“All QM textbooks describe the effects of the Exclusion Principle but its explanation is either avoided or put down to symmetry considerations. The importance of the Exclusion Principle as a foundational pillar of modern physics cannot be overstated since, for example, atomic structure, the rigidity of matter, stellar evolution and the whole of chemistry depend on its operation.” – Mike Towler, “Exchange, antisymmetry and Pauli repulsion. Can we ‘understand’ or provide a physical basis for the Pauli exclusion principle?”, TCM Group, Cavendish Laboratory, University of Cambridge, pdf slide 23.
Japanese physicist Youhei Tsubono, who has a page criticising the spin-orbit coupling, points out that there is an apparent discrepancy between the magnetic field energy for electron alignment and the energy difference between the 1s and 2s states, which creates a question of how the spinning charge (magnetic dipole) alignment mechanism of electrons creates the mechanism for the Pauli exclusion principle.
Referring to Quantum chemistry 6th edition, by Ira N. Levine, p 292, Tsubono argues that the difference in lithium’s energy between having three electrons in the 1s state (forbidden by the Pauli exclusion principle) and having two electrons in the 1s state (with opposite spins) and the third electron in the 2s state is 11 eV, which he claims is far greater than the assumed value of the magnetic dipole (spinning charge) field energy, which he claims is only about 10-5 eV. I can’t resist commenting here to resolve this alleged anomaly:
In a nutshell, the error Tsubono makes here is conflating the energy of alignment of magnetic spins for electrons at a given distance from the nucleus with the energy needed to not only flip spin states but also to move to a greater distance from the nucleus. It is true that the repulsive magnetic dipole field energy between similarly-aligned electron spins is only about 10-5 eV, but because they’re both in the same subshell that’s enough to account for the observed Pauli exclusion principle. The underlying error Tsubono makes is to start from the false model (see left hand side of diagram above) showing three electrons in the 1s state, then raising the rhetorical question of how the small magnetic repulsive energy is able to drive one electron into the 2s state. This situation never arises. The nucleus is formed first of all in fully ionized form by some nuclear reaction. The first electrons therefore approach the nucleus from a large distance. The realistic question therefore is not: “how does the third electron in the 1s state get enough energy to move to the 2s state from the weak magnetic repulsion that causes the Pauli exclusion principle?” The 3rd electron stops in the 2s state because of a mechanism: it’s unable to radiate the energy it would gain in approaching any closer to the nucleus. The electron in the 2s state can only radiate energy in units of hf, so even a small discrepancy in energy is enough to prevent it approaching closer to the nucleus. (Similarly, if an entry ticket costs $10, you don’t get in with $9.99.)
Similarly, the objection Tsubono raises to the supposedly faster-than-light speed of spin of the classical electron radius is false, because the core size of the electron is far smaller than the classical electron radius.
The core can therefore spin fast enough to explain the magnetic dipole moment without violating the speed of light, which would only be the case if the classical electron was true. What’s annoying about Tsubono’s page, like many other popular critics of “modern physics”, is that it tries to throw out the baby with the bathwater. The spinning electron’s dipole magnetic field alignment mechanism for the Pauli exclusion principle is one of a few really impressive, understandable mechanisms in quantum mechanics, and it is therefore important to defend it. Having chucked out the physical mechanism that comes from quantum field theory, Tsubono then argues “quantum field theory is not physics, just maths.”
Richard P. Feynman reviews nonsensical “mathematical” (aka philosophical) attacks on objective critics of quantum dogma in the Feynman Lectures on Physics, volume 3, chapter 2, section 2-6:
“Let us consider briefly some philosophical implications of quantum mechanics. … making observations affects a phenomenon … The problem has been raised: if a tree falls in a forest and there is nobody there to hear it, does it make a noise? A real tree falling in a real forest makes a sound, of course, even if nobody is there. Even if no one is present to hear it, there are other traces left. The sound will shake some leaves … Another thing that people have emphasized since quantum mechanics was developed is the idea that we should not speak about those things which we cannot measure. (Actually relativity theory also said this.) … The question is whether the ideas of the exact position of a particle and the exact momentum of a particle are valid or not. The classical theory admits the ideas; the quantum theory does not. This does not in itself mean that classical physics is wrong.
“When the new quantum mechanics was discovered, the classical people—which included everybody except Heisenberg, Schrödinger, and Born—said: “Look, your theory is not any good because you cannot answer certain questions like: what is the exact position of a particle?, which hole does it go through?, and some others.” Heisenberg’s answer was: “I do not need to answer such questions because you cannot ask such a question experimentally.” … It is always good to know which ideas cannot be checked directly, but it is not necessary to remove them all. … In quantum mechanics itself there is a probability amplitude, there is a potential, and there are many constructs that we cannot measure directly. The basis of a science is its ability to predict. … We have already made a few remarks about the indeterminacy of quantum mechanics. … we cannot predict the future exactly. This has given rise to all kinds of nonsense and questions on the meaning of freedom of will, and of the idea that the world is uncertain. Of course we must emphasize that classical physics is also indeterminate … if we start with only a tiny error it rapidly magnifies to a very great uncertainty. … For already in classical mechanics there was indeterminability from a practical point of view.”
Most QM and QFT textbook authors (excepting Feynman’s 1985 QED) ignore the mechanism for quantum field theory, in order to cater to Pythagorean style mathematical mythology. This mythology is reminiscent of the elitist warning over Plato’s doorway. Only mathematicians are welcome. To enforce this policy, an obfuscation of physical mechanisms is usually undertaken in a pro-“Bohring” effort to convince students that physics at the basic level is merely a matter of dogmatically applying certain mathematics rules from geniuses, which lack any physical understanding. Tsubono has other criticisms of modern dogma, e.g. that dark energy provides a modern ad hoc version of “ether” to make general relativity compatible with observation (just the opposite of Einstein’s basis for special relativity). So why not go back to Lorentz’s mechanism for mass increase and length contraction as being a field interaction accompanied with radiation which occurs upon acceleration? The answer seems to be that there is a widespread resistance to trying to understand physics objectively. It seems that status quo is easier to defend.
There is a widespread journalistic denial of freedom to basic questions in quantum mechanics about what is really going on, what the mechanism is, and efforts are made to close down discussions that could lead revolutionary, unorthodox or heretical direction
“… Bohr … said: ‘… one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up [trying to explain it further].”
‘I would like to put the uncertainty principle in its historical place … If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows for all the ways an event can happen – there is no need for an uncertainty principle!’ … electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that … interference becomes very important, and we have to sum the arrows[*] to predict where an electron is likely to be.’
– Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5, pp. 84-5. [*Arrows = wavefunction amplitudes, each proportional to exp(iS) = cos S + i sin S, where S is the action of the potential path.]
Nobel Laureate Gell-Mann debunked single-wavefunction entanglement using colored socks. A single and thus entangled/collapsible wavefunction for each quantum number of a particle only occurs in non-relativistic 1st quantization QM, such as Schroedinger’s equation. By contrast, in relativistic 2nd quantization, there is a separate wavefunction amplitude for each potential/possible interaction, not merely one wavefunction amplitude per quantum number. This difference gets rid of “wavefunction” collapse, “wavefunction” entanglement philosophy, and so on. Instead of a single wavefunction that becomes deterministic only when measured, we have the path integral, where you add together all the possible wavefunction amplitudes for a particle’s transition. The paths with smallest action compared to Planck’s constant (thus having the smallest energy and/time) are in phase, and contribute most, while paths of larger action (large energy and/or time) have phases that interfere and cancel out.
Virtual (or offshell) particles travel along the cancelled paths of large action, not real (or onshell) particles. So there’s a simple mechanism which replaces the single wavefunction chaos of ordinary quantum mechanics with interference and constructive interference for multiple wavefunctions per particle in quantum field theory, which is the correct, relativistic theory. Single wavefunction theories like Schroedinger’s model of the atom (together with Bell’s inequality, which falsely assumes a single wavefunction per particle, like quantum computing hype) are false, because they are non-relativistic and thus ignore the fact that the Coulomb field is quantized, and the field quanta or virtual photon interactions mediating the force binding an orbital electron to a nucleus. Once you switch to quantum field theory, the chaotic motion of an orbital electron has a natural origin due to its random, discrete interactions with the quantum Coulomb field. (The classical Coulomb field in Schroedinger’s model is a falsehood.)
Relativistic quantum field theory, unlike quantum mechanics (1st quantization) gets over Rutherford’s objection to Bohr’s atomic electron, the emission of radiation by accelerating charge. Charges in quantum field theory have fields which are composed of the exchange of what is effectively offshell radiation: the ground state is thus defined by an equilibrium between emission and reception of virtual radiation. We only “observe” onshell photons emitted while an electron accelerates, because the act of acceleration throws the usual balanced equilibrium (of virtual photon exchange between all charges), temporarily out of equilibrium by preventing the usual complete cancellation of field phases. Evidence: consider Young’s double slit experiment using Feynman’s path integral. We can see that virtual photons go through all slits, in the process interacting with the fields in the electrons on slit edges (causing diffraction), but only the uncancelled field phases arriving on the screen are registered as being a real (onshell) photon. It’s simple.
This is analogous to the history of radiation in thermodynamics. Before Prevost’s suggestion in 1792 that an exchange of thermal energy explains the absence of cooling if all bodies are continuously radiating energy, thermodynamics was in grave difficulties with heroic Niels Bohr “God characters” grandly dismissing as ignorant anyone who discovered an anomaly in the theories of fluid heat like caloric and phlogiston. Today we grasp that a room at 15 C is radiating because it is emitting heat with a radiating temperature of 288 K above absolute zero. Cooling is not synonymous with radiating. If the surrounding parts of the building are also at 15 C, the room will not cool, since the radiating effect is compensated by the receipt of radiation from the rooms, floor and roof. Likewise, the electron in the ground state can radiate energy without spiralling into the nucleus, if it is in equilibrium and is receiving as much energy as it radiates.
False no-go theorems, based on false premises, have always been used to quickly end any progressive suggestions without objective discussion. This censorship deliberately retarded the objective development of new ideas which were contrary to populist dogma. It was only when the populist dogma became excessively boring or when a rival idea was evolved into a really effective replacement, that “anomalies” in the old theory ceased to be taboo. Similarly, the populist and highly misleading Newtonian particle theory of light still acts to prevent objective discussions of multipath interference as the explanation of Young’s double-slit experiment, just as it did in Young’s day:
“Commentators have traditionally asked aloud why the two-slit experiment did not immediately lead to an acceptance of the wave theory of light. And the traditional answers were that: (i) few of Young’s contemporaries were willing to question Newton’s authority, (ii) Young’s reputation was severely damaged by the attacks of Lord Brougham in the Edinburgh Review, and that (iii) Young’s style of presentation, spoken and written, was obscure. Recent historians, however, have looked instead for an explanation in the actual theory and in its corpuscular rivals (Kipnis 1991; Worrall 1976). Young had no explanation at the time for the phenomena of polarization: why should the particles of his ether be more willing to vibrate in one plane than another? And the corpuscular theorists had been dealing with diffraction fringes since Grimaldi described them in the 17th century: elaborate explanations were available in terms of the attraction and repulsion of corpuscles as they passed by material bodies. So Young’s wave theory was thus very much a transitional theory. It is his ‘general law of interference’ that has stood the test of time, and it is the power of this concept that we celebrate on the bicentennial of its publication in his Syllabus of 1802.”
Feynman remarks in his Lectures on Physics that if you deny all “unobservables” like Mach and Bohr does, then you can kiss the wavefunction Psi goodbye. You can observe probabilities and cross-sections via reaction rates, but as Feynman argues, that’s not a direct observation for the existence of the wavefunction. There are lots of things in physics that are founded on indirect evidence, giving rise to the possibility that an alternative theory may explain the same evidence using a different basic model. This is exactly the situation as occurred in explaining sunrise by either the sun orbiting the earth daily, or the earth rotating daily while the sun moves only about one degree across the sky.