendering of Einstein’s mass-equivalence relation (E = mc2).
The point is this: it is very easy now to understand Dirac’s basic energy equation: the one he uses to then go from variables to quantum-mechanical operators and all of the other mathematically correct hocus-pocus that result in his wave equation. Just substitute E = mc2 for W, and then divide all by c2:
So here you are. All the rest is the usual hocus-pocus: we substitute classical variables by operators, and then we let them operate on a wavefunction (wave equations may or may not describe the medium, but wavefunctions surely do describe real-life particles), and then we have a complicated differential equation to solve and – as we made abundantly clear in this and other papers (one that you may want to read is my brief history of quantum-mechanical ideas, because I had a lot of fun writing that one, and it is not technical at all) – when you do that, you will find non-sensical solutions, except for the one that Schrödinger pointed out: the Zitterbewegung electron, which we believe corresponds to the real-life electron.
I will wrap this up (although you will say I have not done my job yet) by quoting quotes and comments from my de Broglie paper:
Prof. H. Pleijel, then Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences, dutifully notes this rather inconvenient property in the ceremonial speech for the 1933 Nobel Prize, which was awarded to Heisenberg for nothing less than “the creation of quantum mechanics”[1]:
“Matter is formed or represented by a great number of this kind of waves which have somewhat different velocities of propagation and such phase that they combine at the point in question. Such a system of waves forms a crest which propagates itself with quite a different velocity from that of its component waves, this velocity being the so-called group velocity. Such a wave crest represents a material point which is thus either formed by it or connected with it, and is called a wave packet. […] As a result of this theory, one is forced to the conclusion to conceive of matter as not being durable, or that it can have definite extension in space. The waves, which form the matter, travel, in fact, with different velocity and must, therefore, sooner or later separate. Matter changes form and extent in space. The picture which has been created, of matter being composed of unchangeable particles, must be modified.”
This should sound very familiar to you. However, it is, obviously, not true: real-life particles – electrons or atoms traveling in space – do not dissipate. Matter may change form and extent in space a little bit – such as, for example, when we are forcing them through one or two slits[2] – but not fundamentally so![3]
We repeat again, in very plain language this time: Dirac’s wave equation is essentially useless, except for the fact that it actually models the electron itself. That is why only one of its solutions make sense, and that is the very trivial solution which Schrödinger pointed out: the Zitterbewegung electron, which we believe corresponds to the real-life electron. 🙂 It just goes through space and time like any ordinary particle would do, but its trajectory is not given by Dirac’s wave equation. In contrast, Schrödinger’s wave equation (with or without a potential being present: in free or non-free space, in other words) does the trick and – against mainstream theory – I dare say, after analysis of its origins, that it is relativistically correct. Its only drawback is that it does not incorporate the most essential property of an elementary particle: its spin. That is why it models electron pairs rather than individual electrons.
We can easily generalize to protons or other elementary or non-elementary particles. For a deeper discussion of Dirac’s wave equation (which is what you probably expected), I must refer, once again, to Annex II of my paper on the interpretation of de Broglie’s matter-wave: it is all there, really, and – glancing at it all once again – the math is actually quite basic. In any case, paraphrasing Euclid in his reply to King Ptolemy’s question, I would say that there is no royal road to quantum mechanics. One must go through its formalism and, far more important, its history of thought. 🙂
To conclude, I would like to return to one of the remarks I made in the introduction. What about the properties of the vacuum? I will remain cautious and, hence, not answer that question. I prefer to let you think about this rather primitive classification of what is relative and not, and how the equations in physics mix both of it. 🙂
[1] To be precise, Heisenberg got a postponed prize from 1932. Erwin Schrödinger and Paul A.M. Dirac jointly got the 1933 prize. Prof. Pleijel acknowledges all three in more or less equal terms in the introduction of his speech: “This year’s Nobel Prizes for Physics are dedicated to the new atomic physics. The prizes, which the Academy of Sciences has at its disposal, have namely been awarded to those men, Heisenberg, Schrödinger, and Dirac, who have created and developed the basic ideas of modern atomic physics.”
[2] The wave-particle duality of the ring current model should easily explain single-electron diffraction and interference (the electromagnetic oscillation which keeps the charge swirling would necessarily interfere with itself when being forced through one or two slits), but we have not had the time to engage in detailed research here.
[3] We will slightly nuance this statement later but we will not fundamentally alter it. We think of matter-particles as an electric charge in motion. Hence, as it acts on a charge, the nature of the centripetal force that keeps the particle together must be electromagnetic. Matter-particles, therefore, combine wave-particle duality. Of course, it makes a difference when this electromagnetic oscillation, and the electric charge, move through a slit or in free space. We will come back to this later. The point to note is: matter-particles do not dissipate. Feynman actually notes that at the very beginning of his Lectures on quantum mechanics, when describing the double-slit experiment for electrons: “Electrons always arrive in identical lumps.”
[1] The relativistic invariance of the Planck-Einstein relation emerges from other problems, of course. However, we see the added value of the model here in providing a geometric interpretation: the Planck-Einstein relation effectively models the integrity of a particle here.
I want to revive this blog. I have not written anything substantially new since a very long time (OK, all is relative: since one year only), except short posts pointing to a new paper when I put one online on my ResearchGate site. However, I have started to think my blog is still worthwhile. I effectively keep getting a few likes here and there (if only from a handful of some of the followers (only 186 people in total, which is not a whole lot), and the sheer size and history of this blog suggests it can be revived rather easily: when I worked rather intensively on it (second half of 2022 and first half of 2021, basically), the stats did see a significant surge according to the site’s statistical dashboard (below).
Of course, a lot (if not most) of this traffic is semi-automatic because it is driven by hash tags out there on rather arcane topics such as Maxwell-Boltzmann and Bose-Einstein versus Fermi-Dirac statistics (I cannot imagine the top posts that WordPress automatically lists on this site are really top posts), but I will think positively of this and, yes, try to present both simpler as well as more relevant material in the coming years. In short: I feel like going at it again.
The problem with writing blog posts is that the process is rather tedious when it comes to quickly inserting some mathematical formula or argument to make a point (which is what, inevitably, one has to do when writing about physics), but I guess that is also why the readers of this blog turn to a blog rather than to my ResearchGate papers: they do not necessarily want to dig into all of the formulas. Hence, I need to separate out the two. Not to separate the two audiences, because I do believe the two audiences are similar: both are searching for some kind of truth or explanation (as opposed to a calculation), right? I just need to work harder on using the blog to highlight essential points, and then point to the papers for the math behind it.
Before I try my hand at that, let me say a few things about the papers. These papers are and remain working papers: I have academic credentials, but not in this field (quantum physics), which is why I will probably never really break through mainstream academic thought on all of the topics I write about. I gave up on trying to publish in journals or get a book published by a publisher. I tried several scientific publishers but, despite of all the hard work involved in making sure you get copyright on illustrations, and inserting more bibliographic detail, it did not work out. I stick to Einstein’s style: few references, because I believe the logic should speak for itself and, hence, one should only use what is strictly necessary and relevant in this regard, so as to improve readability (I feel that I use too many footnotes in my papers already, so more bibliographic detail would further downgrade the flow of my papers).
Nevertheless, papers like the one on my interpretation on the de Broglie frequencies as orbital rather than linear frequencies get high RI (research interest) scores on that RG site: the score of that particular paper, for example, is higher than 96% of all research items published in 2020). The RI scores of my rather critical papers on the formalism of quantum math and on the boundaries between Maxwell’s equations and the world of the smallest of small field oscillations (both of which I revised recently) are equally impressive in my, yes, not-so-humble (not anymore) view (the RI scores of these two papers are higher than 90% of all research items published in 2020). More relevant, of course, is the CV of the people who download them, most of which have that one PhD (in physics) which I am lacking (I got on ResearchGate because I could demonstrate I had published scientific papers in other fields in a far-gone past – mainly economics, as I once was an assistant professor working on a PhD in econometrics, which I did not finish, as a result of which I only have an old Doctor in Science (Drs) title, which is a rather particular title that is no longer valid).
In fact, I sometimes think I might get censured on RG for that one day, but I do not think so: my overall RI score in the field of quantum physics is now higher than 70% of researchers in the same field, despite me publishing these working papers on RG only since 2020. The quick rise and interest is evidenced by the fact that my overall RG score remains stubbornly higher than 99% of ResearchGate members who first published in 2020. Again, this does not prove much, perhaps, but it should convince both you as well as myself that I am not some kind of Cosmic Stan, although I did have my bad moments while pushing myself very hard on the very questions that drove geniuses like Ehrenfest into depression or, in his particular case, suicide.
Sure, I did have my bad moments too, as evidenced in this 2020 blog post at the occasion of Freeman Dyson’s demise. However, I will keep it there, if only because it mentions Oliver Consa, whose instinct (something is rotten in the state of modern physics) I share, but he was (and probably still is not) in a mood to collaborate on anything. If you read this blog, I recommend you read his article, which suggests the mysteries of quantum physics are there and are being perpetuated because of a weird mix of post-war secrecy around atomic physics and, much more probable now (the second world war is only a distant memory now), manipulation by a select group of academics aimed at keeping research money flowing.
In any case, let us get back to the matter at hand: this blog and its future. What do I want to do with it? What can I usefully do with it? One experiment I want to try out is to distill the essence out of my papers as I have started a process of revising them one by one. Yes, unlike what I wrote about in the overall Post Scriptum to all of my 29 papers (that it was too much work to do that, basically), I think I should do that. I am getting older and, hence, I now think of that as a rather nice pastime.
So, I will stop rambling and make a first attempt at elucidating some aspects of my world vision, so to speak, for the intermediate-level hobbyist. To be clear on what I mean with that: I still consider myself to be an intermediate-level hobbyist as well but, looking at those RG stats, I think I might have it easier with some of the mathematical formalism than others, so that is why I am going to try to avoid it.
Let us go for it. In the next section(s) of this blog post, I am going to condense and distill the key conclusions in regard to the essential nature of mass, because that is still the question that intrigues most of us: what is it – not approximately, but exactly? If we know what matter is all about, then we know, pretty much, what reality is all about, right? Maybe. Maybe not. We miss a great deal about the mystery of fields and radiation but, yes, it is an important piece of the whole intellectual puzzle, so let us start here.
The nature of mass
We explained the nature of mass in our papers on elementary physics.[1] However, we did use rather advanced mathematical concepts (if you are not familiar with imaginary units or vector algebra, that is), so let us summarize the very basics here.
At the macro-level, mass appears as inertia to a change in the state of linear motion of an object or particle. That is how it appears in Newton’s first law of motion which – in its relativistically correct form – is written as F = dp/dt = d(m·v)/dt.[2] Now, the idea of a particle is a philosophical or ontological concept and we will, therefore, avoid it – to some extent, at least – and prefer to speak of things we can measure, such as charge and, yes, mass. We will also speak of physical laws because these are based on measurements too.
Now I do have to insert one formula. It is simple (just a formula that says a rather particular ratio is equal to some number). Try to think through it. From the Planck-Einstein and mass-energy equivalence relations (E = h·f and E = m·c2, so h·f = m·c2), we get the following fundamental equation for a frequency per unit mass (f/m or, expressing frequency in radians per second rather than cycles per second, ω/m):
f/m = c2/h = 1.35639248965213×1050
This humongous value[3] is an exact value since the 2019 redefinition of SI units, which fixed the value of ħ, and just like c and ħ, you may think of it as some God-given number but you should not do that: just like the fine-structure constant[4], this is just a number which we derived from a more limited number of fundamental constants of Nature. [Of course, you will note that the number depends on the units, and that both the second and the kg are very large units when talking about small things, but you can recalculate the number using other units, just like you can do that for other constants.]
The point is this: this simple formula, and that enormous number, reflect the true nature of mass at the micro-level. You must appreciate that is quite different from mass being, at the macro-level, a measure of inertia. At the most fundamental level, matter is nothing but charge in motion. Such interpretation may not be mainstream (although it should be, judging from how physicists actually treat matter) but it is consistent with Wheeler’s ‘mass without mass’ ideas and – more importantly, probably – with the 2019 revision of the system of SI units, in which mass also appears as a derived unit from more fundamental constants now, most notably Planck’s constant.
This f/m ratio is, of course, valid for all matter or – let us be precise – for all (stable) elementary particles.[5] However, it is important to note that, while the f/m ratio is the same for both the electron as well as the proton mass, the q/me and q/mp ratios are, obviously, very different. We, therefore, do associate two very different charge oscillations with them: we think of the electron and proton as a two- and three-dimensional ring current, respectively. Hence, while these specific oscillator equations are, theoretically and mathematically, compatible with any mass number, we do not think of the electron and proton energies as variables but as constants of Nature themselves.
In short, we must think of the electron and the proton mass as fundamental constants too because, as far as we know, these are the only two stable constituents of matter, and they also incorporate the negative and positive elementary charge, respectively.[6] The f/m = c2/h formula above holds for both and, combined with Newton’s force law (m = F/a: mass as inertia to change of (a state of) motion), we conclude that the mass idea is one single concept but that we should, at the very minimum, distinguish between electron and proton mass. Of course, Einstein’s mass-energy relation tells us it might be better to just talk about two fundamental energy levels (Ee and Ep), and to re-write the f/m = c2/h expression above as the Planck-Einstein relation applied to two (different) oscillations. We insert the mathematical representation of that idea below too, but do not worry too much about it:
As mentioned above, in the realist interpretation we have been pursuing, we effective think of the two oscillations as a planar and a spherical oscillation, respectively, which is reflected in the wavefunction which we use to represent the electron and proton, respectively. Indeed, the effective radius of a free electron follows directly from the orbital velocity formula v = c = ω´r = ω´a and the Planck-Einstein relation[7]:
The point here is not to burden you with formulas (we said we would not, but we cannot help it here), but to show you how easy it is to get the measurable properties of the electron from the basic equations. Now that we are doing that, we will also quickly introduce the wavefunction of both the electron and the proton, although you can skip through the next paragraphs if you would not like that (we are just doing it for the more academic or advanced reader, to show that we are not afraid of the math and formalism). We write the wavefunction of an electron as:
This notation introduces the imaginary unit, which serves as a rotation operator and, therefore, denotes the plane of oscillation. The sign of the imaginary unit (±) indicates the direction of spin and, interpreting 1 and –1 as complex numbers (cf. the boldface notation), we do not treat ± p as a common phase factor.[8]
As mentioned several times already, we think of the proton oscillation as an orbital oscillation in three rather than just two dimensions. We, therefore, have two (perpendicular) orbital oscillations, with the frequency of each of the oscillators given by ω = E/2ħ = mc2/2ħ (energy equipartition theorem), and with each of the two perpendicular oscillations packing one half-unit of ħ only.[9] Such spherical view of a proton fits with packing models for nucleons and yields the experimentally measured radius of a proton:
The 4 factor here is the one distinguishing the formula for the surface of a sphere (A = 4πr2) from the surface of a disc (A = πr2).[10] So do we consider the (in)famous proton radius puzzle solved? Yes. We do. Let us – for the more advanced reader again – write the proton wavefunction. We think of it as a combination of two elementary wavefunctions:
While the electron and proton oscillation are very different, the calculations of their magnetic moment based on a ring current model (with a square root correction to take the spherical nature of the proton into account) strongly suggest the nature of both oscillations and, therefore, the nature of all mass, is electromagnetic. However, we may refer to the electron and proton mass as electromagnetic and nuclear mass respectively because protons (and neutrons) make up most of the mass of atomic nuclei[11], while electrons explain the electromagnetic interaction(s) between atoms and, therefore, explain molecular shapes and other physical phenomena.
Finally, the two oscillations may be associated with the two lightlike particles we find in Nature: photons and neutrinos. These lightlike particles carry energy (but no charge) but are traditionally associated with electromagnetic and nuclear reactions respectively (emission and/or absorption of photons/neutrinos, respectively), which also explains why referring to the three-dimensional proton oscillation as a nuclear oscillation makes sense.[12]
Is that it, then? You may have a few immediate reactions and one of them would be this: we reduce mass to charge in motion here. So what is charge, then? And can we reduce charge to something else. It would take me quite a bit of text to reply to that, so I will only be short here.
First, getting rid of one concept in physics is already a great simplification, and we cannot get rid of the concept of charge by reducing it to mass. In contrast, we do have this nice ‘mass without mass’ model here, and so that is great. Second, never forget that mass (and energy) are relative: you will measure them differently in different reference frames. In contrast, charge is absolute: the proton and electron charge are a unit of charge that does not change depending on your frame of reference. It is just like the speed of light, or Planck’s constant: these constants are c and h, respectively. They are absolute. So that is why we can get rid of the mass concept, so to speak. We cannot get rid of (electric) charge.
So, this is it. See you next time (for my next post, that is)?
[2] The formula is relativistically correct because both m and v are not constant: they are functions varying in time as well and that is why we cannot easily take them out of the d()/dt brackets.
[3] A number with 50 zeros would be referred to as one hundred quindecillion (using the Anglo-Saxon short scale) or one hundred octillions (using the non-English long scale of naming such astronomic numbers).
[4] The fine-structure constant pops up in electromagnetic theory, and is co-defined with the electric and magnetic constants. Their CODATA values are related as follows:
[5] Note that the electron and proton (and their anti-matter counterparts) are stable, but the neutron (as a free particle, i.e., outside of a nucleus) is not, even if its average lifetime (almost 15 minutes) is very large as compared to other non-stable particles.
[6] As mentioned above, the neutron is only stable inside of the nucleus, and we think of it as a combination of a positive and negative charge. It is, therefore, reducible and, as such, not truly elementary. However, such view is, obviously, part of another speculative model of ours and, hence, should not be a concern to the reader here.
[7] We write this as a vector cross-product, and assume an idealized circular orbital when writing the position vector r as a wavefunction r = ψ = a·e±iθ = a·[cos(±θ) + i · sin(±θ)]. The magnitude ½r½is, obviously, equal to ½a·e±iθ ½ = a. This is a variant of Wheeler’s mass-without-mass model because the model assumes a pointlike (but not necessarily infinitesimally small or zero-dimensional) charge, whose rest mass is zero and, therefore, moves at lightspeed and acquires relativistic mass only. As such, it is photon-like, but photons (light-particles) carry no charge. The a = r notation may be somewhat confusing because a is also used to denote acceleration¾an entirely different concept, of course!
[8] See our paper on Euler’s wavefunction and the double life of -1, October 2018. This paper is one of our very early papers – a time during which we developed early intuitions – and we were not publishing on RG then. We basically take Feynman’s argument on base transformations apart. The logic is valid, but we should probably review and rewrite the paper in light of the more precise intuitions and arguments we developed since then, even if – as mentioned – I have no doubt as to the validity of the argument.
[9] Such half-units of ħ for linearly polarized waves also explains the results of Mach-Zehnder one-photon interference experiments. There is no mystery here.
[10] We also have the same 1/4p factor in the formula for the electric constant, and for exactly the same reason (Gauss’ law).
[11] Binding energy – also electromagnetic in nature – makes up for the rest.
If you would happen to be very young and you want to study something useful, then go for applied science: chemistry, biology or – when you are really smart – engineering or medicine. Something like that. If you want to do physics, go join CERN or something: they probably value engineers or technicians more than theorists there, too! 🙂
Reading Feynman 