Is Chemistry Explained by Quantum Mechanics?

Here are some quotes by famous chemists connecting to the previous post on RealQM as an alternative to textbook StdQM: 

• The great enabler of chemistry, quantum mechanics, also reveals the poverty of our language and concepts. (Roald Hoffmann)
• There is no unique way of defining a chemical bond from quantum mechanics. (Roald Hoffmann)
• The concepts of chemistry are more than the consequences of the Schrödinger equation. (Linus Pauling)
• The concept of the chemical bond is not a real one; it is a figment of our own imagination. A bond does not exist as an observable entity.( Charles Coulson)
• Quantum mechanics does not provide a definition of a chemical bond. (Richard Bader)
• Quantum Mechanics supplies numbers, chemistry supplies meaning. (Henry Eyring)
• Theories of physics cannot explain the principles governing chemical reactions. (Michael Polanyi)
• The exact solution of the Schrödinger equation would not solve the chemical problem. (Per-Olov Löwdin)
• Orbitals, bonds, and structures are models imposed on quantum results, not entities delivered by QM itself. (John C. Slater)
• The chemical bond is not a quantum-mechanical observable. (George C. Pimentel)
• Chemistry is not derivable from quantum mechanics in any straightforward sense. (Hans Primas)
• Orbitals are not physical realities; they are mathematical constructs. (Robert S. Mulliken)
• The microscopic description does not exhaust the meaning of macroscopic phenomena. (Ilya Prigogine)
• Exact quantum dynamics would still not yield chemical concepts such as mechanisms, bonds, or reaction pathways. (William H. Miller)
• Quantum mechanics does not directly provide chemical structure; structure is inferred. (Jerome Karle)
• Quantum numbers and wave functions do not by themselves define chemical individuality. (Friedrich Hund)
• Quantum mechanics explains everything in principle, but nothing in practice — and very little in concept. QM does not define chemical bonds. QM does not uniquely explain molecular structure. Chemical explanation involves conceptual frameworks not present in physics. Chemistry is not simply applied quantum mechanics. Quantum mechanics is indispensable to chemistry, yet insufficient as a chemical explanation. (Consensus)

Compare with what famous physicists claim:

• Quantum electrodynamics is the most accurate theory we have ever had. (Richard Feynman)
• Quantum mechanics is surely the most successful physical theory we have ever discovered. (Steven Weinberg)
• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known. (Paul Dirac)
• Quantum electrodynamics is the most accurate theory known to man. (Julian Schwinger)
• No experimental result has ever contradicted quantum mechanics. (Max Born)
• Quantum mechanics works astonishingly well—better than we have any right to expect. (Frank Wilczek)
• Quantum mechanics is not just correct; it is spectacularly correct. (Sean Carroll)
• Quantum theory has survived every experimental test to which it has been subjected. (David Deutsch)
• The predictions of quantum mechanics are so spectacularly confirmed that it is hard to contemplate abandoning it. (John Bell)
• Quantum mechanics is the most successful predictive framework ever developed, unmatched in accuracy, scope, and experimental confirmation. (Consensus)

Draw your own conclusion.

Basic Mystery of Quantum: Shared vs Individual

The basic mystery of textbook Standard Quantum Mechanics StdQM serving as the foundation of modern physics, is the physical meaning of the wave function $\Psi (x_1,...,x_N)$ for a system with $N$ electrons depending on  $N$ spatial variables $x_1,...,x_N$ each $x_i$ serving as the 3d Euclidean coordinate of a copy $E_i$ of the same Euclidean space $E=\Re^3$, for $i=1,...,N$, with the total coordinate $x=(x_1,...,x_N)$ sweeping over configuration space as $\Re^{3N}$.

The mystery comes from the fact the each $E_i$ is connected to an electron $i$ and so serves as an individual universe for each electron. Very strange. The inspiration maybe came for the Monad Theory of Leibniz where each monad (as form of elementary unit like an electron) has its own universe to dwell in, while taking in blurred perceptions from all other monads.  

But electrons interact through Coulomb potentials 

• $\frac{1}{\vert x_i -x_j\vert}$ with $i\neq j$ 

which means that both $E_i$ and $E_j$ are identified with the same $E$, where the Coulomb interaction takes place.

We see that each $E_i$ serves a double role as both representing an individual and a common shared 3d space. Very confusing. 

The physics of QM has two elements:

1. Coulomb interaction between electrons in a common shared physical 3d space.
2. Kinetic energy from presence of a Laplacian acting in each individual $E_i$. 

Here 1 is shared and 2 individual and QM as the combination of 1 + 2 has to struggle to make sense of this contradictory mix. Ok?

Recall that StdQM is uncomputable because of the $3N$ spatial dimensions. 

RealQM is an alternative to StdQM formulated in terms of a wave function depending on a single physical variable in a 3d Euclidean space E. RealQM is computable because computational complexity scales linearly with $N$. 

It is a mystery that RealQM has been developed only recently, since it is very natural and does not suffer from the many unresolved issues of StdQM. Why not give it a try, after having struggled for 100 years to make sense of StdQM?

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.

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.

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).

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?

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...

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.

What Does the Schrödinger's Equation Say?

Nobel Laureate in Physics Gerhard t' Hooft is not happy with the prime jewel of modern physics in the form of Schrödinger's Equation SE as expressed in Un Unorthodox View on Quantum Mechanics:

• We know very well how to use the equation. The properties of atoms, molecules, elementary particles and the forces between all of these can be derived with perplexing accuracy using it. The way the equation is used is nothing to complain about, but what exactly does it say?
• What do these wave functions represent? In particular the ones that are not asso- ciated to photons (the energy packets of the electromagnetic field, which we think we understand very well). 
• What do those waves stand for that are associated to electrons, or other elementary particles, or even molecules and larger things, including cats, and eventually, physicists? What happens to its wave function when you actually observe a particle?
• Almost a full century has passed since the equation was written down, and fierce discussions have been held, quite a few standpoints were vigorously defended and equally vigorously attacked. We still do not know what or whom to believe, but it still goes on, while others get irritated by all this display of impotence. 
• Why is it that we still do not agree? I think I know the answers, but almost everyone disagrees with me.
• Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly concerning 'what is really going on', but questions such as these may well be essential for finding new ways of constructing models beyond what is now called the Standard Model of the sub-atomic particles.

t' Hooft describes modern physics in a state of stalemate, impotence and irritation and asks for new ways of constructing models. 

I will send RealQM t' Hooft RealQM and will report his reaction. 

Note that t' Hooft repeats the mantra the physicists know very well how to use SE to derive properties of atoms and molecules with perplexing accuracy... there is nothing to complain about. Yet t' Hooft does complain because he does not understand what all this highly accurate information in fact does say? 

Philosophy of Classical Physics vs Modern Physics

Here is a new article in the series about RealQM:

• RealQM vs StdQM: Philosophy

The idea is that philosophy enters into physics when there is a need to clarify the meaning of concepts of physics. The Philosophy of Quantum Mechanics is an academic discipline itself, typically part of a department of philosophy rather than a department of physics, powered by the fact that the Quantum Mechanics is filled with contradictions and mysteries which are not part of classical physics.

 

Why Quantum Mechanics is "Weird"

All leading modern physicists agree that quantum mechanics is so "weird" or "absurd" that it cannot be understood: 

• Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd. (Feynman)
• I think I can safely say that nobody understands Quantum Mechanics. (Feynman)
• If quantum mechanics has not profoundly shocked you, you have not understood it yet. (Bohr)

The "weirdness" of quantum mechanics comes from its foundational principle in the form of Schrödinger's equation based on a Hamiltonian $H_{weird}$ of the following form for an atom with kernel of positive charge $Z$ at the origin of a 3d Euclidean coordinate system $R^3$ surrounded by $N=Z$ electrons labeled $i=1,2,...,N$:

• $H_{weird}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$                                        

where each $x_i$ is a 3d coordinate for a separate copy of $R^3$ and $\Delta_i$ the Laplacian differential operator with respect to $x_i$. The Hamiltonian $H_{weird}$ acts on wave functions $\psi (x_1,x_2,...x_N)$ depending on $N$ 3d spatial variables $x_i$, each $x_i$ serving to represent an electron with presence over the whole of its own copy of $R^3$, thus based on electronic wave functions having global supports.

The weirdness comes from the many dimensions where each electron $i=1,...,N$ is equipped with a separate copy of $R^3$, where it is acted upon by a Laplacian differential operator $\Delta_i$ giving it kinetic energy, yet the electrons interact in a common $R^3$ by the presence of $\vert x_i-x_j\vert$ in the term representing Coulomb electronic repulsion. The electrons thus have both separated individual existence and shared existence. That is weird from classical continuum mechanics point of where a shared single physical 3d space is the only one available. With a travesty of Bohr, one could maybe say

• If from a  knowledge of classical continuum mechanics, you are not shocked by $H_{weird}$, then you have not understood classical continuum mechanics.

Quantum mechanics is thus weird unphysical because it is based on a Hamiltonian $H_{weird}$, which is weird unphysical. Of course, if you are dealing with something which is partly weird, then you have to get rid of the weirdness and keep whatever is not weird and maybe useful.  Efforts to this end e g in the form of Density Functional Theory have been made without however completely getting rid on the weirdness. RealQM is a based on $H_{weird}$ but with a new meaning which is physical and not at all weird, see this post for an intro. 

 

Quantum Physics as Classical Continuum Physics

The fundamental theories of modern physics appearing as revolutions of classical physics at the turn to the 20th century are: 

• Quantum Mechanics QM of atoms and molecules based on Schrödinger's equation. 
• Einstein's General Theory of Relativity GR theory of space, time and gravitation. 

QM offered a fundamentally a new view on the microscopical world of atoms and molecules and GR a likewise fundamentally new view on the cosmology of largest scales, while the macroscopical world of human perception of classical continuum physics such as solid/fluid mechanics and electromagnetics, was left untouched. 

Modern physics offered theories fundamentally different from the well understood and experienced theories of classical continuum physics, which was certainly grand but came with difficulties of understanding from human experience. 

QM described an atom or molecule with $N$ electrons in terms of a Schrödinger wave function $\Psi$ depending on $3N$ spatial variables with electron living in distinct 3d worlds, in a model which did not make sense from classical continuum physics point of view and thus required a new form of physical meaning as the essence of modernity.

But this showed to be very difficult and no consensus on physical meaning has formed despite very serious efforts over 100 years. The message is instead that there is no observation which is not in perfect agreement with computations using QM and so QM is a machine that works perfectly even if it is not understood why. In other words: Shut up and calculate.    

But is it necessarily so that the microscopical world of atoms and molecules must be fundamentally different from the macroscopical world of continuum physics, which we as human beings can experience and understand? Maybe this world is like ours, just a bit smaller?

Let us consider a key example: QM describes the ground state of the Hydrogen atom with one electron as the state minimising the total energy as the sum of "gradient energy" and potential energy.

• $\frac{1}{2}\int\vert\nabla\Psi (x)\vert^2dx-\int\frac{\Psi (x)^2}{\vert x\vert}dx$ 

under the side condition $\int\Psi (x)^2dx =1$, where $\Psi (x)$ is a function depending a 3d spatial variable $x$ with $\Psi (x)^2$ representing electron charge density and $\frac{1}{\vert x\vert}$ is the Coulomb potential of the kernel at $x=0$. The ground state comes out as a multiple of $\exp (-\vert x\vert)$ as an electron charge density decaying away from the kernel with total charge of 1, which seeks to be as close as possible to the kernel at a "gradient cost". 

We can give this problem a different interpretation in classical continuum physics as the basic mode of vibration of an elastic body subject to a potential force with the "gradient cost" expressing an "elastic compression cost".  We can thus, if we want, view the electron of Hydrogen atom as a form of "elastic medium" subject to attraction from the kernel. 

This is not the view of an electron as particle, which is not true physics, but instead as an extended object in 3d space with a certain "elasticity", which appears as true physics.  It is the "gradient energy" which gives the electron extension in space. 

We can thus fully understand the Hydrogen atom as a form of classical continuum physics, with spectrum in spectacular perfect agreement with observation. 

RealQM offers a generalisation into a model of atoms and molecules as classical continuum physics in the form of non-overlapping "elastic" charge densities interacting by Coulomb potentials, which is understandable in the same sense as the Hydrogen atom, and agrees with observations, and is computable in the same efficient way as classical continuum physics. 

RealQM is fundamentally different from the accepted multi-dimensional QM for which physics is missing. 

Note that the novelty of the Schrödinger equation for the Hydrogen atom presented by Schrödinger in 1926, was the appearance of the "gradient energy" of an electron  not present with a particle view as in Bohr's failed atom model. This was a revolution!

Note that the "uncertainty principle" is simply a reflection of the presence of the "gradient energy" forcing an electron density to be distributed over space and so like anything with spatial extension being a bit uncertain as concerns precis point location. Nothing new and strange. 

Note that the fact that a ground state is not radiating, which Bohr tried to explain, is that in the vibrating mode of the ground state the electron density is constant over time. On the other hand excited states give rise to charge densities changing over time and thus radiate.

The paradigm of modern physics is that the microscopical world is fundamentally different from the macroscopical world, and so cannot be understood from human experience.  

RealQM offers a microscopical world of fundamentally the same form as the macroscopical world, just smaller. 

When seeking some response to RealQM from physicists and chemists, I meet attitudes of skepticism, which is natural, of flat neglect, which is understandable, but very little understanding as if classical continuum physics is no longer part of physics and chemistry education. 

It would be sufficient with one physicist/chemist expressing understanding of the basic principles of RealQM and either refuting as unreasonable or accepting them as reasonable. 

ChatGPT: The World Itself Is Weird

After a long conversation with ChatGPT o1 about quantum mechanics, ChatGPT comes to the following conclusion by collecting the collected wisdom of all the great physicists of the 20th century:

• The reason quantum mechanics is weird is that the world itself is weird—but only from the perspective of our classical minds. At the quantum level, the universe simply operates by different rules, ones that are no less valid than those of classical physics. This weirdness is a feature of the universe’s richness and complexity, and it pushes us to continually rethink our understanding of reality. Instead of resisting the weird, we should celebrate it as part of the incredible mystery of existence!

The conclusion that quantum mechanics is weird comes from the fact that the basic mathematical model of Quantum Mechanics QM in the form of the standard linear Schrödinger equation in multidimensional configuration space stdQM, does not describe any form of possible/thinkable physical reality. 

In other words, the stdQM Model of the World is Weird. Does it follow that the World Itself is Weird? 

Only educated physicists like Feynman would be pretentious or brave enough to say: Yes! 

An ordinary intellect/mind would say without hesitation that it is not sure that the World Itself is Weird just because a Model of the World is Weird. That there is a difference between a Model of the World and the World Itself. Ok?

An ordinary intellect/mind would probably also say that the World Itself cannot be Weird, because if is, then it would not exist. Really weird things can exist only as Fantasy not in reality. Something which is both wave and particle at the same time cannot really exist. Something which is both square and circular at the same time cannot exist. 

Ok, so the World Itself cannot really be Weird. What then to do with a Model of the World which is Weird? Can a Weird Model work? Yes, it is possible if the weirdness somehow is cancelled out. 

And Yes, it is possible to get something reasonable out of the standard Schrödinger equation stdQM, if only what is weird is cancelled out and this is what Real Quantum Mechanics RealQM does. 

RealQM is not weird since it has the form of a classical continuum mechanical model in 3d space, which is conceptually well understood. 

The nice thing with ChatGPT is that it makes it possible (for me) to have a conversation with an AI physicist in a situation where all my attempts to have a conversation with a real physicist have turned out in a weird way. Try ChatGPT yourself. It is educating and fun!

ChatGPT as AI does not suffer from the same protective prestige as a real physicist, because it has not been so programmed I guess.

Trauma of Modern Physics: The Wave Function

The root of the present crisis of modern physics can be traced back to Schrödinger's equation for a system of $N$ electrons formulated nearly 100 years ago in terms of a wave function 

• $\Psi (x,t)$ with $x=(x_1,x_2,...x_N)$ 

as a complex number depending on $N$ three dimensional (3d) coordinates $x_i$ for $i=1,..,N$ plus a time coordinate $t$, in total $3N$ spatial coordinates plus time. The Schrödinger equation specifies how $\Psi (x,t)$ changes over time starting from some given initial configuration $\Psi (x,0)$. 

This may look harmless from purely notational point of view, but the wave function is a monster from both conceptual and computational point of view, since it depends on so many spatial coordinates.  

The conceptual difficulty is to give the wave function a physical (ontic) meaning in 3d physical space, and there is no resolution in sight. Physicists have simply given up resorting to "Shut up and calculate".

The computational difficulty is that even a coarse discretisation of each coordinate into say 10 different positions makes $\Psi$ to depend on $10^{3N}$ numbers, which already for $N=10$ is beyond the capacity of any thinkable computer. In particular, the specification of the initial configuration $\Psi (x,0)$ is a daunting task. 

Since modern physics is based on Schrödinger's equation (+ relativity theory), the above difficulties have remained as the deep trauma behind the present crisis, witnessed in many books including:

• The Wave Function (eds Ney and Albert).
• Philosophy of Physics: Quantum Mechanics (Tim Maudlin)  

To get perspective on the nature of $\Psi (x,t)$ let us compare with the Monadology of Leibniz with the world seen as a collection of monads or simple substances each one with its own mind capable of forming its own (blurred) conception of the world in interaction with all other monads. 

The simple particles without mind of early atomism are here given minds capable of perception and so connect to the wave-function. The trouble with such a many-mind theory is that there is no common 3d space as basis for some ontology, only a collection of separate individual views impossible for an external observer to make sense of. 

To make progress, the standard Schrödinger equation with its hopeless wave-function must be replaced by another atomistic model which has an ontic meaning and is computable. Real Quantum Mechanics offers such a model. It may be the model Schrödinger was searching for when realising that his equation did not make sense and so in despair giving up and leaving quantum mechanics to Bohr and Heisenberg.  

Sabine: Stagnation in Physics 1924-2024

Sabine Hossenfelder has taken up the mission to expose the so called crisis in physics, or rather in her words the stagnation of fundamental physics presented in this long interview starting out

• We haven't really made any progress on the big open questions since they occurred a century ago.
• We still do not understand how Quantum Mechanics QM works.
• QM has a problem of inconsistency.

Here Sabine gives reason for the stagnation of fundamental physics ultimately based on QM as atom physics: 

• If we do not understand QM, how can we understand anything based on QM?
• QM is not understandable, because it does not make sense as a theory of physics. 
• A physical theory which does not make sense as real physics cannot be understood in a real sense. 

In this situation, there are two possibilities: 

1. QM is anyway accepted even if does not make sense. This is the current agreement by the physics community. 
2. QM is discarded (since it does not make sense).  

I have followed 2 by developing a different form of atom physics named Real Quantum Mechanics RealQM, which is fundamentally different from the accepted QM which I refer to as Standard QM or StdQM initiated by Schrödinger in 1924.

RealQM is understandable as a physical deterministic continuum mechanics model in 3 space dimensions. The reason StdQM is not understandable, is that it is a statistical model in many-dimensional configurations space without physical meaning. Compare with John Clauser.

Sabine has emerged as a very successful presenter of science, after giving up a career as fundamental physicist, since quantum gravity did not make sense, with particular mission to expose the stagnation in fundamental physics. This is admirable. What is less admirable (from my point of view) is that Sabine does not show any interest in finding some path to progress away from stagnation, such as RealQM.

Maybe this post can open to some communication.  

Science or Magic?

What is the difference between science and magic? Is there less magic and more science in our modern technological society ultimately geared by Human Intelligence HI? Let' see, with connection to recents posts. 

This years Nobel Prizes in Physics and Chemistry were given to Artificial Intelligence AI and not HI as all previous years, which can be seen as an expression of the crisis of modern theoretical physics witnessed by leading physicists in popular science media/web. 

Modern theoretical physics was born 100 years ago in the form of Quantum Mechanics QM for atomic microscopics without gravitation and Einstein's General Theory of Relativity GR for macroscopic gravitation, still today serving as foundation, although incompatible.  

Both QM and GR introduced new elements of magic into theoretical physics, in classical form carried by logic and clarity in the spirit of Leibniz and Euler, as expressed by Nobel Laureates: 

• If quantum theory is correct, it signifies the end of physics as a science. (Einstein 1921)
• If you can fathom QM without getting dizzy, you don't get it. (Bohr 1922)
• It seems clear that the present quantum mechanics is not in its final form. Some day a new quantum mechanics will be discovered ....determinism in the way that Einstein wanted. (Dirac 1933) 
• I don't like QM, and I'm sorry I ever had anything to do with it. (Schrödinger 1933)
• Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored. (Born 1954)

• It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness. (Wigner 1963)
  

• Nobody understands QM. (Feynman 1965) 
• Many people probably felt relieved when told that the world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. (Alfven 1970)
• QM is wrong. QM makes absolutely no sense.(Penrose 2020). 

Nevertheless QM is viewed to have, then apparently by magic, delivered wonders like the atomic bomb and the computer and all physicists confess to GR even if its "four dimensional curved space time" is pure magic.  

We are led to conclude that modern science ultimate based on QM + GR has very strong elements of magic. To this picture we can now add AI as something magical beyond understanding, because the computational optimisation process behind AI is too complex to be inspected and understood. 

The essence of science in a classical sense is to be understandable by HI, while magic is not understandable by HI. Understanding is important because that opens for constructive improvement/advancement, while shear magic does not.  

The crisis of modern theoretical physics can thus be seen as an expression of the difficulty of advancing science based on magic. QM and GR has not evolved since birth 100 years ago and science without advancement is dead science. 

Origin of the mystery of QM.   

QM is based on Schrödinger's Equation SE presented in 1925 for the hydrogen atom with one electron, and then formally extended to atomic systems with $N>1$ electrons, with solutions named wave functions  denoted by $\Psi$ depending on $N$ three-dimensional spatial coordinates altogether $3N$ coordinates and a time coordinate. Theoretical physicists like to speak about $\Psi$ as offering a full description of the World, unfortunately maybe way beyond the imagination of a general public. 

The mystery of QM introduced by Born, is that the wave function $\Psi$ has a meaning only as probability and not as actuality, and since physics concerns actuality the wave function lacks physical meaning. In addition it is uncomputable because computational work scales exponentially with $N$. The effect is that QM describes  physics in terms of wave functions without direct physical meaning, which in addition are uncomputable. The wave function carries information about all possibilities but no single actuality and as such is an uncomputable monster which cannot be used constructively.

In this hopeless situation, physicists compute solutions to simplified SE and adjust computations until fit with experiments. The mantra then reads that QM always gives exact agreement with observation as evidence that QM is a complete success (and as such truly magical). 

The probability interpretation of QM appeared as a necessity from a trivial formal mathematical generalisation of SE for one electron with physical meaning, into a canonical SE for many electrons without physical meaning. Non-physical formality thus dictated resort to probability instead of physical actuality, and the result was mystery beyond HI.

Is there then no hope? Yes, there is a different generalisation from one to many electrons based on physics into a deterministic model in the form of classical continuum mechanics, which we refer to as Real Quantum Mechanics RealQM. This model is understandable and computable and as such can open to advancement of fundamental science. Take a look.  

PS Note that science as magic is not the same as science fiction, which is based on physics albeit fictional.

Modern Physics = Obsession with Measurement. Why?

The previous post Newton's Mechanics Does Not Require Absolute Space and Time recalled Newton's warning to physicists in the introduction to Principia Mathematica:

• Do not confound confound real quantities themselves with their relations and vulgar measures.

Modern physics has done the opposite in both theory of relativity and quantum mechanics as its two pillars. 

Einstein focussed in his Special Theory of Relativity SR from 1905 on coordination of measurements of space and time in different inertial coordinate systems moving with constant velocity with respect to each other, using rigid rods and standard clocks as devices, and discovered entirely new phenomena of space contraction and time dilation never heard of before. 

Bohr reduced quantum mechanics to what can be measured and then faced a seemingly unsurmountable  measurement problem. 

So both Einstein and Bohr focussed on (vulgar) measures of quantities and not quantities themselves in direct negation of Newton's warning. 

Newton viewed physics to be independent of human measurements in an understanding that the Moon follows its path around the Earth even when we cannot see it. That the world/mother continues to exist even when eyes are closed, is something a child gradually discovers. 

But Bohr can only speak about things he can measure and says that anything beyond that is hidden to our perception and understanding. An electron is not in any specific state before measurement, which in fact decides the state after measurement (like spin up or down). 

How is it possible that Bohr's view is passionately embraced by modern physicists, when it is so utterly childish? Of course the world in general goes around without any human observation/measurement.

Of course a "quantities themselves" must have a meaning in the sense that this is needed to make the world evolve from an interplay of quantities, without assistance of human observers. 

The idea of quantum mechanics that atomic reality is decided by measurement originates from the fact that the very act of measurement has an impact on the state of an atom, as a form of destructive test. In macroscopic physics this effect can usually be discarded making measurement non-destructive. 

Quantum mechanics comes with another confusing element in the shape of a multi-dimensional wave function, which has no direct physical meaning, only some statistical meaning. Measuring the wave function is thus impossible and so according to Bohr we would not be able to speak of it, but this is the favourite theme of a modern physicist. 

We recall that a mathematical model describes some physics in concise terms, like Newton's Law of Gravitation studied in recent posts:

•  $\Delta\phi =\rho$,                           (NG)

where $\phi$ is gravitational potential and $\rho$ mass density. (NG) connects two quantities which are quantities themselves (potential and mass) and we can speak about these quantities without having to measure them (which can be difficult). Physical laws thus involve quantities themselves with measured quantities being secondary. 

But we can compute quantities themselves by solving equations like (NG), and so discover their nature without measurement. Computing can be seen as a form of non-destructive testing. An obsession with computing could then be productive. But the many-dimensional wave function is uncomputable.

Paraphrasing Bohr we can say that we can only speak about quantities which can be computed. 

Real Quantum Mechanics gives a new formulation of quantum mechanics in terms of quantities themselves in the form of charge densities and potentials, which are computable.  

Many-Minds Relativity gives an alternative to SR which conforms to the SI standard of meter and second.

PS The ultimate expression of obsession of measurement is the proclaimed detection of gravity waves by LIGO (Nobel Prize in Physics 2017) resulting from the most violent physical event possible (collision of two black holes) supposed to send an echo reaching Earth 1.3 billions of years later, a signal so faint that detection required an accuracy smaller than the width of a human hair over the distance from Earth to the nearest star!  

Objective of Quantum Mechanics to Predict Outcomes of Experiments?

Leading modern theoretical physicists can tell you:

• The objective of quantum mechanics is to predict outcomes of (quantum mechanical) experiments. 

You may find this a bit strange. Isn't the objective of theoretical physics to understand physical processes. In the case of quantum mechanics, that would be to understand the microscopic physics of atoms, electrons, protons, neutrons and more. But this is not possible in the case of quantum mechanics, since in the words of Richard Feynman:

• Nobody understands quantum mechanics.

So what is left is the to predict outcomes of experiments, which seems a bit like betting on a horse race. Or is the theoretical physicist simply mocking with you, to avoid further questions?

Ok, if the experiment agrees with the prediction, then you may view that as support to an idea that the theory is correct, in that specific case. But to confirm a theory by experiments requires massive experiments. It is not enough, in general, to make just one experiment and then say that the theory is correct. Maybe that experiment was very special? 

In any case this practised a lot: To confirm Einstein's General Theory of Relativity GR, it was enough with one observation of a very slight change of the apparent position of a star during the solar eclipse on May 29 in 1919 (the perihelion shift of Mercury was not a prediction). For a second confirmation, we had to wait until the LIGO gravitational wave detection at 09.51 UTC on 14 September 2015 of two ~30 solar mass black holes merging about 1.3 billion light-years from Earth. But that was also a very special case. In any case, GR is now considered to be fully confirmed by two very special/extreme (and questionable) observations. 

Similarly, the Standard Model of fundamental physics is supposed to now be fully confirmed by very special experiments at LHC completed in 2012 showing existence of the Higgs boson after a 40 year long fruitless search, as a little jump on an energy graph. 

But if the experiment does not agree with theoretical prediction, what to do? Throw the theory away because it fails on one experiment? Maybe quite reasonable if the experiment is relevant. The alternative is to modify the theory by e g some new parameter to agree with the experiment, but then the prediction aspect is missing. Of course it is also possible to modify the experiment until agreement with theory, but again without true prediction.

To fully confirm a general theory by experiments is impossible. To confirm a general theory by very special experiments, as seems to be the current standard, is not very convincing to me. 

Newton's theory of gravitation is a general theory, which is supported by a generality of  experiments/observations and contradicted by none, and can be understood from conservation principles. It can serve as the role model for all of theoretical physics.

 

If the element of understanding is missing, then theoretical science seems to reduce to fitting theory to experiment or vice versa. Is this the reason for the current crisis of fundamental physics? 

What then about GR? Again, we have a theory which is very difficult to understand. Einstein said he could not understand it, but how is it possible to formulate a theory without understanding it? Of course a modern physicists would proudly say that there are two main theories of modern physics, quantum mechanics and GR (which happen to be contradictory/incompatible), and then act as if he/she understand these theories quite well, if not in full detail, while showing no willingness to go into a discussion about specifics of the theories and referring instead to the very rich literature explaining GR written by people who really understand GR.  

It means that a modern theoretical physicist will have to struggle with general theories, which cannot be understood nor confirmed by experiments, since only very special experiments are available, if any at all.

At the same time the modern theoretical physicist must give the impression of understanding and presence of confirmation.

  

 

Does a Modern Physicist Know Classical Physics?

Is it possible that fundamental physics can be reduced to combinations of 

• Gravitation governed by Newtonian Mechanics (NM).
• Electromagnetics governed by Maxwell's equations and Coulomb's Law (EM). 

This is true for classical physics, while modern physics is commonly viewed to need other forms of fundamental physics as Special/General Relativity SR/GR and Quantum Mechanics QM. The trouble with modern physics is that GR and QM since 100 years are understood to be incompatible/contradictory with no resolution in sight, which has caused a crisis of modern physics witnessed by many leading physicists, but at the same time denied. The contradiction has driven physicists to seek resolutions on very small scales of $10^{-34}$ m of QM as String Theory, and on the very large scales of the whole Universe as GR, without progress since 50 years, both beyond any form of direct experimental confirmation, thus forms of speculation. 

Of course there were reasons perceived to step out of the NM+EM paradigm, which had worked so amazingly well for all of classical physics, at the turn to modern physics at the beginning of the 20th century. Here is where classical physics stumbled:

1. Instant action at distance in NM: (Einstein GR)
2. Irreversibility in thermodynamics (2nd Law): (Boltzmann Statistics)
3. Absence of the ultra-violet catastrophe in black-body radiation: (Planck Statistics)
4. Null result of the Michelson-Morley experiment: (Einstein SR)

1 was the classical problem left unresolved by Newton, which did not stop classical physics to boom, with 1 and 4 supposedly resolved by Einstein as GR/SR.

2 came out of observations of irreversible transfer of mechanical energy to heat energy in contradiction to the fact that the laws of NM and EM are formally reversible. Boltzmann used a big hammer to resolve this paradox in the form of statistical physics followed by Planck's statistics to explain 3: The very essence of classical physics as deterministic cause-effect physics was given up in a Faustian deal. This started the Fall of Physics. 

3 and 4 were essentially null results, which do not serve well as stepping stones to progress. 

Modern physics thus grew out from efforts to resolve 2-3 by introducing entirely new physics based on statistics taking the form of QM, and SR/GR to resolve 1 and 4.  

Once the Fall was made there was no limit to what new physics could be invented which culminated at the end of the 20th century after 100 years of free fall, with the Standard Model and String Theory beyond observation. The atomic bomb served to give theoretical physicists unlimited resources to create new physics. But the fundamental problems 1-4 were left without credible answers, with only deepened mystery.

In books and blog posts I have suggested resolutions of 1-4 within classical physics. Theoretical physicists have not shown any openness to any form of discussion. Is the reason that a modern physicist does not have to know much about classical physics/mathematics, because it has been replaced by modern physics, like the epicycles of Ptolemy? To understand if 1-4 cannot, or in fact can, be resolved within classical deterministic physics, seems to me to require solid knowledge of classical physics. Is this included in the curriculum for physics education today? Or is it primarily focussed on SR/GR and QM? 

The less you know, the more certain you can be that you are right. (Dunning-Kruger effect)

Steven Weinberg in Dreams of a Final Theory unhappy with the linearity of QM, seeking an alternative but failing:

“This theoretical failure to find a plausible alternative to quantum mechanics, even more than the precise experimental verification of linearity, suggests to me that quantum mechanics is the way it is because any small change in quantum mechanics would lead to logical absurdities. If this is true, quantum mechanics may be a permanent part of physics. Indeed, quantum mechanics may survive not merely as an approximation to a deeper truth, in the way that Newton’s theory of gravitation survives as an approximation to Einstein’s general theory of relativity, but as a precisely valid feature of the final theory.”

In the next post I will briefly indicate how 1-4 can be explained within NM+EM as if that could be the final theory.

Russian Doll Fractal Atomic Physics

Big Doll = Atom with Nucleus = Small Doll .

RealQM presents a new Schrödinger equation for atomic physics as a positive nucleus of size $10^{-15}$ m surrounded by a collection of non-overlapping electrons densities without self-repulsion of size $10^{-10}$ m, which in ground/excited states organise into shells as solution to an energy minimisation packing problem under Coulomb attraction/repulsion.

RealQM is a classical continuum model in 3 spatial dimensions describing deterministic physics, fundamentally different from standardQM in multidimensional configuration space with unclear physics as statistics.  

Similarly RealQM presents a Schrödinger equation for an atomic nucleus of size $10^{-15}$ m as a negative kernel of size $10^{-20}$ m surrounded by a collection of non-overlapping proton densities without self-repulsion of size $10^{-15}$ m organizing into shells under Coulomb attraction/repulsion.

The change of spatial scale between atom and atomic nucleus of $10^5$ is translated to binding energies with the same factor.

The basic case is represented by two possible configurations of 1 proton and 1 electron: As a H atom with proton kernel surrounded by an electron density with binding energy 13.6. eV, and as a neutron N as an electron kernel surrounded by a proton density with binding energy 0.78 MeV with a factor of about $10^5$. 

What emerges is a form of Russian Doll with an H atom as a Big Doll with nucleus as a Small Doll composed in the same way with just a switch of sign of charge. It is possible to think of even bigger dolls built in a similar way such as planet systems around a star. 

In RealQM an atomic nucleus is held together by Coulomb attraction between electron kernel and surrounding proton density thus overpowering proton repulsion, in the same way an atomic ion is held together by Coulomb attraction between proton nucleus and surrounding electron density overpowering electron repulsion. There is here no need to ad hoc introduce a strong force as in the Standard Model. 

The configuration can in principle be repeated with an even smaller doll with positive kernel of even smaller size of $10^{-25}$ m. But that is beyond observation and so it seems reasonable to search for an explanation why there are so to speak only two atomic dolls: Atom = Big Doll and atomic  nucleus = Small Doll. 

That requires that the kernel of an atomic nucleus as a negative charge of strength more than 1 is free of self-repulsion, since it has no positive kernel overpowering repulsion as in Big and Small Doll. This remains to be understood. Can two electrons be compressed to a negative charge density -2 without self-repulsion? Is this possible by some form of quantum gravity? In any case this makes two electrons fundamentally different from two protons for which there is no need of compression to +2 without self-repulsion.

A Russian Doll system as a form of fractal system describing the Universe as a repeating pattern, would thus end with a Small Doll in the form of a nucleus as a negative charge density of size $10^{-20}$ m without self-repulsion surrounded by a collection of non-overlapping proton densities organised into shells as solution to an energy minimisation packing problem. Such a nucleus would be held together by Coulomb attraction overpowering repulsion without need of the strong force of the Standard Model.  

Recall that the early Bohr model of an atom was a planetary system of electrons/planets orbiting a nucleus/Sun. In RealQM this is replaced by a stationary system of non-overlapping electron densities surrounding a nucleus as solution to an energy minimisation packing problem. Compare with Fractal Cosmology. It seems that we can find fractals on largest scales governed by gravitational attraction and smallest scales governed by Coulomb electric attraction, but not on human scales showing more complexity.  

Note that it would be sensational if nuclei show to be held together by Coulomb attraction as classic physics, rather than by a residual of a strong force between quarks as postulated in the Standard Model. 

PS1 When I ask professional physicists if in the existing literature there is something like RealQM, they do not give any answer, but tell me that standard Quantum Mechanics, whatever that is, and the Standard Model are by far the best theories about physics ever created and that they agree with all experiments to an incredible precision and so there is no reason to look at anything else, in particular nothing from a mathematician. In the next moment they tell that in fact both models have severe shortcomings, which motivate more tax payer money to new fundamental theoretical physics to be discovered by a new much bigger Large Hadron Collider.

PS2 From A Search for Exotic Higgs Decays by Burzynski: In spite of the overwhelming successes of the SM, there are several glaring issues with the SM which remain unresolved. First and foremost, there are many fundamental phenomena observed in nature that are not predicted or explained by the SM. These include gravity, the nature of dark matter, neutrino masses, and the matter-antimatter asymmetry observed in the universe, among others. Second, there are theoretical problems with the SM which imply a lack of complete understanding of underlying phenomena. Examples include the hierarchy problem and the strong CP problem.