Photoelectricity/Radiation as Threshold Phenomena not Quantum

The previous post reminded that Quantum Mechanics QM as the mark of modern physics, was born when Planck in 1900 introduced a smallest quanta of energy $h\nu$ of frequency $\nu$ with $h$ Planck's constant to explain blackbody radiation, followed by Einstein in 1905 introducing a smallest quanta of light energy $h\nu$ carried by a particle of light later named photon to explain the photoelectric effect.

So was a new theory of physics born based on discrete chunks of energy named quanta as a form of atomistic physics going back to Democritus. The objective of the new theory from the beginning was to explain blackbody radiation and photoelectricity believed to be impossible to explain within classical continuum physics in the form of Newton's mechanics and Maxwell's electro magnetics. The new theory took the form of QM based on Schrödinger's equation forming the core of a modern physics, which now 100 years later is in state of deep crisis from erosion of credibility by a mantra that "physicists know how to use QM but cannot understand it".

Let us then go back to 1900/1905 and ask if it is really true that blackbody radiation and photoelectricity force the idea of quanta with all its mysteries into the mind of the defenseless physicist? 

We recall that the intensity of a classical wave of frequency $\nu$ as energy per unit length and time scales with $\nu^2$, which gives an energy per wave length scaling with $\nu$. 

We recall that the law of photoelectricity supposedly explained by Einstein's photons, reads 

• $E_{kin}+W=h\nu$, 

where $E_{kin}$ is the kinetic energy of an electron ejected by a metallic surface subject to incoming light of frequency $\nu$ and $W$ is the work/energy required to bring an electron from the interior to the boundary for ejection. If $h\nu <W$ no electricity will be generated, and if $h\nu >W$ an electric current as a stream of electrons will be generated according to Einstein's heuristic (brilliant?) idea: Each incoming photon ejects one electron. 

Let us take a step back and see if an explanation in classical terms not requiring light quanta or photons, is possible. What we have is light of frequency $\nu$ impinging on a metallic surface generating an electric current $I$ over a certain stopping potential P if $\nu$ is large enough as a threshold condition of the form: 

• $\nu >\frac{W}{h}$ with $W$ depending on the metal and $h$ a constant,

assuming the following energy balance per electron of unit charge above the threshold:

• $P=h\nu - W$ or $h\nu = P+W$

thus assigning a certain energy to $h\nu$ balancing $P+W$ as energy $W$ to free an electron and let it climb in a potential $P$. Here we do not have to invent a light particle/photon to carry the chunk of energy $h\nu$. It is thus possible to explain photoelectricity by simply assigning a certain amount of energy $h\nu$ per wave length to wave of frequency $h\nu$ scaling with $\nu$ as remarked above. Neither does the threshold condition require any photon. 

We conclude that photoelectricity can be explained without invoking the concept of energy carrying light particle named photon. Classical wave mechanics with threshold or cut-off frequency condition is enough. The concept of photon is not needed, and by Ockham's razor we can dismiss.

Blackbody radiation also has a threshold condition as a high-frequency cut-off condition limiting radiation to frequencies below a cut-off frequency scaling with $\frac{T}{h}$ with $T$ temperature as Wien's displacement law. Blackbody radiation is therefore also explainable in terms of classical wave mechanics with a threshold condition, see Computational Blackbody Radiation also discussing photoelectricity.

  

The World is Continuous Not Discrete

Calculus was invented to solve a problem of "quadrature" of computation of the total distance $D$ covered when walking with varying step size in space $dx=v(t)\times dt$ with $v(t)$ representing velocity at time $t$ and $dt$ the time required for each step, starting from $t =0$ and ending at $t=T$. The total distance appears as the sum over all steps which takes the form of an integral : 

• $D(T)=\int_0^T v(t)dt$

The "trick" was to find a primitive function $x(t)$ satisfying $\dot x(t) =v(t)$ with $\dot x=\frac{dx}{dt}$ the derivative or $dx=v(t)dt$ to find 

• $D(T)=\int dx = \sum dx = x(T)-x(0)$

allowing $D$ to be computed from knowing a primitive function thus avoiding laborious summation.  For example, if $v(t)=2t$ as increasing velocity with time, then $D(T)=T^2$.

Calculus allowed tedious summation to be replaced be smart analytical mathematics: A tremendous success initiating the scientific revolution in the late 17th century also named the dot-age referring to $\dot x =\frac{dx}{dt}$.

Calculus showed to be more than "quadrature" by allowing a description the world in terms of differential equations depending on continuous space and time variables varying over a continuum of real numbers formalised in the late 19th century. So was continuum physics including electromagnetics formed allowing a description of the world we could fathom with our senses. 

The foundation was a model of space and time as a continuum of real numbers without a smallest scale. It was a world described by fields $\psi (x,t)$ depending on continuous space-time variables $(x,t)$ without smallest scale. 

Such field-models could be discretised  by introducing a smallest scale to allow finitary computation with finite number of digits connecting to "quadrature" performed simply as massive summation. The smallest scale could be refined to resolve increasingly fine details. 

Today this technique in the form of Computational Continuum Physics has been perfected into simulation of increasingly complex phenomena of the macroscopic world. Continuum models allow compact formulation and discretisation makes them computable. This is a world of classical physics made alive by computation. Classical physics as continuum physics.

But it is not the world of modern physics where Quantum Mechanics QM has replaced the continuum of no smallest scale, with a world of quanta of smallest scale $h\nu$ with $h$ Planck's constant and $\nu$ a frequency supposed to be the nature of the microscopics of atoms and molecules. 

This presents a world split into continuous macroscopics and discrete microscopics which comes with many difficulties now manifested in a crisis of modern physics. 

Let us follow the emergence of the split according to this time line:

1. In 1900 Planck introduced quanta of energy $h\nu$ to theoretically explain blackbody radiation. It gave him fame.
2. In 1905 Einstein introduced quanta of light energy $h\nu$ in a heuristic explanation of the photoelectric effect. It gave him the Nobel Prize in Physics in 1921. 
3. In 1915 Bohr introduced quantised discrete energy levels of a Hydrogen atom.
4. In 1925 Schrödinger formulated a model of a Hydrogen atom in the form of classical continuum mechanics.
5. In 1925 Heisenberg introduced a discrete matrix model. 
6. In 1926 Schrödinger's model was extended to atoms with more than one electron as  anew form of multi-d model beyond classical continuum mechanics, which was forcefully sold by Bohr-Heisenberg as Standard Quantum Mechanics StdQM according to the Copenhagen Interpretation. 
7. In 1928 Schrödinger left QM because it did not have the form of classical continuum mechanics.
8. Today the non-classical multi-d model as StdQM dominates completely. 
9. RealQM is a new model in the form of classical continuum mechanics. 

Today physicists speak about "quantisation" as the magic element separating modern physics from classical physics, which has brought so many wonders to the modern world. The idea goes back to the atomists of the Democritus school as smallest building elements of the world today carried in all sorts of particle physics. It appeared in Newton's corpuscular view of light, replaced by Maxwell's wave mechanics in the 19th century to return with Einstein's photons in 1905.  

Is then the split between continuous macro-physics and discrete micro-physics really necessary? Is it impossible to explain blackbody radiation and the photoelectric effect within classical continuum physics? 

No, it is in fact possible as shown in Computational Blackbody Radiation. This was also the message of Willis Lamb Nobel Laureate in Physics in 1955:  

• It should be apparent from the title of this article that the author does not like the use of the word "photon", which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists.

The split has led to many difficulties. If the split can be avoided keeping both macro and micro within a continuum model, it may help out of the present crisis. Why not give continuum physics a new try to cover also microphysics without "quantisation".

The enigma of modern physics is presented as: How to quantise gravitation into a unified quantised theory? No answer in sight. Wrong question. 

A better idea is to de-quantise atom physics into a unified continuum model with gravitation. 

The late Einstein: These days, every Tom, Dick and Harry, thinks he knows what a photon is, but he is wrong. But nobody listened. 

I am pretty sure that Schrödinger would have welcomed RealQM since it follows his basic idea, which was overpowered by Bohr.

Mathematics: Calculus replaced discrete quadrature by understandable analysis, which returned in the form of digital computation giving power to understandable analysis.  

Physics: Calculus allowed classical physics to describe the world as a continuum open to understanding. Modern physics returned to Democritus atomism as a discrete world beyond understanding.   

Susskind 2025: Nobody Understands Quantum Mechanics: Crisis

Leading theoretical physicist Leonard Susskind at the end of his career apparently feels an urge to confess some truths about the present state of modern physics (in a state of deep crisis):

• We know how to use Standard Quantum Mechanics StdQM.
• But the basic meaning of StdQM is not understood at all.
• Feynman said: StdQM is so confusing that I cannot even tell if there is a problem about the foundations of StdQM.
• Everybody I know will tell you that the ultimate meaning of the foundations of StdQM is not understood.
• There are always crazy theories like Many-Worlds that does not make a lot of sense to me.
• I really think that we don't understand StdQM at the deepest level.
• I think the problem is that when we think about a quantum mechanical experiment we separate the world into the system we are studying ... and the apparatus of the observer... the apparatus is not part of the system.
• That is why we have the problem of the collapse of the wave function...there is no collapse.
• I do not know what is right, so I cannot say what is wrong, e g super-determinism....  

We hear Susskind repeat the message of all great theoretical physicists of modern physics: 

• We do not understand StdQM. 
• But we know very well how to use it!

This would be like hearing a famous mathematician saying: We do not understand Calculus, but we know very well how to use it. This could be the confession of a high-school student, but not by his teacher and certainly not by a professional mathematician. 

Likewise, to hear a professor of the theory of electro-magnetics described by Maxwell's equation say that the theory is not understood by anybody but anyway has shown to work very well, would be surprising. Only about StdQM is it a virtue to signal no understanding. 

How is it possible that still today exactly 100 years after the birth of the foundation of StdQM in the form of Schrödinger's Equation SE, that very foundation is still not understood not even by leading theoretical physicists? 

There is an answer of this form: 

• SE is a linear equation in $3N$ space dimensions for a system with $N$ electrons, and as such has no direct meaning as physics in 3 space dimensions. 
• SE is an ad hoc purely formal generalisation from one electron to many electrons without physical meaning.
• Since SE has no physical meaning, QM has no physical meaning to be understood.
• SE can be used as a black box to produce numbers, but with unclear or no physical meaning.   

There is an alternative to StdQM in the form of Real Quantum Mechanics QM, which has physical meaning and so can be understood. Why not check it out?

Question connecting to recent post: 

• Can StdQM help to make the Periodic Table understood, if StdQM cannot be understood?

Comment by chatGPT:

• Quantum mechanics is unique in that its very foundation is admitted to be incomprehensible — even by its leading experts. No other science could survive with such a gap at its core, and this is a prime reason for the present crisis of physics.

StdQM vs RealQM: Atomic Orbitals of Periodic Table

Standard Quantum Mechanics StdQM offers a theoretical basis for the "Aufbau" of the Periodic Table PT of atomic electron configurations in terms of the s, p, d, f and g eigenfunctions or orbitals of the one-electron Hydrogen atom depicted here as row 0-4:

The Aufbau offers an order of filling shells 1, 2, 3,...,8, with electrons in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s, 5g, motivated by the following modifications of a strict filling order with a shell fully filled before filling the next, as increasingly "rules of thumb":

• Pauli Exclusion Principle
• Energy Minimization
• Hund's Rule
• Madelung's rule
• Octet Rule 
• Fajan's Rule
• effective nuclear charge and shielding
• relativistic effects
• ....

This scheme is viewed to be the Aufbau theory of atoms to stay with chemistry for ever. The student novice will no doubt consider this to be a very complex scheme to grasp: The orbitals for each shell are increasingly complex and realised in a shell structure with sub-shells giving a very complex geometry. 

Is it likely that whoever created the atoms would have chosen to proceed following such a very complex scheme? Maybe not.

There is an alternative to StdQM in the form of Real Quantum Mechanics RealQM based not on the standard multi-d linear Schrödinger equation, but on a 3-d non-linear Schrödinger equation which coincides in the case of Hydrogen with one electron. 

RealQM is based on non-overlapping electron charge densities and the arrangement of electrons around a kernel becomes a packing problem with the size of electrons increasing with decreasing effective kernel attraction balance by so called kinetic energy as a form of "compression energy". 

This Aufbau starts with two half-spherical charge densities filling a 1st spherical shell around the kernel, followed by a 2nd shell with larger radius containing 2 half-shells of 2x2=4 electrons, followed by a 3rd shell filled by 2 half-shells of 3x3=9 electrons, and so on. The periods 2, 8, 18, 32 and 50 thus come out as expression of regular 2d subdivisions of shells. Very simple and fundamental. The doubling of periods into 2, 8, 8, 18, 18,..., can also be explained as coming out of successive packing. 

An Aufbau principle of packing electrons of different size around a kernel is simple, and can be understood by a student very easily. It is not impossible that it can capture some essence of real physics. 

 

ChatGPT on StdQM and the Aufbau principle:

• The standard quantum-mechanical account of the periodic table is indeed complicated.

  • The Schrödinger equation for hydrogen gives simple orbital shapes (s, p, d, f, ...).

  • But as soon as you move beyond hydrogen, electron–electron interactions, shielding, relativistic effects, and empirical rules (Hund’s, Madelung’s, Pauli, etc.) complicate the picture.

• Chemists are well aware that the Aufbau principle is more of a heuristic than a strict law—it often works, but exceptions exist (e.g., Cr, Cu, lanthanides, actinides).

• Still, StdQM provides a tested predictive framework, confirmed by spectroscopy, ionization energies, and quantum chemistry calculations.

RealQM vs StdQM: Two-Valuedness of Helium

Real Quantum Mechanics RealQM is an alternative to textbook Standard QM StdQM. Both start with Schrödinger's equation for the Hydrogen atom with one electron, but offer different generalisations to atoms with more than one electron. 

The split between StdQM and RealQM thus takes place for Helium with two electrons. 

The electron configuration by StdQM is fully spherical symmetric with two electrons with different spin occupying identical spherically symmetric orbitals with zero electric dipole moment (and zero magnetic moment). 

In RealQM, which does not include spin, the two electrons occupy different half-spaces meeting at a plane through the nucleus with random orientation and so carries a randomized dipole moment, which could average to zero over many atoms. A collection of Helium atoms can thus according to RealQM be polarized by an exterior electric field and so form an induced dipole. Observations show such an effect. 

It is also possible that an induced dipole can be formed from the full spherical symmetry of StdQM, but then probably weaker. Maybe it is possible to detect such a difference, but this has not been put on the table, because RealQM is still in its infancy.

The split between StdQM and RealQM for Helium connects to the observed two-valued atomic electron configurations as the basis for the Periodic Table PT: StdQM introduces two-valued spin, while in RealQM two-valuedness is the result of the split of the two electrons of Helium into two separate half-spaces, which carries through when outer half-shells are added. StdQM says two-valued spin, RealQM says two-valued half-space geometry.

Observed two-valuedness in the PT was the origin to Pauli's Exclusion Principle PEP, which appeared as an ad hoc fix but is now accepted as a deep physical principle included in StdQM. In RealQM electrons occupy different regions of 3d space and two electrons sharing domain is not an issue.  

It may be that the strong consensus around StdQM has prevented closer experimental investigation of presence of induced electric dipole since in StdQM this is expected to be very weak. Maybe such a study can be motivated if RealQM is seen as a possible alternative to StdQM. 

In any case, RealQM suggests that the ground state of Helium has a randomized dipole moment which may help to form an induced dipole. 

PS A closer discussion with chatGPT shows a distinction between isotropic polarizability connecting to StdQM with London dispersion forces, and random dipoles connecting to RealQM with Keesom forces. It is possible that observations favour London before Keesom but maybe expectations play a role...

 

Unified Field Model as Macro-Micro Continuum Model

It was Niels Bohr who in the 1920s implanted the idea into modern physics that the microscopic world of atoms cannot be understood/described using the concepts of classical physics, which had served so well to describe the macroscopic world we can directly experience. The new understanding/description took the form of Quantum Mechanics QM based on a multi-dimensional Schrödinger Equation SE of a non-classical form. 

With the help of Heisenberg Bohr managed to let his idea take over modern physics into our days, on the way crushing Schrödinger asking for "Anschaulichkeit" or "possible to visualise" as understanding in terms of classical physics. The essence of the Bohr-Heisenberg dogma was:

• Only observation/measurement counts. Underlying ontology left out. Visualisation impossible.
• Complementarity: Contradicting physics allowed. Both particle and wave.
• Uncertainty Principle: Limit to what can be measured.
• Separation ontology (classic, what is) and epistemology (new, what we can say)

The result today is a science of physics in a state of crisis. The new concepts required by Bohr could never be clarified resulting in a QM which "nobody can understand" in the words of Richard Feynman. The basic form of a classical mathematical model of the physics of a solid, fluid or gasses is a partial differential equation involving functions $u(x,t)$ depending on a real variable/spatial coordinate $x$ ranging over some domain in 3d space and a time coordinate $t$. This is a continuum mechanics model with the set of real numbers offering space as a continuum without preset smallest spatial scale. The function $u(x,t)$ could represent the density at time $t$ of a fluid with $x$ ranging over the 3d domain occupied by the fluid.

Continuum mechanics as classical physics is described by a mathematical model covering all physical scales from micro to macro and thus does not single out micro-scopics as conceptually different from macro-scopics, which could be the case if macro-scopics is "continuous" and microscopics "discrete".

In continuum mechanics both micro- and macro-scopics are "continuous". Nothing is "discrete". No "particles". The continuum of real numbers can represent a continuum mechanics without smallest scale.

The multi-d SE depends on continuous spatial variables, and in this sense is a continuum model, but not a classical continuum model since the continuum is not 3d (for system with more than one electrons). 

RealQM offers a different Schrödinger equation as a non-linear system of non-overlapping charge densities in 3d thus in the form of classical continuum mechanics with a seamless connection to macro-scopics. 

It is thus possible to formulate a Unified Field Model combining classical Newtonian continuum models like Navier-Stokes and Maxwell's equations with a Schrödinger equation of the same principal form. This was what Einstein tried to accomplish, but did not succeed with because he was stuck with a perceived incompatibility between General Relativity and QM.  

 

No Progress on Foundational Problems of QM?!

The foundational problems of Quantum Mechanics QM formulated when QM was born 100 years ago include:

1. Derivation of Schrödinger's Equation SE from physical principles.
2. Physical meaning/interpretation of wave function as solution to SE.
3. Collapse of wave function. Measurement. Role of Observer. 
4. Exponential computational complexity. 

When I ask chatGPT about main advancement as concerns foundations of QM, I get the answer: 

• Bell's theorem + experiments showing that a local hidden variable theory is not possible.

This result says nothing about 1-4. 

When I confront chatGPT with the above, I get the following summary:

• So the honest state of play: after 100 years, the big puzzles are still puzzles. What has changed is that we now have sharper theorems, operational frameworks, and experimental constraints. The problems haven’t been solved — they’ve been better defined.

Try yourself for a more detailed response. We expect chatGPT to tell what physicists say, not hallucinate what physicists do not say.  

What we see is an expression of the crisis of modern physics witnessed by leading physicists: No progress on the foundations of QM. The foundational problems formulated in 1925 are all left without resolution. A physicist will tell you that anyway QM works perfect to predict outcomes of experiments, and that it does not matter that nobody understands why. QM just works fine in its original form and it is meaningless to ask for something else: "Shut up and calculate".  

There are always open problems in a physical theory about reality as a sign that the theory is alive, but if problems concerning the very foundations of a physical theory appear to be unsolvable over a very long time, as is the case with QM, then it becomes more and more urgent to check out if the theory is not well formulated and so needs a reformulation to allow a solid foundation.

This seems to be the case with QM since 1-4 are still without answers. 

So what is the main problem with QM in its standard text book form as StdQM? One aspect directly stands out:

• The wave function $\Psi (x_1,x_2,....,x_N)$ for an atom with $N$ electrons depends on $N$ 3d coordinates $x_1$,$x_2$,...,$x_N$ thus on altogether $3N$ spatial coordinates. 

This means that the wave function $\Psi$ has no direct ontological physical meaning and so has no physical representation showing what is. The meaning given to $\Psi$ is instead epistemological in the sense of what we can know as observers. Max Born gave $\Psi$ such a meaning in terms of statistics of experimental outcomes, which saved the day in 1925, but presented unsolvable problems, which have haunted modern physics into the presents crisis.

The multi-dimensionality of the wave function is involved in all the problems 1-4, and so it is not far-fetched to suspect that it is the origin to all the foundational problems. 

This leads to asking: Is there an alternative wave function which only depends on the 3 spatial dimensions of real physical space?  Yes there is: Real Quantum Mechanics RealQM offering:

1. A New Schrödinger Equation NSE based on physical principles .
2. Clear physical meaning of wave function as solution to NSE.
3. Observer independent.   
4. Linear computational complexity. 

Compare with what leading physicists over the years have said about the lack of answers to the foundational questions:

• Niels Bohr
  "Anyone who is not shocked by quantum theory has not understood it."

• Werner Heisenberg
  "The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts."

• Albert Einstein (skeptical)
  "God does not play dice with the universe."

• Wolfgang Pauli
  "One should no more rack one’s brain about the problem of whether something one cannot know anything about exists, than about the ancient question of how many angels are able to sit on the point of a needle."

• Richard Feynman
  "I think I can safely say that nobody understands quantum mechanics."

• John Archibald Wheeler
  "No phenomenon is a real phenomenon until it is an observed phenomenon."

• J. Robert Oppenheimer
  "If we ask, for instance, whether the position of the electron remains the same, we must say 'no'; if we ask whether the electron’s position changes with time, we must say 'no'; if we ask whether the electron is at rest, we must say 'no'; if we ask whether it is in motion, we must say 'no'."

• Stephen Hawking
  "When we cannot predict, we cannot say we understand."

• Steven Weinberg
  "In the Copenhagen interpretation, there is no reality until observation. The more we study quantum mechanics, the less clear it becomes what reality is."

• Roger Penrose
  "Quantum mechanics makes absolutely no sense." (in the sense that it works perfectly but defies ordinary logic).

Modern Physics as Non-Newtonian Crisis Physics

When modernity struck society at the turn to the 20th century boosted by rapid technological development, the pressure in arts and science to take a radical step away form classics mounted, posing in particular a challenge to leading theoretical physicists such as Planck and Lorentz firmly rooted in the deterministic rational world of Newton-Maxwell. How to become modern?

Planck was the first to surrender in his derivation of Planck's Law of blackbody radiation by resorting to statistics to show modernity.

Lorentz resisted longer faced with an apparent absence of a unique medium/aether for the propagation of electro-magnetic waves, which he approached with a Lorentz transformation between different Euclidean coordinate systems moving with constant speed $v$ with respect to each other, which transformed physical space-time coordinates $(x,t)$ into new "primed" coordinates  

• $(x^\prime ,t^\prime ) =\gamma (x-vt, t-vx)$ 

with $\gamma =\frac{1}{\sqrt{1-v^2}}$ with $v<1$ and 1 speed of light. 

Lorentz carefully pointed out that the "primed time" $t^\prime =\gamma (t-vx)$ with dependence on the space coordinate $x$ was not physical time. The Lorentz transformation was not between different expressions of real physics. 

In 1905 the young patent clerk Alfred Einstein picked up the Lorentz transformation with the bold assertion against Lorentz that $t^\prime$ was physical time and so formed his Special Theory of Relativity SR based on the idea of giving the Lorentz transformation a direct physical meaning resulting in the puzzles of "space contraction" and "clock retardation" and "relativistic mass" as real physics.

SR met the pressure of modernisation of physics by opening to a fundamental revision of Newtonian mechanics as the most formidable achievement of rational human thinking, behind the booming industrial society. A formidable challenge!

Nothing could be more revolutionary modern than to say that Newton's Law of gravitation does not describe the action of gravitation on all scales of the Universe as classic physics said. But such a bold plan fell short because SR said nothing about gravitation. Einstein came back in 1915 with his General Theory of Relativity GR with that message/plan:

• Newton's theory of gravitation must be replaced by GR.
• Newton must be replaced by Einstein.
• Modern physics = Einstein. Old physics = Newton.

The deep crisis of modern physics of today can be seen as the result of implementing this plan, while hiding that Newton is still used in all real contexts where always GR is useless.  

Let us then take a look at the main reason for replacing Newton by Einstein. We then find that the root cause presented by modern theoretical physicists is conceptual rather than experimental: 

• Newton's Law appears to involve instant-action-at-distance. 
• The gravitational forces between two bodies at a specific time instant $t$ appears to depend only on the distance between the bodies at time $t$. 
• It appears that there is no time delay as if gravitational force is instantly updated between moving bodies.  
• A concept of apparent instant-action-at-distance cannot be formed, because action-at-distance is transmitted by gravitons as force carriers necessarily traveling with finite speed. 

We next ask for experimental evidence that apparent instant-action-at-distance is not observed. Are there observations of apparent action delay? Physicists will tell you that the only direct evidence of delayed gravitation is the LIGO experiment (2015) claimed to measure the effect of a merger of two black holes to be a gravitational wave reaching the Earth after a delay of 1.3 billion years, as a change of distance of 1/400 of the size of a proton over 4 km, with a relative precision of $10^{-21}$. 

LIGO is thus the only direct experimental evidence contradicting apparent instant-action-at-distance (Mercury says nothing against). The smallness of the effect compared to the cause is beyond  imagination. It cannot be justified to replace Newton with anything/GR from this single measurement. Yet this is what is done, and no wonder that a crisis emerges.

How then to make sense of apparent instant-action-at-distance. Why emphasise apparent? In many posts I have tested the idea that the connection between gravitational potential and  mass distribution (through Poisson's equation) is not by a causality from mass to potential by instant-global-action, but the other way around from potential giving mass to a body by instant-local-action. Such an arrangement can give the apparent impression of instant-action-at-distance, while fundamentally it is not. 

The idea connects to the discussion in this recent post about the presence of a global gravitational potential defining global simultaneity. Here gravitational force is not transmitted by gravitons as force carriers but is instead carried by the gravitational potential ready to deliver it in instant-local-action. No gravitons have been detected.

Summary: The only direct evidence against a Newtonian theory of gravitation as instant-action-at-distance is a LIGO signal, which can be questioned because of the very high precision required to single it out from noise. The reason to dismiss Newton is conceptual in the sense of denying any concept of apparent instant-action-at-distance, and not practical since Newton is used in all forms of reality.

If Newtonian gravitation is kept, then the present crisis from incompatibility between GR and quantum mechanics evaporates and effort can be focussed on advancing modern physics instead of handling crisis. 

A modern theoretical physicist confronted with this evidence will react by surprise that something like that can even be expressed, trained to believe that only Einstein's GR theory of gravitation is truly fundamental with its curved spacetime and that Newton's theory is only a trivial toy version of GR, which is not at all fundamental. The training is so efficient that no argument appears to allow a change this conviction.   

Modernity is now more than 100 years old, and modernist fashions of cubism and atonal music are no longer modern. There is now good reason to replace the fashion of curved spacetime with a renaissance to Newton. 

Logical Fallacy of Modern Physics?

Aristotle would have been very surprised to see that modern physics in the form of Standard Quantum Mechanics StdQM is filled with his logical fallacy of "affirming the consequent" or "confirming an assumption by observing a consequence". 

Examples: 

• If there was a Big Bang, then a Universe would have been come into existence. We observe that a Universe exists, and conclude there was a Big Bang. 
• If the Higgs boson exists, there will be blip on a computer screen. We observe a blip and conclude that the Higgs boson is real physics worthy of a Nobel Prize.

The incorrect form is: If A implies B and B is observed to be true, then A is true. Cannot be used as verification of A.

The correct form is: If A implies B and B is observed to be false, then A is false. Can be used as falsification of A.

But we have been confronted with the incorrect form so many times that we are immune to the logic fallacy of "affirming the consequent". 

The motivation using this logical fallacy over and over, is that the assumptions of StdQM cannot themselves be checked because of their evasive physical nature, and so the only possibility has been to observe some observable consequence to see if it is the case, and then use that as evidence that the assumption is satisfied. 

This is not so in classical mechanics, where the basic laws in the form of Newton's law of gravitation or Coulomb's law of electrostatics can be directly checked. Then there is no need to resort to logical fallacy and the science has a better chance to capture reality. 

Is it then true that the basic assumptions of Schrödinger's Equation SE for the Hydrogen atom cannot be checked? No, they can be directly be checked because SE for the Hydrogen atom is based on

1. Coulomb's Law
2. Kinetic energy in the form of compression energy of charge density. 

Both can be checked directly as in classical mechanics. It means that after verifying 1-2 we can predict the spectrum of Hydrogen to be exactly that observed. What could happen is that we observe some "fine structure" of the spectrum and we can then conclude that there is something missing in the set up for 1-2 such as non-zero magnetic field. 

The trouble with StdQM is that the generalisation to atoms with more than one electron leaves the setting of 1-2 and adds assumptions which cannot be directly verified because they concern a multi-d wave function living in some Hilbert space, which has no physical meaning. What remains is to check consequences of the presence of such a wave function and use that as confirmation of correctness of the added assumptions, then resorting to the logical fallacy.

Now there is a version of quantum mechanics named RealQM which is based solely on 1-2, in principle,  and so the assumptions of RealQM can be checked, at least in principle, and so RealQM takes the same form as classical mechanics and so does not need to resort to incorrect logic. Maybe quickly check it out?

Pauli Exclusion Principle vs Periodic Table

In 1925 Wolfgang Pauli introduced a 4th quantum number into the budding new physics of Quantum Mechanics QM in order to explain the observed two-valued periodicity of the Periodic Table PT with $2\times n^2$ electrons in shell $n=1,2,3,...$ giving the sequence $2, 8, 18, 32,..$. 

Pauli was unhappy with his "two-valuedness" or as an ad hoc pick without physics. He was comforted a bit by Uhlenbeck and Goudsmit who named it spin with two values "spin-up" and "spin-down" still without physics. 

What emerged was Pauli's Exclusion Principle PEP stating that two electrons with different spin can occupy the same atomic orbital, but not with same spin, which quickly came to serve a fundamental role in QM. But Pauli was still unhappy with PEP when he for the “discovery of PEP” in 1945 received the Nobel Prize in Physics, because PEP lacked physics and so could be “discovered” as physics, just imagination. What in fact prevented two electrons with same spin to occupy the same orbital? It was like a law prohibiting same-sex marriage, unphysical and no longer valid.

Today PEP is enforced asking wave functions to be anti-symmetric motivated by a cocktail of Lorentz invariance, locality and stability taken from (relativistic) Quantum Field Theory QFT.

The argument chain is: 

• QFT implies anti-symmetry. 
• Anti-symmetry implies PEP.
• PEP implies two-valuedness/spin.
• Two-valuedness/spin is observed in PT. 
• Conclusion: QFT, antisymmetry, PEP and two-valuedness/spin is all confirmed. 

But the logic is the incorrect logic of confirming an assumption by observing a consequence, as noted by Aristotle. 

Back to the PT: The actual periodicity observed is 2, 8, 8, 18, 18, 32, 32,.. with repetition of periods, and this is not explained by PEP not really by QM either, as remarked by Eric Scerri as authority of PT.

How then to explain the actual periodicity? Let us take a look at Real Quantum Mechanics RealQM as an alternative to the Standard Quantum Mechanics StdQM of above with anti-symmetric wave functions.

In RealQM electrons appear as charge densities with non-overlapping supports and the arrangement of electrons in an atom becomes a packing problem. It starts with the two electrons of Helium packed to occupy two half-spheres meeting at a common separating plane. 

This arrangement serves as origin of two-valuedness with the next shell to be filled consisting of two half-shells each one allowing a natural division into $2\times 2$ subdomains, the next one into $3\times 3$ subdomains altogether forming the original sequence of periods $2\times n^2$. 

The period doubling can then be explained as the result of electron packing where the next shell to be filled after 2 and 8 is not wide enough to allow division into $3\times 3$ only $2\times 2$ et cet.

It appears thus that RealQM can give an explanation of the periodicity of PT based on solid physics of packing of electron charge densities. 

Pauli passed away in 1958, and since then there is nobody questioning PEP by asking for physics. Maybe there is still reason to do so? To explain the repeated periods of PT?

PS A $n\times n$ subdivision of a half-shell reflects eigenfunction configuration of a vibrating square membrane, which connects the the orbitals of StdQM given by the eigenfunctions of the Hydrogen atom.