Schrödinger Equation Anniversary 1926-2026

In March 1926 the 39 year old Austrian physicist Erwin Schrödinger published an article entitled Quantisation as Eigenvalue Problem presenting a mathematical model of a Hydrogen atom with one electron in terms of classical continuum mechanics, which kick-started modern physics into the era of Quantum Mechanics, since it exactly captured the observed spectrum of Hydrogen.

The success was complete, and Schrödinger was very happy with his one-electron mathematical model as a wave equation in terms of a wave function representing electron charge density of clear physical nature like any density of classical continuum mechanics. 

But the happiness did not last long, since his one-electron model was quickly generalised to atoms with $N>1$ electrons in the hands of Bohr-Born-Heisenberg BBM in terms of a wave function $\Psi$ depending on $3N$ spatial coordinates, which could only be given a probabilistic meaning and so could not be accepted by Schrödinger with his deep conviction of physics as reality. The effect was that Schrödinger was quickly "cancelled" and had to spend the rest of his life as outsider without any say. The success was turned into its opposite.      

At a Dublin 1952 Colloquium Schrödinger restated his deep conviction carried for 26 lonely years that history took the wrong turn after March 1926 when his Schrödinger equation for Hydrogen was hijacked by Bohr-Born-Heisenberg to form the Copenhagen Interpretation as Standard Quantum Mechanics StdQM, which has filled text books, students and physicists minds for 100 years and still does:    

• Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today,
• I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.
• It has been worked out in great detail to form a scheme of admirable logical consistency that has been inculcated ever since to every young student of theoretical physics.
• The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it. 
• It is, as I said, the probability view of quantum mechanics. You know how it pervades the whole system. It is always implied in everything a quantum theorist tells you. Nearly every result he pronounces is about the probability of this or that or that ... happening-with usually a great many alternatives. The idea that they be not alternatives but all really happen simultaneously seems lunatic to him, just impossible. 
• He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. 
• It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way-namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation, which need, of course, not be a scientific observation.
• Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it. 
• And I wonder that he is not afraid, when he puts a ten pound-note {his wrist-watch} into his drawer in the evening, he might  find it dissolved in the morning, because he has not kept watching it.

Real Quantum Mechanics RealQM is an alternative to StdQM formed in the spirit of Schrödinger. It is quite possible that RealQM would have made Schrödinger happy again. If you are unhappy with StdQM, try RealQM! To get started check out recent posts e g the previous on Unified Field Theory with RealQM.

Unified Field Theory: Newton + Maxwell + RealQM

Schrödinger created Quantum Mechanics by formulating in 1926 a mathematical model within classical continuum mechanics in terms of a wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ satisfying a wave equation named Schrödinger's Equation SE: 

• $i\frac{\partial\psi}{\partial t}+H\psi =0$     (SE)

with 

• $H=-\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$ a Hamiltonian differential operator.

The eigenvalues of SE showed to exactly fit with the observed spectrum of a Hydrogen atom and so was the answer to a search begun by Bohr 15 years before. The success was complete: SE revealed the secret of the Hydrogen atom as an eigenvalue problem for a Hamiltonian with time-independent normalised real-valued eigenfunctions $\Psi (x)$ with energies as sum of kinetic and potential energies appearing as eigenvalues:

• $E = E_{kin}+E_{pot}=\frac{1}{2}\int\vert\nabla\Psi\vert^2dx-\int\frac{\Psi^2(x)}{\vert x\vert}dx.$ 

The ground state of a Hydrogen atom took the physical form of a charge density $\Psi^2(x)$ with minimal energy appearing as a compromise of negative $E_{pot}$ by concentration near $x=0$ balanced by a positive $E_{kin}=-\frac{1}{2}E_{pot}$ appearing as a form of "compression energy".

SE took the form of classical continuum mechanics with a clear physical interpretation as charge density and so represented a complete success of classical mathematical physics suddenly expanding its excellent service from macroscopics into atomic microscopics. 

SE combines perfectly with Newtonian gravitation giving $\Psi^2(x)$ a double role as both charge density and mass density, as well as with Maxwell's electro-magnetics. The resulting Newton-Maxwell Schrödinger NMS model was a Unified-Field-Theory covering all of Hydrogen physics from galactic to atomic scales. A tremendous success of mathematical modelling of real physics! Since Hydrogen accounts for 74% of the mass of the Universe NMS captured nearly everything.

But 25% is Helium and 1% all the other atoms, and so SE had to be extended to atoms with more than one electron like Helium with two electrons to qualify as UFT. But how?

A quick formal resolution lay on the table: Give each new electron a whole set of 3d coordinates and trivially extend (SE) to any atom with a stroke of a pen. That gave a wave function depending on $3N$ space coordinates for an atom $N$ electrons. Easy to do but without clear physical meaning. 

Schrödinger refused to take this step, but Bohr-Born-Heisenberg jumped on the band wagon of Standard Quantum Mechanics StdQM based on a multi-d Schrödinger equation forming the foundation of modern physics under heavy protests from Schrödinger because it replaced causality and physicality by non-physical probabilities of observer measurement outcomes. 

In short StdQM is viewed to be the result of a process of quantisation preventing unification with the classical continuum physics of Newton and Maxwell, which has grown out into the deep crisis of modern physics of today.

Since Maxwell and Newton represent perfect theories, without any need of quantification, the natural idea to form a UFT is to search for a form of QM without quantification. But this has been prevented for 100 years by the very strong domination of the Copenhagen Interpretation of Bohr-Born-Heisenberg. Efforts have been made of  "dequantisation" of StdQM bringing it back to classic continuum physics (e g Bohmian mechanics), but without success because quantification cannot be reversed. 

RealQM offers a generalisation of SE for Hydrogen to atoms with more than one electrons, which stays within the realm of classical continuum physics, and so combines perfectly with Newton and Maxwell into a UFT.  

 

Radiative Equilibrium Without Quanta: Normality

Consider a Hydrogen atom described by Schrödinger's Equation SE in radiative equilibrium with light of a certain frequency $\nu$ described by Maxwell's equations as an  electromagnetic wave. This means that there is a gap $\Delta E$ in the distribution of eigenvalues $E$ or spectrum such that $\Delta E =h\nu$ with $h$ a scaling factor, in classical literature named Plank's constant. 

The SE for Hydrogen is a partial differential equation of classical continuum form in terms of a wave function which changes continuously in space and time during the process of establishing and maintaining radiation at the resonance frequency $\nu$. The energy gap $\Delta E$ scales with the frequency $\nu$ over  the spectrum. 

What is discrete is the spectrum, just as in classical continuum mechanics, while wave functions are continuous and do not take any discrete "jumps" in state/energy.  

Conclusion: The Schrödinger's Equation SE for a Hydrogen atom takes the form of classical continuum mechanics. QM for a Hydrogen atom is classical continuum physics. No need for quantisation. The fact that the spectrum is discrete is not evidence that any non-classical process of quantisation is really needed. See also this post.

chatGPT: Maxwell + Schrödinger looks good:

• Treat the atom quantum mechanically (Schrödinger equation).

• Treat the radiation as a classical wave (Maxwell).

• That explains a lot: absorption spectra, stimulated emission, radiative equilibrium, Rabi oscillations.

• Everything looks continuous.

This model works surprisingly well in many normal conditions.

end chatGPT

But a modern theoretical physicist is not happy with normality of classical continuum physics as description of the basic problem of atom physics of a radiating atom, because it is not modern new physics. And so the modern physicist goes on to confront the radiating atom as classical continuum physics with some extreme circumstances such as very very weak forcing so weak that the continuity breaks down. Like running your car engine with only a very weak slow irregular ignition making the engine start to malfunction. This is called appeal to extremes often used in debate.

By focussing on some extreme case, the classical model covering the normal case can be downplayed as "wrong" even if it works fine, to prepare the way for some new bold modern theory, which is more "fundamentally correct". In this way all the victories of the classic theory for all normal cases can be cashed in for the new theory to which can then be added anything extreme even if vague. 

This is what is done when General Relativity replaces Newton's theory of gravitation as being more "fundamentally correct". Or when QFT replaces QM which replaces Schrödinger+Maxwell. More and more extreme to downplay the normal.

So can unsuccessful explanation of something normal within classical continuum mechanics, be covered up by focussing the interest onto something more fundamental and extreme, and the possibility of a classical explanation can be missed, as that of RealQM.   

The Spell of Quantisation = Crisis of Modern Physics

The fundamental difference between modern physics in the form of Quantum Mechanics QM and classical physics in the form of Continuum Mechanics, is something named 

• Quantisation. 

After a long discussion with chatGPT the following conclusion as "Honest Summary" is reached:

• Quantisation means: interactions are granular, in units of Planck's constant $h$.
• It is detected physically through indivisible events (photoelectrons, Compton recoils, detector clicks).
• It is explained mathematically by replacing classical observables with operators whose spectra are discrete.
• But the mechanical reason why nature enforces this is not known. 
• It is a foundational mystery.

On the way we have learned that what Quantisation is not:

• Not simply probabilistic interpretation of wave function. 
• Not simply discrete spectrum of a continuous vibrating string/atom.
• Not simply discreteness of electron unit charge.
• Not discrete "light particles/photons".
• Not discrete "lumps of energy".  
• Not really QM but rather Quantum Field Theory for continuous fields with discrete excitations. 

But not really anything concrete beyond formalism mystery of what Quantisation is. 

The trouble with Quantisation is that it forces a split between classical continuum physics and modern quantised physics which prevents a unification of macroscopic physics of gravitation with microscopic physics of atoms including electromagnetics. 

Without knowing what Quantisation is, it is very difficult to check if the split with continuum physics is really necessary. 

The fact that modern physics has not been able to form a Unified Field Theory UFT represents a monumental failure, which is now causing a deep credibility crisis of theoretical physics. 

Modern physics is thus confronted with the following spell:

1. Quantisation is necessary.
2. Quantisation prevents a UFT.
3. Lack of UFT is the root cause to the present deep crisis of theoretical physics.
4. Quantisation is a mystery.

But based on 4. it is natural to ask if 1. is true? 

To question 1. requires a QM without Quantisation and there is a candidate for such a thing in the form of Real Quantum Mechanics RealQM which has the form of classical continuum mechanics and so allows unification. 

With RealQM the spell of Quantisation evaporates and a UFT appears as a real possibility to explore. Want to try it? 

Recall that the 1. is the leading idea today of professional physicists: The only way forward towards unification is quantising gravitation, and the only hope went to String Theory emerging 50 years ago, but this hope is now quickly eroding. No hope any more for quantising gravity. 

The only way forward is to dequantise QM. This is what RealQM offers. 

Quantum Mechanics Without Quantisation

Schrödinger's Equation SE for the Hydrogen atom with one electron has the form of a classical continuum mechanical wave equation in a complex-valued wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ with $\vert\psi (x,t)\vert^2$ assigned the clear physical meaning of electron charge density at $(x,t)$ with total charge of one unit. The model captures the observed spectrum of Hydrogen as a discrete set of eigenvalues of normalised eigenfunctions in fully classical continuum mechanical form. 

Yet this model has been taken as starting point for a fundamental reformation of classical physics into a fundamentally new form of physics named quantum mechanics resulting from a process of quantisation. In the case of the Hydrogen atom this radical step reduces to a reinterpretation of $\vert\psi (x,t)\vert^2$ as a probability density thus replacing charge density (with physical meaning) with probability (without physical meaning). In this case the reformation makes no sense: The Emperor's New Clothes. Smallest quantum of energy has no physical meaning. 

The reason for the reformation appeared along with the generalisation of SE to atoms with more than one electron, which was the problem facing Schrödinger in 1926 after formulating SE for the Hydrogen atom with one electron, which propelled him to fame. But it was not evident how to proceed and so Schrödinger gave in to a purely formal generalisation introducing a new set of 3d spatial variables for each new electron forming a multi-d SE with only probabilistic interpretation possible and as such aggressively promoted by Bohr-Born-Heisenberg overpowering Schrödinger's request for real physics as ontology instead of unphysical probability as epistemology.

So was the modern physics of quantum mechanics born from a formal process of quantisation, which boiled down to replacing classical deterministic continuum physics by probabilistic physics without determinism and physical meaning. Schrödinger deeply regretted ever to be involved in this project forming 20th century physics. 

Could history have taken a different route by a different generalisation staying within classical continuum physics if Schrödinger had just resisted the onslaught from Bohr-Born-Heisenberg at bit longer? Yes, this would have been possible if only Schrödinger had tried the idea of Real  Quantum Mechanics RealQM of forming a SE in terms of non-overlapping charge densities with direct physical meaning and without any need of reformation by quantisation into probabilities. 

RealQM offers a model of atomic physics in the form of classical continuum physics without any need of quantisation and probabilities. RealQM combines seamlessly with classical electro-magnetics and Newtonian mechanics and so opens to the formation of a Unified Field Theory UFT, which both Schrödinger and Einstein struggled to find throughout the later halfs of their scientific lives, but couldn't do.....Schrödinger died in Vienna in 1961 73 years old... 

Schrödinger in his Nobel Lecture 1933 showing his resistance to Bohr-Born-Heisenberg:

• We cannot, however, manage to make do with such old, familiar, and seemingly indispensible terms as "real" or "only possible"; we are never in a position to say what really is or what really happens, but we can only say what will be observed in any concrete individual case. 
• Will we have to be permanently satisfied with this. . . ? On principle, yes. On principle, there is nothing new in the postulate that in the end exact science should aim at nothing more than the description of what can really be observed. 
• The question is only whether from now on we shall have to refrain from tying description to a clear hypothesis about the real nature of the world. 
• There are many who wish to pronounce such abdication even today. But I believe that this means making things a little too easy for oneself.

ChatGPT about Schrödinger's struggle find a UFT:

• After inventing wave mechanics, Schrödinger spent decades searching for a unified continuum field theory of matter and forces, resisting the idea that nature is fundamentally quantised — but his attempts never succeeded against the empirical dominance of quantum field theory.

• Goal: Matter = continuous wave fields, not particles.

• Method:

  • Original 1926 wave mechanics: electrons as standing waves.

  • Later: attempts to merge wave mechanics with Einstein’s relativity → affine field theory, complex scalar fields.

• Belief: Quantisation is not fundamental, but an artifact of wave modes and stability conditions.

• Outcome: His “unified field theory” never matched experiments; the community rejected it once QED and QFT succeeded.

• Spirit: Continuity is real, discreteness is emergent.

  
  

The Deep Secret of $E=h\nu$ Uncovered = 0

The value of Planck's constant $h$ is supposed to carry a deep secret of the atomic physics captured in the Schrödinger Equation SE of Quantum Mechanics QM as the foundation of modern physics. A deep secret of a microscopic world which is fundamentally different from the macroscopic world we can fathom by direct experience. A strange world of the modern physics emerging in the beginning of the 20th century, which "nobody understands" including the physical meaning of Planck's constant $h$. 

In the new 2019 SI standard of units, the value of $h$ is specified to be exactly $h=6.62607015\times 10^{−34}$ Joule-seconds, which is a very small number viewed to hide a deep secret, while appearing as an arbitrary unit conversion factor. 

Let us seek to untangle the secret in detail. We recall the message of modern physics of the existence of a smallest quantum of energy $h\nu$ associated to a wave of frequency of $\nu$ showing that the microscopic world is discrete and not continuous like the macroscopic world so well described by continuum mechanics. More precisely, light as a wave phenomenon is viewed to consist of a stream of light particles named photons each one carrying exactly the energy $h\nu$. Mind boggling, suggesting some deep secret.

Let us now trace the connection to SE for the Hydrogen atom taking the form: 

• $ih\frac{\partial\psi}{\partial t} + H\psi =0$                (SE)

where $\psi (x.t)$ is a complex-valued wave function depending on a 3d spatial coordinate $x$ and a time variable $t$ and $H$ is a (Hermitian) operator acting on $\psi$ with a discrete spectrum of real eigenvalues $E$ representing energies of normalised eigenfunctions $\Psi (x)$ satisfying $H\Psi =E\Psi$, which give wave solutions to (SE) of the form 

• $\psi (x,t)=\exp(i\frac{E}{h}t)\Psi (x)=\exp(i\nu t)\Psi (x)$ with
• $\nu =\frac{E}{h}$ or $E=h\nu$.  

We thus see a direct connection between the smallest quantum of energy $h\nu$ and energies $E=h\nu$ of eigenstates/functions of a Hydrogen atom, as a direct reflection of the form of (SE) including a first time derivative: Energy $E$ scales linearly with frequency $\nu$. 

The other way around, one can see (SE) as being formed by Schrödinger to include the connection $E=h\nu$ between energy $E$ and frequency $\nu$ (as a linear dispersion relation), because that fits with observed spectrum of the Hydrogen atom. Mathematical modeling to fit observation.   

More precisely, the spectrum of a Hydrogen atom comes out from differences of eigenvalues/energies $\Delta E$ translated to frequencies by $\Delta E =h\nu$. 

The basic heuristic idea of Einstein in 1905 was that  the energy of the electron of a Hydrogen atom can "jump" from one energy level to another by receiving/delivering exactly one photon of energy $\Delta E =h\nu$ in radiative equilibrium with light of frequency $\nu$: 

• Transition from one energy level to another with an energy jump $\Delta E$ of the electron of a Hydrogen atom involves receiving/delivering exactly the energy $\Delta E=h\nu$ of one photon of frequency $\nu =\frac{E}{h}$. 

This idea is supposed to convince us that the world of a Hydrogen atom is discrete operating with discrete chunks of energy $h\nu$ carried by discrete light particles/photons.

But this is an invented discreteness: SE is a continuum model of classical form in a wave function $\psi$ with $\vert\psi (x,t)\vert^2$ representing charge density, which has a discrete set of eigenvalues just like a vibrating string. The association of energy to frequency by $E=h\nu$ is simply a scaling of between energy and frequency with a scaling factor of $h$ with a value depending on choice of units.

From (SE) it follows that size of a Hydrogen atom scales with $h^2$ which connects to the discreteness of a Hydrogen atom with its only electron, which is described by the continuous model (SE) of classical continuum form. 

We thus find nothing fundamentally different from classical continuum mechanics point of view in the (SE) model of a Hydrogen atom in terms of a charge density. The association of an energy jump $\Delta E =h\nu $ to exactly one photon of frequency $\nu$ lacks real physical meaning and is just a convention which appeared as a heuristic idea in Einstein's mind in 1905. Planck's constant $h$ does not say that the microscopic world is discrete making it fundamentally different from a continuous macroscopic world. Planck's constant has a meaning as setting the physical scale of a Hydrogen atom, but not as a deep secret about the world. Of course atoms have spatial size just as specific macroscopic material objects with specific spatial extension. A Hydrogen atom is a like a continuous string of a violin of certain length and tension. No quantum.

In short, the quantum world of a Hydrogen atom can be understood in terms of classical continuum mechanics. 

The split appears when generalising (SE) to atoms with $N>1$ electrons following the route of Standard QM by Born-Bohr-Heisenberg into a linear wave equation in $3N$ spatial dimensions, with the wave function given a probabilistic unphysical meaning which makes StdQM "not understandable".

RealQM offers a fundamentally different generalisation without split away from classical continuum mechanics, which is understandable.  

Summary: 

1. Planck's constant $h$ serves as a formal conversion factor between energy $\Delta E$ and frequency $\nu$ with $\Delta E=h\nu$ in the setting of a radiating  Hydrogen atom. The size of a Hydrogen atom scales with $h^2$ which gives the specific value of Planck's constant $h$ a physical meaning, which is not some deep secreted of smallest quantum of energy. 
2. The generalisation to any atom by StdQM leaves classical continuum mechanics into a probabilistic quantum world "nobody can understand" where Planck's constant appears as a deep secret.
3. RealQM offers a generalisation staying within the form of classical continuum mechanics which "everybody can understand" where Planck's constant remains the simple conversion factor of 1. = No Secret = 0.
4. RealQM appears as "Quantum Mechanics without Quantum" which opens to unification with electromagnetics-Newtonian gravitation into a Unifies Field Theory as unfinished dream of Einstein. Let's get to work! 

Brief Quantum Story 1900 - 1905 - 1925 - 2025

The first form of the Schrödinger equation presented by Schrödinger in 1926  offered a mathematical model of the Hydrogen atom with one electron in the form of a linear wave equation of classical continuum mechanical form in terms of a (complex valued) wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ with $\vert\psi (x,t)\vert^2$ representing charge density at $(x,t)$ with total unit electron charge. The corresponding classical eigenvalue problem with discrete eigenvalues showed to fit exactly with the observed discrete spectrum of Hydrogen. 

The success was immense and Schrödinger rocketed to fame by giving birth to a new form physics of atoms to be named Quantum Mechanics QM, but it was not Schrödinger who coined the concept of quantum, and in fact he disliked it from the bottom of his heart:

• If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.

Recall from recent posts that that the quantum was the result of desperate actions by first Planck in 1905 introducing a quantum of energy $h\nu$ associated with radiation of frequency $\nu$ with $h$ a very small constant indicating that a quantum of energy is a very small quantity. Einstein followed in 1905 by suggesting that light of frequency $\nu$ could be thought of (heuristically only!) as a stream of light particles or photons each photon carrying exactly one quantum of energy $h\nu$. Vivid fantasy.

Then 20 years passed with the idea of the quantum of energy $h\nu$ kept as a form of easy fix to explain blackbody radiation and photoelectricity believed to be impossible within classical continuum physics. 

Schrödinger gave his revolutionary Hydrogen article the title "Quantisation as Eigenvalue Problem" thus connecting back to the a concept of "quantisation" suggested earlier by Bohr and de Broglie and coming out in Heisenberg's matrix mechanics, which he now reformulated as an eigenvalue problem of the form of classical continuum physics. Schrödinger's goal was to show that the new quantum mechanics of atoms in fact could take the form of classical continuum mechanics. Schrödinger never gave up that goal but could only reach it in the case of the Hydrogen atom with one electron, since already the Helium atom with two electrons appeared to require a new model outside classical continuum mechanics, and so Schrödinger left QM in 1928 disgusted, to let it be formed by Bohr-Heisenberg as a fundamentally new form of physics as QM, which has come to serve as the foundation of modern physics, without Schrödinger the founder of QM 

But back to Schrödinger's equation for the Hydrogen atom, which does not ask for any quantum of energy $h\nu$ carried by a photon. It is a classical continuum physics eigenvalue problem with discrete spectrum of eigenvalues $E_1<E_2<E_3,...$ representing energies of excited states staring from a ground state energy $E_1$. Differences of eigenvalues $E_n-E_m$ with $E_n>E_m$ match with frequencies $\nu$ in the observed spectrum of Hydrogen under scaling with a certain constant $h$. There is here only a superficial connection between a classical continuum physics eigenvalue problem and the new concept of quantum of energy scaling with frequency $\nu$.  Schrödinger managed to turn quantisation into a classical eigenvalue problem. 

Once the Hydrogen atom was secured within classical continuum physics without the real need of any quantum of energy $h\nu$, which he disliked so much, Schrödinger took on the Helium atom with two electrons. And this is where history took a turn with far-reaching consequences into our time. Instead of staying within classical continuum physics, Schrödinger and everyone else took the easy way out by generalising from one electron to many electrons by a purely formal procedure leaving out physics. For some reason, Schrödinger and everyone else missed the possibility demonstrated in Real Quantum Mechanics RealQM of staying within classical continuum physics without need for any quantum of energy. 

The result of taking the easy formal route when generalising Schrödinger's equation from one electron to many and so form StdQM as the textbook version of QM today, is that "nobody understands QM", simply because the easy formal route does not make sense from physical point of view. What does not make sense cannot be understood, and if something cannot be understood, it is because it does not make sense. 

What about giving RealQM a try, if you want to understand QM? RealQM offers an understanding of blackbody radiation and photoelectric effect with a frame of classical continuum physics!

Recall this statement by Lieb and Thirring from this post concerning the easy way out:

• An important historical point is to be noted here. It might have been thought that the correct generalization for N particles is to use N functions of one variable instead of one function of N variables. 
• Such a ‘wrong turn’ did not happen historically, which is, after all, remarkable.

What did not happen was RealQM and so when it now happens 100 years later it may be remarkable.

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?