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

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

The proton radius puzzle solved

I thought I’d stop blogging, but I can’t help it: I think you’d find this topic interesting – and my comments are actually too short for a paper or article, so I thought it would be good to throw it out here.

If you follow the weird world of quantum mechanics with some interest, you will have heard the latest news: the ‘puzzle’ of the charge radius of the proton has been solved. To be precise, a more precise electron-proton scattering experiment by the PRad (proton radius) team using the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab has now measured the root mean square (rms) charge radius of the proton as[1]:

rp = 0.831 ± 0.007stat ± 0.012syst fm

If a proton would, somehow, have a pointlike elementary (electric) charge in it, and if it it is in some kind of circular motion (as we presume in Zitterbewegung models of elementary particles), then we can establish a simple relation between the magnetic moment (μ) and the radius (a) of the circular current.

Indeed, the magnetic moment is the current (I) times the surface area of the loop (πa2), and the current is just the product of the elementary charge (qe) and the frequency (f), which we can calculate as f = c/2πa, i.e. the velocity of the charge[2] divided by the circumference of the loop. We write:F1Using the Compton radius of an electron (ae = ħ/mec), this yields the correct magnetic moment for the electron[3]:F2What radius do we get when applying the a = μ/0.24…´10–10 relation to the (experimentally measured) magnetic moment of a proton? I invite the reader to verify the next calculation using CODATA values:F3When I first calculated this, I thought: that’s not good enough. I only have the order of magnitude right. However, when multiplying this with √2, we get a value which fits into the 0.831 ± 0.007 interval. To be precise, we get this:

Of course, you will wonder: how can we justify the √2 factor? I am not sure. It is a charge radius. Hence, the electrons will bounce off because of the electromagnetic fields. The magnetic field of the current ring will be some envelope to the current ring itself. We would, therefore, expect the measured charge radius to be larger than the radius of the current ring (a). There are also the intricacies related to the definition of a root mean square (rms) radius.

I feel this cannot be a coincidence: the difference between our ‘theoretical’ value (0.83065 fm) and the last precision measurement (0.831 fm) is only 0.00035 fm, which is only 5% of the statistical standard deviation (0.007 fm). Proton radius solved?

Maybe. Maybe not. The concluding comments of Physics Today were this: “The PRad radius result, about 0.83 fm, agrees with the smaller value from muonic and now electronic hydrogen spectroscopy measurements. With that, it seems the puzzle is resolved, and the discrepancy was likely due to measurement errors. Unfortunately, the conclusion requires no new physics.” (my italics)

I wonder what kind of new physics they are talking about.

Jean Louis Van Belle, 24 January 2020

PS: I did make a paper out of this (see my academia.edu or viXra.org publications), and I shared it with the PRad team at JLAB. Prof. Dr. Ashot Gasparian was kind enough to acknowledge my email and thought “the approach and numbers are interesting.” Let us see what comes out of it. I need to get back to my day job. 🙂

[1] See: https://www.nature.com/articles/s41586-019-1721-2. See also: https://www.jlab.org/prad/collaboration.html and https://www.jlab.org/experiment-research.

[2] Zitterbewegung models assume an electron consists of a pointlike charge whizzing around some center. The rest mass of the pointlike charge is zero, which is why its velocity is equal to the speed of light. However, because of its motion, it acquires an effective mass – pretty much like a photon, which has mass because of its motion. One can show the effective mass of the pointlike charge – which is a relativistic mass concept – is half the rest mass of the electron: mγ = me/2.

[3] The calculations do away with the niceties of the + or – sign conventions as they focus on the values only. We also invite the reader to add the SI units so as to make sure all equations are consistent from a dimensional point of view. For the values themselves, see the CODATA values on the NIST website (https://physics.nist.gov/cuu/Constants/index.html).

Wikipedia censorship

I started to edit and add to the rather useless Wikipedia article on the Zitterbewegung. No mention of Hestenes or more recent electron models (e.g. Burinskii’s Kerr-Newman geometries. No mention that the model only works for electrons or leptons in general – not for non-leptonic fermions. It’s plain useless. But all the edits/changes/additions were erased by some self-appointed ‘censor’. I protested but then I got reported to the administrator ! What can I say? Don’t trust Wikipedia. Don’t trust any ‘authority’. We live in weird times. The mindset of most professional physicists seems to be governed by ego and the Bohr-Heisenberg Diktatur.

For the record, these are the changes and edits I tried to make. You can compare and judge for yourself. Needless to say, I told them I wouldn’t bother to even try to contribute any more. I published my own article on the Vixrapedia e-encyclopedia. Also, as Vixrapedia did not have an entry on realist interpretations of quantum mechanics, I created one: have a look and let me know what you think. 🙂

Zitterbewegung (“trembling” or “shaking” motion in German) – usually abbreviated as zbw – is a hypothetical rapid oscillatory motion of elementary particles that obey relativistic wave equations. The existence of such motion was first proposed by Erwin Schrödinger in 1930 as a result of his analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces what appears to be a fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of ω = 2mc2/ħ, or approximately 1.5527×1021 radians per second. Paul Dirac was initially intrigued by it, as evidenced by his rather prominent mention of it in his 1933 Nobel Prize Lecture (it may be usefully mentioned he shared this Nobel Prize with Schrödinger):

“The variables give rise to some rather unexpected phenomena concerning the motion of the electron. These have been fully worked out by Schrödinger. It is found that an electron which seems to us to be moving slowly, must actually have a very high frequency oscillatory motion of small amplitude superposed on the regular motion which appears to us. As a result of this oscillatory motion, the velocity of the electron at any time equals the velocity of light. This is a prediction which cannot be directly verified by experiment, since the frequency of the oscillatory motion is so high and its amplitude is so small. But one must believe in this consequence of the theory, since other consequences of the theory which are inseparably bound up with this one, such as the law of scattering of light by an electron, are confirmed by experiment.”[1]

In light of Dirac’s later comments on modern quantum theory, it is rather puzzling that he did not pursue the idea of trying to understand charged particles in terms of the motion of a pointlike charge, which is what the Zitterbewegung hypothesis seems to offer. Dirac’s views on non-leptonic fermions – which were then (1950s and 1960s) being analyzed in an effort to explain the ‘particle zoo‘ in terms of decay reactions conserving newly invented or ad hoc quantum numbers such as strangeness[2] – may be summed up by quoting the last paragraph in the last edition of his Principles of Quantum Mechanics:

“Now there are other kinds of interactions, which are revealed in high-energy physics. […] These interactions are not at present sufficiently well understood to be incorporated into a system of equations of motion.”[3]

Indeed, in light of this stated preference for kinematic models, it is somewhat baffling that Dirac did not follow up on this or any of the other implications of the Zitterbewegung hypothesis, especially because it should be noted that a reexamination of Dirac theory shows that interference between positive and negative energy states is not a necessary ingredient of Zitterbewegung theories.[4] The Zitterbewegung hypothesis also seems to offer interesting shortcuts to key results of mainstream quantum theory. For example, one can show that, for the hydrogen atom, the Zitterbewegung produces the Darwin term which plays the role in the fine structure as a small correction of the energy level of the s-orbitals.[5] This is why authors such as Hestenes refers to it as a possible alternative interpretation of mainstream quantum mechanics, which may be an exaggerated claim in light of the fact that the zbw hypothesis results from the study of electron behavior only.

Zitterbewegung models have mushroomed[6] and it is, therefore, increasingly difficult to distinguish between them. The key to understanding and distinguishing the various Zitterbewegung models may well be Wheeler‘s ‘mass without mass’ idea, which implies a distinction between the idea of (i) a pointlike electric charge (i.e. the idea of a charge only, with zero rest mass) and (ii) the idea of an electron as an elementary particle whose equivalent mass is the energy of the zbw oscillation of the pointlike charge.[7] The ‘mass without mass’ concept requires a force to act on a charge – and a charge only – to explain why a force changes the state of motion of an object – its momentum p = mγ·v(with γ referring to the Lorentz factor) – in accordance with the (relativistically correct) F = dp/dt force law.

History

As mentioned above, the zbw hypothesis goes back to Schrödinger’s and Dirac’s efforts to try to explain what an electron actually is. Unfortunately, both interpreted the electron as a pointlike particle with no ‘internal structure’.David Hestenes is to be credited with reviving the Zitterbewegung hypothesis in the early 1990s. While acknowledging its origin as a (trivial) solution to Dirac’s equation for electrons, Hestenes argues the Zitterbewegung should be related to the intrinsic properties of the electron (charge, spin and magnetic moment). He argues that the Zitterbewegung hypothesis amounts to a physical interpretation of the elementary wavefunction or – more boldly – to a possible physical interpretation of all of quantum mechanics: “Spin and phase [of the wavefunction] are inseparably related — spin is not simply an add-on, but an essential feature of quantum mechanics. […] A standard observable in Dirac theory is the Dirac current, which doubles as a probability current and a charge current. However, this does not account for the magnetic moment of the electron, which many investigators conjecture is due to a circulation of charge. But what is the nature of this circulation? […] Spin and phase must be kinematical features of electron motion. The charge circulation that generates the magnetic moment can then be identified with the Zitterbewegung of Schrödinger “[8] Hestenes’ interpretation amounts to an kinematic model of an electron which can be described in terms of John Wheeler‘s mass without mass concept.[9] The rest mass of the electron is analyzed as the equivalent energy of an orbital motion of a pointlike charge. This pointlike charge has no rest mass and must, therefore, move at the speed of light (which confirms Dirac’s en Schrödinger’s remarks on the nature of the Zitterbewegung). Hestenes summarizes his interpretation as follows: “The electron is nature’s most fundamental superconducting current loop. Electron spin designates the orientation of the loop in space. The electron loop is a superconducting LC circuit. The mass of the electron is the energy in the electron’s electromagnetic field. Half of it is magnetic potential energy and half is kinetic.”[10]

Hestenes‘ articles and papers on the Zitterbewegung discuss the electron only. The interpretation of an electron as a superconducting ring of current (or as a (two-dimensional) oscillator) also works for the muon electron: its theoretical Compton radius rC = ħ/mμc ≈ 1.87 fm falls within the CODATA confidence interval for the experimentally determined charge radius.[11] Hence, the theory seems to offer a remarkably and intuitive model of leptons. However, the model cannot be generalized to non-leptonic fermions (spin-1/2 particles). Its application to protons or neutrons, for example, is problematic: when inserting the energy of a proton or a neutron into the formula for the Compton radius (the rC = ħ/mc formula follows from the kinematic model), we get a radius of the order of rC = ħ/mpc ≈ 0.21 fm, which is about 1/4 of the measured value (0.84184(67) fm to 0.897(18) fm). A radius of the order of 0.2 fm is also inconsistent with the presumed radius of the pointlike charge itself. Indeed, while the pointlike charge is supposed to be pointlike, pointlike needs to be interpreted as ‘having no internal structure’: it does not imply the pointlike charge has no (small) radius itself. The classical electron radius is a likely candidate for the radius of the pointlike charge because it emerges from low-energy (Thomson) scattering experiments (elastic scattering of photons, as opposed to inelastic Compton scattering). The assumption of a pointlike charge with radius re = α·ħ/mpc) may also offer a geometric explanation of the anomalous magnetic moment.[12]

In any case, the remarks above show that a Zitterbewegung model for non-leptonic fermions is likely to be somewhat problematic: a proton, for example, cannot be explained in terms of the Zitterbewegung of a positron (or a heavier variant of it, such as the muon- or tau-positron).[13] This is why it is generally assumed the large energy (and the small size) of nucleons is to be explained by another force – a strong force which acts on a strong charge instead of an electric charge. One should note that both color and/or flavor in the standard quarkgluon model of the strong force may be thought of as zero-mass charges in ‘mass without mass’ kinematic models and, hence, the acknowledgment of this problem does not generally lead zbw theorists to abandon the quest for an alternative realist interpretation of quantum mechanics.

While Hestenes‘ zbw interpretation (and the geometric calculus approach he developed) is elegant and attractive, he did not seem to have managed to convincingly explain an obvious question of critics of the model: what keeps the pointlike charge in the zbw electron in its circular orbit? To put it simply: one may think of the electron as a superconducting ring but there is no material ring to hold and guide the charge. Of course, one may argue that the electromotive force explains the motion but this raises the fine-tuning problem: the slightest deviation of the pointlike charge from its circular orbit would yield disequilibrium and, therefore, non-stability. [One should note the fine-tuning problem is also present in mainstream quantum mechanics. See, for example, the discussion in Feynman’s Lectures on Physics.] The lack of a convincing answer to these and other questions (e.g. on the distribution of (magnetic) energy within the superconducting ring) led several theorists working on electron models (e.g. Alexander Burinskii[14][15]) to move on and explore alternative geometric approaches, including Kerr-Newman geometries. Burinskii summarizes his model as follows: “The electron is a superconducting disk defined by an over-rotating black hole geometry. The charge emerges from the Möbius structure of the Kerr geometry.”[16] His advanced modelling of the electron also allows for a conceptual bridge with mainstream quantum mechanics, grand unification theories and string theory: “[…] Compatibility between gravity and quantum theory can be achieved without modifications of Einstein-Maxwell equations, by coupling to a supersymmetric Higgs model of symmetry breaking and forming a nonperturbative super-bag solution, which generates a gravity-free Compton zone necessary for consistent work of quantum theory. Super-bag is naturally upgraded to Wess-Zumino supersymmetric QED model, forming a bridge to perturbative formalism of conventional QED.”[17]

The various geometric approaches (Hestenes’ geometric calculus, Burinskii’s Kerr-Newman model, oscillator models) yield the same results (the intrinsic properties of the electron are derived from what may be referred to as kinematic equations or classical (but relativistically correct) equations) – except for a factor 2 or 1/2 or the inclusion (or not) of variable tuning parameters (Burinskii’s model, for example, allows for a variable geometry) – but the equivalence of the various models that may or may not explain the hypothetical Zitterbewegung still needs to be established.

The continued interest in zbw models may be explained because Zitterbewegung models – in particular Hestenes’ model and the oscillator model – are intuitive and, therefore, attractive. They are intuitive because they combine the Planck-Einstein relation (E = hf) and Einstein’s mass-energy equivalence (E = mc2): each cycle of the Zitterbewegung electron effectively packs (i) the unit of physical action (h) and (ii) the electron’s energy. This allows one to understand Planck’s quantum of action as the product of the electron’s energy and the cycle time: h = E·T = h·f·T = h·f/f = h. In addition, the idea of a centripetal force keeping some zero-mass pointlike charge in a circular orbit also offers a geometric explanation of Einstein’s mass-energy equivalence relation: this equation, therefore, is no longer a rather inexplicable consequence of special relativity theory.

The section below offers a general overview of the original discovery of Schrödinger and Dirac. It is followed by further analysis which may or may not help the reader to judge whether the Zitterbewegung hypothesis might, effectively, amount to what David Hestenes claims it actually is: an alternative interpretation of quantum mechanics.

Theory for a free fermion

[See the article: the author of this section does not seem to know – or does not mention, at least – that the Zitterbewegung hypothesis only applies to leptons (no strong charge).]

Experimental evidence

The Zitterbewegung may remain theoretical because, as Dirac notes, the frequency may be too high to be observable: it is the same frequency as that of a 0.511 MeV gamma-ray. However, some experiments may offer indirect evidence. Dirac’s reference to electron scattering experiments is also quite relevant because such experiments yield two radii: a radius for elastic scattering (the classical electron radius) and a radius for inelastic scattering (the Compton radius). Zittebewegung theorists think Compton scattering involves electron-photon interference: the energy of the high-energy photon (X- or gamma-ray photons) is briefly absorbed before the electron comes back to its equilibrium situation by emitting another (lower-energy) photon (the difference in the energy of the incoming and the outgoing photon gives the electron some extra momentum). Because of this presumed interference effect, Compton scattering is referred to as inelastic. In contrast, low-energy photons scatter elastically: they seem to bounce off some hard core inside of the electron (no interference).

Some experiments also claim they amount to a simulation of the Zitterbewegung of a free relativistic particle. First, with a trapped ion, by putting it in an environment such that the non-relativistic Schrödinger equation for the ion has the same mathematical form as the Dirac equation (although the physical situation is different).[18][19] Then, in 2013, it was simulated in a setup with Bose–Einstein condensates.[20]

The effective mass of the electric charge

The 2m factor in the formula for the zbw frequency and the interpretation of the Zitterbewegung in terms of a centripetal force acting on a pointlike charge with zero rest mass leads one to re-explore the concept of the effective mass of an electron. Indeed, if we write the effective mass of the pointlike charge as mγ = γm0 then we can derive its value from the angular momentum of the electron (L = ħ/2) using the general angular momentum formula L = r × p and equating r to the Compton radius:

This explains the 1/2 factor in the frequency formula for the Zitterbewegung. Substituting m for mγ in the ω = 2mc2/ħ yields an equivalence with the Planck-Einstein relation ω = mγc2/ħ. The electron can then be described as an oscillator (in two dimensions) whose natural frequency is given by the Planck-Einstein relation.[21]