Deep electron orbitals and the essence of quantum physics

After a long break (more than six months), I have started to engage again in a few conversations. I also looked at the 29 papers on my ResearchGate page, and I realize some of them would need to be re-written or re-packaged so as to ensure a good flow. Also, some of the approaches were more productive than others (some did not lead anywhere at all, actually), and I would need to point those out. I have been thinking about how to approach this, and I think I am going to produce an annotated version of these papers, with comments and corrections as mark-ups. Re-writing or re-structuring all of them would require to much work.

The mark-up of those papers is probably going to be based on some ‘quick-fire’ remarks (a succession of thoughts triggered by one and the same question) which come out of the conversation below, so I thank these thinkers for having kept me in the loop of a discussion I had followed but not reacted to. It is an interesting one – on the question of ‘deep electron orbitals’ (read: the orbitals of negative charge inside of a nucleus exist and, if so, how one can model them. If one could solve that question, one would have a theoretical basis for what is referred to as low-energy nuclear reactions. That was known formerly as cold fusion, but that got a bit of a bad name because of a number of crooks spoiling the field, unfortunately.

PS: I leave the family names of my correspondents in the exchange below out so they cannot be bothered. One of them, Jerry, is a former American researcher at SLAC. Andrew – the key researcher on DEPs – is a Canadian astrophysicist, and the third one – Jean-Luc – is a rather prominent French scientist in LENR.]

From: Jean Louis Van Belle
Sent: 18 November 2021 22:51
Subject: Staying engaged (5)

Oh – and needless to say, Dirac’s basic equation can, of course, be expanded using the binomial expansion – just like the relativistic energy-momentum relation, and then one can ‘cut off’ the third-, fourth-, etc-order terms and keep the first and second-order terms only. Perhaps it is equations like that kept you puzzled (I should check your original emails). In any case, this way of going about energy equations for elementary particles is a bit the same as those used in perturbation equations in which – as Dirac complained – one randomly selects terms that seem to make sense and discard others because they do not seem to make sense. Of course, Dirac criticized perturbation theory much more severely than this – and rightly so. 😊 😊 JL

From: Jean Louis Van Belle
Sent: 18 November 2021 22:10
Subject: Staying engaged (4)

Also – I remember you had some questions on an energy equation – not sure which one – but so I found Dirac’s basic equation (based on which he derives the ‘Dirac’ wave equation) is essentially useless because it incorporates linear momentum only. As such, it repeats de Broglie’s mistake, and that is to interpret the ‘de Broglie’ wavelength as something linear. It is not: frequencies, wavelengths are orbital frequencies and orbital circumferences. So anything you would want to do with energy equations that are based on that, lead nowhere – in my not-so-humble opinion, of course. To illustrate the point, compare the relativistic energy-momentum relation and Dirac’s basic equation in his Nobel Prize lecture (I hope the subscripts/superscripts get through your email system so they display correctly):

m₀²c⁴ = E² – p²c² (see, for example, Feynman-I-16, formula 16-3)

Divide the above by c² and re-arrange and you get Dirac’s equation: W²/c² – p_r² – m²/c² = 0 (see his 1933 Nobel Prize Lecture)

So that cannot lead anywhere. It’s why I totally discard Dirac’s wave equation (it has never yielded any practical explanation of a real-life phenomenon anyway, if I am not mistaken).

Cheers – JL

From: Jean Louis Van Belle
Sent: 18 November 2021 21:49
Subject: Staying engaged (3)

Just on ‘retarded sources’ and ‘retarded fields’ – I have actually tried to think of the ‘force mechanism’ inside of an electron or a proton (what keeps the pointlike charge in this geometric orbit around a center of mass?). I thought long and hard about some kind of model in which we have the charge radiate out a sub-Planck field, and that its ‘retarded effects’ might arrive ‘just in time’ to the other side of the orbital (or whatever other point on the orbital) so as to produce the desired ‘course correction’ might explain it. I discarded it completely: I am now just happy that we have ‘reduced’ the mystery to this ‘Planck-scale quantum-mechanical oscillation’ (in 2D or 3D orbitals) without the need for an ‘aether’, or quantized spacetime, or ‘virtual particles’ actually ‘holding the thing together’.

Also, a description in terms of four-vectors (scalar and vector potential) does not immediately call for ‘retarded time’ variables and all that, so that is another reason why I think one should somehow make the jump from E-B fields to scalar and vector potential, even if the math is hard to visualize. If we want to ‘visualize’ things, Feynman’s discussion of the ‘energy’ and ‘momentum’ flow in https://www.feynmanlectures.caltech.edu/II_27.html might make sense, because I think analyses in terms of Poynting vectors are relativistically current, aren’t they? It is just an intuitive idea…

Cheers – JL

From: Jean Louis Van Belle
Sent: 18 November 2021 21:28
Subject: Staying engaged (2)

But so – in the shorter run – say, the next three-six months, I want to sort out those papers on ResearchGate. The one on the de Broglie’s matter-wave (interpreting the de Broglie wavelength as the circumference of a loop rather than as a linear wavelength) is the one that gets most downloads, and rightly so. The rest is a bit of a mess – mixing all kinds of things I tried, some of which worked, but other things did not. So I want to ‘clean’ that up… 😊 JL

From: Jean Louis Van Belle
Sent: 18 November 2021 21:21
Subject: Staying engaged…

Please do include me in the exchanges, Andrew – even if I do not react, I do read them because I do need some temptation and distraction. As mentioned, I wanted to focus on building a credible n = p + e model (for free neutrons but probably more focused on a Schrodinger-like D = p + e + p Platzwechsel model, because the deuteron nucleus is stable). But so I will not do that the way I studied the zbw model of the electron and proton (I believe that is sound now) – so that’s with not putting in enough sleep. I want to do it slowly now. I find a lot of satisfaction in the fact that I think there is no need for complicated quantum field theories (fields are quantized, but in a rather obvious way: field oscillations – just like matter-particles – pack Planck’s quantum of (physical) action which – depending on whether you freeze time or positions as a variable, expresses itself as a discrete amount of energy or, alternatively, as a discrete amount of momentum), nor is there any need for this ‘ontologization’ of virtual field interactions (sub-Planck scale) – the quark-gluon nonsense.

Also, it makes sense to distinguish between an electromagnetic and a ‘strong’ or ‘nuclear’ force: the electron and proton have different form factors (2D versus 3D oscillations, but that is a bit of a non-relativistic shorthand for what might be the case) but, in addition, there is clearly a much stronger force at play within the proton – whose strength is the same kind of ‘scale’ as the force that gives the muon-electron its rather enormous mass. So that is my ‘belief’ and the ‘heuristic’ models I build (a bit of ‘numerology’ according to Dr Pohl’s rather off-hand remarks) support it sufficiently for me to make me feel at peace about all these ‘Big Questions’.

I am also happy I figured out these inconsistencies around 720-degree symmetries (just the result of a non-rigorous application of Occam’s Razor: if you use all possible ‘signs’ in the wavefunction, then the wavefunction may represent matter as well as anti-matter particles, and these 720-degree weirdness dissolves). Finally, the kind of ‘renewed’ S-matrix programme for analyzing unstable particles (adding a transient factor to wavefunctions) makes sense to me, but even the easiest set of equations look impossible to solve – so I may want to dig into the math of that if I feel like having endless amounts of time and energy (which I do not – but, after this cancer surgery, I know I will only die on some ‘moral’ or ‘mental’ battlefield twenty or thirty years from now – so I am optimistic).

So, in short, the DEP question does intrigue me – and you should keep me posted, but I will only look at it to see if it can help me on that deuteron model. 😊 That is the only ‘deep electron orbital’ I actually believe in. Sorry for the latter note.

Cheers – JL

From: Andrew
Sent: 16 November 2021 19:05
To: Jean-Luc; Jerry; Jean Louis
Subject: Re: retarded potential?

Dear Jean-Louis,

Congratulations on your new position. I understand your present limitations, despite your incredible ability to be productive. They must be even worse than those imposed by my young kids and my age. Do you wish for us to not include you in our exchanges on our topic? Even with no expectation of your contributing at this point, such emails might be an unwanted temptation and distraction.

Dear Jean-Luc,

Thank you for the Wiki-Links. They are useful. I agree that the 4-vector potential should be considered. Since I am now considering the nuclear potentials as well as the deep orbits, it makes sense to consider the nuclear vector potentials to have an origin in the relativistic Coulomb potentials. I am facing this in my attempts to calculate the deep orbits from contributions to the potential energies that have a vector component, which non-rel Coulomb potentials do not have.

For examples: do we include the losses in Vcb (e.g., from the binding energy BE) when we make the relativistic correction to the potential; or, how do we relativistically treat pseudo potentials such as that of centrifugal force? We know that for equilibrium, the average forces must cancel. However, I’m not sure that it is possible to write out a proper expression for “A” to fit such cases.

Best regards to all,

Andrew

_ _ _

On Fri, Nov 12, 2021 at 1:42 PM Jean-Luc wrote:

Dear all,

I totally agree with the sentence of Jean-Louis, which I put in bold in his message, about vector potential and scalar potential, combined into a 4-vector
potential A, for representing EM field in covariant formulation. So EM representation by 4-vector A has been very developed, as wished by JL,
in the framework of QED.

We can note the simplicity of Lorentz gauge written by using A.
   https://en.wikipedia.org/wiki/Lorenz_gauge_condition

We can see the reality of vector potential
in the Aharonov-Bohm effect:
    https://en.wikipedia.org/wiki/Aharonov-Bohm_effect.
In fact, we can see that vector potential contains more information than E,B fields.
Best regards

   Jean-Luc
Le 12/11/2021 à 05:43, Jean Louis Van Belle a écrit :

Hi All – I’ve been absent in the discussion, and will remain absent for a while. I’ve been juggling a lot of work – my regular job at the Ministry of Interior (I got an internal promotion/transfer, and am working now on police and security sector reform) plus consultancies on upcoming projects in Nepal. In addition, I am still recovering from my surgery – I got a bad flue (not C19, fortunately) and it set back my auto-immune system, I feel. I have a bit of a holiday break now (combining the public holidays of 11 and 15 November in Belgium with some days off to bridge so I have a rather nice super-long weekend – three in one, so to speak).

As for this thread, I feel like it is not ‘phrasing’ the discussion in the right ‘language’. Thinking of E-fields and retarded potential is thinking in terms of 3D potential, separating out space and time variables without using the ‘power’ of four-vectors (four-vector potential, and four-vector space-time). It is important to remind ourselves that we are measuring fields in continuous space and time (but, again, this is relativistic space-time – so us visualizing a 3D potential at some point in space is what it is: we visualize something because our mind needs that – wants that). The fields are discrete, however: a field oscillation packs one unit of Planck – always – and Planck’s quantum of action combines energy and momentum: we should not think of energy and momentum as truly ‘separate’ (discrete) variables, just like we should not think of space and time as truly ‘separate’ (continuous) variables.

I do not quite know what I want to say here – or how I should further work it out. I am going to re-read my papers. I think I should further develop the last one (https://www.researchgate.net/publication/351097421_The_concepts_of_charge_elementary_ring_currents_potential_potential_energy_and_field_oscillations), in which I write that the vector potential is more real than the electric field and the scalar potential should be further developed, and probably it is the combined scalar and vector potential that are the ’real’ things. Not the electric and magnetic field. Hence, illustrations like below – in terms of discs and cones in space – do probably not go all that far in terms of ‘understanding’ what it is going on… It’s just an intuition…

Cheers – JL

From: Andrew
Sent: 23 September 2021 17:17
To: Jean-Luc; Jerry; Jean Louis
Subject: retarded potential?

Dear Jean-Luc,

Becasue of the claim that gluons are tubal, I have been looking at the disk-shaped E-field lines of the highly-relativistic electron and comparing it to the retarded potential, which, based on timing, would seem to give a cone rather than a disk (see figure). This makes a difference when we consider a deep-orbiting electron. It even impacts selection of the model for impact of an electron when considering diffraction and interference.

Even if the field appears to be spreading out as a cone, the direction of the field lines are that of a disk from the retarded source. However, how does it interact with the radial field of a stationary charge?

Do you have any thoughts on the matter.

Best regards,

Andrew

_ _ _

On Thu, Sep 23, 2021 at 5:05 AM Jean-Luc wrote:

Dear Andrew, Thank you for the references. Best regards, Jean-Luc

Le 18/09/2021 à 17:32, Andrew a écrit :
> This might have useful thoughts concerning the question of radiation
> decay to/from EDOs.
>
> Quantum Optics Electrons see the quantum nature of light
> Ian S. Osborne
> We know that light is both a wave and a particle, and this duality
> arises from the classical and quantum nature of electromagnetic
> excitations. Dahan et al. observed that all experiments to date in
> which light interacts with free electrons have been described with
> light considered as a wave (see the Perspective by Carbone). The
> authors present experimental evidence revealing the quantum nature of
> the interaction between photons and free electrons. They combine an
> ultrafast transmission electron microscope with a silicon-photonic
> nanostructure that confines and strengthens the interaction between
> the light and the electrons. The “quantum” statistics of the photons
> are imprints onto the propagating electrons and are seen directly in
> their energy spectrum.
> Science, abj7128, this issue p. 1324; see also abl6366, p. 1309

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 V_eff = 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 theorem. Of course, now I know that using your V_eff 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.

All you need to know 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: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics), 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 Geistes, Vorrede, 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!]

The Nature of Antimatter (dark matter)

The electromagnetic force has an asymmetry: the magnetic field lags the electric field. The phase shift is 90 degrees. We can use complex notation to write the E and B vectors as functions of each other. Indeed, the Lorentz force on a charge is equal to: F = qE + q(v×B). Hence, if we know the (electric field) E, then we know the (magnetic field) B: B is perpendicular to E, and its magnitude is 1/c times the magnitude of E. We may, therefore, write:

B = –iE/c

The minus sign in the B = –iE/c expression is there because we need to combine several conventions here. Of course, there is the classical (physical) right-hand rule for E and B, but we also need to combine the right-hand rule for the coordinate system with the convention that multiplication with the imaginary unit amounts to a counterclockwise rotation by 90 degrees. Hence, the minus sign is necessary for the consistency of the description. It ensures that we can associate the aeⁱ^E^t^/^ħ and ae^–ⁱ^E^t^/^ħ functions with left and right-handed spin (angular momentum), respectively.

Now, we can easily imagine a antiforce: an electromagnetic antiforce would have a magnetic field which precedes the electric field by 90 degrees, and we can do the same for the nuclear force (EM and nuclear oscillations are 2D and 3D oscillations respectively). It is just an application of Occam’s Razor principle: the mathematical possibilities in the description (notations and equations) must correspond to physical realities, and vice versa (one-on-one). Hence, to describe antimatter, all we have to do is to put a minus sign in front of the wavefunction. [Of course, we should also take the opposite of the charge(s) of its antimatter counterpart, and please note we have a possible plural here (charges) because we think of neutral particles (e.g. neutrons, or neutral mesons) as consisting of opposite charges.] This is just the principle which we already applied when working out the equation for the neutral antikaon (see Annex IV and V of the above-referenced paper):

Don’t worry if you do not understand too much of the equations: we just put them there to impress the professionals. 🙂 The point is this: matter and antimatter are each other opposite, literally: the wavefunctions aeⁱ^E^t^/^ħ and –aeⁱ^E^t^/^ħ add up to zero, and they correspond to opposite forces too! Of course, we also have lightparticles, so we have antiphotons and antineutrinos too.

We think this explains the rather enormous amount of so-called dark matter and dark energy in the Universe (the Wikipedia article on dark matter says it accounts for about 85% of the total mass/energy of the Universe, while the article on the observable Universe puts it at about 95%!). We did not say much about this in our YouTube talk about the Universe, but we think we understand things now. Dark matter is called dark because it does not appear to interact with the electromagnetic field: it does not seem to absorb, reflect or emit electromagnetic radiation, and is, therefore, difficult to detect. That should not be a surprise: antiphotons would not be absorbed or emitted by ordinary matter. Only anti-atoms (i.e. think of a antihydrogen atom as a antiproton and a positron here) would do so.

So did we explain the mystery? We think so. 🙂

We will conclude with a final remark/question. The opposite spacetime signature of antimatter is, obviously, equivalent to a swap of the real and imaginary axes. This begs the question: can we, perhaps, dispense with the concept of charge altogether? Is geometry enough to understand everything? We are not quite sure how to answer this question but we do not think so: a positron is a positron, and an electron is an electron¾the sign of the charge (positive and negative, respectively) is what distinguishes them! We also think charge is conserved, at the level of the charges themselves (see our paper on matter/antimatter pair production and annihilation).

We, therefore, think of charge as the essence of the Universe. But, yes, everything else is sheer geometry! 🙂

The End of Physics?

There are two branches of physics. The nicer branch studies equilibrium states: simple laws, stable particles (electrons and protons, basically), the expanding (oscillating?) Universe, etcetera. This branch includes the study of dynamical systems which we can only describe in terms of probabilities or approximations: think of kinetic gas theory (thermodynamics) or, much simpler, hydrostatics (the flow of water, Feynman, Vol. II, chapters 40 and 41), about which Feynman writes this:

“The simplest form of the problem is to take a pipe that is very long and push water through it at high speed. We ask: to push a given amount of water through that pipe, how much pressure is needed? No one can analyze it from first principles and the properties of water. If the water flows very slowly, or if we use a thick goo like honey, then we can do it nicely. You will find that in your textbook. What we really cannot do is deal with actual, wet water running through a pipe. That is the central problem which we ought to solve some day, and we have not.” (Feynman, I-3-7)

Still, we believe first principles do apply to the flow of water through a pipe. In contrast, the second branch of physics – we think of the study of non-stable particles here: transients (charged kaons and pions, for example) or resonances (very short-lived intermediate energy states). The class of physicists who studies these must be commended, but they resemble econometrists modeling input-output relations: if they are lucky, they will get some kind of mathematical description of what goes in and what goes out, but the math does not tell them how stuff actually happens. It leads one to think about the difference between a theory, a calculation and an explanation. Simplifying somewhat, we can represent such input-output relations by thinking of a process that will be operating on some state |ψ⟩ to produce some other state |ϕ⟩, which we write like this:

⟨ϕ|A|ψ⟩

A is referred to as a Hermitian matrix if the process is reversible. Reversibility looks like time reversal, which can be represented by taking the complex conjugate ⟨ϕ|A|ψ⟩* = ⟨ψ|A†|ϕ⟩: we put a minus sign in front of the imaginary unit, so we have –i instead of i in the wavefunctions (or i instead of –i with respect to the usual convention for denoting the direction of rotation). Processes may not reversible, in which case we talk about symmetry-breaking: CPT-symmetry is always respected so, if T-symmetry (time) is broken, CP-symmetry is broken as well. There is nothing magical about that.

Physicists found the description of these input-output relations can be simplified greatly by introducing quarks (see Annex II of our paper on ontology and physics). Quarks have partial charge and, more generally, mix physical dimensions (mass/energy, spin or (angular) momentum). They create some order – think of it as some kind of taxonomy – in the vast zoo of (unstable) particles, which is great. However, we do not think there was a need to give them some kind of ontological status: unlike plants or insects, partial charges do not exist.

We also think the association between forces and (virtual) particles is misguided. Of course, one might say forces are being mediated by particles (matter- or light-particles), because particles effectively pack energy and angular momentum (light-particles – photons and neutrinos – differ from matter-particles (electrons, protons) in that they carry no charge, but they do carry electromagnetic and/or nuclear energy) and force and energy are, therefore, being transferred through particle reactions, elastically or non-elastically. However, we think it is important to clearly separate the notion of fields and particles: they are governed by the same laws (conservation of charge, energy, and (linear and angular) momentum, and – last but not least – (physical) action) but their nature is very different.

W.E. Lamb (1995), nearing the end of his very distinguished scientific career, wrote about “a comedy of errors and historical accidents”, but we think the business is rather serious: we have reached the End of Science. We have solved Feynman’s U = 0 equation. All that is left, is engineering: solving practical problems and inventing new stuff. That should be exciting enough. 🙂

Post scriptum: I added an Annex (III) to my paper on ontology and physics, with what we think of as a complete description of the Universe. It is abstruse but fun (we hope!): we basically add a description of events to Feynman’s U = 0 (un)worldliness formula. 🙂

On the Universe and Aliens

I was a bit bored today (Valentine’s Day but no Valentine playing for me), and so I did a video on the Universe and (the possibility) of Life elsewhere. It is simple (I managed to limit it to 40 minutes!) but it deals with all of the Big Questions: fundamental forces and distance scales; the geometric approach to gravity and the curvature of the Universe; Big Bang(s) and – who knows? – an oscillating Universe; and, yes, Life here and, perhaps, elsewhere. Enjoy ! The corresponding paper is available on ResearchGate.

PS: I’ve also organized my thoughts on quarks in a (much more) moderate annex to my paper on ontology and physics. Quite a productive Valentine’s Day – despite the absence of a Valentina ! 🙂 JL