Those who read this blog, or my papers, know that the King of Science, physics, is in deep trouble. [In case you wonder, the Queen of Science is math.]

The problem is rather serious: a lack of credibility. It would kill any other business, but things work differently in academics. The question is this: how many professional physicists would admit this? An even more important question is: how many of those who admit this, would try to do something about it?

We hope the proportion of both is increasing – so we can trust that at least the dynamics of all of this are OK. I am hopeful – but I would not bet on it.

Post scriptum: A researcher started a discussion on ResearchGate earlier this year. The question for discussion is this: “In September 2019, the New York Times printed an opinion piece by Sean Carroll titled”Even Physicists Don’t Understand Quantum Mechanics. Worse, they don’t seem to want to understand it.” (https://www.nytimes.com/2019/09/07/opinion/sunday/quantum-physics.html) Is it true that physicists don’t want to understand QM? And if so then why?” I replied this to it:

“Sean Carroll is one of the Gurus that is part of the problem rather than the solution: he keeps peddling approaches that have not worked in the past, and can never be made to work in the future. I am an amateur physicist only, but I have not come across a problem that cannot be solved by ‘old’ quantum physics, i.e. a combination of Maxwell’s equations and the Planck-Einstein relation. Lamb shift, anomalous magnetic moment, electron-positron pair creation/annihilation (a nuclear process), behavior of electrons in semiconductors, superconduction etc. There is a (neo-)classical solution for everything: no quantum field and/or perturbation theories are needed. Proton and electrons as elementary particles (and neutrons as the bound state of an proton and a nuclear electron), and photons and neutrinos as lightlike particles, carrying electromagnetic and strong field energy respectively. That’s it. Nothing more. Nothing less. Everyone who thinks otherwise is ‘lost in math’, IMNSHO.”

Brutal? Yes. Very much so. The more important question is this: is it true? I cannot know for sure, but it comes across as being truthful to me.

Needless to say, this quantization of space looks very different depending on the situation: the order of magnitude of the radius of orbital motion around a nucleus is about 150 times the electron’s Compton radius[2] so, yes, that is very different. However, the basic idea is always the same: a pointlike charge going round and round in a rather regular fashion (otherwise our idea of a cycle time (T = 1/f) and an orbital would not make no sense whatsoever), and that oscillation then packs a certain amount of energy as well as Planck’s quantum of action (h). In fact, that’s just what the Planck-Einstein relation embodies: E = h·f. Frequencies and, therefore, radii and velocities are very different (we think of the pointlike charge inside of an electron as whizzing around at lightspeed, while the order of magnitude of velocities of the electron in an atomic or molecular orbital is also given by that fine-structure constant: v = α·c/n (n is the principal quantum number, or the shell in the gross structure of an atom), but the underlying equations of motion – as Dirac referred to it – are not fundamentally different.

We can look at these oscillations in two very different ways. Most Zitterbewegung theorists (or realist thinkers, I might say) think of it as a self-perpetuating current in an electromagnetic field. David Hestenes is probably the best known theorist in this class. However, we feel such view does not satisfactorily answer the quintessential question: what keeps the charge in its orbit? We, therefore, preferred to stick with an alternative model, which we loosely refer to as the oscillator model.

However, truth be told, we are aware this model comes with its own interpretational issues. Indeed, our interpretation of this oscillator model oscillated between the metaphor of a classical (non-relativistic) two-dimensional oscillator (think of a Ducati V2 engine, with the two pistons working in tandem in a 90-degree angle) and the mathematically correct analysis of a (one-dimensional) relativistic oscillator, which we may sum up in the following relativistically correct energy conservation law:

dE/dt = d[kx^{2}/2 + mc^{2}]/dt = 0

More recently, we actually noted the number of dimensions (think of the number of pistons of an engine) should actually not matter at all: an old-fashioned radial airplane engine has 3, 5, 7, or more cylinders (the non-even number has to do with the firing mechanism for four-stroke engines), but the interplay between those pistons can be analyzed just as well as the ‘sloshing back and forth’ of kinetic and potential energy in a dynamic system (see our paper on the meaning of uncertainty and the geometry of the wavefunction). Hence, it seems any number of springs or pistons working together would do the trick: somehow, linear becomes circular motion, and vice versa. But so what number of dimensions should we use for our metaphor, really?

We now think the ‘one-dimensional’ relativistic oscillator is the correct mathematical analysis, but we should interpret it more carefully. Look at the dE/dt = d[kx^{2}/2 + mc^{2}]/dt = = d(PE + KE)/dt = 0 once more.

For the potential energy, one gets the same kx^{2}/2 formula one gets for the non-relativistic oscillator. That is no surprise: potential energy depends on position only, not on velocity, and there is nothing relative about position. However, the (½)m_{0}v^{2} term that we would get when using the non-relativistic formulation of Newton’s Law is now replaced by the mc^{2} = γm_{0}c^{2} term. Both energies vary – with position and with velocity respectively – but the equation above tells us their sum is some constant. Equating x to 0 (when the velocity v = c) gives us the total energy of the system: E = mc^{2}. Just as it should be. 🙂 So how can we now reconcile this two models? One two-dimensional but non-relativistic, and the other relativistically correct but one-dimensional only? We always get this weird 1/2 factor! And we cannot think it away, so what is it, really?

We still don’t have a definite answer, but we think we may be closer to the conceptual locus where these two models might meet: the key is to interpret x and v in the equation for the relativistic oscillator as (1) the distance along an orbital, and (2) v as the tangential velocity of the pointlike charge along this orbital.

Huh? Yes. Read everything slowly and you might see the point. [If not, don’t worry about it too much. This is really a minor (but important) point in my so-called realist interpretation of quantum mechanics.]

If you get the point, you’ll immediately cry wolf and say such interpretation of x as a distance measured along some orbital (as opposed to the linear concept we are used to) and, consequently, thinking of v as some kind of tangential velocity along such orbital, looks pretty random. However, keep thinking about it, and you will have to admit it is a rather logical way out of the logical paradox. The formula for the relativistic oscillator assumes a pointlike charge with zero rest mass oscillating between v = 0 and v = c. However, something with zero rest mass will always be associated with some velocity: it cannot be zero! Think of a photon here: how would you slow it down? And you may think we could, perhaps, slow down a pointlike electric charge with zero rest mass in some electromagnetic field but, no! The slightest force on it will give it infinite acceleration according to Newton’s force law. [Admittedly, we would need to distinguish here between its relativistic expression (F = dp/dt) and its non-relativistic expression (F = m_{0}·a) when further dissecting this statement, but you get the idea. Also note that we are discussing our electron here, in which we do have a zero-rest-mass charge. In an atomic or molecular orbital, we are talking an electron with a non-zero rest mass: just the mass of the electron whizzing around at a (significant) fraction (α) of lightspeed.]

Hence, it is actually quite rational to argue that the relativistic oscillator cannot be linear: the velocity must be some tangential velocity, always and – for a pointlike charge with zero rest mass – it must equal lightspeed, always. So, yes, we think this line of reasoning might well the conceptual locus where the one-dimensional relativistic oscillator (E = m·a^{2}·ω^{2}) and the two-dimensional non-relativistic oscillator (E = 2·m·a^{2}·ω^{2}/2 = m·a^{2}·ω^{2}) could meet. Of course, we welcome the view of any reader here! In fact, if there is a true mystery in quantum physics (we do not think so, but we know people – academics included – like mysterious things), then it is here!

Post scriptum: This is, perhaps, a good place to answer a question I sometimes get: what is so natural about relativity and a constant speed of light? It is not so easy, perhaps, to show why and how Lorentz’ transformation formulas make sense but, in contrast, it is fairly easy to think of the absolute speed of light like this: infinite speeds do not make sense, both physically as well as mathematically. From a physics point of view, the issue is this: something that moves about at an infinite speed is everywhere and, therefore, nowhere. So it doesn’t make sense. Mathematically speaking, you should not think of v reaching infinite but of a limit of a ratio of a distance interval that goes to infinity, while the time interval goes to zero. So, in the limit, we get a division of an infinite quantity by 0. That’s not infinity but an indeterminacy: it is totally undefined! Indeed, mathematicians can easily deal with infinity and zero, but divisions like zero divided by zero, or infinity divided by zero are meaningless. [Of course, we may have different mathematical functions in the numerator and denominator whose limits yields those values. There is then a reasonable chance we will be able to factor stuff out so as to get something else. We refer to such situations as indeterminate forms, but these are not what we refer to here. The informed reader will, perhaps, also note the division of infinity by zero does not figure in the list of indeterminacies, but any division by zero is generally considered to be undefined.]

[1] It may be extra electron such as in, for example, the electron which jumps from place to place in a semiconductor (see our quantum-mechanical analysis of electric currents). Also, as Dirac first noted, the analysis is actually also valid for electron holes, in which case our atom or molecule will be positively ionized instead of being neutral or negatively charged.

[2] We say 150 because that is close enough to the 1/α = 137 factor that relates the Bohr radius to the Compton radius of an electron. The reader may not be familiar with the idea of a Compton radius (as opposed to the Compton wavelength) but we refer him or her to our Zitterbewegung (ring current) model of an electron.

It is done! My last paper on the mentioned topic (available on Phil Gibbs’s site, my ResearchGate page or academia.edu) should conclude my work on the QED sector. It is a thorough exploration of the hitherto mysterious concept of the effective mass and all that.

The result I got is actually very nice: my calculation of the order of magnitude of the kb factor in the formula for the energy band (the conduction band, as you may know it) shows that the usual small angle approximation of the formula does not make all that much sense. This shows that some ‘realist’ thinking about what is what in these quantum-mechanical models does constrain the options: we cannot just multiply wave numbers with some random multiple of π or 2π. These things have a physical meaning!

So no multiverses or many worlds, please! One world is enough, and it is nice we can map it to a unique mathematical description.

I should now move on and think about the fun stuff: what is going on in the nucleus and all that? Let’s see where we go from here. Downloads on ResearchGate have been going through the roof lately (a thousand reads on ResearchGate is better than ten thousand on viXra.org, I guess), so it is all very promising. 🙂

I wrote a lot of papers but most of them – if not all – deal with very basic stuff: the meaning of uncertainty (just statistical indeterminacy because we have no information on the initial condition of the system), the Planck-Einstein relation (how Planck’s quantum of action models an elementary cycle or an oscillation), and Schrödinger’s wavefunctions (the solutions to his equation) as the equations of motion for a pointlike charge. If anything, I hope I managed to restore a feeling that quantum electrodynamics is not essentially different from classical physics: it just adds the element of a quantization – of energy, momentum, magnetic flux, etcetera.

Importantly, we also talked about what photons and electrons actually are, and that electrons are pointlike but not dimensionless: their magnetic moment results from an internal current and, hence, spin is something real – something we can explain in terms of a two-dimensional perpetual current. In the process, we also explained why electrons take up some space: they have a radius (the Compton radius). So that explains the quantization of space, if you want.

We also talked fields and told you – because matter-particles do have a structure – we should have a dynamic view of the fields surrounding those. Potential barriers – or their corollary: potential wells – should, therefore, not be thought of as static fields. They result from one or more charges moving around and these fields, therefore, vary in time. Hence, a particle breaking through a ‘potential wall’ or coming out of a potential ‘well’ is just using an opening, so to speak, which corresponds to a classical trajectory.

We, therefore, have the guts to say that some of what you will read in a standard textbook is plain nonsense. Richard Feynman, for example, starts his lecture on a current in a crystal lattice by writing this: “You would think that a low-energy electron would have great difficulty passing through a solid crystal. The atoms are packed together with their centers only a few angstroms apart, and the effective diameter of the atom for electron scattering is roughly an angstrom or so. That is, the atoms are large, relative to their spacing, so that you would expect the mean free path between collisions to be of the order of a few angstroms—which is practically nothing. You would expect the electron to bump into one atom or another almost immediately. Nevertheless, it is a ubiquitous phenomenon of nature that if the lattice is perfect, the electrons are able to travel through the crystal smoothly and easily—almost as if they were in a vacuum. This strange fact is what lets metals conduct electricity so easily; it has also permitted the development of many practical devices. It is, for instance, what makes it possible for a transistor to imitate the radio tube. In a radio tube electrons move freely through a vacuum, while in the transistor they move freely through a crystal lattice.” [The italics are mine.]

It is nonsense because it is not the electron that is traveling smoothly, easily or freely: it is the electrical signal, and – no ! – that is not to be equated with the quantum-mechanical amplitude. The quantum-mechanical amplitude is just a mathematical concept: it does not travel through the lattice in any physical sense ! In fact, it does not even travel through the lattice in a logical sense: the quantum-mechanical amplitudes are to be associated with the atoms in the crystal lattice, and describe their state – i.e. whether or not they have an extra electron or (if we are analyzing electron holes in the lattice) if they are lacking one. So the drift velocity of the electron is actually very low, and the way the signal moves through the lattice is just like in the game of musical chairs – but with the chairs on a line: all players agree to kindly move to the next chair for the new arrival so the last person on the last chair can leave the game to get a beer. So here it is the same: one extra electron causes all other electrons to move. [For more detail, we refer to our paper on matter-waves, amplitudes and signals.]

But so, yes, we have not said much about semiconductors, lasers and other technical stuff. Why not? Not because it should be difficult: we already cracked the more difficult stuff (think of an explanation of the anomalous magnetic moment, the Lamb shift, or one-photon Mach-Zehnder interference here). No. We are just lacking time ! It is, effectively, going to be an awful lot of work to rewrite those basic lectures on semiconductors – or on lasers or other technical matters which attract students in physics – so as to show why and how the mechanics of these things actually work: not approximately, but how exactly – and, more importantly, why and how these phenomena can be explained in terms of something real: actual electrons moving through the lattice at lower or higher drift speeds within a conduction band (and then what that conduction band actually is).

The same goes for lasers: we talk about induced emission and all that, but we need to explain what that might actually represent – while avoiding the usual mumbo-jumbo about bosonic behavior and other useless generalizations of properties of actually matter- and light-particles that can be reasonably explained in terms of the structure of these particles – instead of invoking quantum-mechanical theorems or other dogmatic or canonical a priori assumptions.

So, yes, it is going to be hard work – and I am not quite sure if I have sufficient time or energy for it. I will try, and so I will probably be offline for quite some time while doing that. Be sure to have fun in the meanwhile ! 🙂

Post scriptum: Perhaps I should also focus on converting some of my papers into journal articles, but then I don’t feel like it’s worth going through all of the trouble that takes. Academic publishing is a weird thing. Either the editorial line of the journal is very strong, in which case they do not want to publish non-mainstream theory, and also insist on introductions and other credentials, or, else, it is very weak or even absent – and then it is nothing more than vanity or ego, right? So I think I am just fine with the viXra collection and the ‘preprint’ papers on ResearchGate now. I’ve been thinking it allows me to write what I want and – equally important – how I want to write it. In any case, I am writing for people like you and me. Not so much for dogmatic academics or philosophers. The poor experience with reviewers of my manuscript has taught me well, I guess. I should probably wait to get an invitation to publish now.

A few days ago, I mentioned I felt like writing a new book: a sort of guidebook for amateur physicists like me. I realized that is actually fairly easy to do. I have three very basic papers – one on particles (both light and matter), one on fields, and one on the quantum-mechanical toolbox (amplitude math and all of that). But then there is a lot of nitty-gritty to be written about the technical stuff, of course: self-interference, superconductors, the behavior of semiconductors (as used in transistors), lasers, and so many other things – and all of the math that comes with it. However, for that, I can refer you to Feynman’s three volumes of lectures, of course. In fact, I should: it’s all there. So… Well… That’s it, then. I am done with the QED sector. Here is my summary of it all (links to the papers on Phil Gibbs’ site):

The last paper is interesting because it shows statistical indeterminism is the only real indeterminism. We can, therefore, use Bell’s Theorem to prove our theory is complete: there is no need for hidden variables, so why should we bother about trying to prove or disprove they can or cannot exist?

Jean Louis Van Belle, 21 October 2020

Note: As for the QCD sector, that is a mess. We might have to wait another hundred years or so to see the smoke clear up there. Or, who knows, perhaps some visiting alien(s) will come and give us a decent alternative for the quark hypothesis and quantum field theories. One of my friends thinks so. Perhaps I should trust him more. 🙂

As for Phil Gibbs, I should really thank him for being one of the smartest people on Earth – and for his site, of course. Brilliant forum. Does what Feynman wanted everyone to do: look at the facts, and think for yourself. 🙂

I ended my post on particles as spacetime oscillations saying I should probably write something about the concept of a field too, and why and how many academic physicists abuse it so often. So I did that, but it became a rather lengthy paper, and so I will refer you to Phil Gibbs’ site, where I post such stuff. Here is the link. Let me know what you think of it.

As for how it fits in with the rest of my writing, I already jokingly rewrote two of Feynman’s introductory Lectures on quantum mechanics (see: Quantum Behavior and Probability Amplitudes). I consider this paper to be the third. 🙂

Post scriptum: Now that I am talking about Richard Feynman – again ! – I should add that I really think of him as a weird character. I think he himself got caught in that image of the ‘Great Teacher’ while, at the same (and, surely, as a Nobel laureate), he also had to be seen to a ‘Great Guru.’ Read: a Great Promoter of the ‘Grand Mystery of Quantum Mechanics’ – while he probably knew classical electromagnetism combined with the Planck-Einstein relation can explain it all… Indeed, his lecture on superconductivity starts off as an incoherent ensemble of ‘rocket science’ pieces, to then – in the very last paragraphs – manipulate Schrödinger’s equation (and a few others) to show superconducting currents are just what you would expect in a superconducting fluid. Let me quote him:

“Schrödinger’s equation for the electron pairs in a superconductor gives us the equations of motion of an electrically charged ideal fluid. Superconductivity is the same as the problem of the hydrodynamics of a charged liquid. If you want to solve any problem about superconductors you take these equations for the fluid [or the equivalent pair, Eqs. (21.32) and (21.33)], and combine them with Maxwell’s equations to get the fields.”

So… Well… Looks he too is all about impressing people with ‘rocket science models’ first, and then he simplifies it all to… Well… Something simple. 😊

Having said that, I still like Feynman more than modern science gurus, because the latter usually don’t get to the simplifying part.

I don’t know where I would start a new story on physics. I am also not quite sure for whom I would be writing it – although it would be for people like me, obviously: most of what we do, we do for ourselves, right? So I should probably describe myself in order to describe the audience: amateur physicists who are interested in the epistemology of modern physics – or its ontology, or its metaphysics. I also talk about the genealogy or archaeology of ideas on my ResearchGate site. All these words have (slightly) different meanings but the distinctions do not matter all that much. The point is this: I write for people who want to understand physics in pretty much the same way as the great classical physicist Hendrik Antoon Lorentz who, just a few months before his demise, at the occasion of the (in)famous 1927 Solvay Conference, wanted to understand the ‘new theories’:

“We are representing phenomena. We try to form an image of them in our mind. Till now, we always tried to do using the ordinary notions of space and time. These notions may be innate; they result, in any case, from our personal experience, from our daily observations. To me, these notions are clear, and I admit I am not able to have any idea about physics without those notions. The image I want to have when thinking physical phenomena has to be clear and well defined, and it seems to me that cannot be done without these notions of a system defined in space and in time.”

Note that H.A. Lorentz understood electromagnetism and relativity theory as few others did. In fact, judging from some of the crap out there, I can safely say he understood stuff as few others do today still. Hence, he should surely not be thought of as a classical physicist who, somehow, was stuck. On the contrary: he understood the ‘new theories’ better than many of the new theorists themselves. In fact, as far as I am concerned, I think his comments or conclusions on the epistemological status of the Uncertainty Principle – which he made in the same intervention – still stand. Let me quote the original French:

“Je pense que cette notion de probabilité [in the new theories] serait à mettre à la fin, et comme conclusion, des considérations théoriques, et non pas comme axiome a priori,quoique je veuille bien admettre que cette indétermination correspond aux possibilités expérimentales. Je pourrais toujours garder ma foi déterministe pour les phénomènes fondamentaux, dont je n’ai pas parlé. Est-ce qu’un esprit plus profond ne pourrait pas se rendre compte des mouvements de ces électrons. Ne pourrait-on pas garder le déterminisme en en faisant l’objet d’une croyance? Faut-il nécessairement ériger l’ indéterminisme en principe?”

What a beautiful statement, isn’t it? Why should we elevate indeterminism to a philosophical principle? Indeed, now that I’ve inserted some French, I may as well inject some German. The idea of a particle includes the idea of a more or less well-known position. Let us be specific and think of uncertainty in the context of position. We may not fully know the position of a particle for one or more of the following reasons:

The precision of our measurements may be limited: this is what Heisenberg referred to as an Ungenauigkeit.

Our measurement might disturb the position and, as such, cause the information to get lost and, as a result, introduce an uncertainty: this is what we may translate as an Unbestimmtheit.

The uncertainty may be inherent to Nature, in which case we should probably refer to it as an Ungewissheit.

So what is the case? Lorentz claims it is either the first or the second – or a combination of both – and that the third proposition is a philosophical statement which we can neither prove nor disprove. I cannot see anything logical (theory) or practical (experiment) that would invalidate this point. I, therefore, intend to write a basic book on quantum physics from what I hope would be Lorentz’ or Einstein’s point of view.

My detractors will immediately cry wolf: Einstein lost the discussions with Bohr, didn’t he? I do not think so: he just got tired of them. I want to try to pick up the story where he left it. Let’s see where I get. 🙂

My very first publication on Phil Gibb’s site – The Quantum-Mechanical Wavefunction as a Gravitational Wave – reached 500+ downloads. I find that weird, because I warn the reader in the comments section that some of these early ideas do not make sense. Indeed, while my idea of modelling an electron as a two-dimensional oscillation has not changed, the essence of the model did. My theory of matter is based on the idea of a naked charge – with zero rest mass – orbiting around some center, and the energy in its motion – a perpetual current ring, really – is what gives matter its (equivalent) mass. Wheeler’s idea of ‘mass without mass’. The force is, therefore, definitelynot gravitational.

It cannot be: the force has to grab onto something, and all it can grab onto is the naked charge. The force must, therefore, be electromagnetic. So I now look at that very first paper as an immature essay. However, I leave it there because that paper does ask all of the right questions, and I should probably revisit it – because the questions I get on my last paper on the subject – De Broglie’s Matter-Wave: Concept and Issues, which gets much more attention on ResearchGate than on Phil Gibb’s site (so it is more serious, perhaps) – are quite similar to the ones I try to answer in that very first paper: what is the true nature of the matter-wave? What is that fundamental oscillation?

I have been thinking about this for many years now, and I may never be able to give a definite answer to the question, but yesterday night some thoughts came to me that may or may not make sense. And so to be able to determine whether they might, I thought I should write them down. So that is what I am going to do here, and you should not take it very seriously. If anything, they may help you to find some answers for yourself. So if you feel like switching off because I am getting too philosophical, please do: I myself wonder how useful it is to try to interpret equations and, hence, to write about what I am going to write about here – so I do not mind at all if you do too!

That is too much already as an introduction, so let us get started. One of my more obvious reflections yesterday was this: the nature of the matter-wave is not gravitational, but it is an oscillation in space and in time. As such, we may think of it as a spacetime oscillation. In any case, physicists often talk about spacetime oscillations without any clear idea of what they actually mean by it, so we may as well try to clarify it in this very particular context here: the explanation of matter in terms of an oscillating pointlike charge. Indeed, the first obvious point to make is that any such perpetual motion may effectively be said to be a spacetime oscillation: it is an oscillation in space – and in time, right?

As such, a planet orbiting some star – think of the Earth orbiting our Sun – may be thought of a spacetime oscillation too ! Am I joking? No, I am not. Let me elaborate this idea. The concept of a spacetime oscillation implies we think of space as something physical, as having an essence of sorts. We talk of a spacetime fabric, a (relativistic) aether or whatever other term comes to mind. The Wikipedia article on aether theories quotes Robert B. Laughlin as follows in this regard: “It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word ‘ether’ has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum.”

I disagree with that. I do not think about the vacuum in such terms: the vacuum is the Cartesian mathematical 3D space in which we imagine stuff to exist. We should not endow this mathematical space with any physical qualities – with some essence. Mathematical concepts are mathematical concepts only. It is the difference between size and distance. Size is physical: an electron – any physical object, really – has a size. But the distance between two points is a mathematical concept only.

The confusion arises from us expressing both in terms of the physical distance unit: a meter, or a pico- or femtometer – whatever is appropriate for the scale of the things that we are looking at. So it is the same thing when we talk about a point: we need to distinguish a physical point – think of our pointlike charge here – and a mathematical point. That should be the key to understanding matter-particles as spacetime oscillations – if we would want to understand them as such, that is – which is what we are trying to do here. So how should we think of this? Let us start with matter-particles. In our realist interpretation of physics, we think of matter-particles as consisting of charge – in contrast to, say, photons, the particles of light, which (also) carry energy but no charge. Let us consider the electron, because the structure of the proton is very different and may involve a different force: a strong force – as opposed to the electromagnetic force that we are so familiar with. Let me use an animated gif from the Wikipedia Commons repository to recapture the idea of such (two-dimensional) oscillation.

Think of the green dot as the pointlike charge: it is a physical point moving in a mathematical space – a simple 2D plane, in this case. So it goes from here to there, and here and there are two mathematical points only: points in the 3D Cartesian space which – as H.A. Lorentz pointed out when criticizing the new theories – is a notion without which we cannot imagine any idea in physics. So we have a spacetime oscillation here alright: an oscillation in space, and in time. Oscillations in space are always oscillations in time, obviously – because the idea of an oscillation implies the idea of motion, and the idea of motion always involves the notion of space as well as the notion of time. So what makes this spacetime oscillation different from, say, the Earth orbiting around the Sun?

Perhaps we should answer this question by pointing out the similarities first. A planet orbiting around the sun involves perpetual motion too: there is an interplay between kinetic and potential energy, both of which depend on the distance from the center. Indeed, Earth falls into the Sun, so to speak, and its kinetic energy gets converted into potential energy and vice versa. However, the centripetal force is gravitational, of course. The centripetal force on the pointlike charge is not: there is nothing at the center pulling it. But – Hey ! – what is pulling our planet, exactly? We do not believe in virtual gravitons traveling up and down between the Sun and the Earth, do we? So the analogy may not be so bad, after all ! It is just a very different force: its structure is different, and it acts on something different: a charge versus mass. That’s it. Nothing more. Nothing less.

Or… Well… Velocities are very different, of course, but even there distinctions are, perhaps, less clear-cut than they appear to be at first. The pointlike charge in our electron has no mass and, therefore, moves at lightspeed. The electron itself, however, acquires mass and, therefore, moves at a fraction of lightspeed only in an atomic or molecular orbital. And much slower in a perpetual current in superconducting material. [Yes. When thinking of electrons in the context of superconduction, we have an added complication: we should think of electron pairs (Cooper pairs) rather than individual electrons, it seems. We are not quite sure what to make of this – except to note electrons will also want to lower their energy by pairing up in atomic or molecular orbitals, and we think the nature of this pairing must, therefore, be the same.]

Did we clarify anything? Maybe. Maybe not. Saying that an electron is a pointlike charge and a two-dimensional oscillation, or saying that it’s a spacetime oscillation itself, appears to be a tautology here, right? Yes. You are right. So what’s the point, then?

We are not sure, except for one thing: when defining particles as spacetime oscillations, we do definitely not need the idea of virtual particles. That’s rubbish: an unnecessary multiplication of concepts. So I think that is some kind of progress we got out of this rather difficult philosophical reflections, and that is useful, I think. To illustrate this point, you may want to think of the concept of heat. When there is heat, there is no empty space. There is no vacuum anymore. When we heat a space, we fill it with photons. They bounce around and get absorbed and re-emitted all of the time. in fact, we, therefore, also need matter to imagine a heated space. Hence, space here is no longer the vacuum: it is full of energy, but this energy is always somewhere – and somewhere specifically: it’s carried by a photon, or (temporarily) stored as an electron orbits around a nucleus in an excited state (which amounts to the same as saying it is being stored by an atom or some molecular structure consisting of atoms). In short, heat is energy but it is being ‘transmitted’ or ‘transported’ through space by photons. Again, the point is that the vacuum itself should not be associated with energy: it is empty. It is a mathematical construct only.

We should try to think this through – even further than we already did – by thinking how photons – or radiation of heat – would disturb perpetual currents: in an atom, obviously (the electron orbitals), but also perpetual superconducting currents at the macro-scale: unless the added heat from the photons is continuously taken away by the supercooling helium or whatever is used, radiation or heat will literally bounce the electrons into a different physical trajectory, so we should effectively associate excited energy states with different patterns of motion: a different oscillation, in other words. So it looks like electrons – or electrons in atomic/molecular orbitals – do go from one state into another (excited) state and back again but, in whatever state they are, we should think of them as being in their own space (and time). So that is the nature of particles as spacetime oscillations then, I guess. Can we say anything more about it?

I am not sure. At this moment, I surely have nothing more to say about it. Some more thinking about how superconduction – at the macro-scale – might actually work could, perhaps, shed more light on it: is there an energy transfer between the two electrons in a Cooper pair? An interplay between kinetic and potential energy? Perhaps the two electrons behave like coupled pendulums? If they do, then we need to answer the question: how, exactly? Is there an exchange of (real) photons, or is the magic of the force the same: some weird interaction in spacetime which we can no further meaningfully analyze, but which gives space not only some physicality but also causes us to think of it as being discrete, somehow. Indeed, an electron is an electron: it is a whole. Thinking of it as a pointlike charge in perpetual motion does not make it less of a whole. Likewise, an electron in an atomic orbital is a whole as well: it just occupies more space. But both are particles: they have a size. They are no longer pointlike: they occupy a measurable space: the Cartesian (continuous) mathematical space becomes (discrete) physical space.

I need to add another idea here – or another question for you, if I may. If superconduction can only occur when electrons pair up, then we should probably think of the pairs as some unit too – and a unit that may take up a rather large space. Hence, the idea of a discrete, pointlike, particle becomes somewhat blurred, right? Or, at the very least, it becomes somewhat less absolute, doesn’t it? 🙂

I guess I am getting lost in words here, which is probably worse than getting ‘lost in math‘ (I am just paraphrasing Sabine Hossenfelder here) but, yes, that is why I am writing a blog post rather than a paper here. If you want equations, read my papers. 🙂 Oh – And don’t forget: fields are real as well. They may be relative, but they are real. And it’s not because they are quantized (think of (magnetic) flux quantization in the context of superconductivity, for example) that they are necessarily discrete – that we have field packets, so to speak. I should do a blog post on that. I will. Give me some time. 🙂

Post scriptum: What I wrote above on there not being any exchange of gravitons between an orbiting planet and its central star (or between double stars or whatever gravitational trajectories out there), does not imply I am ruling out their existence. I am a firm believer in the existence of gravitational waves, in fact. We should all be firm believers because – apart from some marginal critics still wondering what was actually being measured – the LIGO detections are real. However, whether or not these waves involve discrete lightlike particles – like photons and, in the case of the strong force, neutrinos – is a very different question. Do I have an opinion on it? I sure do. It is this: when matter gets destroyed or created (remember the LIGO detections involved the creation and/or destruction of matter as black holes merge), gravitational waves must carry some of the energy, and there is no reason to assume that the Planck-Einstein relation would not apply. Hence, we will have energy packets in the gravitational wave as well: the equivalent of photons (and, most probably, of neutrinos), in other words. All of this is, obviously, very speculative. Again, just think of this whole blog post as me freewheeling: the objective is, quite simply, to make you think as hard as I do about these matters. 🙂

As for my remark on the Cooper pairs being a unit or not, that question may be answered by thinking about what happens if Cooper pairs are broken, which is a topic I am not familiar with, so I cannot say anything about it.

I’ve been asked a couple of times: “What about Bell’s No-Go Theorem, which tells us there are no hidden variables that can explain quantum-mechanical interference in some kind of classical way?” My answer to that question is quite arrogant, because it’s the answer Albert Einstein would give when younger physicists would point out that his objections to quantum mechanics (which he usually expressed as some new thought experiment) violated this or that axiom or theorem in quantum mechanics: “Das ist mir wur(sch)t.”

In English: I don’t care. Einstein never lost the discussions with Heisenberg or Bohr: he just got tired of them. Like Einstein, I don’t care either – because Bell’s Theorem is what it is: a mathematical theorem. Hence, it respects the GIGO principle: garbage in, garbage out. In fact, John Stewart Bell himself – one of the third-generation physicists, we may say – had always hoped that some “radical conceptual renewal”[1] might disprove his conclusions. We should also remember Bell kept exploring alternative theories – including Bohm’s pilot wave theory, which is a hidden variables theory – until his death at a relatively young age. [J.S. Bell died from a cerebral hemorrhage in 1990 – the year he was nominated for the Nobel Prize in Physics. He was just 62 years old then.]

So I never really explored Bell’s Theorem. I was, therefore, very happy to get an email from Gerard van der Ham, who seems to have the necessary courage and perseverance to research this question in much more depth and, yes, relate it to a (local) realist interpretation of quantum mechanics. I actually still need to study his papers, and analyze the YouTube video he made (which looks much more professional than my videos), but this is promising.

To be frank, I got tired of all of these discussions – just like Einstein, I guess. The difference between realist interpretations of quantum mechanics and the Copenhagen dogmas is just a factor 2 or π in the formulas, and Richard Feynman famously said we should not care about such factors (Feynman’s Lectures, III-2-4). Modern physicists fudge them away consistently. They’ve done much worse than that, actually. They are not interested in truth. Convention, dogma, indoctrination – non-scientific historical stuff – seems to prevent them from that. And modern science gurus – the likes of Sean Carroll or Sabine Hossenfelder etc. – play the age-old game of being interesting: they pretend to know something you do not know or – if they don’t – that they are close to getting the answers. They are not. They have them already. They just don’t want to tell you that because, yes, it’s the end of physics.

[1] See: John Stewart Bell, Speakable and unspeakable in quantum mechanics, pp. 169–172, Cambridge University Press, 1987.

My manuscript offers a somewhat sacrilegious but intuitive explanation of (special) relativity theory (The Emperor Has No Clothes: the force law and relativity, p. 24-27). It is one of my lighter and more easily accessible pieces of writing. The argument is based on the idea that we may define infinity or infinite velocities as some kind of limit (or some kind of limiting idea), but that we cannot really imagine it: it leads to all kinds of logical inconsistencies.

Let me give you a very simple example here to illustrate these inconsistencies: if something is traveling at an infinite velocity, then it is everywhere and nowhere at the same time, and no theory of physics can deal with that.

Now, if I would have to rewrite that brief introduction to relativity theory, I would probably add another logical argument. One that is based on our definition or notion of time itself. What is the definition of time, indeed? When you think long and hard about this, you will have to agree we can only measure time with reference to some fundamental cycle in Nature, right? It used to be the seasons, or the days or nights. Later, we subdivided a day into hours, and now we have atomic clocks. Whatever you can count and meaningfully communicate to some other intelligent being who happens to observe the same cyclical phenomenon works just fine, right?

Hence, if we would be able to communicate to some other intelligent being in outer space, whose position we may or may not know but both he/she/it (let us think of a male Martian for ease of reference) and we/me/us are broadcasting our frequency- or amplitude-modulated signals wide enough so as to ensure ongoing communication, then we would probably be able to converge on a definition of time in terms of the fundamental frequency of an elementary particle – let us say an electron to keep things simple. We could, therefore, agree on an experiment where he – after receiving a pre-agreed start signal from us – would starting counting and send us a stop signal back after, say, three billion electron cycles (not approximately, of course, but three billion exactly). In the meanwhile, we would be capable, of course, to verify that, inbetween sending and receiving the start and stop signal respectively (and taking into account the time that start and stop signal needs to travel between him and us), his clock seems to run somewhat differently than ours.

So that is the amazing thing, really. Our Martian uses the same electron clock, but our/his motion relative to his/ours leads us to the conclusion his clock works somewhat differently, and Einstein’s (special) relativity theory tells ushow, exactly: time dilation, as given by the Lorentz factor.

Does this explanation make it any easier to truly understand relativity theory? Maybe. Maybe not. For me, it does, because what I am describing here is nothing but the results of the Michelson-Morley experiment in a slightly more amusing context which, for some reason I do not quite understand, seems to make them more comprehensible. At the very least, it shows Galilean relativity is as incomprehensible – or as illogical or non-intuitive, I should say – as the modern-day concept of relativity as pioneered by Albert Einstein.

You may now think (or not): OK, but what about relativistic mass? That concept is, and will probably forever remain, non-intuitive. Right? Time dilation and length contraction are fine, because we can now somehow imagine the what and why of this, but how do you explain relativistic mass, really?

The only answer I can give you here it to think some more about Newton’s law: mass is a measure of inertia, so that is a resistance to a change in the state of motion of an object. Motion and, therefore, your measurement of any acceleration or deceleration (i.e. a change in the state of motion) will depend on how you measure time and distance too. Therefore, mass has to be relativistic too.

QED: quod erat demonstrandum. In fact, it is not a proof, so I should not say it’s QED. It’s SE: a satisfactory explanation. Why is an explanation and not a proof? Because I take the constant speed of light for granted, and so I kinda derive the relativity of time, distance and mass from my point of departure (both figuratively and literally speaking, I’d say).

Post scriptum: For the mentioned calculation, we do need to know the (relative) position of the Martian, of course. Any event in physics is defined by both its position as well as its timing. That is what (also) makes it all very consistent, in fact. I should also note this short story here (I mean my post) is very well aligned with Einstein’s original 1905 article, so you can (also) go there to check the math. The main difference between his article and my explanation here is that I take the constant speed of light for granted, and then all that’s relative derives its relativity from that. Einstein looked at it the other way around, because things were not so obvious then. 🙂