Read question here in PSE:
https://tinyurl.com/umc9678p What is your opinion?
IMPORTANT UPDATE 15 AUGUST 2025: To my surprise my question in PSE was removed by the moderators! Must have hit some nerve there. Anyway, here is the question replicated on RG:
Watching this very interesting video, https://www.youtube.com/watch?v=piC8T2HnzrU about the known concept among physicists of why the electron or else called Bohr Magneton, cannot have a classical physical spin although it has an intrinsic spin classical angular momentum, I realized that the atomic bound Bohr electron was used in these calculations and not the free electron, in conjunction with the outdated and wrong Bohr model depiction of the atom where the electron orbits the nucleus as a small sphere of radius equal to the "classical radius" of the electron!
Question: But in this calculation of the physical spin speed, should not the Bohr radius 5.29177×10−11 m of the electron as suggested by its wavefunction of the atomic bound electron be used instead the much smaller classical radius of the free electron of 2.82 fm which is exclusively referring to the unbound free electron and not to the atomic H-1 ground state bound electron?
This whole concept is mislabeled in my opinion because it is based and used in the calculations, of the false image of the electron being a small sphere orbiting the nucleus of the atom whereas the ground state wavefunction suggests that the electron is actually a cloud or thin shell encompassing the whole nucleus at a distance and inside the nucleus. Therefore, the Bohr radius of the electron should be used which is (5.29177×10−11 m)>10−12 m and therefore does not violate Special Relativity (SR).
I believe that it is a mistake, to use in these calculations for the atomic bound Bohr electron the classical radius of the free electron and not the obvious Bohr radius for the electron.
The electron being a point in superposition (i.e. in all places simultaneously) all around and inside the nucleus of the atom is just a mathematical representation describing a cloud or shell around the nucleus at the Bohr distance and not physical. Thus, the Bohr electron (i.e. shortest distance electron from the nucleus in an atom ) is possible to physically spin at subluminal speed and is not violating SR. A more accurate depiction of the Bohr electron used in these calculation would be the following for the H-1 atom:
see animation:
https://www.horntorus.com/particle-model/H-1-m-flux.html
and also attached image Fig.1 Bohr electron of the H-1 atom. The blue lines manifold animation represents the Bohr electron wavefunction encompassing all around the nucleus of the atom (nucleus shown as a red sphere) at the center and also inside the nucleus.
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Note 1: This example is emphasizing the inability of QM to ontologically describe the physical sub-atomic microworld of the excited states of H-1 atom. The only QM wavefuncion than can represented classically in this case is the ground state of the H-1 atom shown in the animationand fig.1 with an electron as a point particle forming in superposition a thin shell horn spheroid around the nucleus and inside the nucleus:
In the ground state, the electron's wavefunction shown classically with the blue manifold in the above animation has no orbital angular momentum but only spin angular momentum as described by QM.
However, in an excited state QM says that the electron in superposition has both spin and orbital angular momentum which is not possible to drawn classically. The only way I can imagine it is if the whole spinning sphere in the above animation besides its equatorial spin starts in an exited state, wobbling around a small circle around the nucleus but always keeping the nucleus (i.e. proton) inside the electron wavefunction (i.e. blue manifold with the nucleus inside)?
Note 2: The superposition concept is only an artifact of the QM theory and not real physical. How else would you draw a thin shell around and inside the nucleus at an instance of time using only a single point? That's right, you make it in superposition occupying all points in the wavefunction surface at the same instance in time!
First of all the premise (that an electron can't have a classical spin) is wrong, since relativistic particles are labeled by two invariants, their mass and their spin and both are classical quantities. Second, the electron radius is a misleading quantity, since the electron is a point, whether classically or quantum mechanically. And finally, the speed of any object, subject to quantum fluctuations, is described by a probability distrubution. So the definition of the speed is given by an operator equation, from which the moments can be unambiguously deduced and, from them, the probability distribution.
That the electron is a point and not a sphere is NOT just a mathematical statement, it's a physical statement. It's not an approximation, within either quantum mechanics, or quantum field theory. It's an assumption about the physics, whether in quantum physics or classical physics. And the consequences of this assumption can be and have been tested.
It is possible to define a length scale-but the statement that this length scale is the radius of the electron requires proof. In classical physics it is possible to describe the properties of a charged extended object; in quantum physics it's considerably harder (Drac tried in 1962). It is possible to show that the description of the electron as a point object is consistent, both mathematically and with experiment, however.
The Bohr radius is NOT the radius of the electron, incidentally; it’s the average value of the size of the hydrogen atom, the bound state of an electron and a proton, whose probability distribution can be computed. And it doesn’t have anything to do with the speed of the spin of the electron and is related with the probability distribution of the orbital angular momentum of the electron.
Since opinions are requested in a general manner, I will give mine.
Ignorance about the fact that the electron is a "charged" elementary particle has reached such a depth in mainstream that nobody seems to remember, or to even know that this major characteristic of the electron is what determines its state of motion.
Nobody except engineers who use the Lorentz force equation are still aware of the importance of the electron charge, because electrons can be made to move only by means of calibrated E-fields and guided on utterly precise curved trajectories only by additional calibrated B-fields acting on this "charge" of the electron as in cathode ray tubes (like old style CRT television sets), which is a characteristic that proves that the electron cannot be a mathematical "point" nor a classical solid small mass deformable with velocity, but is made of a fixed amount of electromagnetic energy oscillating at a very specific frequency about its "center-of-presence" in space.
Put in perspective in this paper:
Article From E=mc2 in normal space to E=m0cIcK in the complex config...
From this perspective of the electron being a stabilized electromagnetic energy quantum oscillating at a given frequency, its spin can in no way be an intrinsic mechanical rotating property, but can only be a relative magnetic property that involves the presence of minimally 2 such particles to be meaningful.
Analysis available in Sections 10 and 11 of this chapter that concretizes the synchronization of kinematic mechanics with electromagnetic mechanics, that encompasses a larger set of electron characteristics than classical kinematic mechanics, according to Wilhelm Wien's project formulated in his 1901 paper:
Article Electromagnetic and Kinematic Mechanics Synchronized in thei...
The peer review opinions about this chapter which is a more complete republication upon invitation of a journal paper published only 6 month previously are available at this link:
https://peerreviewarchive.com/review-history/6575b
One of which was:
"The chapter is written carefully and interesting for academic level students and researchers. It contains many precious topics related to synchronized kinematic and electromagnetic mechanics. This chapter is important because it provides an accurate scientific description of synchronized kinematic and electromagnetic mechanics and helps students and researchers to solve issues related to this field. This chapter will help those interested and specialists to understand more the importance of synchronized kinematic and electromagnetic mechanics and its applications."
Hopefully, the upcoming generation of researchers will integrate this forgotten information in their worldviews and restart progress about the fundamental subatomic level of magnitude.
These papers are part of a series designed so that careful reading and studying of the sequence in order of publication dates, with personal numerical confirmation of each equation by means of a pocket scientific calculator, amounts to one undergrad session in electromagnetic mechanics study:
Article INDEX -Electromagnetic Mechanics (The 3-Spaces Model)
The question
“Wrong calculation of the possible physical spin speed of the Bohr electron?”
- looks as rather, if too, strange - a particle’s spin is angular momentum - the cross-product “M=rxP”, where “bold” menas “vector”, P is limear momentum, P=mV, m is a particle mass, V is velocity that has absolute value “speed”, r is particle’s radius-vector in some coordinate system. So wording “physical spin speed” is, again, strange – speed only particles have in space, and at that can have some angular momentum, or – if there is no some point in space, relating to which in a physical task is necessary to define M - not.
Though the above relates only to 3DXYZ space, since in the mainstream classical physics Matter’s spacetime is 4D one with metrics (ct,X,Y,Z), only in this case [besides some mathematical exotics] angular momentum [further AM is a vector. If a space has more dimensions, the cross-product isn’t a vector, and so, say, yet in Minkowski 4D space the “4-angular momentum” is the tensor.
If under action of some attractive force some m moves in the 3D space along some closed orbit, vector M is “orbital momentum; besides a rotating macro body has “intrinsic” AM, which is the sum of orbital momentums of particles that constitute body relating to rotation axis [body isn’t a point, and the particles are distributed in the body on principally non-zero distances from the axis]; at orbital motion it can be summed with orbital momentum.
As that, say, happens with electrons on atoms’ orbitals.
Including on QM scale particles have some parameter that looks and behaves in 3DXYZ space as some intrinsic AM, while in mainstream QM
“…the electron radius is a misleading quantity, since the electron is a point, whether classically or quantum mechanically. ….”
- i.e, in a particle there is no no-zero distances at all, and really in mainstream QM the experimentally observed“spin” is introduced really as some completely transcendent/ weird something that for/by some transcendent reason/way behaves as intrinsic AM.
The post is rather long, so now
Cheers
[Continuation of the post above]
This fundamental QM weirdnesses, including the above can be, and are, rigorously scientifically rationally clarified only in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this concrete case it is enough to read one of two main papers https://www.researchgate.net/publication/391209088_The_Informational_Conception_and_Basic_Physics.
In the model,, in accordance with some of really utmost fundamental in XX century von Weizsäcker and Fredkin-Toffoli findings, it is postulated that Matter is based on a binary reversible logics, and so the ultimate and utmost universal base of Matter is [5]4D dense lattice of primary elementary logical structures – binary reversible fundamental logical elements [FLE] that have [5]4 utmost universal – “kinematical” degreases of freedom at changing its state – “FLE binary flip”
The lattice is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), where cτ,X,Y,Z, are 4 space dimensions, ct is the time dimension. FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP.
Correspondingly everything in Matter is/are some specific disturbances in the lattice; disturbances “particles “ are created if some the lattice FLE is impacted with transmission to it some 4D linear momentum and energy, what causes in the lattice sequential FLE-by-FLE flipping propagation. Since anything in the lattice cannot propagate with a 4D speed more that c=lP/tP, the flipping FLEs precess, and so the “flipping FLE” trajectory is a 4D helix, that has radius, for having rest mass particles [“T-particles in the link above”] at small 3DXYZ speeds the helix radius is the particle’s Compton length λ=ћ/mc, and so 4D AM of the flipping point, i.e. intrinsic 4D AM of fundamental particles is equal to ћ.
So yeah, any particle, including electron, really always exists and interacts as having Planck length “point”, however at the, including at humans’ experiments ones, interactions the interactions points are distributed as are on some “wave” – what is observed as the also weird in the mainstream “wave-particle duality”.
Etc., including in the mainstream experimentally observed 3D “spin” of fundamental particles be equal ћ/2 is the specific 3D projection of the 4D spin= ћ above; particles “photons” are created by 3DXYZ momentums, and so have “whole” spin ћ; since neutrinos are fermions they for sure are created [by cτ-components of] 4D momentums, and so for sure have weird in the mainstream rest masses.
More see the link above; though to understand what are “interactions” is necessary to read at least section 6.“Mediation of the fundamental forces in complex systems” in
https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics ;
Cheers
Recent SS posts in https://www.researchgate.net/post/Probability_What_are_the_implications_of_non-classical_probability_theories_in_modeling_uncertain_systems_in_quantum_mechanics/2, pages 1,2,
- are relevant to this thread question.
Cheers
An addition to the SS posts above about “Bohr electron”.
Really in this case rather evident problem exists [ https://en.wikipedia.org/wiki/Bohr_model]:
- in the Bohr model in ground state orbital angular momentum, in, say, H-atom, is equal L=ħ, while experimentally it is equal to zero.
In mainstream QM there are a few solutions of this problem:
[semiclassical one] “…an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to revolve "around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus).….”
- but this “…model fails to explain the fact that the lowest energy state is spherically symmetric – it doesn't point in any particular direction.….”
So in the mainstream
“…In modern quantum mechanics, the electron in hydrogen is a spherical cloud of probability that grows denser near the nucleus. The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius……”
- what looks as too strange something. Electron is a particle, which - as any other particle, as that is rigorously shown in the SS&VT Planck scale informational physical model, see two linked papers in 2-nd SS post August 2, with well more zero approximation always exists and interacts as “FLE flipping point”, which has size ~ Planck length, though these points are on the 4D helix, which in 3DXYZ space is observed as “wave”;
- but by no means this is some transcendent mystic “cloud of probability”.
Really [see https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics, section 6.“Mediation of the fundamental forces in complex systems”]
- at/in any particles’ interactions by at least fundamental Nature Gravity, Electric, and Nuclear/Strong ,forces the particles exchange by the Forces real mediators that are radiated by the Forces charges.
At that in the H-atom [not only, though] ground s-state the radiated by proton Electric Force mediators hit in the “electron-point” rather rarely, so after a hit in some space point electron moves before next hit on space distance more than r, and so the next hit [or a few hits] returns the electron back. I.e. really just the “semiclassical” solution is much more scientific than the “modern quantum mechanics” one. Though yerah, the hits are distributed in the space fundamentally randomly, and so the “electrons-points” are in the space distributed in accordance with the H-atom wave “cloud of probability”.function.
Cheers
The Bohr Magneton in the H-1 atom at ground state (with zero orbital angular momentum and only having spin angular momentum) can be physically visualized as a vacuum flux manifold around and inside the nucleus of the H-1 atom (i.e. single proton), similar to the field around and inside an air electric solenoid like in this animation:
https://www.horntorus.com/particle-model/H-1-m-flux.html
The blue lines manifold is the wavefunction which essentially represents a massive dimesnionless point-like electron in superposition according to QM. The superposition concept is only an artifact of the QM theory and not real physical. How else would you draw a thin shell around and inside the nucleus at an instance of time using only a single point? That's right, you make it in superposition occupying all points in the wavefunction surface at the same instance in time!
From the electromagntic perspective, the Bohr magneton turns out to be related to the energy induced in the electron at mean Bohr radius distance in an isolated hydrogen atom. It then is a property of the carrying energy of the electron at this distance from the proton.
Its apparent anomalous experimental measurement then turns out to be related to the gyroradius of its B field at this distance from the proton.
Analyzed in this paper published in an engineering journal in 2013:
Article On The Electron Magnetic Moment Anomaly
My hidden assumption: Everything matter and light is made of fundamental EM vacuum flux thus coherent distortions in the vacuum medium. The vacuum flux is more elementary than the SM "elementary" particles.
Quote: "My hidden assumption: Everything matter and light is made of fundamental EM vacuum flux thus coherent distortions in the vacuum medium. The vacuum flux is more elementary than the SM "elementary" particles."
This makes sense to me, since there seems to be an underlying permanent magnetic energy field everywhere in the universe. The Sun's magnetic field reaches way further than pluto's orbit, for example. There is little doubt in my mind that all stars in the galaxy are immesed in the global magnetic energy field of the set.
Noel Coughlin even identified a relationship between electromagnetic theory and Buckminster Fuller's Synergetics' isometric vector sums of stable close packed tetrahedral structures that seem relatable to elementary particles that would gain in my view by being further analyzed (beyond my level of expertise to address):
Summarized with tentative first draft conclusions in this preprint:
Preprint Correlation of the electromagnetic mechanics of elementary p...
The thread question is really scientifically clarified in the 4 SS posts on page 1.
Cheers
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