Mainstream QM: A Bright Shining Lie

Yesterday night, I got this email from a very bright young physicist: Dr. Oliver Consa. He is someone who – unlike me – does have the required Dr and PhD credentials in physics (I have a drs. title in economics) – and the patience that goes with it – to make some more authoritative statements in the weird world of quantum mechanics. I recommend you click the link in the email (copied below) and read the paper. Please do it! 

It is just 12 pages, and it is all extremely revealing. Very discomforting, actually, in light of all the other revelations on fake news in other spheres of life.

Many of us – and, here, I just refer to those who are reading my post – all sort of suspected that some ‘inner circle’ in the academic circuit had cooked things up:the Mystery Wallahs, as I refer to them now. Dr. Consa’s paper shows our suspicion is well-founded.

QUOTE

Dear fellow scientist,

I send you this mail because you have been skeptical about Foundations of Physics. I think that this new paper will be of your interest. Feel free to share it with your colleagues or publish it on the web. I consider it important that this paper serves to open a public debate on this subject.

Something is Rotten in the State of QED
https://vixra.org/pdf/2002.0011v1.pdf

Abstract
“Quantum electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is based on a single experimental value: the anomalous magnetic moment of the electron (g-factor). An examination of QED history reveals that this value was obtained using illegitimate mathematical traps, manipulations and tricks. These traps included the fraud of Kroll & Karplus, who acknowledged that they lied in their presentation of the most relevant calculation in QED history. As we will demonstrate in this paper, the Kroll & Karplus scandal was not a unique event. Instead, the scandal represented the fraudulent manner in which physics has been conducted from the creation of QED through today.”  (12 pag.)

Best Regards,
Oliver Consa
oliver.consa@gmail.com

UNQUOTE

Mr. Feynman and boson-fermion theory

I’ve been looking at chapter 4 of Feynman’s Lectures on Quantum Mechanics (the chapter on identical particles) for at least a dozen times now—probably more. This and the following chapters spell out the mathematical framework and foundations of mainstream quantum mechanics: the grand distinction between fermions and bosons, symmetric and asymmetric wavefunctions, Bose-Einstein versus Maxwell-Boltzmann statistics, and whatever else comes out of that—including the weird idea that (force) fields should also come in lumps (think of quantum field theory here). These ‘field lumps’ are then thought of as ‘virtual’ particles that, somehow, ‘mediate’ the force.

The idea that (kinetic and/or potential) energy and (linear and/or angular) momentum are being continually transferred – somehow, and all over space – by these ‘messenger’ particles sounds like medieval philosophy to me. However, to be fair, Feynman does actually not present these more advanced medieval ideas in his Lectures on Quantum Physics. I have always found that somewhat strange: he was about to receive a Nobel Prize for his path integral formulation of quantum mechanics and other contributions to what has now become the mainstream interpretation of quantum mechanics, so why wouldn’t he talk about it to his students, for which he wrote these lectures? In contrast, he does include a preview of Gell-Mann’s quark theory, although he does say – in a footnote – that “the material of this section is longer and harder than is appropriate at this point” and he, therefore, suggests to skip it and move to the next chapter.

[As for the path integral formulation of QM, I would think the mere fact that we have three alternative formulations of QM (matrix, wave-mechanical and path integral) would be sufficient there’s something wrong with these theories: reality is one, so we should have one unique (mathematical) description of it).]

Any case. I am probably doing too much Hineininterpretierung here. Let us return to the basic stuff that Feynman wanted his students to accept as a truthful description of reality: two kinds of statistics. Two different ways of interaction. Two kinds of particles. That’s what post-WW II gurus such as Feynman – all very much inspired by the ‘Club of Copenhagen’—aka known as the ‘Solvay Conference Club‘ – want us to believe: interactions with ‘Bose particles’ – this is the term Feynman uses in this text of 1963  – involve adding amplitudes with a + (plus) sign. In contrast, interactions between ‘Fermi particles’ involve a minus (−) sign when ‘adding’ the amplitudes.

The confusion starts early on: Feynman makes it clear he actually talks about the amplitude for an event to happen or not. Two possibilities are there: two ‘identical’ particles either get ‘swapped’ after the collision or, else, they don’t. However, in the next sections of this chapter – where he ‘proves’ or ‘explains’ the principle of Bose condensation for bosons and then the Pauli exclusion principle for fermions – it is very clear the amplitudes are actually associated with the particles themselves.

So his argument starts rather messily—conceptually, that is. Feynman also conveniently skips the most basic ontological or epistemological question here: how would a particle ‘know‘ how to choose between this or that kind of statistics? In other words, how does it know it should pick the plus or the minus sign when combining its amplitude with the amplitude of the other particle? It makes one think of Feynman’s story of the Martian in his Lecture on symmetries in Nature: what handshake are we going to do here? Left or right? And who sticks out his hand first? The Martian or the Earthian? A diplomat would ask: who has precedence when the two particles meet?

The question also relates to the nature of the wavefunction: if it doesn’t describe anything real, then where is it? In our mind only? But if it’s in our mind only, how comes we get real-life probabilities out of them, and real-life energy levels, or real-life momenta, etcetera? The core question (physical, epistemological, philosophical, esoterical or whatever you’d want to label it) is this: what’s the connection between these concepts and whatever it is that we are trying to describe? The only answer mainstream physicists can provide here is blabber. That’s why the mainstream interpretation of physics may be acceptable to physicists, but not to the general public. That’s why the debate continues to rage: no one believes the Standard Model. Full stop. The intuition of the masses here is very basic and, therefore, probably correct: if you cannot explain something in clear and unambiguous terms, then you probably do not understand it.

Hence, I suspect mainstream academic physicists probably do not understand whatever it is they are talking about. Feynman, by the way, admitted as much when writing – in the very first lines of the introduction to his Lectures on Quantum Mechanics – that “even the experts do not understand it the way they would like to.”

I am actually appalled by all of this. Worse, I am close to even stop talking or writing about it. I only kept going because a handful of readers send me a message of sympathy from time to time. I then feel I am actually not alone in what often feels like a lonely search in what a friend of mine refers to as ‘a basic version of truth.’ I realize I am getting a bit emotional here – or should I say: upset? – so let us get back to Feynman’s argument again.

Feynman starts by introducing the idea of a ‘particle’—a concept he does not define – not at all, really – but, as the story unfolds, we understand this concept somehow combines the idea of a boson and a fermion. He doesn’t motivate why he feels like he should lump photons and electrons together in some more general category, which he labels as ‘particles’. Personally, I really do not see the need to do that: I am fine with thinking of a photon as an electromagnetic oscillation (a traveling field, that is), and of electrons, protons, neutrons and whatever composite particle out there that is some combination of the latter as matter-particles. Matter-particles carry charge: electric charge and – who knows – perhaps some strong charge too. Photons don’t. So they’re different. Full stop. Why do we want to label everything out there as a ‘particle’?

Indeed, when everything is said and done, there is no definition of fermions and bosons beyond this magical spin-1/2 and spin-1 property. That property is something we cannot measure: we can only measure the magnetic moment of a particle: any assumption on their angular momentum assumes you know the mass (or energy) distribution of the particle. To put it more plainly: do you think of a particle as a sphere, a disk, or what? Mainstream physicists will tell you that you shouldn’t think that way: particles are just pointlike. They have no dimension whatsoever – in their mathematical models, that is – because all what experimentalists is measuring scattering or charge radii, and these show the assumption of an electron or a proton being pointlike is plain nonsensical.

Needless to say, besides the perfect scattering angle, Feynman also assumes his ‘particles’ have no spatial dimension whatsoever: he’s just thinking in terms of mathematical lines and points—in terms of mathematical limits, not in terms of the physicality of the situation.

Hence, Feynman just buries us under a bunch of tautologies here: weird words are used interchangeably without explaining what they actually mean. In everyday language and conversation, we’d think of that as ‘babble’. The only difference between physicists and us commoners is that physicists babble using mathematical language.

[…]

I am digressing again. Let us get back to Feynman’s argument. So he tells us we should just accept this theoretical ‘particle’, which he doesn’t define: he just thinks about two of these discrete ‘things’ going into some ‘exchange’ or ‘interaction’ and then coming out of it and going into one of the two detectors. The question he seeks to answer is this: can we still distinguish what is what after the ‘interaction’?

The level of abstraction here is mind-boggling. Sadly, it is actually worse than that: it is also completely random. Indeed, the only property of this mystical ‘particle’ in this equally mystical thought experiment of Mr. Feynman is that it scatters elastically with some other particle. However, that ‘other’ particle is ‘of the same kind’—so it also has no other property than that it scatters equally elastically from the first particle. Hence, I would think the question of whether the two particles are identical or not is philosophically empty.

To be rude, I actually wonder what Mr. Feynman is actually talking about here. Every other line in the argument triggers another question. One should also note, for example, that this elastic scattering happens in a perfect angle: the whole argument of adding or subtracting amplitudes effectively depends on the idea of a perfectly measurable angle here. So where is the Uncertainty Principle here, Mr. Feynman? It all makes me think that Mr. Feynman’s seminal lecture may well be the perfect example of what Prof. Dr. John P. Ralston wrote about his own profession:

“Quantum mechanics is the only subject in physics where teachers traditionally present haywire axioms they don’t really believe, and regularly violate in research.” (1)

Let us continue exposing Mr. Feynman’s argument. After this introduction of this ‘particle’ and the set-up with the detectors and other preconditions, we then get two or three paragraphs of weird abstract reasoning. Please don’t get me wrong: I am not saying the reasoning is difficult (it is not, actually): it is just weird and abstract because it uses complex number logic. Hence, Feynman implicitly requests the reader to believe that complex numbers adequately describes whatever it is that he is thinking of (I hope – but I am not so sure – he was trying to describe reality). In fact, this is the one point I’d agree with him: I do believe Euler’s function adequately describes the reality of both photons and electrons (see our photon and electron models), but then I also think +i and −i are two very different things. Feynman doesn’t, clearly.

It is, in fact, very hard to challenge Feynman’s weird abstract reasoning here because it all appears to be mathematically consistent—and it is, up to the point of the tricky physical meaning of the imaginary unit: Feynman conveniently forgets the imaginary unit represents a rotation of 180 degrees and that we, therefore, need to distinguish between these two directions so as to include the idea of spin. However, that is my interpretation of the wavefunction, of course, and I cannot use it against Mr. Feynman’s interpretation because his and mine are equally subjective. One can, therefore, only credibly challenge Mr. Feynman’s argument by pointing out what I am trying to point out here: the basic concepts don’t make any sense—none at all!

Indeed, if I were a student of Mr. Feynman, I would have asked him questions like this:

“Mr. Feynman, I understand your thought experiment applies to electrons as well as to photons. In fact, the argument is all about the difference between these two very different ‘types’ of ‘particles’. Can you please tell us how you’d imagine two photons scattering off each other elastically? Photons just pile on top of each other, don’t they? In fact, that’s what you prove next. So they don’t scatter off each other, do they? Your thought experiment, therefore, seems to apply to fermions only. Hence, it would seem we should not use it to derive properties for bosons, isn’t it?”

“Mr. Feynman, how should an electron (a fermion – so you say we should ‘add’ amplitudes using a minus sign) ‘think’ about what sign to use for interaction when a photon is going to hit it? A photon is a boson – so its sign for exchange is positive – so should we have an ‘exchange’ or ‘interaction’ with the plus or the minus sign then? More generally, who takes the ‘decisions’ here? Do we expect God – or Maxwell’s demon – to be involved in every single quantum-mechanical event?”

Of course, Mr. Feynman might have had trouble answering the first question, but he’d probably would not hesitate to produce some kind of rubbish answer to the second: “Mr. Van Belle, we are thinking of identical particles here. Particles of the same kind, if you understand what I mean.”

Of course, I obviously don’t understand what he  means but so I can’t tell him that. So I’d just ask the next logical question to try to corner him:

“Of course, Mr. Feynman. Identical particles. Yes. So, when thinking of fermion-on-fermion scattering, what mechanism do you have in mind? At the very least, we should be mindful of the difference between Compton versus Thomson scattering, shouldn’t we? How does your ‘elastic’ scattering relate to these two very different types of scattering? What is your theoretical interaction mechanism here?”

I can actually think of some more questions, but I’ll leave it at this. Well… No… Let me add another one:

“Mr. Feynman, this theory of interaction between ‘identical’ or ‘like’ particles (fermions and bosons) looks great but, in reality, we will also have non-identical particles interacting with each other—or, more generally speaking, particles that are not ‘of the same kind’. To be very specific, reality sees many electrons and many photons interacting with each other—not just once, at the occasion of some elastic collision, but all of the time, really. So could we, perhaps, generalize this to some kind of ‘three- or n-particle problem’?”

This sounds like a very weird question, which even Mr. Feynman might not immediately understand. So, if he didn’t shut me up already, he may have asked me to elaborate: “What do you mean, Mr. Van Belle? What kind of three- or n-particle problem are you talking about?” I guess I’d say something like this:

“Well… Already in classical physics, we do not have an analytical solution for the ‘three-body problem’, but at least we have the equations. So we have the underlying mechanism. What are the equations here? I don’t see any. Let us suppose we have three particles colliding or scattering or interacting or whatever it is we are trying to think of. How does any of the three particles know what the other two particles are going to be: a boson or a fermion? And what sign should they then use for the interaction? In fact, I understand you are talking amplitudes of events here. If three particles collide, how many events do you count: one, two, three, or six?”

One, two, three or six? Yes. Do we think of the interaction between three particles as one event, or do we split it up as a triangular thing? Or is it one particle interacting, somehow, with the two other, in which case we’re having two events, taking into account this weird plus or minus sign rule for interaction.

Crazy? Yes. Of course. But the questions are logical, aren’t they? I can think of some more. Here is one that, in my not-so-humble view, shows how empty these discussions on the theoretical properties of theoretical bosons and theoretical fermions actually are:

“Mr. Feynman, you say a photon is a boson—a spin-one particle, so its spin state is either 1, 0 or −1. How comes photons – the only boson that we actually know to exist from real-life experiments – do not have a spin-zero state? Their spin is always up or down. It’s never zero. So why are we actually even talking about spin-one particles, if the only boson we know – the photon – does not behave like it should behave according to your boson-fermion theory?” (2)

Am I joking? I am not. I like to think I am just asking very reasonable questions here—even if all of this may sound like a bit of a rant. In fact, it probably is, but so that’s why I am writing this up in a blog rather than in a paper. Let’s continue.

The subsequent chapters are about the magical spin-1/2 and spin-1 properties of fermions and bosons respectively. I call them magical, because – as mentioned above – all we can measure is the magnetic moment. Any assumption that the angular momentum of a particle – a ‘boson’ or a ‘fermion’, whatever it is – is ±1 or ±1/2, assumes we have knowledge of some form factor, which is determined by the shape of that particle and which tells us how the mass (or the energy) of a particle is distributed in space.

Again, that may sound sacrilegious: according to mainstream physicists, particles are supposed to be pointlike—which they interpret as having no spatial dimension whatsoever. However, as I mentioned above, that sounds like a very obvious oxymoron to me.

Of course, I know I would never have gotten my degree. When I did the online MIT course, the assistants of Prof. Dr. Zwieback also told me I asked too many questions: I should just “shut up and calculate.” You may think I’m joking again but, no: that’s the feedback I got. Needless to say, I went through the course and did all of the stupid exercises, but I didn’t bother doing the exams. I don’t mind calculating. I do a lot of calculations as a finance consultant. However, I do mind mindless calculations. Things need to make sense to me. So, yes, I will always be an ‘amateur physicist’ and a ‘blogger’—read: someone whom you shouldn’t take very seriously. I just hope my jokes are better than Feynman’s.

I’ve actually been thinking that getting a proper advanced degree in physics might impede understanding, so it’s good I don’t have one. I feel these mainstream courses do try to ‘brainwash’ you. They do not encourage you to challenge received wisdom. On the contrary, it all very much resembles rote learning: memorization based on repetition. Indeed, more modern textbooks – I looked at the one of my son, for example – immediately dive into the hocus-pocus—totally shamelessly. They literally start by saying you should not try to understand and that you just get through the math and accept the quantum-mechanical dogmas and axioms! Despite the appalling logic in the introductory chapters, Mr. Feynman, in contrast, at least has the decency to try to come up with some classical arguments here and there (although he also constantly adds that the student should just accept the hocus-pocus approach and the quantum-mechanical dogmas and not think too much about what it might or might not represent).

My son got high marks on his quantum mechanics exam: a 19/20, to be precise, and so I am really proud of him—and I also feel our short discussions on this or that may have helped him to get through it. Fortunately, he was doing it as part of getting a civil engineering degree (Bachelor’s level), and he was (also) relieved he would never have to study the subject-matter again. Indeed, we had a few discussions and, while he (also) thinks I am a bit of a crackpot theorist, he does agree “the math must describe something real” and that “therefore, something doesn’t feel right in all of that math.” I told him that I’ve got this funny feeling that, 10 or 20 years from now, 75% (more?) of post-WW II research in quantum physics – most of the theoretical research, at least (3) – may be dismissed as some kind of collective psychosis or, worse, as ‘a bright shining lie’ (title of a book I warmly recommend – albeit on an entirely different topic). Frankly, I think many academics completely forgot Boltzmann’s motto for the physicist:

“Bring forward what is true. Write it so that it is clear. Defend it to your last breath.”

[…]

OK, you’ll say: get real! So what is the difference between bosons and fermions, then? I told you already: I think it’s a useless distinction. Worse, I think it’s not only useless but it’s also untruthful. It has, therefore, hampered rather than promoted creative thinking. I distinguish matter-particles – electrons, protons, neutrons – from photons (and neutrinos). Matter-particles carry charge. Photons (and neutrinos) do not. (4) Needless to say, I obviously don’t believe in ‘messenger particles’ and/or ‘Higgs’ or other ‘mechanisms’ (such as the ‘weak force’ mechanism). That sounds too much like believing in God or some other non-scientific concept. [I don’t mind you believing in God or some other non-scientific concept – I actually do myself – but we should not confuse it with doing physics.]

And as for the question on what would be my theory of interaction? It’s just the classical theory: charges attract or repel, and one can add electromagnetic fields—all in respect of the Planck-Einstein law, of course. Charges have some dimension (and some mass), so they can’t take up the same space. And electrons, protons and neutrons have some structure, and physicists should focus on modeling those structures, so as to explain the so-called intrinsic properties of these matter-particles. As for photons, I think of them as an oscillating electromagnetic field (respecting the Planck-Einstein law, of course), and so we can simply add them. What causes them to lump together? Not sure: the Planck-Einstein law (being in some joint excited state, in other words) or gravity, perhaps. In any case: I am confident it is something real—i.e. not Feynman’s weird addition or subtraction rules for amplitudes.

However, this is not the place to re-summarize all of my papers. I’d just sum them up by saying this: not many physicists seem to understand Planck’s constant or, what amounts to the same, the concept of an elementary cycle. And their unwillingness to even think about the possible structure of photons, electrons and protons is… Well… I’d call it criminal. :-/

[…]

I will now conclude my rant with another down-to-earth question: would I recommend reading Feynman’s Lectures? Or recommend youngsters to take up physics as a study subject?

My answer in regard to the first question is ambiguous: yes, and no. When you’d push me on this, I’d say: more yes than no. I do believe Feynman’s Lectures are much better than the modern-day textbook that was imposed on my son during his engineering studies and so, yes, I do recommend the older textbooks. But please be critical as you go through them: do ask yourself the same kind of questions that I’ve been asking myself while building up this blog: think for yourself. Don’t go by ‘authority’. Why not? Because the possibility that a lot of what labels itself as science may be nonsensical. As nonsensical as… Well… All what goes on in national and international politics for the moment, I guess. 🙂

In regard to the second question – should youngsters be encouraged to study physics? – I’d say what my father told me when I was hesitating to pick a subject for study: “Do what earns respect and feeds your family. You can do philosophy and other theoretical things on the side.”

With the benefit of hindsight, I can say he was right. I’ve done the stuff I wanted to do—on the side, indeed. So I told my son to go for engineering – rather than pure math or pure physics. 🙂 And he’s doing great, fortunately !

Jean Louis Van Belle

Notes:

(1) Dr. Ralston’s How To Understand Quantum Mechanics is fun for the first 10 pages or so, but I would not recommend it. We exchanged some messages, but then concluded that our respective interpretations of quantum mechanics are very different (I feel he replaces hocus-pocus by other hocus-pocus) and, hence, that we should not “waste any electrons” (his expression) on trying to convince each other.

(2) It is really one of the most ridiculous things ever. Feynman spends several chapters on explaining spin-one particles to, then, in some obscure footnote, suddenly write this: “The photon is a spin-one particle which has, however, no “zero” state.” From all of his jokes, I think this is his worst. It just shows how ‘rotten’ or ‘random’ the whole conceptual framework of mainstream QM really is. There is, in fact, another glaring inconsistency in Feynman’s Lectures: in the first three chapters of Volume III, he talks about adding wavefunctions and the basic rules of quantum mechanics, and it all happens with a plus sign. In this chapter, he suddenly says the amplitudes of fermions combine with a minus sign. If you happen to know a physicist who can babble his way of out this inconsistency, please let me know.

(3) There are exceptions, of course. I mentioned very exciting research in various posts, but most of it is non-mainstream. The group around Herman Batalaan at the University of Nebraska and various ‘electron modellers’ are just one of the many examples. I contacted a number of these ‘particle modellers’. They’re all happy I show interest, but puzzled themselves as to why their research doesn’t get all that much attention. If it’s a ‘historical accident’ in mankind’s progress towards truth, then it’s a sad one.

(4) We believe a neutron is neutral because it has both positive and negative charge in it (see our paper on protons and neutrons). as for neutrinos, we have no idea what they are, but our wild guess is that they may be the ‘photons’ of the strong force: if a photon is nothing but an oscillating electromagnetic field traveling in space, then a neutrino might be an oscillating strong field traveling in space, right? To me, it sounds like a reasonable hypothesis, but who am I, right? 🙂 If I’d have to define myself, it would be as one of Feynman’s ideal students: someone who thinks for himself. In fact, perhaps I would have been able to entertain him as much as he entertained me— and so, who knows, I like to think he might actually have given me some kind of degree for joking too ! 🙂

(5) There is no (5) in the text of my blog post, but I just thought I would add one extra note here. 🙂 Herman Batelaan and some other physicists wrote a Letter to the Physical Review Journal back in 1997. I like Batelaan’s research group because – unlike what you might think – most of Feynman’s thought experiments have actually never been done. So Batelaan – and some others – actually did the double-slit experiment with electrons, and they are doing very interesting follow-on research on it.

However, let me come to the point I want to mention here. When I read these lines in that very serious Letter, I didn’t know whether to laugh or to cry:

“Bohr’s assertion (on the impossibility of doing a Stern-Gerlach experiment on electrons or charged particles in general) is thus based on taking the classical limit for ħ going to 0. For this limit not only the blurring, but also the Stern-Gerlach splitting vanishes. However, Dehmelt argues that ħ is a nonzero constant of nature.”

I mean… What do you make of this? Of course, ħ is a nonzero constant, right? If it was zero, the Planck-Einstein relation wouldn’t make any sense, would it? What world were Bohr, Heisenberg, Pauli and others living in? A different one than ours, I guess. But that’s OK. What is not OK, is that these guys were ignoring some very basic physical laws and just dreamt up – I am paraphrasing Ralston here – “haywire axioms they did not really believe in, and regularly violated themselves.” And they didn’t know how to physically interpret the Planck-Einstein relation and/or the mass-energy equivalence relation. Sabine Hossenfelder would say they were completely lost in math. 🙂

The Mystery Wallahs

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

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

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

Outright fascinating. Brilliant ! […]

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

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

JL

A common-sense interpretation of (quantum) physics

This is my summary of what I refer to as a common-sense interpretation of quantum physics. It’s a rather abstruse summary of the 40 papers I wrote over the last two years.

1. A force acts on a charge. The electromagnetic force acts on an electric charge (there is no separate magnetic charge) and the strong force acts on a strong charge. A charge is a charge: a pointlike ‘thing’ with zero rest mass. The idea of an electron combines the idea of a charge and its motion (Schrödinger’s Zitterbewegung). The electron’s rest mass is the equivalent mass of the energy in its motion (mass without mass). The elementary wavefunction represents this motion.

2. There is no weak force: a force theory explaining why charges stay together must also explain when and how they separate. A force works through a force field: the idea that forces are mediated by virtual messenger particles resembles 19th century aether theory. The fermion-boson dichotomy does not reflect anything real: we have charged and non-charged wavicles (electrons versus photons, for example).

3. The Planck-Einstein law embodies a (stable) wavicle. A stable wavicle respects the Planck-Einstein relation (E = hf) and Einstein’s mass-energy equivalence relation (E = m·c2). A wavicle will, therefore, carry energy but it will also pack one or more units of Planck’s quantum of action. Planck’s quantum of action represents an elementary cycle in Nature. An elementary particle embodies the idea of an elementary cycle.

4. The ‘particle zoo’ is a collection of unstable wavicles: they disintegrate because their cycle is slightly off (the integral of the force over the distance of the loop and over the cycle time is not exactly equal to h).

5. An electron is a wavicle that carries charge. A photon does not carry charge: it carries energy between wavicle systems (atoms, basically). It can do so because it is an oscillating field.

6. An atom is a wavicle system. A wavicle system has an equilibrium energy state. This equilibrium state packs one unit of h. Higher energy states pack two, three,…, n units of h. When an atom transitions from one energy state to another, it will emit or absorb a photon that (i) carries the energy difference between the two energy states and (ii) packs one unit of h.

7. Nucleons (protons and neutrons) are held together because of a strong force. The strong force acts on a strong charge, for which we need to define a new unit: we choose the dirac but – out of respect for Yukawa, we write one dirac as 1 Y. If Yukawa’s function models the strong force correctly, then the strong force – which we denote as FN – can be calculated from the Yukawa potential:

F1

This function includes a scale parameter a and a nuclear proportionality constant υ0. Besides its function as an (inverse) mathematical proportionality constant, it also ensures the physical dimensions on the left- and the right-hand side of the force equation are the same. We can choose to equate the numerical value of υ0 to one.

8. The nuclear force attracts two positive electric charges. The electrostatic force repels them. These two forces are equal at a distance r = a. The strong charge unit (gN) can, therefore, be calculated. It is equal to:

F2

9. Nucleons (protons or neutrons) carry both electric as well as strong charge (qe and gN). A kinematic model disentangling both has not yet been found. Such model should explain the magnetic moment of protons and neutrons.

10. We think of a nucleus as wavicle system too. When going from one energy state to another, the nucleus emits or absorbs neutrinos. Hence, we think of the neutrino as the photon of the strong force. Such changes in energy states may also involve the emission and/or absorption of an electric charge (an electron or a positron).

Does this make sense? I look forward to your thoughts. 🙂

[…]

Because the above is all very serious, I thought it would be good to add something that will make you smile. 🙂

saint-schrodinger-as-long-as-the-tomb-is-closed-jesus-is-both-dead-and-alive

The virtuality of virtual particles

I’ve did what I promised to do – and that is to start posting on my other blog. On quantum chromodynamics, that is. But I think this paper deserves wider distribution. 🙂

The paper below probably sort of sums up my views on quantum field theory. I am not sure if I am going to continue to blog. I moved my papers to an academia.edu site and… Well… I think that’s about it. 🙂

0123456789p10p11p12

God’s Number explained

My posts on the fine-structure constant – God’s Number as it is often referred to – have always attracted a fair amount of views. I think that’s because I have always tried to clarify this or that relation by showing how and why exactly it pops us in this or that formula (e.g. Rydberg’s energy formula, the ratio of the various radii of an electron (Thomson, Compton and Bohr radius), the coupling constant, the anomalous magnetic moment, etcetera), as opposed to what most seem to try to do, and that is to further mystify it. You will probably not want to search through all of my writing so I will just refer you to my summary of these efforts on the viXra.org site: “Layered Motions: the Meaning of the Fine-Structure Constant.

However, I must admit that – till now – I wasn’t quite able to answer this very simple question: what is that fine-structure constant? Why exactly does it appear as a scaling constant or a coupling constant in almost any equation you can think of but not in, say, Einstein’s mass-energy equivalence relation, or the de Broglie relations?

I finally have a final answer (pun intended) to the question, and it’s surprisingly easy: it is the radius of the naked charge in the electron expressed in terms of the natural distance unit that comes out of our realist interpretation of what an electron actually is. [For those who haven’t read me before, this realist interpretation is based on Schrödinger’s discovery of the Zitterbewegung of an electron.] That natural distance unit is the Compton radius of the electron: it is the effective radius of an electron as measured in inelastic collisions between high-energy photons and the electron. I like to think of it as a quantum of space in which interference happens but you will want to think that through for yourself. 

The point is: that’s it. That’s all. All the other calculations follow from it. Why? It would take me a while to explain that but, if you carefully look at the logic in my classical calculations of the anomalous magnetic moment, then you should be able to  understand why these calculations are somewhat more fundamental than the others and why we can, therefore, get everything else out of them. 🙂

Post scriptum: I quickly checked the downloads of my papers on Phil Gibbs’ site, and I am extremely surprised my very first paper (the quantum-mechanical wavefunction as a gravitational wave) of mine still gets downloads. To whomever is interested in this paper, I would say: the realist interpretation we have been pursuing – based on the Zitterbewegung model of an electron – is based on the idea of a naked charge (with zero rest mass) orbiting around some center. The energy in its motion – a perpetual current ring, really – gives the electron its (equivalent) mass. That’s just Wheeler’s idea of ‘mass without mass’. But the force is definitely not gravitational. It cannot be. The force has to grab onto something, and all it can grab onto here is that naked charge. The force is, therefore, electromagnetic. It must be. I now look at my very first paper as a first immature essay. It did help me to develop some basic intuitive ideas on what any realist interpretation of QM should look like, but the quantum-mechanical wavefunction has nothing to do with gravity. Quantum mechanics is electromagnetics: we just add the quantum. The idea of an elementary cycle. Gravity is dealt with by general relativity theory: energy – or its equivalent mass – bends spacetime. That’s very significant, but it doesn’t help you when analyzing the QED sector of physics. I should probably pull this paper of the site – but I won’t. Because I think it shows where I come from: very humble origins. 🙂

The metaphysics of physics

I realized that my last posts were just some crude and rude soundbites, so I thought it would be good to briefly summarize them into something more coherent. Please let me know what you think of it.

The Uncertainty Principle: epistemology versus physics

Anyone who has read anything about quantum physics will know that its concepts and principles are very non-intuitive. Several interpretations have therefore emerged. The mainstream interpretation of quantum mechanics is referred to as the Copenhagen interpretation. It mainly distinguishes itself from more frivolous interpretations (such as the many-worlds and the pilot-wave interpretations) because it is… Well… Less frivolous. Unfortunately, the Copenhagen interpretation itself seems to be subject to interpretation.

One such interpretation may be referred to as radical skepticism – or radical empiricism[1]: we can only say something meaningful about Schrödinger’s cat if we open the box and observe its state. According to this rather particular viewpoint, we cannot be sure of its reality if we don’t make the observation. All we can do is describe its reality by a superposition of the two possible states: dead or alive. That’s Hilbert’s logic[2]: the two states (dead or alive) are mutually exclusive but we add them anyway. If a tree falls in the wood and no one hears it, then it is both standing and not standing. Richard Feynman – who may well be the most eminent representative of mainstream physics – thinks this epistemological position is nonsensical, and I fully agree with him:

“A real tree falling in a real forest makes a sound, of course, even if nobody is there. Even if no one is present to hear it, there are other traces left. The sound will shake some leaves, and if we were careful enough we might find somewhere that some thorn had rubbed against a leaf and made a tiny scratch that could not be explained unless we assumed the leaf were vibrating.” (Feynman’s Lectures, III-2-6)

So what is the mainstream physicist’s interpretation of the Copenhagen interpretation of quantum mechanics then? To fully answer that question, I should encourage the reader to read all of Feynman’s Lectures on quantum mechanics. But then you are reading this because you don’t want to do that, so let me quote from his introductory Lecture on the Uncertainty Principle: “Making an observation affects the phenomenon. The point is that the effect cannot be disregarded or minimized or decreased arbitrarily by rearranging the apparatus. When we look for a certain phenomenon we cannot help but disturb it in a certain minimum way.” (ibidem)

It has nothing to do with consciousness. Reality and consciousness are two very different things. After having concluded the tree did make a noise, even if no one was there to  hear it, he wraps up the philosophical discussion as follows: “We might ask: was there a sensation of sound? No, sensations have to do, presumably, with consciousness. And whether ants are conscious and whether there were ants in the forest, or whether the tree was conscious, we do not know. Let us leave the problem in that form.” In short, I think we can all agree that the cat is dead or alive, or that the tree is standing or not standing¾regardless of the observer. It’s a binary situation. Not something in-between. The box obscures our view. That’s all. There is nothing more to it.

Of course, in quantum physics, we don’t study cats but look at the behavior of photons and electrons (we limit our analysis to quantum electrodynamics – so we won’t discuss quarks or other sectors of the so-called Standard Model of particle physics). The question then becomes: what can we reasonably say about the electron – or the photon – before we observe it, or before we make any measurement. Think of the Stein-Gerlach experiment, which tells us that we’ll always measure the angular momentum of an electron – along any axis we choose – as either +ħ/2 or, else, as -ħ/2. So what’s its state before it enters the apparatus? Do we have to assume it has some definite angular momentum, and that its value is as binary as the state of our cat (dead or alive, up or down)?

We should probably explain what we mean by a definite angular momentum. It’s a concept from classical physics, and it assumes a precise value (or magnitude) along some precise direction. We may challenge these assumptions. The direction of the angular momentum may be changing all the time, for example. If we think of the electron as a pointlike charge – whizzing around in its own space – then the concept of a precise direction of its angular momentum becomes quite fuzzy, because it changes all the time. And if its direction is fuzzy, then its value will be fuzzy as well. In classical physics, such fuzziness is not allowed, because angular momentum is conserved: it takes an outside force – or torque – to change it. But in quantum physics, we have the Uncertainty Principle: some energy (force over a distance, remember) can be borrowed – so to speak – as long as it’s swiftly being returned – within the quantitative limits set by the Uncertainty Principle: ΔE·Δt = ħ/2.

Mainstream physicists – including Feynman – do not try to think about this. For them, the Stern-Gerlach apparatus is just like Schrödinger’s box: it obscures the view. The cat is dead or alive, and each of the two states has some probability – but they must add up to one – and so they will write the state of the electron before it enters the apparatus as the superposition of the up and down states. I must assume you’ve seen this before:

|ψ〉 = Cup|up〉 + Cdown|down〉

It’s the so-called Dirac or bra-ket notation. Cup is the amplitude for the electron spin to be equal to +ħ/2 along the chosen direction – which we refer to as the z-direction because we will choose our reference frame such that the z-axis coincides with this chosen direction – and, likewise, Cup is the amplitude for the electron spin to be equal to -ħ/2 (along the same direction, obviously). Cup and Cup will be functions, and the associated probabilities will vary sinusoidally – with a phase difference so as to make sure both add up to one.

The model is consistent, but it feels like a mathematical trick. This description of reality – if that’s what it is – does not feel like a model of a real electron. It’s like reducing the cat in our box to the mentioned fuzzy state of being alive and dead at the same time. Let’s try to come up with something more exciting. 😊

[1] Academics will immediately note that radical empiricism and radical skepticism are very different epistemological positions but we are discussing some basic principles in physics here rather than epistemological theories.

[2] The reference to Hilbert’s logic refers to Hilbert spaces: a Hilbert space is an abstract vector space. Its properties allow us to work with quantum-mechanical states, which become state vectors. You should not confuse them with the real or complex vectors you’re used to. The only thing state vectors have in common with real or complex vectors is that (1) we also need a base (aka as a representation in quantum mechanics) to define them and (2) that we can make linear combinations.

The ‘flywheel’ electron model

Physicists describe the reality of electrons by a wavefunction. If you are reading this article, you know how a wavefunction looks like: it is a superposition of elementary wavefunctions. These elementary wavefunctions are written as Ai·exp(-iθi), so they have an amplitude Ai  and an argument θi = (Ei/ħ)·t – (pi/ħ)·x. Let’s forget about uncertainty, so we can drop the index (i) and think of a geometric interpretation of A·exp(-iθ) = A·eiθ.

Here we have a weird thing: physicists think the minus sign in the exponent (-iθ) should always be there: the convention is that we get the imaginary unit (i) by a 90° rotation of the real unit (1) – but the rotation is counterclockwise rotation. I like to think a rotation in the clockwise direction must also describe something real. Hence, if we are seeking a geometric interpretation, then we should explore the two mathematical possibilities: A·eiθ and A·e+iθ. I like to think these two wavefunctions describe the same electron but with opposite spin. How should we visualize this? I like to think of A·eiθ and A·e+iθ as two-dimensional harmonic oscillators:

eiθ = cos(-θ) + i·sin(-θ) = cosθ – i·sinθ

e+iθ = cosθ + i·sinθ

So we may want to imagine our electron as a pointlike electric charge (see the green dot in the illustration below) to spin around some center in either of the two possible directions. The cosine keeps track of the oscillation in one dimension, while the sine (plus or minus) keeps track of the oscillation in a direction that is perpendicular to the first one.

Figure 1: A pointlike charge in orbit

Circle_cos_sin

So we have a weird oscillator in two dimensions here, and we may calculate the energy in this oscillation. To calculate such energy, we need a mass concept. We only have a charge here, but a (moving) charge has an electromagnetic mass. Now, the electromagnetic mass of the electron’s charge may or may not explain all the mass of the electron (most physicists think it doesn’t) but let’s assume it does for the sake of the model that we’re trying to build up here. The point is: the theory of electromagnetic mass gives us a very simple explanation for the concept of mass here, and so we’ll use it for the time being. So we have some mass oscillating in two directions simultaneously: we basically assume space is, somehow, elastic. We have worked out the V-2 engine metaphor before, so we won’t repeat ourselves here.

Figure 2: A perpetuum mobile?

V2

Previously unrelated but structurally similar formulas may be related here:

  1. The energy of an oscillator: E = (1/2)·m·a2ω2
  2. Kinetic energy: E = (1/2)·m·v2
  3. The rotational (kinetic) energy that’s stored in a flywheel: E = (1/2)·I·ω2 = (1/2)·m·r2·ω2
  4. Einstein’s energy-mass equivalence relation: E = m·c2

Of course, we are mixing relativistic and non-relativistic formulas here, and there’s the 1/2 factor – but these are minor issues. For example, we were talking not one but two oscillators, so we should add their energies: (1/2)·m·a2·ω2 + (1/2)·m·a2·ω2 = m·a2·ω2. Also, one can show that the classical formula for kinetic energy (i.e. E = (1/2)·m·v2) morphs into E = m·c2 when we use the relativistically correct force equation for an oscillator. So, yes, our metaphor – or our suggested physical interpretation of the wavefunction, I should say – makes sense.

If you know something about physics, then you know the concept of the electromagnetic mass – its mathematical derivation, that is – gives us the classical electron radius, aka as the Thomson radius. It’s the smallest of a trio of radii that are relevant when discussing electrons: the other two radii are the Bohr radius and the Compton scattering radius respectively. The Thomson radius is used in the context of elastic scattering: the frequency of the incident particle (usually a photon), and the energy of the electron itself, do not change. In contrast, Compton scattering does change the frequency of the photon that is being scattered, and also impacts the energy of our electron. [As for the Bohr radius, you know that’s the radius of an electron orbital, roughly speaking – or the size of a hydrogen atom, I should say.]

Now, if we combine the E = m·a2·ω2 and E = m·c2 equations, then a·ω must be equal to c, right? Can we show this? Maybe. It is easy to see that we get the desired equality by substituting the amplitude of the oscillation (a) for the Compton scattering radius r = ħ/(m·c), and ω (the (angular) frequency of the oscillation) by using the Planck relation (ω = E/ħ):     

a·ω = [ħ/(m·c)]·[E/ħ] = E/(m·c) = m·c2/(m·c) = c

We get a wonderfully simple geometric model of an electron here: an electric charge that spins around in a plane. Its radius is the Compton electron radius – which makes sense – and the radial velocity of our spinning charge is the speed of light – which may or may not make sense. Of course, we need an explanation of why this spinning charge doesn’t radiate its energy away – but then we don’t have such explanation anyway. All we can say is that the electron charge seems to be spinning in its own space – that it’s racing along a geodesic. It’s just like mass creates its own space here: according to Einstein’s general relativity theory, gravity becomes a pseudo-force—literally: no real force. How? I am not sure: the model here assumes the medium – empty space – is, somehow, perfectly elastic: the electron constantly borrows energy from one direction and then returns it to the other – so to speak. A crazy model, yes – but is there anything better? We only want to present a metaphor here: a possible visualization of quantum-mechanical models.

However, if this model is to represent anything real, then many more questions need to be answered. For starters, let’s think about an interpretation of the results of the Stern-Gerlach experiment.

Precession

A spinning charge is a tiny magnet – and so it’s got a magnetic moment, which we need to explain the Stern-Gerlach experiment. But it doesn’t explain the discrete nature of the electron’s angular momentum: it’s either +ħ/2 or -ħ/2, nothing in-between, and that’s the case along any direction we choose. How can we explain this? Also, space is three-dimensional. Why would electrons spin in a perfect plane? The answer is: they don’t.

Indeed, the corollary of the above-mentioned binary value of the angular momentum is that the angular momentum – or the electron’s spin – is never completely along any direction. This may or may not be explained by the precession of a spinning charge in a field, which is illustrated below (illustration taken from Feynman’s Lectures, II-35-3).

Figure 3: Precession of an electron in a magnetic fieldprecession

So we do have an oscillation in three dimensions here, really – even if our wavefunction is a two-dimensional mathematical object. Note that the measurement (or the Stein-Gerlach apparatus in this case) establishes a line of sight and, therefore, a reference frame, so ‘up’ and ‘down’, ‘left’ and ‘right’, and ‘in front’ and ‘behind’ get meaning. In other words, we establish a real space. The question then becomes: how and why does an electron sort of snap into place?

The geometry of the situation suggests the logical angle of the angular momentum vector should be 45°. Now, if the value of its z-component (i.e. its projection on the z-axis) is to be equal to ħ/2, then the magnitude of J itself should be larger. To be precise, it should be equal to ħ/√2 ≈ 0.7·ħ (just apply Pythagoras’ Theorem). Is that value compatible with our flywheel model?

Maybe. Let’s see. The classical formula for the magnetic moment is μ = I·A, with I the (effective) current and A the (surface) area. The notation is confusing because I is also used for the moment of inertia, or rotational mass, but… Well… Let’s do the calculation. The effective current is the electron charge (qe) divided by the period (T) of the orbital revolution: : I = qe/T. The period of the orbit is the time that is needed for the electron to complete one loop. That time (T) is equal to the circumference of the loop (2π·a) divided by the tangential velocity (vt). Now, we suggest vt = r·ω = a·ω = c, and the circumference of the loop is 2π·a. For a, we still use the Compton radius a = ħ/(m·c). Now, the formula for the area is A = π·a2, so we get:

μ = I·A = [qe/T]·π·a2 = [qe·c/(2π·a)]·[π·a2] = [(qe·c)/2]·a = [(qe·c)/2]·[ħ/(m·c)] = [qe/(2m)]·ħ

In a classical analysis, we have the following relation between angular momentum and magnetic moment:

μ = (qe/2m)·J

Hence, we find that the angular momentum J is equal to ħ, so that’s twice the measured value. We’ve got a problem. We would have hoped to find ħ/2 or ħ/√2. Perhaps it’s  because a = ħ/(m·c) is the so-called reduced Compton scattering radius…

Well… No.

Maybe we’ll find the solution one day. I think it’s already quite nice we have a model that’s accurate up to a factor of 1/2 or 1/√2. 😊

Post scriptum: I’ve turned this into a small article which may or may not be more readable. You can link to it here. Comments are more than welcome.

A Survivor’s Guide to Quantum Mechanics?

When modeling electromagnetic waves, the notion of left versus right circular polarization is quite clear and fully integrated in the mathematical treatment. In contrast, quantum math sticks to the very conventional idea that the imaginary unit (i) is – always! – a counter-clockwise rotation by 90 degrees. We all know that –i would do just as an imaginary unit as i, because the definition of the imaginary unit says the only requirement is that its square has to be equal to –1, and (–i)2 is also equal to –1.

So we actually have two imaginary units: i and –i. However, physicists stubbornly think there is only one direction for measuring angles, and that is counter-clockwise. That’s a mathematical convention, Professor: it’s something in your head only. It is not real. Nature doesn’t care about our conventions and, therefore, I feel the spin ‘up’ versus spin ‘down’ should correspond to the two mathematical possibilities: if the ‘up’ state is represented by some complex function, then the ‘down’ state should be represented by its complex conjugate.

This ‘additional’ rule wouldn’t change the basic quantum-mechanical rules – which are written in terms of state vectors in a Hilbert space (and, yes, a Hilbert space is an unreal as it sounds: its rules just say you should separate cats and dogs while adding them – which is very sensible advice, of course). However, they would, most probably (just my intuition – I need to prove it), avoid these crazy 720 degree symmetries which inspire the likes of Penrose to say there is no physical interpretation on the wavefunction.

Oh… As for the title of my post… I think it would be a great title for a book – because I’ll need some space to work it all out. 🙂

Quantum math: garbage in, garbage out?

This post is basically a continuation of my previous one but – as you can see from its title – it is much more aggressive in its language, as I was inspired by a very thoughtful comment on my previous post. Another advantage is that it avoids all of the math. 🙂 It’s… Well… I admit it: it’s just a rant. 🙂 [Those who wouldn’t appreciate the casual style of what follows, can download my paper on it – but that’s much longer and also has a lot more math in it – so it’s a much harder read than this ‘rant’.]

My previous post was actually triggered by an attempt to re-read Feynman’s Lectures on Quantum Mechanics, but in reverse order this time: from the last chapter to the first. [In case you doubt, I did follow the correct logical order when working my way through them for the first time because… Well… There is no other way to get through them otherwise. 🙂 ] But then I was looking at Chapter 20. It’s a Lecture on quantum-mechanical operators – so that’s a topic which, in other textbooks, is usually tackled earlier on. When re-reading it, I realize why people quickly turn away from the topic of physics: it’s a lot of mathematical formulas which are supposed to reflect reality but, in practice, few – if any – of the mathematical concepts are actually being explained. Not in the first chapters of a textbook, not in its middle ones, and… Well… Nowhere, really. Why? Well… To be blunt: I think most physicists themselves don’t really understand what they’re talking about. In fact, as I have pointed out a couple of times already, Feynman himself admits so much:

“Atomic behavior appears peculiar and mysterious to everyone—both to the novice and to the experienced physicist. Even the experts do not understand it the way they would like to.”

So… Well… If you’d be in need of a rather spectacular acknowledgement of the shortcomings of physics as a science, here you have it: if you don’t understand what physicists are trying to tell you, don’t worry about it, because they don’t really understand it themselves. 🙂

Take the example of a physical state, which is represented by a state vector, which we can combine and re-combine using the properties of an abstract Hilbert space. Frankly, I think the word is very misleading, because it actually doesn’t describe an actual physical state. Why? Well… If we look at this so-called physical state from another angle, then we need to transform it using a complicated set of transformation matrices. You’ll say: that’s what we need to do when going from one reference frame to another in classical mechanics as well, isn’t it?

Well… No. In classical mechanics, we’ll describe the physics using geometric vectors in three dimensions and, therefore, the base of our reference frame doesn’t matter: because we’re using real vectors (such as the electric of magnetic field vectors E and B), our orientation vis-á-vis the object – the line of sight, so to speak – doesn’t matter.

In contrast, in quantum mechanics, it does: Schrödinger’s equation – and the wavefunction – has only two degrees of freedom, so to speak: its so-called real and its imaginary dimension. Worse, physicists refuse to give those two dimensions any geometric interpretation. Why? I don’t know. As I show in my previous posts, it would be easy enough, right? We know both dimensions must be perpendicular to each other, so we just need to decide if both of them are going to be perpendicular to our line of sight. That’s it. We’ve only got two possibilities here which – in my humble view – explain why the matter-wave is different from an electromagnetic wave.

I actually can’t quite believe the craziness when it comes to interpreting the wavefunction: we get everything we’d want to know about our particle through these operators (momentum, energy, position, and whatever else you’d need to know), but mainstream physicists still tell us that the wavefunction is, somehow, not representing anything real. It might be because of that weird 720° symmetry – which, as far as I am concerned, confirms that those state vectors are not the right approach: you can’t represent a complex, asymmetrical shape by a ‘flat’ mathematical object!

Huh? Yes. The wavefunction is a ‘flat’ concept: it has two dimensions only, unlike the real vectors physicists use to describe electromagnetic waves (which we may interpret as the wavefunction of the photon). Those have three dimensions, just like the mathematical space we project on events. Because the wavefunction is flat (think of a rotating disk), we have those cumbersome transformation matrices: each time we shift position vis-á-vis the object we’re looking at (das Ding an sich, as Kant would call it), we need to change our description of it. And our description of it – the wavefunction – is all we have, so that’s our reality. However, because that reality changes as per our line of sight, physicists keep saying the wavefunction (or das Ding an sich itself) is, somehow, not real.

Frankly, I do think physicists should take a basic philosophy course: you can’t describe what goes on in three-dimensional space if you’re going to use flat (two-dimensional) concepts, because the objects we’re trying to describe (e.g. non-symmetrical electron orbitals) aren’t flat. Let me quote one of Feynman’s famous lines on philosophers: “These philosophers are always with us, struggling in the periphery to try to tell us something, but they never really understand the subtleties and depth of the problem.” (Feynman’s Lectures, Vol. I, Chapter 16)

Now, I love Feynman’s Lectures but… Well… I’ve gone through them a couple of times now, so I do think I have an appreciation of the subtleties and depth of the problem now. And I tend to agree with some of the smarter philosophers: if you’re going to use ‘flat’ mathematical objects to describe three- or four-dimensional reality, then such approach will only get you where we are right now, and that’s a lot of mathematical mumbo-jumbo for the poor uninitiated. Consistent mumbo-jumbo, for sure, but mumbo-jumbo nevertheless. 🙂 So, yes, I do think we need to re-invent quantum math. 🙂 The description may look more complicated, but it would make more sense.

I mean… If physicists themselves have had continued discussions on the reality of the wavefunction for almost a hundred years now (Schrödinger published his equation in 1926), then… Well… Then the physicists have a problem. Not the philosophers. 🙂 As to how that new description might look like, see my papers on viXra.org. I firmly believe it can be done. This is just a hobby of mine, but… Well… That’s where my attention will go over the coming years. 🙂 Perhaps quaternions are the answer but… Well… I don’t think so either – for reasons I’ll explain later. 🙂

Post scriptum: There are many nice videos on Dirac’s belt trick or, more generally, on 720° symmetries, but this links to one I particularly like. It clearly shows that the 720° symmetry requires, in effect, a special relation between the observer and the object that is being observed. It is, effectively, like there is a leather belt between them or, in this case, we have an arm between the glass and the person who is holding the glass. So it’s not like we are walking around the object (think of the glass of water) and making a full turn around it, so as to get back to where we were. No. We are turning it around by 360°! That’s a very different thing than just looking at it, walking around it, and then looking at it again. That explains the 720° symmetry: we need to turn it around twice to get it back to its original state. So… Well… The description is more about us and what we do with the object than about the object itself. That’s why I think the quantum-mechanical description is defective.

Should we reinvent wavefunction math?

Preliminary note: This post may cause brain damage. 🙂 If you haven’t worked yourself through a good introduction to physics – including the math – you will probably not understand what this is about. So… Well… Sorry. 😦 But if you have… Then this should be very interesting. Let’s go. 🙂

If you know one or two things about quantum math – Schrödinger’s equation and all that – then you’ll agree the math is anything but straightforward. Personally, I find the most annoying thing about wavefunction math are those transformation matrices: every time we look at the same thing from a different direction, we need to transform the wavefunction using one or more rotation matrices – and that gets quite complicated !

Now, if you have read any of my posts on this or my other blog, then you know I firmly believe the wavefunction represents something real or… Well… Perhaps it’s just the next best thing to reality: we cannot know das Ding an sich, but the wavefunction gives us everything we would want to know about it (linear or angular momentum, energy, and whatever else we have an operator for). So what am I thinking of? Let me first quote Feynman’s summary interpretation of Schrödinger’s equation (Lectures, III-16-1):

“We can think of Schrödinger’s equation as describing the diffusion of the probability amplitude from one point to the next. […] But the imaginary coefficient in front of the derivative makes the behavior completely different from the ordinary diffusion such as you would have for a gas spreading out along a thin tube. Ordinary diffusion gives rise to real exponential solutions, whereas the solutions of Schrödinger’s equation are complex waves.”

Feynman further formalizes this in his Lecture on Superconductivity (Feynman, III-21-2), in which he refers to Schrödinger’s equation as the “equation for continuity of probabilities”. His analysis there is centered on the local conservation of energy, which makes me think Schrödinger’s equation might be an energy diffusion equation. I’ve written about this ad nauseam in the past, and so I’ll just refer you to one of my papers here for the details, and limit this post to the basics, which are as follows.

The wave equation (so that’s Schrödinger’s equation in its non-relativistic form, which is an approximation that is good enough) is written as:formula 1The resemblance with the standard diffusion equation (shown below) is, effectively, very obvious:formula 2As Feynman notes, it’s just that imaginary coefficient that makes the behavior quite different. How exactly? Well… You know we get all of those complicated electron orbitals (i.e. the various wave functions that satisfy the equation) out of Schrödinger’s differential equation. We can think of these solutions as (complex) standing waves. They basically represent some equilibrium situation, and the main characteristic of each is their energy level. I won’t dwell on this because – as mentioned above – I assume you master the math. Now, you know that – if we would want to interpret these wavefunctions as something real (which is surely what want to do!) – the real and imaginary component of a wavefunction will be perpendicular to each other. Let me copy the animation for the elementary wavefunction ψ(θ) = a·ei∙θ = a·ei∙(E/ħ)·t = a·cos[(E/ħ)∙t]  i·a·sin[(E/ħ)∙t] once more:

Circle_cos_sin

So… Well… That 90° angle makes me think of the similarity with the mathematical description of an electromagnetic wave. Let me quickly show you why. For a particle moving in free space – with no external force fields acting on it – there is no potential (U = 0) and, therefore, the Vψ term – which is just the equivalent of the the sink or source term S in the diffusion equation – disappears. Therefore, Schrödinger’s equation reduces to:

∂ψ(x, t)/∂t = i·(1/2)·(ħ/meff)·∇2ψ(x, t)

Now, the key difference with the diffusion equation – let me write it for you once again: ∂φ(x, t)/∂t = D·∇2φ(x, t) – is that Schrödinger’s equation gives us two equations for the price of one. Indeed, because ψ is a complex-valued function, with a real and an imaginary part, we get the following equations:

  1. Re(∂ψ/∂t) = −(1/2)·(ħ/meffIm(∇2ψ)
  2. Im(∂ψ/∂t) = (1/2)·(ħ/meffRe(∇2ψ)

Huh? Yes. These equations are easily derived from noting that two complex numbers a + i∙b and c + i∙d are equal if, and only if, their real and imaginary parts are the same. Now, the ∂ψ/∂t = i∙(ħ/meff)∙∇2ψ equation amounts to writing something like this: a + i∙b = i∙(c + i∙d). Now, remembering that i2 = −1, you can easily figure out that i∙(c + i∙d) = i∙c + i2∙d = − d + i∙c. [Now that we’re getting a bit technical, let me note that the meff is the effective mass of the particle, which depends on the medium. For example, an electron traveling in a solid (a transistor, for example) will have a different effective mass than in an atom. In free space, we can drop the subscript and just write meff = m.] 🙂 OK. Onwards ! 🙂

The equations above make me think of the equations for an electromagnetic wave in free space (no stationary charges or currents):

  1. B/∂t = –∇×E
  2. E/∂t = c2∇×B

Now, these equations – and, I must therefore assume, the other equations above as well – effectively describe a propagation mechanism in spacetime, as illustrated below:

propagation

You know how it works for the electromagnetic field: it’s the interplay between circulation and flux. Indeed, circulation around some axis of rotation creates a flux in a direction perpendicular to it, and that flux causes this, and then that, and it all goes round and round and round. 🙂 Something like that. 🙂 I will let you look up how it goes, exactly. The principle is clear enough. Somehow, in this beautiful interplay between linear and circular motion, energy is borrowed from one place and then returns to the other, cycle after cycle.

Now, we know the wavefunction consist of a sine and a cosine: the cosine is the real component, and the sine is the imaginary component. Could they be equally real? Could each represent half of the total energy of our particle? I firmly believe they do. The obvious question then is the following: why wouldn’t we represent them as vectors, just like E and B? I mean… Representing them as vectors (I mean real vectors here – something with a magnitude and a direction in a real space – as opposed to state vectors from the Hilbert space) would show they are real, and there would be no need for cumbersome transformations when going from one representational base to another. In fact, that’s why vector notation was invented (sort of): we don’t need to worry about the coordinate frame. It’s much easier to write physical laws in vector notation because… Well… They’re the real thing, aren’t they? 🙂

What about dimensions? Well… I am not sure. However, because we are – arguably – talking about some pointlike charge moving around in those oscillating fields, I would suspect the dimension of the real and imaginary component of the wavefunction will be the same as that of the electric and magnetic field vectors E and B. We may want to recall these:

  1. E is measured in newton per coulomb (N/C).
  2. B is measured in newton per coulomb divided by m/s, so that’s (N/C)/(m/s).

The weird dimension of B is because of the weird force law for the magnetic force. It involves a vector cross product, as shown by Lorentz’ formula:

F = qE + q(v×B)

Of course, it is only one force (one and the same physical reality), as evidenced by the fact that we can write B as the following vector cross-product: B = (1/c)∙ex×E, with ex the unit vector pointing in the x-direction (i.e. the direction of propagation of the wave). [Check it, because you may not have seen this expression before. Just take a piece of paper and think about the geometry of the situation.] Hence, we may associate the (1/c)∙ex× operator, which amounts to a rotation by 90 degrees, with the s/m dimension. Now, multiplication by i also amounts to a rotation by 90° degrees. Hence, if we can agree on a suitable convention for the direction of rotation here, we may boldly write:

B = (1/c)∙ex×E = (1/c)∙iE

This is, in fact, what triggered my geometric interpretation of Schrödinger’s equation about a year ago now. I have had little time to work on it, but think I am on the right track. Of course, you should note that, for an electromagnetic wave, the magnitudes of E and B reach their maximum, minimum and zero point simultaneously (as shown below). So their phase is the same.

E and B

In contrast, the phase of the real and imaginary component of the wavefunction is not the same, as shown below.wavefunction

In fact, because of the Stern-Gerlach experiment, I am actually more thinking of a motion like this:

Wavefunction 2But that shouldn’t distract you. 🙂 The question here is the following: could we possibly think of a new formulation of Schrödinger’s equation – using vectors (again, real vectors – not these weird state vectors) rather than complex algebra?

I think we can, but then I wonder why the inventors of the wavefunction – Heisenberg, Born, Dirac, and Schrödinger himself, of course – never thought of that. 🙂

Hmm… I need to do some research here. 🙂

Post scriptum: You will, of course, wonder how and why the matter-wave would be different from the electromagnetic wave if my suggestion that the dimension of the wavefunction component is the same is correct. The answer is: the difference lies in the phase difference and then, most probably, the different orientation of the angular momentum. Do we have any other possibilities? 🙂

P.S. 2: I also published this post on my new blog: https://readingeinstein.blog/. However, I thought the followers of this blog should get it first. 🙂