Photon Energy =$ h\nu$ as Deep Secret of Modern Physics?

In a classical wave equation the frequency in time $\nu$ scales with $\sqrt{E}$ with $E$ wave energy, or the other way around energy $E\sim \nu^2$. To see this recall that a classical wave appears as a real-valued solution $\phi (x,t)$ to the following classical wave equation (with $\phi_t$ the derivative with respect to $t$):

• $\phi_{tt}-\phi_{xx} =0$ for $0<x<\pi$ and $t>0$,                         (1)
• $\phi (0,t)=\phi(\pi ,t)$ for $t>0$,
• $\phi (x,0)$ and $\phi_{t}(x,0)$ given initial values.

A typical solution has the form 

• $\phi(x,t)=\cos(\nu t)\sin(\nu x)$ with $\nu =1,2,3,..$ as natural number, 
• with energy $E\equiv \int_0^\pi\vert\phi_{xx}\vert ^2dx\sim \nu^2$
• thus with frequency $\nu\sim \sqrt{E}$.  

On the other hand we know the convention of assigning the energy $E=h\nu$ to a photon in Standard Quantum Mechanics, thus as $E\sim \nu$, with $h$ a constant, which can be anything but is  prescribed to have a certain standard value in the SI Standard.  

So in classical wave mechanics $E\sim\nu^2$ and in quantum mechanics $E\sim\nu$, which to a student must be confusing, in particular since $E=h\nu$ is supposed to have a deep secret meaning. 

So why this difference? The reason is that the wave equation of quantum mechanics does not take the above form, but instead the following complex form with only one derivative in time:

• $i\phi_{t}-\phi_{xx}$ for $0<x<\pi$ and $t>0$,                         (2)
• $\phi (0,t)=\phi(\pi ,t)$ for $t>0$,
• $\phi (x,0)$ given initial value,

with typical solution 

• $\phi(x,t)=\exp(i\nu^2 t)\sin(\nu x)$ with $\nu =1,2,3,..$,  
• with energy $E\equiv \int_0^\pi\vert\phi_{xx}\vert ^2dx\sim \nu^2$,
• thus with frequency $\nu\sim E$.  

We understand that the complex form (2) can be reduced to real form:

• $\phi_{tt}-\phi_{xxxx}$,

to be compared with the classical $\phi_{tt}-\phi_{xx}$, which explains the switch from $E\sim \nu^2$ to $E\sim\nu$. 

We have learned that the connection $E=h\nu$ simply reflects the nature of the wave equation adopted and as such carries no deep secret per se and only represents an ad hoc division of global energy into little quanta which have no realisation in physics. 

If we connect an atom naturally described by (2) to light naturally described by (1), the we have to take the difference in chosen wave equations into account when connecting atomic energy and light energy recalling that incoming wave energy scales like $\nu^2$ resulting from $\nu$ incoming energy quanta of size $\nu$ per unit of time. 

The post points to basic aspects and does not seek to give a detailed account using 3d Maxwell equations for light and Schrödinger's eq for an atom. The idea is to decode the proclaimed deep secret of light particles/photons carrying energy quanta $h\nu$.

Notice that the macroscopic wave equation (1) describes waves which move rectilinearly in space, while (2) describes atomic waves which rather rotate on the spot while keeping charge density constant.  Schrödinger's equation thus connects to (2) in direct opposition to any concept of electrons moving around a nucleus.  

Classical Normal Physics vs Modern Extreme Physics

This is a reflection on the previous post opening to a "quantum mechanics without quantum" as a continuum world possible to describe by the fields of classical continuum physics. If indeed this is a real possibility, it might be worthwhile to pursue. Ok?

To learn about some physics there are two fundamentally different approaches: (i) start with the normal and (ii) start with the extreme. For example, to learn about the physics of sailing you may (i) start with normal conditions or (ii) start with the extremes of no wind or hurricane. What would be your advice?

With the opposites of normal and extreme, we can identify:

1. Classical Physics = reality of continuum we see as normal physics. Illusion of discreteness on all scales.  
2. Modern Physics = reality of small scale discrete/quantum we see only as extreme physics. Illusion of continuity on large scales. 

This is the split between continuum physics and quantum physics which has haunted the science of physics for 100 years into the present deep crisis, because 2 has been adopted to direct the efforts following the legacy of Bohr-Born-Heisenberg, which made 1 into fringe physics carried by Schrödinger-Einstein.

The big trouble with 2. is the break with 1. preventing unified physics on all scales leading to a crisis.

The fundamental idea of 2. is "quantisation" as a vague procedure to split things into little pieces not in physical meaning, but into some form of book-keeping units of "quanta". This is the idea of "quantisation of light", which is a continuous electromagnetic wave phenomenon very well described by Maxwell's wave equation over a 3d spatial continuum, by insisting that a wave of frequency $\nu$ can be chopped up in small units of energy $h\nu$ named photons where $h$ is a very small constant. This is a form of book-keeping without physics, since the physics of a photon has never been made clear.  

In any case, to support 2. experiments have been set up to prove the existence of photons simply by identifying a single photon experimentally. Since $h\nu$ is very small that requires an extremely sensitive detector which gives exactly "one click per photon". The assumption is then that since a click is discrete, what makes the click appear must also have been discrete and that is the photon! So can the existence of the photons as real discrete physics be proved by a click on a screen. The same with the Higgs boson proved to exist by a blip on a screen in 2015 in an extreme LHC experiment! LIGO also extremely extreme!

 

Thus major efforts have been spent on supporting 2. as the essence of modern physics, while 1. has been kept short to be pursued in philosophical circles without experimental devices capable of detecting normality.

With the deepening crisis resulting from 2. it may now be possible to open for a renewed focus on 1. as a continuum world of normality of great complexity. That is the objective of RealQM. 

My question to chatGPT: Which experiment forced quantisation (upon resisting physicists)?

Answer:

• Planck (1900): introduced quantisation as a desperate fix.

• Einstein (1905): pushed photons as real, but not widely accepted.

• Bohr (1913): extended discreteness to atoms.

• Compton (1923): gave overwhelming evidence photons are real quanta. → This was the true turning point.

By the mid-1920s, physicists gave up resisting. Quantum mechanics (Schrödinger 1926, Heisenberg 1925) became the new framework.

My comment: All of the above phenomena can be explained as continuum physics as discussed in previous posts and shown in Computational Blackbody Radiation. It appears that physicists have been more than willing to be forced into extreme positions to fill the need of sensation headline physics of modernity. It may also seem heroic to stick to an extreme principle under heavy skepticism from normality: We simply "have to give up" the rationality of the normal because physics is "weird" and something that "nobody can understand". But maybe we do not have to do that?

Maybe the time for Big Physics as extreme physics is coming to an end, in the deepening crisis, where the  next even bigger Large Hadron Collider for extreme physics will not be built, because there is nothing more of the extreme to be detected because physics is exhausted on extremely small scales, and that the real complex physics of interest takes place on scales larger than the smallest, which can be detected by affordable apparatus.

Here is a problem for normal physics still open after 100 years: 

• Explain the Periodic Table by QM,  in particular the periodicity 2,8,8,18,18,32,32,... 

Theoretical physicist: This was done long ago, in principle, but details were left to chemists. 

Theoretical chemist: I have been trying for a long time without much success. A basic problem is that I do not understand QM well enough and I get no help from a theoretical physicist who says that an explanation was given long ago, in principle....

Quantum Mechanics Without Quantum

Recent posts have identified the roots of  textbook Standard Quantum Mechanics StdQM, as the essence of modern atomic physics, in the works by Planck in 1900 on blackbody radiation and by Einstein in 1905 on photoelectricity. 

Let us retrace how StdQM as based on Schrödinger's Equation SE from 1925 for the Hydrogen atom, connects back to the early work by Planck-Einstein who did not know of atoms.  

We recall that in an act of desperation Planck introduced the concept of smallest quantum (chunk) of energy $E=h\nu$ of a wave with frequency $\nu$ and $h$ a constant later named Planck's constant, in order to explain why the ultra-violet catastrophe of blackbody radiation does not take place, as the prime challenge to theoretical physics in 1900. Planck as leading physicist of the German Empire simply had to come up with an explanation. In a Faustian deal Planck gave up his soul deeply rooted in classical physics for statistics of quanta and saved the day to the German Empire, which he deeply regretted but could not reverse.

Einstein followed in 1905 by connecting the smallest quantum of energy $h\nu$ to an idea of light as consisting of particles later named photons carrying exactly the energy $h\nu$. Einstein used this idea to come up with an explanation of photoelectricity in his position as patent clerk in Bern, in desperate need of scientific publications to open the door to a university position.

So was a smallest chunk or quantum of energy $h\nu$ and a light particle/photon supposed to carry that quantum of energy, introduced into physics in desperate attempts to gain attention, but the scientific community remained skeptical. 

The SE of a Hydrogen atom of 1925 took the form of classical continuum wave mechanical model in terms of an electron charge density $\psi (x)$ depending on a 3d spatial coordinate $x$ in Coulomb interaction with a kernel, while carrying a certain energy measured by $\vert\nabla\phi (x)\vert^2$ named kinetic energy. The observed spectrum of Hydrogen as a certain set of discrete frequencies $\nu$ showed to fit very precisely with differences of eigenvalues of SE representing differences of energy levels of the electron representing beat frequencies of an electron oscillating between levels. This connected energy to frequency in the same way as Planck's energy quantum $E=h\nu$ and Einstein's photon of energy $h\nu$.

So was a connection created between (i) a concept of smallest quantum of energy $h\nu$ and (ii) the discrete spectrum of a classical continuous wave equation without presence of any smallest quantum of energy. 

So was stdQM born to form the essence of modern physics as radically new form of physics based on a radically new idea of a smallest quantum of energy, which was based on a mathematical model of classical form as SE where the smallest quantum of energy had no role to play.  

The result is a mismatch between classical continuum physics in the form of SE without quantum, and a proclaimed new form of physics with quantum. No wonder that StdQM is surrounded by confusion expressed as "nobody understands QM". 

RealQM is an alternative to StdQM in the form of classical continuum physics without quantum. Computational Blackbody Radiation explains blackbody radiation and photoelectricity without quantum.The mismatch is gone. 

  

 

Why "Nobody Understands Quantum Mechanics"

This is a continuation of recent posts on the present crisis of modern physics. 

The essence of classical physics as a science is that it can be understood as a theory about the real world that makes sense to a human mind asking for logic and rationality. 

In 1900 a shift was initiated by Planck in his study of blackbody radiation followed by Einstein in his 1905 study of the photoelectric effect, which 20 years later was used to motivate a new form of physics named Quantum Mechanics QM, which became the trade mark of modern physics into present time. 

The trouble with QM is that all leading physicists say and have said for 100 years that "nobody understands QM". The result is a crisis of a modern physics based on QM.

But science is about understanding and so the fact that QM is not understandable, asks for an explanation. 

One way of forming a theory qualifying for not being understandable is to take some triviality and in the spirit of Einstein "elevate it to a Postulate" as a very deep truth about the world. The apparent clash between triviality and deep truth will cause confusion coming out as "nobody understands". This is like viewing 1+1=2 to be a deep truth of mathematics (instead of trivial definition), which if believed would express "nobody understands mathematics"? 

Let us see if this is in fact what happened with a QM growing out from Einstein's "heuristic explanation of the photoelectric effect" in 1905. Einstein started with the following observations made long before 1905:

• Light of frequency $\nu$ impinging on a metallic surface generates a current of electrons only if $\nu$ is bigger than a threshold value characteristic of the metal.
• The energy of electrons scales linearly with the frequency above the threshold, with energy identified with a stopping potential.    

It was believed that this could not be explained within the classical understandable wave theory of light by Maxwell, simply because that theory was not viewed to include the interaction between light and matter manifested in the photoelectric effect. 

Something more appeared to be needed and that was what Einstein offered in his "heuristic explanation" of the form "one incoming photon ejects one electron" or "one photon = one electron" or "one person = one vote":

• Energy balance gives "photon energy  = electron energy + electron release energy". 
• Define "photon energy" =$h\nu$ with $h$ a constant. 
• Conclude "$h\nu$ = electron energy + electron release energy" as the Law of Photoelectricity.  

Einstein here introduced the idea of a photon as "quanta of light" with an energy $h\nu$ picked from Planck. The essence was the scaling of energy with frequency $\nu$ and not amplitude of light, which connected to the nature of the threshold as a demand on frequency and not amplitude.

Einstein thus gave a "heuristic explanation" of the already observed Law of Photoelectricity, which gave him the 1921 Nobel Prize in Physics "for his discovery of the Law of Photoelectricity" as a misconception from "not understanding".

What Einstein did was to associate the energy $h\nu$ to something named "photon", which could be anything and still is not identified as to physical reality, but with the definite ability to kick out an electron from a metallic surface with the same energy $h\nu$ minus a release energy. For sure this was a "heuristic explanation" where the physics of "kicking out an electron" was hidden. It was thus a triviality made into a deep truth, and as such causing confusion ultimately leading to "nobody understands QM".

Is it then impossible to explain the Law of Photoelectricity in classical terms? If we look at the ingredients of incoming light and outgoing electrical current and stopping potential everything looks classical. Even the threshold on frequency can be accepted as classical as a form wave length precision required to release an electron tied to an atom. The energy of a classical wave of frequency $\nu$ scales with $\nu^2$ thus setting incoming light energy per unit length and time. The observed scaling with $\nu$ can then be obtained by partitioning incoming energy into wave length pieces each with energy scaling with $\nu$ into a totality of $\nu$ incoming pieces per unit of time. 

It is thus possible to give a "heuristic explanation" of the Law of Photoelectricity within classical wave physics, because it only involves classical concepts, which is as good as Einstein's resorting to discrete chunks of energy $h\nu$. 

Einstein did not get the Nobel Prize for explaining the Law of Photoelectricity, because his explanation convinced nobody, only for discovering a law that was already discovered. 

Computational Blackbody Radiation gives an explanation of blackbody radiation and photoelectricity in terms of classical wave mechanics without mystery, which can be understood by a high-school student. 

Altogether a basic reason that "nobody understands QM" is that it starts from a triviality of "quantisation" presented as a deep truth about reality as being discrete chopped up in little "quanta".  See also RealQM as "quantum mechanics without quanta" as understandable physics.

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 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 $h$ is 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 to make it climb the 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 a threshold or high-frequency cut-off condition, is enough. The concept of photon is not needed, and by Ockham's razor we can dismiss this idea as irrelevant.

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.

RealQM presents a new Schrödinger equation as the basis of a QM without quanta. Since nobody knows what a quanta is from physical point of view, this may helå to cope with crisis born from introducing this concept, which both Planck and Einstein deeply regretted.

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. 

 

Mixing Time into Space: Not Physics!

Modern physics is based on Einstein's Special and General Theory of Relativity SR and GR based on concept of spacetime where time is mixed into space as expressed in particular by the Lorentz Transformation LT as the essence of SR. This makes modern physics counter-intuitive with surprising strange effects of time dilation, space contraction and relativistic mass.

Let us take a fresh look at the idea of mixing time into space and ask if it can be possible from physical point of view. Consider a physical world composed of physical bodies with the following characteristics:

1. A physical body has extension in space coming with positive mass. 
2. Extension in space is manifested as existence of the body as the collection of its parts at the same time, that is simultaneous spatial existence/configuration. 
3. It is not meaningful to consider spatial existence of an extended body without simultaneity.  
4. Change of spatial configuration of a body can be seen as a body clock measuring progression of object time in terms of spatial change.
5. Two objects can interact by spatial contact, which synchronises object clocks to read the same.
6. Spatial contact between the parts of a body establishes simultaneity over the body.
7. A physical world does not carry a coordinate system to monitor its changing state. Object configurations change by simultaneous contact, which is represented by changing object configurations without need of representation in human made coordinate systems.
8. A human made spatial coordinate system can be a 3d Euclidean coordinate system fixed to the Earth, Sun or distant galaxy. 
9. Simultaneity of contact respects causality between two objects in the sense that agreement of order in time is possible.  

Notice that SR breaks 2-3. Spatial existence in SR has no extension in space and does not include simultaneity, which means that causality as order in time cannot be secured. Physics without causality cannot work.

So far this is a mechanical world without gravitation, governed by contact. Gravitation can be added by introducing a gravitational potential which depends on simultaneous spatial existence of all the physical bodies of the world asking for complete object time synchronisation (OS). 

Is (OS) possible? How can two far away bodies synchronise time without contact? Is it possible that  the gravitational potential as a massless field carries a master clock and gives birth to object/mass configurations along with object clocks synchronized to the master clock? This connects to the need of "absolute time" in Newtonian mechanics. It represents a non-standard form of causality where the gravitational potential is primary and mass distribution secondary, or possibly have equal roles in a perfect harmony in the sense of Leibniz. 

The gravitational potential of the Universe would thus as extended field carry a simultaneity of presence like that of an extended material body, a simultaneity instantly transmitted to material bodies as gravitational force synchronising all object clocks.

We thus arrive at a material world connected by simultaneity carried by changing spatial configurations connected to a master gravitational potential. 

In any case there will be no mixing of space into time upsetting simultaneity. This is fundamentally the view of Leibniz.  

Summary: In world without gravitation simultaneity is established by spatial  contact, and serves no role without contact. In a world with gravitation, a master gravitational potential can establish global simultaneity, to be used in electromagnetics. 

Einstein in Alice Wonderland

This a follow up of the previous post.

The mathematician Lewis Carroll anticipated Einstein's Special Theory of Relativity SR (1905) in his famous Alice's Adventures in Wonderland (1865) filled with "space contraction" and "time dilation" as core themes of the book. Very amusing and mind boggling! Einstein must have read the book in his youth, although he did not read much, since the connections cannot be accidental. 

In a further discussion with chatGPT representing mainstream professional physicists view, the following is made clear:

• A matter-only world is a Newton world to be Galilean invariant. 
• Adding light changes this matter-only world to be instead Lorentz invariant, even if there is no interaction between light and matter.
• Adding light to a matter-only world "reveals the true spacetime structure" to be Lorentzian and not Galilean as only an approximation of Lorentzian. 

This is really a very Grand Plan for the world and it is important to see what the basis is. We thus recall the form of a Galilean transformation and a Lorentz transformation between two space-time coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ in two inertial systems moving with speed $v$ with respect to each other, assuming  speed of light = 1:

• Galilean: $x^\prime = x-vt$ and $t^\prime =t$.
• Lorentz: $x^\prime = \gamma (x-vt)$ and $t^\prime =\gamma (t-vx)$ with $\gamma =\frac{1}{\sqrt{1-v^2}}$.

We see two very simple linear transformations so simple that even Alice would understand the mathematics. We see the "time dilation" aspect of Lorentz in the dependence in the primed time coordinate $t^\prime =\gamma (t-vx)$ on the space coordinate $x$. In short, a Lorentz transformation mixes space and time, which a Galilean does not. 

The idea carried by modern physics is now that a Lorentz transformation reveals the "true nature of spacetime," which thus is not that of a Galilean transformation. 

But is this credible? How can a simple linear transformation reveal the true nature of a spacetime without physics? 

A Galilean transformation expresses that measurement of velocity depends on chosen coordinate system in a specific simple way, while Nature does not use any coordinate system at all. Physicists are thus free to chose coordinate system as they like and Nature will not protest.

Lorentz clearly stated that a Lorentz transformation has no physical meaning. But a Galilean transformation can be given direct physical meaning in the form of meter sticks moving with constant velocity keeping their length and clocks unaffected by such motion. 

But this kind of argumentation is dismissed by a modern physicist because it questions Wonderland Science. The Lorentz transformation in all its simplicity is claimed to reveal the "true nature of spacetime" and there is nothing more to say. Discussion closed. Forget what Lorentz said!

SR was from the beginning met with neglect or skepticism and in the motivation for the 1921 Nobel Prize in Physics to Einstein the Nobel Committee explicitly expressed that the Prize was given to Einstein despite his SR physics never done before or after. In the 1920s quantum mechanics took over with a Galilean invariant Schrödinger equation (1925) followed by a Lorentz invariant Dirac equation (1928), which took over the scene when Schrödinger left the field quickly thereafter. Dirac's equation gave SR respectability, while Einstein was removed from the scene by Bohr. 

Today SR is kept like a toy model with amusing properties, but is no longer subject to scientific study. But the idea of spacetime with time mixed into space is alive in Einstein's General Theory of Relativity GR also believed to reveal the "true nature of space time" now as "curved spacetime". But no Nobel Prize to GR either. Maybe the true nature of space and time is not revealed in a coordinate transformation…

  

Einstein: Both Maxwell and Newton are Wrong!

In recent posts I have been searching for an explanation of the current crisis of modern physics, which is deep and sadly acknowledged by all prominent physicists and philosophers of physics. 

One striking aspect of modern physics is that it is presented as "strange", "weird", "counter-intuitive", "paradoxical" with unsettled "foundational problems" since 100 years without progress. To be compared with classical physics, which is rational and understandable and not strange at all although it can exhibit very complex dynamics showing surprising emergence.

The new aspect of strangeness into physics was introduced by Einstein in 1905 in his Special Theory of Relativity SR to be the academic work opening an academic career from his position as patent clerk in Bern with little training in mathematics and physics. Einstein gambled high: Derive new physics from  very few very general principles or Postulates with this Grand Plan:

• Show "Maxwell is wrong" because he assumes a "unique aether" for propagation of electromagnetic waves/light.
• Show "Newton is wrong" because he assumes "absolute space" and "absolute time".
• In particular: Show "no-aether" and "relative space-time."

Einstein then decided to start from the following Postulates:

1. Laws of physics take the same form in all inertial systems.
2. The speed of light is the same in all inertial systems 

Here inertial systems = standard Euclidean space-time coordinate systems moving with constant velocity with respect to each other.

To facilitate showing "Maxwell is wrong" Einstein attributed "unique aether" to Maxwell, which is not correct since Maxwell works well with any inertial system, and so Maxwell is a "many-aether" theory,  as many aethers as inertial systems. Maxwell without any aether/inertial system does not make sense because without, Maxwell's equations cannot even be formulated.

To facilitate showing "Newton is wrong" Einstein attributed "absolute space" to Newton, which is not correct since already Galileo understood that Newton's equations read the same in all inertial systems connected by a Galilean transformation, and so Newton is also a "many-aether" theory.  

We observe that Maxwell satisfies Postulate 1+2 and so cannot be wrong within SR as being based on these two Postulates. Einstein's attempt to prove "Maxwell wrong" thus failed and so he ended up with "Maxwell is right" which was what everybody said then and still says. SR said nothing not already very well known about Maxwell/light.

As concerns if "Newton is wrong" follows from the Postulates, we observe that Newton satisfies Postulate 1 under Galilean transformation and Postulate 2 about speed of light does not concern Newton because Newton does not speak about light but about matter. Einstein's attempt to prove "Newton is wrong" from Postulate 1+2 thus failed.

We conclude that Einstein's Grand Plan of proving "Maxwell is wrong" and "Newton is wrong" from SR based on Postulate 1+2,  thus failed. Compare Summary below!

We may now ask if anyway SR contains some physics of interest as derived by Einstein from Postulates 1+2? 

This was addressed in this post concerning Einstein's "derivation" of the Lorentz transformation by identifying two different light signals to be the same by disrespecting physics. 

In any case, after having derived the Lorentz transformation on loose grounds, Einstein concluded that "Newton is wrong" by not being Lorentz invariant, which did not make sense since Lorentz invariance is born out of Maxwell's equations for light and so does not connect to Newton's material mechanics. 

We conclude that SR does not prove either Maxwell nor Newton to be wrong. This should be welcomed by modern physicists trained to believe the opposite and then having to accept that "physics is strange". Maxwell and Newton are not strange, only Einstein!

If you want to dig more into Maxwell as a "many-aether" theory, take a look at Many-Minds Relativity.

In particular it would be a big relief if "Newton is right" could be reinstalled into physics. This would open to a Unified Field Theory since Newton and Maxwell are fully compatible as mass-based Newtonian gravitation and light without mass leaving possible interaction open to some new additional physics. 

Unfortunately modern physics has given in to adopt Einstein's "Newton is wrong because of SR" taken to represent stunning progress beyond classical physics. But experimental evidence must then be presented and that has shown to be very difficult to collect, to be honest. This is what usually is presented by modern physicists as best evidence that "Newton is wrong":

• Perihelion Precession of Mercury (1859)
• Michelson–Morley Experiment (1887)
• Deflection of Light (1919 eclipse expedition)
• Time Dilation of Muons (1949).
• Gravitational Time Dilation of photons (1959)

We understand that only the Perihelion Precession of Mercury concerns Newton's mechanics, the other concern essentially light, and we have in this post inspected the evidence and seen that it is weak, in particular because it is not SR which is claimed to show "Newton is wrong", but General Relativity GR.

We thus see that modern physics has to struggle very hard to show that "Newton is wrong". Of course this is expected when remembering that Newton's law of gravitation follows from conservation of energy and force in a gravitating material system, as the message of many posts. 

We conclude that Einstein's research plan to show "Newton is wrong" was based on ignorance combined with great ambition, and so did not work as science, but miraculously it worked politically to make Einstein the greatest physicist all times, securely displacing Newton to a second place. It is here much of the crisis of modern physics is rooted.  

You can always find a reason to dismiss a scientific theory by finding some irrelevant aspect which "is wrong". You may e g dismiss Newton's law of gravitation because it does not say anything about gravitational bending of light, because it says nothing about light at all, only about matter. But that lacks scientific reason and so could have only political reason. What is most important with a theory is that it is correct in a certain sense under certain circumstances, not that it does not apply to everything and does not tell everything.

If it so happens that light is affected by matter-based Newtonian gravitation by some physical mechanism yet to be discovered, then that could be added to Newton. But it would not mean that "Newton is wrong" as concerns matter. Yes, there are claims of "relativistic effects" appearing when matter reaches velocities near the speed of light, but that can only be achieved experimentally in supercolliders stretching physics to the extreme.  

Although the above arguments are logical and simple, they will meet opposition from a modern physics community carefully trained to believe that "Newton is simple+wrong" and "Einstein is strange+right".  Physics becomes much more manageable under a banner of "Newton is simple+right" rather than the opposite.  

Summary of SR agreed with chatGPT:

• SR does not add anything to Maxwell as theory of light.
• SR claims "Newton is wrong" because "Newton is not Lorentz invariant". But the nature of Newton/matter/mechanics is to be Galilean invariant and so the claim lacks logic.

What apparently happened is that Einstein became so taken away by "elevating" the Lorentz invariance of Maxwell's equations to a "general principle of relativity" demanding "all physical laws to be Lorentz invariant" as if playing God. What happens if you "elevate" a special case to a General Principle?

Another thing is that the Lorentz invariance of Maxwell's equations has to be handled with care since the Lorentz transformation mixes time into space in an unphysical way. This is was what Lorentz said when inspecting his transformation carefully pointing out that the "transformed time was not physical time", which Einstein failed to understand and so went on to form SR relativistic mechanics without physics. But Einstein succeeded with his Grand Plan to become the greatest physicist all times! Now Einstein is gone since 70 years and maybe it is time to move on without him and leave "strange physics" to the history of  failed attempts from "elevating" some special case to General Principle.

Tim Maudlin: Philosophy of Quantum Mechanics

This is follow up of the previous post on formalistic vs realistic physics.

Tim Maudlin is a realist philosopher of quantum physics in the following sense declared in the Introduction to Philosophy of Physics: Quantum Theory (interview here):

• A physical theory should clearly and forthrightly address two fundamental questions: what there is, and what it does. 
• The answer to the first question is provided by the ontology of the theory, and the answer to the second by its dynamics. 
• The ontology should have a sharp mathematical description, and the dynamics should be implemented by precise equations describing how the ontology will, or might, evolve.

Maudlin then proceeds to describe three theories (Collapse, Many-Worlds and Pilot Wave theories) which meet these demands, starting with a declaration that the Copenhagen Interpretation does not.

Maudlin does not like the term "realist", "realistic" or the opposite, claiming that "physical theories" are neither "realist" or the opposite, but the above declaration I think qualifies him to be a realist like Schrödinger rather than formalist like Born-Heisenberg. 

The question is then if the three above theories really satisfy the demands given. Already the fact that there is more than one theory raises questions, if there is only one reality. If not, then Many-Worlds comes in, but that ontology is very shaky. Collapse Theory and Pilot Wave Theory concern the One-World we are part of and build on a multi-dimensional Schrödinger Equation SE. The trouble with SE is that multi-dimensionality is way beyond the three dimensions of the observable world and so has been given no physical meaning at all,  or as last straw a statistical meaning as somehow describing different possibilities rather than realities. To replace what is with a wide range of possibilities and to argue that realism is not destroyed, requires a bit of good work and it is not clear that Maudlin succeeds. Note that he prepares for success by offering might evolve as alternative to will evolve, thus opening to statistics and the Copenhagen Interpretation he does not like...

In any case, the multi-dimensionality of SE in its standard form as the basis for both Collapse and Pilot Wave theories is the root trouble when seeking a description of what is and what it does. RealQM offers an alternative in 3d meeting these descriptions. 

Let me ask Maudlin to take a look at RealQM to see if his demands are satisfied in this case keeping the strict will evolve and not just might evolve.

Added: 

It seems that Maudlin answers that the Pilot Wave theory fulfills his demands of reality because the particles carried by the Pilot Wave are real, and then the multi-d Pilot Wave as solution to Schrödinger's equation also must be real. Something telling/carrying real particles what to do that in some real way and so must itself be real in some sense. The problem is that the what is and what it does of that Pilot Wave is hidden or maybe not there at all...

Realists vs Formalists: Modern Physics vs Mathematics

In the 1930s two main battles were shaping (quantum) physics and mathematics into our time, between realists and formalists with the following main actors:

• Physics formalists: Bohr-Born-Heisenberg.
• Physics realists: Schrödinger-Einstein.
• Mathematics formalist: Hilbert.
• Mathematics realist: Brouwer. 

The outcome of the battles were opposite. In physics Bohr-Born-Heisenberg took over completely and kicked out Schrödinger-Einstein. In mathematics Hilbert was defeated by Brouwer assisted by Gödel and Turing. 

Thus formalism took over physics and realism took over mathematics, opposite to the natural idea of (classical) physics as connected to reality and mathematics to formality. Very surprising and strange.

Mathematics as realism of constructivism/computing is today booming with AI the remarkable reality of Large Language Models LLM.

Physics as formalism is today in a state of deep crisis detached from reality back to medieval scholastics about interpretations of formalistic quantum mechanics without conclusion. 

Is it possible to bring back realism into quantum physics, not by another interpretation of the given formalism, but by replacing the formalism by realism? Maybe, in any case Real Quantum Mechanics RealQM is an attempt to do so. Why not take a look?

A position as realist is comfortable: There is a reality out there independent of any observation. The objective of physics is to describe this reality in constructive mathematical terms allowing computational simulation and comparison with observation. Reality cannot be "weird". 

A position as formalist is awkward: If there is no reality corresponding to the formalism, it is just a game. It is thus necessary to somehow connect formality to reality, but starting as formality, the connecting physics to be invented may come out as "weird", which is how Feynman-Bohr were selling quantum mechanics and then very successfully because "weird physics" suited media.

The formalists took over quantum physics because the basic model of quantum mechanics in the form of the multi-dimensional Schrödinger Equation SE was not derived from only assumptions about physical reality, but also included an element referred to as "kinetic energy" obtained as an analog of classical kinetic energy $\frac{p^2}{m}$ with $p=mv$ momentum with $m$ mass and $v$ velocity, by simply replacing the quantity $p$ by the differential operator $i\nabla$. Black magic formalism with a new form of "kinetic energy" without connection to motion! 

RealQM is based on a different SE where the "kinetic energy" appears as a "compression energy" of realistic classical mechanics. 

Since the multi-dimensional SE was accepted as fallen from the sky without origin in physics, it became impossible to question SE on objective physical grounds and the debate fell apart into endless quarrel about interpretations. 

To take a step out of the crisis it necessary to question the multi-d SE and seek to find a formulation based in physics and not in pure formalism. Ok?

Quantum Paradoxes and Physical Reality: Harvey Brown

Harvey Brown is a philosopher of physics with a realist approach developed in his book Quantum Paradoxes and Physical Reality starting with the following basic questions of modern physics:

1. Do the basic entities of atomic physics, such as electrons, photons, and so on, actually exist independently of the observations performed by physicists?
2. If the answer to the previous question is positive, is it possible to comprehend the structure of atomic objects and the evolution of atomic processes, in the sense of forming spacetime images somehow in correspondence with their reality?
3. Should one formulate physical laws in such a way that one or several causes are given for all observed effects?

Harvey maps positive answers to opponents of quantum mechanics:

• Ehrenfest, Planck, Einstein, Schrödinger and de Broglie, 

and negative to defenders of quantum mechanics: 

• Sommerfeld, Born, Bohr, Pauli, Heisenberg, Jordan, and Dirac. 

Basically a split between realists and formalists.

The situation today is that the formalist attitude is completely dominating, and that a realist attitude is shown only by a few realist philosophers of physics such as Tim Maudlin and Harvey Brown himself. 

To the realist camp I can add RealQM with positive answers to 1-3. It may be that positive realist answers tmay help progress better than negative formalist.