Physical humbug

A good thing and a bad thing today:

1. The good thing is: I expanded my paper which deals with more advanced questions on this realist interpretation of QM (based on mass-without-mass models of elementary particles that I have been pursuing). I think I see everything clearly now: Maxwell’s equations only make sense as soon as the concepts of charge densities (expressed in coulomb per volume or area unit: C/m3 or C/m2) and currents (expressed in C/s) start making sense, which is only above the threshold of Planck’s quantum of action and within the quantization limits set by the Planck-Einstein relation. So, yes, we can, finally, confidently write this:

Quantum Mechanics = All of Physics = Maxwell’s equations + Planck-Einstein relation

2. The bad thing: I had an annoying discussion on ResearchGate on the consistency of quantum physics with one of those people who still seem to doubt both special as well as general relativity theory.

To get my frustration out, I copy the exchange below – as it might be informative when you are confronted with weirdos on some scientific forum too! It starts with a rather non-sensical remark on the reality of infinities, and an equally non-sensical question on how we get quantization from classical equations (Maxwell’s equations and then Gauss and Stokes theorem), to which the answer has to be: we do not, of course! For that, you need to combine them with the Planck-Einstein relation!

Start of the conversation: Jean Louis Van Belle, I found Maxwell quite consistent with, for instance Stokes aether model. Can you explain how he ‘threw it out‘. It was a firm paradigm until Einstein removed it’s power to ‘change‘ light speed, yet said “space without aether is unthinkable.” (Leiden ’21). He then mostly re-instated it in his ’52 paper correcting 1905 interpretations in bounded ‘spaces in motion within spaces) completed in the DFM. ‘QM’ then emerges.

My answer: Dear Peter – As you seem to believe zero-dimensional objects can have properties and, therefore, exist, and also seem to believe infinity is also real (not just a mathematical idealization), then we’re finished talking, because – for example – no sensible interpretation of the Planck-Einstein relation is possible in such circumstances. Also, all of physics revolves around conjugate variables, and these combine in products or product sums that have very small but finite values (think of typical canonic commutator relations, for example): products of infinity and zero are undefined – in mathematics too, by the way! I attach a ‘typically Feynman’ explanation of one of these commutator relations, which talks about the topic rather well. I could also refer to Dirac’s definition of the Dirac function (real probability functions do not collapse into an infinite probability density), or his comments on the infinities appearing in the perturbation theory he himself had developed, and which he then distanced himself from exactly because it generated infinities, which could not be ‘real’ according to him. I’ve got the feeling you’re stuck in 19th century classical physics. Perhaps you missed one or two other points from Einstein as well (apart from the references you give).To relate this discussion to the original question of this thread, I’d say: physicists who mistake mathematical idealizations for reality do obviously not understand quantum mechanics. Cheers – JL

PS: We may, of course, in our private lives believe that God ‘exists’ and that he is infinite and whatever, but that’s personal conviction or opinion: it is not science, nothing empirical that has been verified and can be verified again at any time. Oh – and to answer your specific question on Maxwell’s equations and vector algebra (Gauss and Stokes theorem), they do not incorporate the Planck-Einstein relation. That’s all. Planck-Einstein (quantization of reality) + Maxwell (classical EM) = quantum physics.

Immediate reply: Jean Louis Van Belle , I don’t invoke either zero dimensional objects, infinity or God! Neither the Planck length or Wolframs brilliant 10-93 is ‘zero’. Fermion pair scale is the smallest ‘Condensed Matter‘ but I suggest we must think beyond that to the condensate & ‘vacuum energy’ scales to advance understanding. More 22nd than 19th century! Einstein is easy to ‘cherry pick’ but his search for SR’s ‘physical’ state bore fruit in 1952!

[This Peter actually did refer to infinities and zeroes in math as being more than mathematical idealizations, but then edited out these specific stupidities.]

My answer: Dear Peter – I really cannot understand why you want to disprove SRT. SRT (or, at least, the absoluteness of lightspeed) comes out of Maxwell’s equations. Einstein just provided a rather heuristic argument to ‘prove’ it. Maxwell’s equations are the more ‘real thing’ – so to speak. And then GRT just comes from combining SRT and Mach’s principle. What problem are you trying to solve? I understand that, somehow, QM does NOT come across as ‘consistent’ to you (so I do not suffer from that: all equations look good to me – I just have my own ‘interpretation’ of it, but I do not question their validity). You seem to suspect something is wrong with quantum physics somewhere, but I don’t see exactly where.

Also, can you explain in a few words what you find brilliant about Wolfram’s number? I find the f/m = c2/h = 1.35639248965213E50 number brilliant, because it gives us a frequency per unit mass which is valid for all kinds of mass (electron, proton, or whatever combination of charged and neutral matter you may think of), but so that comes out of the E = mc2 and E = hf, and so it is not some new ‘God-given’ number or something ‘very special’: it is just a straight combination of two fundamental constants of Nature that we already know. I also find the fine-structure constant (and the electric/magnetic constants) ‘brilliant numbers’ but, again, I don’t think they are something mysterious. So what is Wolfram’s number about? What kind of ratio or combination of functions or unexplained explanation or new undiscovered simplification of existing mainstream explanations does it bring? Is it a new proportionality constant – some elasticity of spacetime, perhaps? A combination of Planck-scale units? Does it connect g and the electric constant? An update of (the inverse of) Eddington’s estimate of the number of protons in the Universe based on latest measurements of the cosmological constant? Boltzmann’s number and Avogadro’s constant (or, in light of the negative exponent, their inverse) – through the golden ratio or a whole new ‘holographic’ theory? New numbers are usually easy to explain in terms of existing theory – or in terms of what they propose to change to existing theory, no?

Perhaps an easy start is to give us a physical dimension for Wolfram’s number. My 1.35639248965213E50 number is the (exact) number of oscillations per kg, for example – not oscillations of ‘aether’ or something, but of charge in motion. Except for the fine-structure constant, all numbers in physics have a physical dimension (except if they’re scaling or coupling constants, such as the fine-structure constant), even if it’s only a scalar (plain number), it’s a number describing x units of something) or a density (then it is x per m3 or m2, per J, per kg, per coulomb, per ampere, etcetera – whatever SI unit or combination of SI units you want to choose).

On a very different note, I think that invoking some statement or a late paper of Einstein in an attempt to add ‘authority’ to some kind of disproof of SRT invokes the wrong kind of authority. 🙂 If you would say Heisenberg or Bohr or Dirac or Feynman or Oppenheimer started doubting SRT near the end of their lives, I’d look up and say: what? Now, no. Einstein had the intellectual honesty to speak up, and speak up rather loudly (cf. him persuading the US President to build the bomb).

As for the compatibility between SRT and GRT and quantum mechanics, the relativistically invariant argument of the wavefunction shows no such incompatibility is there (see Annex II and III of The Zitterbewegung hypothesis and the scattering matrix). Cheers – JL


Personal conclusion: I think I’ll just stay away from ResearchGate discussions for a while. They are not always good for one’s peace of mind. :-/

All of physics

This five-pager has it: all you ever wanted to know about the Universe. Electron mass and proton mass are seen as input to the model. To the most famous failed experiment in all of classical physics – the 1887 Michelson-Morley experiment, which disproved aether theories and established the absoluteness of lightspeed – we should add the Kamioka Nucleon Decay Experiment, which firmly established that protons do not decay. All the rest is history. 🙂

Post scriptum (26 April): I added another five-pager on fundamental concepts on ResearchGate, which may or may not help to truly understand what might be the case (I am paraphrasing Wittgenstein’s definition of reality here). It is on potentials, and it explains why thinking in terms of neat 1/r or 1/r2 functions is not all that helpful: reality is fuzzier than that. Even a simple electrostatic potential may be not very simple. The fuzzy concept of near and far fields remains useful.

I am actually quite happy with the paper, because it sort of ‘completes’ my thinking on elementary particles in terms of ring currents. It made me feel like it is the first time I truly understand the complementarity/uncertainty principle – and that I invoke it to make an argument.

The nuclear force and gauge

I just wrapped up a discussion with some mainstream physicists, producing what I think of as a final paper on the nuclear force. I was struggling with the apparent non-conservative nature of the nuclear potential, but now I have the solution. It is just like an electric dipole field: not spherically symmetric. Nice and elegant.

I can’t help copying the last exchange with one of the researchers. He works at SLAC and seems to believe hydrinos might really exist. It is funny, and then it is not. :-/

Me: “Dear X – That is why I am an amateur physicist and don’t care about publication. I do not believe in quarks and gluons. Do not worry: it does not prevent me from being happy. JL”

X: “Dear Jean Louis – The whole physics establishment believes that neutron is composed of three quarks, gluons and a see of quark-antiquark pairs. How does that fit into your picture? Best regards, X”

Me: “I see the neutron as a tight system between positive and negative electric charge – combining electromagnetic and nuclear force. The ‘proton + electron’ idea is vague. The idea of an elementary particle is confusing in discussions and must be defined clearly: stable, not-reducible, etcetera. Neutrons decay (outside of the nucleus), so they are reducible. I do not agree with Heisenberg on many fronts (especially not his ‘turnaround’ on the essence of the Uncertainty Principle) so I don’t care about who said what – except Schroedinger, who fell out with both Dirac and Heisenberg, I feel. His reason to not show up at the Nobel Prize occasion in 1933 (where Heisenberg received the prize of the year before, and Dirac/Schroedinger the prize of the year itself) was not only practical, I think – but that’s Hineininterpretierung which doesn’t matter in questions like this. JL”

X: “Dear Jean Louis – I want to to make doubly sure. Do I understand you correctly that you are saying that neutron is really a tight system of proton and electron ? If that is so, it is interesting that Heisenberg, inventor of the uncertainty principle, believed the same thing until 1935 (I have it from Pais book). Then the idea died because. Pauli’s argument won, that the neutron spin 1/2 follows the Fermi-Dirac statistics and this decided that the neutron is indeed an elementary particle. This would very hard sell, if you now, after so many years, agree with Heisenberg. By the way, I say in my Phys. Lett. B paper, which uses k1/r + k2/r2 potential, that the radius of the small hydrogen is about 5.671 Fermi. But this is very sensitive to what potential one is using. Best regards, X.”

Quaternions and the nuclear wave equation

In this blog, we talked a lot about the Zitterbewegung model of an electron, which is a model which allows us to think of the elementary wavefunction as representing a radius or position vector. We write:

ψ = r = a·e±iθ = a·[cos(±θ) + i · sin(±θ)]

It is just an application of Parson’s ring current or magneton model of an electron. Note we use boldface to denote vectors, and that we think of the sine and cosine here as vectors too! You should note that the sine and cosine are the same function: they differ only because of a 90-degree phase shift: cosθ = sin(θ + π/2). Alternatively, we can use the imaginary unit (i) as a rotation operator and use the vector notation to write: sinθ = i·cosθ.

In one of our introductory papers (on the language of math), we show how and why this all works like a charm: when we take the derivative with respect to time, we get the (orbital or tangential) velocity (dr/dt = v), and the second-order derivative gives us the (centripetal) acceleration vector (d2r/dt2 = a). The plus/minus sign of the argument of the wavefunction gives us the direction of spin, and we may, perhaps, add a plus/minus sign to the wavefunction as a whole to model matter and antimatter, respectively (the latter assertion is very speculative though, so we will not elaborate that here).

One orbital cycle packs Planck’s quantum of (physical) action, which we can write either as the product of the energy (E) and the cycle time (T), or the momentum (p) of the charge times the distance travelled, which is the circumference of the loop λ in the inertial frame of reference (we can always add a classical linear velocity component when considering an electron in motion, and we may want to write Planck’s quantum of action as an angular momentum vector (h or ħ) to explain what the Uncertainty Principle is all about (statistical uncertainty, nothing ontological), but let us keep things simple as for now):

h = E·T = p·λ

It is important to distinguish between the electron and the charge, which we think of being pointlike: the electron is charge in motion. Charge is just charge: it explains everything and its nature is, therefore, quite mysterious: is it really a pointlike thing, or is there some fractal structure? Of these things, we know very little, but the small anomaly in the magnetic moment of an electron suggests its structure might be fractal. Think of the fine-structure constant here, as the factor which distinguishes the classical, Compton and Bohr radii of the electron: we associate the classical electron radius with the radius of the poinlike charge, but perhaps we can drill down further.

We also showed how the physical dimensions work out in Schroedinger’s wave equation. Let us jot it down to appreciate what it might model, and appreciate why complex numbers come in handy:

Schroedinger’s equation in free space

This is, of course, Schroedinger’s equation in free space, which means there are no other charges around and we, therefore, have no potential energy terms here. The rather enigmatic concept of the effective mass (which is half the total mass of the electron) is just the relativistic mass of the pointlike charge as it whizzes around at lightspeed, so that is the motion which Schroedinger referred to as its Zitterbewegung (Dirac confused it with some motion of the electron itself, further compounding what we think of as de Broglie’s mistaken interpretation of the matter-wave as a linear oscillation: think of it as an orbital oscillation). The 1/2 factor is there in Schroedinger’s wave equation for electron orbitals, but he replaced the effective mass rather subtly (or not-so-subtly, I should say) by the total mass of the electron because the wave equation models the orbitals of an electron pair (two electrons with opposite spin). So we might say he was lucky: the two mistakes together (not accounting for spin, and adding the effective mass of two electrons to get a mass factor) make things come out alright. 🙂

However, we will not say more about Schroedinger’s equation for the time being (we will come back to it): just note the imaginary unit, which does operate like a rotation operator here. Schroedinger’s wave equation, therefore, must model (planar) orbitals. Of course, the plane of the orbital itself may be rotating itself, and most probably is because that is what gives us those wonderful shapes of electron orbitals (subshells). Also note the physical dimension of ħ/m: it is a factor which is expressed in m2/s, but when you combine that with the 1/m2 dimension of the ∇2 operator, then you get the 1/s dimension on both sides of Schroedinger’s equation. [The ∇2 operator is just the generalization of the d2r/dx2 but in three dimensions, so x becomes a vector: x, and we apply the operator to the three spatial coordinates and get another vector, which is why we call ∇2 a vector operator. Let us move on, because we cannot explain each and every detail here, of course!]

We need to talk forces and fields now. This ring current model assumes an electromagnetic field which keeps the pointlike charge in its orbit. This centripetal force must be equal to the Lorentz force (F), which we can write in terms of the electric and magnetic field vectors E and B (fields are just forces per unit charge, so the two concepts are very intimately related):

F = q·(E + v×B) = q·(E + c×E/c) = q·(E + 1×E) = q·(E + j·E) = (1+ j)·q·E

We use a different imaginary unit here (j instead of i) because the plane in which the magnetic field vector B is going round and round is orthogonal to the plane in which E is going round and round, so let us call these planes the xy– and xz-planes respectively. Of course, you will ask: why is the B-plane not the yz-plane? We might be mistaken, but the magnetic field vector lags the electric field vector, so it is either of the two, and so now you can check for yourself of what we wrote above is actually correct. Also note that we write 1 as a vector (1) or a complex number: 1 = 1 + i·0. [It is also possible to write this: 1 = 1 + i·0 or 1 = 1 + i·0. As long as we think of these things as vectors – something with a magnitude and a direction – it is OK.]

You may be lost in math already, so we should visualize this. Unfortunately, that is not easy. You may to google for animations of circularly polarized electromagnetic waves, but these usually show the electric field vector only, and animations which show both E and B are usually linearly polarized waves. Let me reproduce the simplest of images: imagine the electric field vector E going round and round. Now imagine the field vector B being orthogonal to it, but also going round and round (because its phase follows the phase of E). So, yes, it must be going around in the xz– or yz-plane (as mentioned above, we let you figure out how the various right-hand rules work together here).

Rotational plane of the electric field vector

You should now appreciate that the E and B vectors – taken together – will also form a plane. This plane is not static: it is not the xy-, yz– or xz-plane, nor is it some static combination of two of these. No! We cannot describe it with reference to our classical Cartesian axes because it changes all the time as a result of the rotation of both the E and B vectors. So how we can describe that plane mathematically?

The Irish mathematician William Rowan Hamilton – who is also known for many other mathematical concepts – found a great way to do just that, and we will use his notation. We could say the plane formed by the E and B vectors is the EB plane but, in line with Hamilton’s quaternion algebra, we will refer to it as the k-plane. How is it related to what we referred to as the i– and j-planes, or the xy– and xz-plane as we used to say? At this point, we should introduce Hamilton’s notation: he did write i and j in boldface (we do not like that, but you may want to think of it as just a minor change in notation because we are using these imaginary units in a new mathematical space: the quaternion number space), and he referred to them as basic quaternions in what you should think of as an extension of the complex number system. More specifically, he wrote this on a now rather famous bridge in Dublin:

i2 = -1

j2 = -1

k2 = -1

i·j = k

j·i= k

The first three rules are the ones you know from complex number math: two successive rotations by 90 degrees will bring you from 1 to -1. The order of multiplication in the other two rules ( i·j = k and j·i = –k ) gives us not only the k-plane but also the spin direction. All other rules in regard to quaternions (we can write, for example, this: i ·j·k = -1), and the other products you will find in the Wikipedia article on quaternions) can be derived from these, but we will not go into them here.

Now, you will say, we do not really need that k, do we? Just distinguishing between i and j should do, right? The answer to that question is: yes, when you are dealing with electromagnetic oscillations only! But it is no when you are trying to model nuclear oscillations! That is, in fact, exactly why we need this quaternion math in quantum physics!

Let us think about this nuclear oscillation. Particle physics experiments – especially high-energy physics experiments – effectively provide evidence for the presence of a nuclear force. To explain the proton radius, one can effectively think of a nuclear oscillation as an orbital oscillation in three rather than just two dimensions. The oscillation is, therefore, driven by two (perpendicular) forces rather than just one, with the frequency of each of the oscillators being equal to ω = E/2ħ = mc2/2ħ.

Each of the two perpendicular oscillations would, therefore, pack one half-unit of ħ only. The ω = E/2ħ formula also incorporates the energy equipartition theorem, according to which each of the two oscillations should pack half of the total energy of the nuclear particle (so that is the proton, in this case). This spherical view of a proton fits nicely with packing models for nucleons and yields the experimentally measured radius of a proton:

Proton radius formula

Of course, you can immediately see that the 4 factor is the same factor 4 as the one appearing in the formula for the surface area of a sphere (A = 4πr2), as opposed to that for the surface of a disc (A = πr2). And now you should be able to appreciate that we should probably represent a proton by a combination of two wavefunctions. Something like this:

Proton wavefunction

What about a wave equation for nuclear oscillations? Do we need one? We sure do. Perhaps we do not need one to model a neutron as some nuclear dance of a negative and a positive charge. Indeed, think of a combination of a proton and what we will refer to as a deep electron here, just to distinguish it from an electron in Schroedinger’s atomic electron orbitals. But we might need it when we are modeling something more complicated, such as the different energy states of, say, a deuteron nucleus, which combines a proton and a neutron and, therefore, two positive charges and one deep electron.

According to some, the deep electron may also appear in other energy states and may, therefore, give rise to a different kind of hydrogen (they are referred to as hydrinos). What do I think of those? I think these things do not exist and, if they do, they cannot be stable. I also think these researchers need to come up with a wave equation for them in order to be credible and, in light of what we wrote about the complications in regard to the various rotational planes, that wave equation will probably have all of Hamilton’s basic quaternions in it. [But so, as mentioned above, I am waiting for them to come up with something that makes sense and matches what we can actually observe in Nature: those hydrinos should have a specific spectrum, and we do not such see such spectrum from, say, the Sun, where there is so much going on so, if hydrinos exist, the Sun should produce them, right? So, yes, I am rather skeptical here: I do think we know everything now and physics, as a science, is sort of complete and, therefore, dead as a science: all that is left now is engineering!]

But, yes, quaternion algebra is a very necessary part of our toolkit. It completes our description of everything! 🙂

The physics of the wave equation

The rather high-brow discussions on deep electron orbitals and hydrinos with a separate set of interlocutors, inspired me to write a paper at the K-12 level on wave equations. Too bad Schroedinger did not seem to have left any notes on how he got his wave equation (which I believe to be correct in every way (relativistically correct, too), unlike Dirac’s or others).

The notes must be somewhere in some unexplored archive. If there are Holy Grails to be found in the history of physics, then these notes are surely one of them. There is a book about a mysterious woman, who might have inspired Schrödinger, but I have not read it, yet: it is on my to-read list. I will prioritize it (read: order it right now).

Oh – as for the math and physics of the wave equation, you should also check the Annex to the paper: I think the nuclear oscillation can only be captured by a wave equation when using quaternion math (an extension to complex math).

The cosmological constant

I wrote a brief paper on the sense and nonsense of standard cosmology, basically arguing dark matter/energy is just antimatter, and providing a logical explanation of why it is ‘dark’ (antiphotons and antineutrons are hard to detect because they do no interact with matter). But all of that was written before I checked the Wikipedia article on the cosmological constant, according to which  the expansion of the universe is actually accelerating! So that has nothing to do with dark matter/energy, but it does suggest a whole new mystery. I quote:

“In 1998 two teams of astrophysicists, one led by Saul Perlmutter, the other led by Brian Schmidt and Adam Riess, carried out measurements on distant supernovae and show that the speed of galaxies recession in relation to the Milky Way increases over time. The universe is in accelerated expansion. […] The universe would contain a mysterious dark energy producing a repulsive force that counterbalances the gravitational braking produced by the matter contained in the universe (see standard cosmological model). For this work, Perlmutter (American), Schmidt (American-Australian), and Riess (American) jointly received the Nobel Prize in physics in 2011.”

I am sure there must be a rational explanation for this. Perhaps the Universe is just a blob in a larger cluster of Universes, which we cannot see because they originated from other Big Bangs. So these other Universes would be tearing ours apart, so to speak. It would surely explain the rather incredible speed of current expansion (2c/3). And, of course, it also makes us feel less lonely, doesn’t it? 🙂   

Hot and cold fusion: just hot air?

I just finished a very short paper recapping the basics of my model of the nuclear force. I wrote it a bit as a reaction to a rather disappointing exchange that is still going on between a few researchers who seem to firmly believe some crook who claims he can produce smaller hydrogen atoms (hydrinos) and get energy out of them. I wrote about my disappointment on one of my other blogs (I also write on politics and more general matters). Any case, the thing I want to do here, is to firmly state my position in regard to cold and hot fusion: I do not believe in either. Theoretically, yes. Of course. But, practically speaking, no. And that’s a resounding no!

The illustration below (from Wikimedia Commons) shows how fusion actually happens in our Sun (I wrote more about that in one of my early papers). As you can see, there are several pathways, and all of these pathways are related through critical masses of radiation and feedback loops. So it is not like nuclear fission, which (mainly) relies on cascaded neutron production. No. It is much more complicated, and you would have to create and contain a small star on Earth to recreate the conditions that are prevalent in the Sun. Containing a relatively small amount of hydrogen plasma in incredibly energy-intensive electromagnetic fields will not do the trick. First, the reaction will peter out. Second, the reaction will yield no net energy: the plasma and electromagnetic fields that are needed to contain the plasma will suck everything up, and much more than that. So, yes, The ITER project is a huge waste of taxpayers’ money.

As for cold fusion, I believe the small experiments showing anomalous heat reactions (or low-energy nuclear reactions as these phenomena are also referred to) are real (see my very first blog post on these) but (1) researchers have done a poor job at replicating these experiments consistently, (2) have failed to provide a firm theoretical basis for those reactions, and (3) whatever theory there is, also strongly hints we should not hope to ever get net energy out of it. This explains why public funding for cold fusion is very limited. Furthermore, scientists who continue to support frauds like Dr. Mills will soon erase whatever credibility smaller research labs in this field have painstakingly built up. So, no, it won’t happen. Too bad, because LENR research itself is quite interesting, and may yield more insights than the next mega-project of CERN, SLAC and what have you. :-/

Post scriptum: On the search for hydrinos (hypothetical small hydrogen), following exchange with a scientist working for a major accelerator lab in the US – part of a much longer one – is probably quite revealing. When one asks why it has not been discovered yet, the answer is invariably the same: we need a new accelerator project for that. I’ll hide the name of the researcher by calling him X.

Dear Jean Louis – They cannot be produced in the Sun, as electron has to be very relativistic. According to my present calculation one has to have a total energy of Etotal ~34.945 MeV. Proton of the same velocity has to have total energy Etotal ~64.165 GeV. One can get such energies in very energetic evens in Universe. On Earth, it would take building special modifications of existing accelerators. This is why it has not been discovered so far.

Best regards, [X]

From: Jean Louis Van Belle <>
Date: Wednesday, March 31, 2021 at 9:24 AM
To: [X]
Cc: [Two other LENR/CF researchers]
Subject: Calculations and observations…

Interesting work, but hydrino-like structures should show a spectrum with gross lines, split in finer lines and hyperfine lines (spin coupling between nucleon(s) and (deep) electron. If hydrinos exist, they should be produced en masse in the Sun. Is there any evidence from unusual spectral lines? Until then, I think of the deep electron as the negative charge in the neutron or in the deuteron nucleus. JL

The Language of Physics

The meaning of life in 15 pages ! Or… Well… At least a short description of the Universe… Not sure it helps in sense-making. 🙂

Post scriptum (25 March 2021): Because this post is so extremely short and happy, I want to add a sad anecdote which illustrates what I have come to regard as the sorry state of physics as a science.

A few days ago, an honest researcher put me in cc of an email to a much higher-brow researcher. I won’t reveal names, but the latter – I will call him X – works at a prestigious accelerator lab in the US. The gist of the email was a question on an article of X: “I am still looking at the classical model for the deep orbits. But I have been having trouble trying to determine if the centrifugal and spin-orbit potentials have the same relativistic correction as the Coulomb potential. I have also been having trouble with the Ademko/Vysotski derivation of the Veff = V×E/mc2 – V2/2mc2 formula.”

I was greatly astonished to see X answer this: “Hello – What I know is that this term comes from the Bethe-Salpeter equation, which I am including (#1). The authors say in their book that this equation comes from the Pauli’s theory of spin. Reading from Bethe-Salpeter’s book [Quantum mechanics of one and two electron atoms]: “If we disregard all but the first three members of this equation, we obtain the ordinary Schroedinger equation. The next three terms are peculiar to the relativistic Schroedinger theory”. They say that they derived this equation from covariant Dirac equation, which I am also including (#2). They say that the last term in this equation is characteristic for the Dirac theory of spin ½ particles. I simplified the whole thing by choosing just the spin term, which is already used for hyperfine splitting of normal hydrogen lines. It is obviously approximation, but it gave me a hope to satisfy the virial theoremOf course, now I know that using your Veff potential does that also. That is all I know.” [I added the italics/bold in the quote.]

So I see this answer while browsing through my emails on my mobile phone, and I am disgusted – thinking: Seriously? You get to publish in high-brow journals, but so you do not understand the equations, and you just drop terms and pick the ones that suit you to make your theory fit what you want to find? And so I immediately reply to all, politely but firmly: “All I can say, is that I would not use equations which I do not fully understand. Dirac’s wave equation itself does not make much sense to me. I think Schroedinger’s original wave equation is relativistically correct. The 1/2 factor in it has nothing to do with the non-relativistic kinetic energy, but with the concept of effective mass and the fact that it models electron pairs (two electrons – neglect of spin). Andre Michaud referred to a variant of Schroedinger’s equation including spin factors.”

Now X replies this, also from his iPhone: “For me the argument was simple. I was desperate trying to satisfy the virial theorem after I realized that ordinary Coulomb potential will not do it. I decided to try the spin potential, which is in every undergraduate quantum mechanical book, starting with Feynman or Tippler, to explain the hyperfine hydrogen splitting. They, however, evaluate it at large radius. I said, what happens if I evaluate it at small radius. And to my surprise, I could satisfy the virial theorem. None of this will be recognized as valid until one finds the small hydrogen experimentally. That is my main aim. To use theory only as a approximate guidance. After it is found, there will be an explosion of “correct” theories.” A few hours later, he makes things even worse by adding: “I forgot to mention another motivation for the spin potential. I was hoping that a spin flip will create an equivalent to the famous “21cm line” for normal hydrogen, which can then be used to detect the small hydrogen in astrophysics. Unfortunately, flipping spin makes it unstable in all potential configurations I tried so far.”

I have never come across a more blatant case of making a theory fit whatever you want to prove (apparently, X believes Mills’ hydrinos (hypothetical small hydrogen) are not a fraud), and it saddens me deeply. Of course, I do understand one will want to fiddle and modify equations when working on something, but you don’t do that when these things are going to get published by serious journals. Just goes to show how physicists effectively got lost in math, and how ‘peer reviews’ actually work: they don’t. :-/

A simple explanation of quantum-mechanical operators

I added an Annex to a paper that talks about all of the fancy stuff quantum physicists like to talk about, like scattering matrices and high-energy particle events. The Annex, however, is probably my simplest and shortest summary of the ordinariness of wavefunction math, including a quick overview of what quantum-mechanical operators actually are. It does not make use of state vector algebra or the usual high-brow talk about Gilbert spaces and what have you: you only need to know what a derivative is, and combine it with our realist interpretation of what the wavefunction actually represents.

I think I should do a paper on the language of physics. To show how (i) rotations (i, j, k), (ii) scalars (constants or just numerical values) and (iii) vectors (real vectors (e.g. position vectors) and pseudovectors (e.g. angular frequency or momentum)), and (iv) operators (derivatives of the wavefunction with respect to time and spatial directions) form ‘words’ (e.g. energy and momentum operators), and how these ‘words’ then combine into meaningful statements (e.g. Schroedinger’s equation).

All of physics can then be summed up in half a page or so. 🙂

PS: You only get collapsing wavefunctions when adding uncertainty to the models (i.e. our own uncertainty about the energy and momentum). The ‘collapse’ of the wavefunction (let us be precise: the collapse of the dissipating wavepacket) thus corresponds to the ‘measurement’ operation. 🙂

PS2: Incidentally, the analysis also gives an even more intuitive explanation of Einstein’s mass-energy equivalence relation, which I summarize in a reply to one of the many ‘numerologist’ physicists on ResearchGate (copied below).

All about cosmology…

I just did a short paper with, yes, all you need to know about cosmology. It recapitulates my theory of dark matter (antimatter), how we might imagine the Big Bang (not a single one, probably!), the possibility of an oscillating Universe, possible extraterrestrial life, interstellar communication, and, yes, life itself. It also tries to offer a more intuitive explanation of SRT/GRT based on an analysis of the argument of the quantum-mechanical wavefunction – although it may not come across as being very ‘intuitive’ (my math is, without any doubt, much more intuitive to me than to you – if only because it is a ‘language’ I developed over years!).

I introduced the paper with a rather long comment on one of the ResearchGate discussion threads: Is QM consistent?. I copy it here for the convenience of my readers. 🙂

The concept of ‘dimension’ may well be the single most misunderstood concept in physics. The bare minimum rule to get out of the mess and have fruitful exchanges with other (re)searchers is to clearly distinguish between mathematical and physical dimensions. Physical dimensions are covered by the 2019 revision of SI units, which may well be the most significant consolidation of theory which science has seen over the past hundred years or so (since Einstein’s SRT/GRT theories, in fact). Its definitions (e.g. the definition of the fine-structure constant) – combined with the CODATA values for commonly repeated measurements – sum up all of physics.

A few months before his untimely demise, H.A. Lorentz delivered his last contributions to quantum physics (Solvay Conference, 1927, General Discussion). He did not challenge the new physics, but did remark it failed to prove a true understanding of what was actually going on by not providing a consistent interpretation of the equations (which he did not doubt were true, in the sense of representing scientifically established facts and repeated measurements) in other words. Among various other remarks, he made this one: “We are trying to represent 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.”

Systems of equations may be reduced or expanded to include more or less mathematical (and physical) dimensions, but one has to be able to reduce them to the basic laws of physics (the mass-energy equivalence relation, the relativistically correct expression of Newton’s force law, the Planck-Einstein relation, etcetera), whose dimensions are physical. The real and imaginary part of the wavefunction represents kinetic and potential energy sloshing back and forth in a system, always adding up to the total energy of the system. The sum of squares of the real and imaginary part adding up to give us the energy density (non-normalized wavefunction) at each point in space or, after normalization, a probability P(r) to find the electron as a function of the position vector r. The argument of the wavefunction itself is invariant and, therefore, is consistent with both SRT as well as GRT (see Annex I and II of The Finite Universe).

The quantum-mechanical wavefunction is, therefore, the pendant to both the Planck-Einstein relation and the mass-energy equivalence relation. Indeed, all comes out of the E = h·f = p·λ and E = mc2 equations (or their reduced forms) combined with Maxwell’s equations written in terms of the scalar and vector potential. The indeterminacy in regard to the position is statistical only: it arises because of the high velocity of the pointlike charge, which makes it impossible to accurately determine its position at any point in time. In other words, the problem is that we are not able to determine the initial condition of the system. If we would be able to do so, we would be able to substitute the indefinite integrals used to derive and define the quantum-mechanical operators to definite integrals, and so we would have a completely defined system. [See: The Meaning of Uncertainty and the Geometry of the Wavefunction.]

Quarks make sense as mathematical form factors only: they reduce the complexity of the scattering matrix, but they are no equivalent to a full and consistent application to the conservation and symmetry laws (conservation of energy, linear and angular momentum, physical action, and elementary charge). The quark hypothesis suffers from the same defect or weakness as the one that H.A. Lorentz noted in regard to the Uncertainty Principle, or in regard to 19th century aether theories. I paraphrase: “The conditions of an experiment are such that, from a practical point of view, we would have indeterminism, but there is no need to elevate indeterminism to a philosophical principle.” Likewise, the elevation of quarks – the belief that these mathematical form factors have some kind of ontological status – may satisfy some kind of deeper religious thirst for knowledge, but that is all there is to it.

Post-WWII developments saw a confluence of (Cold War) politics and scientific dogma – which is not at all unusual in the history of thought, but which has been documented now sufficiently well to get over it (see: Oliver Consa, February 2020, Something is rotten in the state of QED). Of course, there was also a more innocent driver here, which Feynman writes about rather explicitly: students were no longer electing physics as a study because everything was supposed to be solved in that field, and all that was left was engineering. Hence, Feynman and many others probably did try to re-establish an original sense of mystery and wonder to attract the brightest. As Feynman’s writes in the epilogue to his Lectures: “The main purpose of my teaching has not been to prepare you for some examination—it was not even to prepare you to serve industry or the military. I [just] wanted most to give you some appreciation of the wonderful world and the physicist’s way of looking at it, which, I believe, is a major part of the true culture of modern times.”

In any case, I think Caltech’s ambitious project to develop an entirely new way of presenting the subject was very successful. I see very few remaining fundamental questions, except – perhaps – the questions related to the nature of electric charge (fractal?), but all other questions mentioned as ‘unsolved problems’ on Wikipedia’s list for physics and cosmology (see:, such as the question of dark matter (antimatter), the arrow of time, one-photon Mach-Zehnder interference, the anomaly in the magnetic moment of an electron, etcetera, come across as comprehensible and, therefore, ‘solved’ to me. As such, I repeat what I think of as a logical truth: quantum physics is fully consistent. ‘Numerical’ interpretations of quantum physics (such as SO(4), for example) may not be wrong, but they do not provide me with the kind of understanding I was looking for, and finally – after many years of deep questioning myself and others – have found.

Feynman is right that the Great Law of Nature may be summarized as U = 0 (Lectures, II-25-6) but also notes this: “This simple notation just hides the complexity in the definitions of symbols: it is just a trick.” It is like talking of “the night in which all cows are equally black” (Hegel, Phänomenologie des GeistesVorrede, 1807). Hence, the U = 0 equation needs to be separated out. I note a great majority of people on this forum try to do that in a very sensible way, i.e. they are aware that science differs from religion in that it seeks to experimentally verify its propositions: it measures rather than believes, and these measurements are cross-checked by a global community and, thereby, establish a non-subjective reality, of which I feel part. A limited number of searchers may believe their version of truth is more true than mainstream views, but I would suggest they do some more reading before trying to re-invent the wheel.

For the rest, we should heed Wittgenstein’s final philosophical thesis on this forum, I think: “Wovon man nicht sprechen kann, darüber muß man schweigen.” Again, this applies to scientific discourse only, of course. We are all free to publish whatever nonsense we want on other forums. Chances are more people would read me there, but as the scope for some kind of consensus decreases accordingly, I try to refrain from doing so.

PS: To understand relativity theory, one must agree on the notion of ‘synchronized clocks’. Synchronization in the context of SRT does not correspond to the everyday usage of the concept. It is not a matter of making them ‘tick’ the same: we must simply assume that the clock that is used to measure the distance from A to B does not move relative to the clock that is used to measure the distance from B to A: clocks that are moving relative to each other cannot be made to tick the same. An observer in the inertial reference frame can only agree to a t = t’ = 0 point (or, as we are talking time, a t = t’ = 0 instant, we should say). From an ontological perspective, this entails both observers can agree on the notion of an infinitesimally small point in space and an infinitesimally small instant of time. Again, these notions are mathematical concepts and do not correspond to the physical concept of quantization of energy, which is given by the Planck-Einstein relation. But the mathematical or philosophical notion does not come across as problematic to me. Likewise, the idea of instantaneous or momentaneous momentum may or may not correspond to a physical reality, but I do not think of it as problematic. When everything is said and done, we do need math to describe physical reality. Feynman’s U = 0 (un)worldliness equation is, effectively, like a very black cow in a very dark night: I just cannot ‘see’ it. 🙂 The notion of infinitesimally small time and distance scales is just like reading the e-i*pi = -1 identity, the ei0 = e0 = 1 or i2 = -1 relations for me. Interpreting i as a rotation by 90 degrees along the circumference of a circle ensures these notions come across as obvious logical (or mathematical/philosophical) truths. 🙂 What is amazing is that complex numbers describe Nature so well, but then mankind took a long time to find that out! [Remember: Euler was an 18th century mathematician, and Louis de Broglie a 20th century physicist so, yes, they are separated by two full centuries!]