An Impossible Task: Quantum Chemistry

Here is a prompt I gave to chatGPT:

• Is it so that chemists have been given the task by physicists to make sense of quantum physics in chemistry, a very difficult if not impossible task?

This is the answer by chatGPT, which is very interesting definitely showing intelligence rarely found in real life. Read and contemplate.

Short answer: yes—historically, chemists were effectively handed that task, and it may well be impossible in the strong sense that was implicitly expected. Let me explain carefully, without rhetoric.

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1. How the Task Was Framed (Mostly by Physicists)

A canonical statement is due to Paul Dirac, who famously wrote (1929) that the fundamental laws needed for chemistry were already known, and that the difficulty was “only” their application.

This framed the division of labor as follows:

• Physicists: discover the fundamental laws (quantum mechanics).

• Chemists: apply them to atoms, molecules, reactions, bonding.

Implicit assumption:

Chemical concepts already exist in quantum mechanics and only need to be extracted.

That assumption is now known to be false.

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2. What Chemists Actually Found

When chemists tried to “apply” quantum mechanics, they discovered something unexpected:

• Quantum mechanics gives wavefunctions and energies.

• Chemistry needs molecules, bonds, structures, reactions.

• These do not appear in the fundamental formalism.

As shown rigorously by Hans Primas and by Robert Woolley, exact quantum mechanics contains:

• no molecular structure,

• no localized bonds,

• no chemically distinguishable molecules.

So the task chemists were given was not “apply the theory,” but rather:

Invent a chemical ontology that quantum mechanics itself does not provide.

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3. Why This Task May Be Impossible (in Principle)

The impossibility is not practical but conceptual.

To succeed fully, chemists would need to:

• derive bond, structure, and molecule uniquely and invariantly

• from the exact quantum formalism

• without arbitrary approximations.

But:

• there is no bond operator,

• no structure observable,

• no unique partition of electrons or space,

• no preferred basis.

All chemically meaningful entities arise only after:

• Born–Oppenheimer separation,

• symmetry breaking,

• orbital localization,

• model-dependent idealizations.

This is why Robin Hendry argues that chemical structure is not derivable but emergent.

So if the original task was:

“Recover chemistry from quantum mechanics”

then yes—it is likely impossible, not just difficult.

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4. Why Chemists Still “Succeeded”

Chemists did succeed—but by changing the task.

Instead of deriving chemistry from physics, they:

• built powerful model frameworks (VB, MO, DFT),

• accepted approximation as constitutive,

• treated bonds and structures as pragmatic theoretical entities.

This made quantum chemistry:

• extraordinarily predictive,

• technologically indispensable,

• but not conceptually foundational.

In effect, chemists became mediators, not applicators:
they made quantum mechanics usable by adding chemistry to it, not extracting chemistry from it.

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5. Was This a Category Error from the Start?

Arguably, yes.

Physics aims to describe:

• universal, invariant, minimal ontology.

Chemistry aims to describe:

• stable, manipulable, explanatory entities at an intermediate scale.

Expecting one to directly ground the other may have been a mistake about how scientific levels relate, not a failure of chemistry.

As Eric Scerri later acknowledged:

dependence does not imply derivability.

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6. So Who Gave Whom an Impossible Job?

Not maliciously, but structurally:

• Physics claimed ontological completeness.

• Chemistry was told to “just apply it.”

• The application required creating concepts the theory does not contain.

That is why quantum chemistry feels permanently provisional:
it is asked to do ontological work with tools that are not ontological.

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7. The Clean Conclusion

Yes—in hindsight, chemists were implicitly asked to do something extraordinarily hard, and possibly impossible:

to recover chemically meaningful entities from a theory that does not contain them.

Chemists responded not by failing, but by quietly redefining success:
from conceptual derivation to predictive control.

The real mistake was not made by chemists,
but by the early belief—common in physics—that

having the fundamental laws automatically gives you the higher-level world.

H₂ showed, at the very first step, that this belief was wrong.

Quantum Chemistry: Success or Failure?

Chemistry as the science of molecules is based on Quantum Mechanics as the science of atoms forming the 250 million known molecules by chemical bonding. In other words, the theoretical/computational foundation of Chemistry is Quantum Chemistry QC, since there is no alternative.  

Let us seek an evaluation of the functionality of QC in this role. We let chatGPT collect some views (references below): 

• Quantum mechanics does not contain chemical structure or bonding in its ontology, so chemistry is not reducible to physics even in principle. (Primas 1981)
• The exact quantum‐mechanical description of matter contains no molecules or structures at all; these appear only through approximations such as the Born–Oppenheimer separation. (Woolley & Sutcliffe 2012) 
• Molecular structure is not part of the ontology of quantum mechanics and emerges only through symmetry breaking and modeling, not derivation from the fundamental theory. (Hendry 2010)
• Although chemistry depends on quantum mechanics, key chemical concepts such as bonding and periodicity cannot be derived from it, so reduction fails conceptually even if physical dependence holds. (Scerri 2007)
• Core chemical concepts like bond and structure do not correspond to entities in quantum mechanics and therefore cannot be reduced to physical descriptions. (van Brakel 2000)
• Chemical phenomena such as reactions and transformations are not definable in physical terms, showing that quantum theory predicts outcomes without providing chemical explanations. (Needham 2008)
• There is no operator or unique quantity in quantum mechanics corresponding to the chemical bond, making the bond a model-dependent construct rather than a fundamental entity. (Shaik & Hiberty 2007)
• The exact quantum‐mechanical treatment of molecules is not only computationally intractable; it is also chemically uninformative. The representations that make quantum mechanics useful in chemistry are not derived by straightforward solution of the Schrödinger equation, but by introducing approximations and conceptual structures that are not part of the fundamental theory. (Woody 2000)
• Quantum chemistry is empirically powerful but fails to conceptually ground molecules, bonds, and structure in its own ontology, so it cannot serve as a foundational explanation of chemistry despite its predictive success. (Summary by chatGPT)

What can we learn from this? That QC is a success as theoretical/computational foundation of Chemistry? Is it possible to twist the above statements indicating failure, into success? After all, QC takes massive super-computer resources. 

In this situation of apparent failure, RealQM offers an alternative foundation with theory directly translated to computer code with linear complexity, see this article submitted to Foundations of Chemistry.

Here is a comment to the post by chatGPT:

• This gets to a real weakness of quantum chemistry: the exact Schrödinger equation does not actually produce molecules, bonds, or reactions in any chemically meaningful way. All the structure chemists care about only appears after imposing strong approximations (Born–Oppenheimer, orbitals, potential surfaces, damping, etc.) that are not part of the fundamental theory. As Andrea Woody and others have argued, the exact quantum description is not just intractable but chemically uninformative. In that sense, quantum chemistry “works” only by departing from the very framework it is supposed to be based on.

Here is what chatGPT delivers when asked to defend against the above views:

• The criticism confuses foundational purity with scientific success. It’s true that the bare Schrödinger equation does not hand us bonds, orbitals, or reaction pathways in closed form—but no physical theory does that for complex systems without modeling, idealization, and coarse-graining. What matters is whether those approximations are physically grounded and empirically reliable. In quantum chemistry they are: from Hartree–Fock and post-HF to DFT and ab initio dynamics, the framework routinely predicts structures, spectra, reaction energies, and mechanisms with quantitative accuracy verified against experiment. That is not a philosophical afterthought—it is the core of how modern chemistry, materials science, and drug design actually work. So quantum chemistry does not “fail”; it succeeds precisely because it shows how rich chemical behavior emerges from quantum laws when treated with disciplined, testable approximations.

Your choice? Note that even in defence mode is it acknowledged that bonds and reaction pathways of prime interest, are not handed. 

I then ask if Philosophy of Chemistry PC can resolve the opposing views of critique and defence and get this response: 

• Philosophy of chemistry does not “fix” the disagreement by choosing a winner, but by showing that the two views use different standards of success. The critics are right that chemistry is not strictly reducible to the bare Schrödinger equation: chemical concepts, structures, and reactions are not derivable without strong approximations and representational choices. But defenders are equally right that quantum chemistry is an extraordinary scientific success, because those approximations are physically motivated, systematically improvable, and empirically validated.

• Philosophy of chemistry resolves the apparent contradiction by reframing it: quantum chemistry fails as a literal, foundational reduction, yet succeeds as an effective, unifying, and predictive theory. What it cannot do—and should not try to do—is eliminate the need for modeling, idealization, and emergence in complex systems. The tension is not a flaw in chemistry, but a feature of how science actually connects fundamental laws to higher-level phenomena.

It seems that the role of PC is to make the devastating critique acceptable into a business as usual. In politics the ruling party can claim complete success even under heavy criticism from the opposition, but the general public has the chance to make a verdict in the next election. 

But in science there is no general public and so the ruling paradigm can resist very strong criticism, until something happens...remember phlogistons...corpuscular theory of light...

References: 

• Primas, H. (1981). Chemistry, Quantum Mechanics and Reductionism. Springer.
• Sutcliffe, B. T., & Woolley, R. G. (2012). “On the quantum theory of molecules.” Journal of Chemical Physics, 137, 22A544.
• Hendry, R. F. (2010). “Molecular structure and the philosophy of chemistry.” In Philosophy of Chemistry (Scerri & McIntyre, eds.).
• Scerri, E. R. (2007). The Periodic Table: Its Story and Its Significance. Oxford University Press.
• van Brakel, J. (2000). The Philosophy of Chemistry. Leuven University Press.
• Needham, P. (2008). “What is the problem with reduction?” Studies in History and Philosophy of Modern Physics, 39(4), 763–776.
• Shaik, S., & Hiberty, P. C. (2007). A Chemist’s Guide to Valence Bond Theory. Wiley.
• Woody, A, (2000). Putting Quantum Mechanics to Work in Chemistry: The Power of Diagrammatic Representation, Philosophy of Science 67.

Why Is Chemical Bonding Still a Mystery?

Chemistry is formed by chemical bonding of atoms into molecules, but the physical nature of a chemical bond appears to be unknown even today 100 years after Quantum Mechanics was formed as the physics of atoms and molecules:

• There is no unique way of defining a chemical bond from quantum mechanics. (Roald Hoffmann)
• 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)
• 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)
• Exact quantum dynamics would still not yield chemical concepts such as mechanisms, bonds, or reaction pathways. (William H. Miller)

The lack of a single convincing theoretical explanation of the physics of chemical bonding, questions the credibility of Chemistry as a science, which is met by (instead of one correct theory) a battery of different explanations including Lewis, VB, MO, CFT, LFT, Band Theory, Quantum Chemistry (HF/DFT), supposed to capture different aspects while partly being contradictory.

But in this rather desperate situation of confusion there may be hope the form of  

• Alternative Computational Foundation of Chemistry 

offering an analysis of covalent chemical bond based on a new form of Schrödinger's equation in physical space with clear physical meaning. If you have ever wondered why one neutral Hydrogen atom $H$ can attract another neutral H to form a $H_2$ molecule as a stable relation, this is for you.

Is is natural to trace the unclear physics of covalent chemical bonding back to the lack of clear physics of Schrödinger's equation in its textbook form. Chemical bonding must rely on clear physics to work, and so cannot be explained by unclear physics. 

Chemistry is real physics and cannot rely on a Schrödinger equation without meaning as real physics. RealQM offers a new Schrödinger equation as real physics, and thus a new foundation of chemistry.

 

Why Philosophy of Physics?

Philosophy of Physics today is largely Philosophy of Quantum Mechanics PQM struggling to give meaning to a QM formed 100 years ago by physicists as modern physics without clear physical meaning. 

PQM then has the double role of (i) cover up lack of meaning and (ii) expose lack of meaning. In either case PQM has a difficult task, which rarely can be pursued at a physics department and so may rather be part of a department of philosophy without physics. Here (ii) invites the critical mind to easy catches, while (i) to be successful requires clever argumentation. 

In both cases the real problem of finding a form of QM with physical meaning is left aside and no progress will take place. The result is that none of the questions about the physical meaning of Schrödinger's equation, formulated in 1926 and still serving as the basis of QM, has been given an answer accepted by the physics community. 

Here RealQM may have something meaningful to offer as a mathematical model of the form of continuum mechanics in physical 3d space with clear ontology. If indeed RealQM does show to function as a physical model of atoms and molecules, then PQM will face a new situation without need to take care of (i)+(ii), and so will have to find a new role, maybe as a challenge to philosophers. 

Leibniz's PII vs RealQM vs StdQM

Leibniz's Principle of the Identity of Indiscernibles PII clashes with the basic idea of identical particles of textbook StdQM: If the electrons of a molecule are identical, that is indiscernible, then they would according to Leibniz be identical and so there would be only one electron present, maybe then in the form of a super-electron distributed over the molecule? 

Leibniz today would object to the idea of identical electrons of StdQM, and so would welcome RealQM where electrons have identity/individuality by occupying separate regions in space with continuity in time. 

Electron individuality has a special role in RealQM with Coulomb repulsion present only between charge densities of different electrons, not within individual charge densities. 

But without individuality, lack of self-repulsion cannot be safely built in, which means that in StdQM self-repulsion has to be actively removed as exchange, which presents a major difficulty.

Recall that the electronic wave-functions of StdQM are required to be anti-symmetric,  that is change sign under swapping of electron labels, while labelling of identical electrons appears as strange as well as sign change without reason. 

Why Philosophy of Chemistry?

This is a comment to the previous post on submission of a RealQM article to Foundations of Chemistry edited by Eric Scerri founder of the 21st century discipline Philosophy of Chemistry. 

What can be the role of a philosophy of chemistry? Why was it formed only recently? To seek answers we ask chatGPT to take on both a defensive and a critical attitude and ask about the role of Quantum Mechanics QM as foundation of chemistry, to get the following condensed answer:

Defense (QM as a strong foundation)

Quantum mechanics is the fundamental theory governing electrons and nuclei, so all chemical phenomena ultimately arise from it. Atoms, bonds, spectra, and periodic trends are, in principle, consequences of quantum laws. Chemical concepts (orbitals, bonds, valence) are higher-level descriptions of underlying quantum reality. Quantum chemistry shows that structures, energies, and reactions can be derived from first principles, even if approximations are needed in practice. Thus, chemistry is autonomous in use but reducible in principle to QM.

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Critique (QM as a limited foundation)

Quantum mechanics constrains what is physically possible, but it does not supply the concepts chemistry depends on. Molecular structure, bonds, functional groups, and mechanisms are not contained in the fundamental equations and must be imposed through approximations and conventions. QM provides calculations, not chemical explanations; multiple quantum descriptions can map onto the same “structure,” showing underdetermination. Quantum chemistry relies on chemical input and interpretation rather than replacing chemical reasoning. Thus, QM is necessary but not sufficient: chemistry remains conceptually and explanatorily autonomous.

 New prompt: Is the role of philosophy of chemistry to handle the contradiction between the two statements?

chatGPT: The philosophy of chemistry addresses the apparent contradiction by clarifying what “based on” means. It distinguishes physical dependence from theoretical reduction and explanatory grounding, showing that chemistry can obey quantum laws without being conceptually derived from them. It analyzes reduction versus emergence, evaluates what counts as explanation, and studies actual scientific practice in quantum chemistry and laboratory work. In doing so, it reframes the conflict: quantum mechanics underwrites chemistry at the physical level, while chemistry retains autonomy in its concepts and explanations.

Summary: We find that a main role of Philosophy of Chemistry is to handle two contradictory views on the functionality of QM as foundation of chemistry. RealQM appears to offer a new foundation with new functionality, where there is no contradiction, and if successful will reduce the need of philosophy to reconcile contradictions.

 

First Submission of RealQM Article

The first of a series of articles about RealQM has been submitted to Foundations of Chemistry with here an updated version:

• Alternative Computational Foundation of Chemistry    (download to get active hyperlinks)

A basic idea is to view formation of a molecule as a form of dynamic analog computation seeking balance of physical forces which can be simulated by digital computation in a new Schrödinger equation with linear computational complexity of the form of classical multi-phase continuum mechanics. This offers a foundation of chemistry as computational mathematical physics.  

RealQM is to be compared with textbook QM based on a multi-dimensional Schrödinger equation with exponential computational complexity. 

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.

Mathematical Foundation of Chemistry?

Let us start the 2026 Anniversary Year of Schrödinger's equation by asking about the role of Mathematics in Chemistry.  

August Comte in his Cours de Philosophie Positive (1830-42) stated

• All attempts to bring chemical questions into the domain of mathematics must be regarded as profoundly irrational, and antipathetic to the nature of these phenomena. 

This cannot be true today, right? Mathematical physicists like Dirac already 90 years ago claimed that chemistry is only a branch of applied atomic physics, which is fully described by Schrödinger/Dirac's differential equation as the mathematical model of textbook Standard Quantum Mechanics StdQM, with the only little caveat that analytical solutions are unknown and numerical solutions are only available in drastically simplified form.  

The result is that physicists today say that chemistry is explained by StdQM, in principle, while chemists facing reality see that chemical bonding is not well explained, because it is not within the scope of StdQM as being restricted to energies leaving out forces. 

If you want to find some hope as a chemist or layman, take a look at this new article:    

• Alternative Computational Foundation of Chemistry

where computational mathematics and real physics are seen to merge into explanations. 

Comment by chatGPT on prompt: Give comment to this text:

This article presents an ambitious and provocative proposal—RealQM—as an alternative computational and conceptual foundation for quantum chemistry. Its central idea, modeling electrons as non-overlapping charge densities in real three-dimensional space with a free-boundary formulation, is original and intellectually stimulating. The work stands out for its explicit dissatisfaction with the interpretational and computational burdens of Standard Quantum Mechanics (StdQM) and for attempting to restore locality, physical intuition, and linear computational scaling.

Strengths and contributions

1. Clear ontological stance
   The paper adopts a consistently realist ontology, treating electron densities as physical objects rather than probabilistic constructs. This addresses a long-standing discomfort many chemists and physicists have with the configuration-space formalism of StdQM and aligns with Schrödinger’s original intuitions.

2. Computational motivation
   The emphasis on linear scaling with the number of electrons and the reduction to a “three-line code” is compelling. If robust, this would represent a genuine breakthrough for ab initio simulations, particularly for large systems where StdQM-based methods require severe approximations.

3. Unified continuum framework
   Casting atomic and molecular structure as a multi-phase continuum mechanics problem with free boundaries is mathematically elegant and conceptually coherent. The analogy with classical variational principles and gradient flows is one of the paper’s strongest aspects.

4. Concrete demonstrations
   The article goes beyond philosophical critique by presenting numerical results for atoms, molecules, shell structure, bonding, and even speculative nuclear models. This breadth is unusual and commendable.

Points requiring clarification or strengthening

1. Status of non-overlap and exclusion
   The assumption of non-overlapping electron densities replaces Pauli exclusion, antisymmetry, and spin with geometric separation. While this is internally consistent, the paper would benefit from a clearer argument explaining why non-overlap is physically justified rather than merely effective. At present, it risks being perceived as a built-in constraint that substitutes, rather than explains, fermionic behavior.

2. Empirical scope and validation
   Agreement with selected ground-state energies is encouraging, but chemistry is ultimately judged by predictive power across a wide range of observables: excitation spectra, reaction barriers, response properties, magnetic effects, and spin-dependent phenomena. The absence of spin, exchange, and correlation needs to be addressed not only philosophically but also empirically.

3. Excited states and spectroscopy
   The discussion of excited states and radiation via beat frequencies is intriguing, but it remains qualitative. It is unclear whether RealQM can systematically reproduce selection rules, fine structure, or multiplet splittings that are central to atomic and molecular spectroscopy.

4. Free-boundary dynamics and uniqueness
   The Bernoulli free-boundary formulation is central to the theory, yet questions of uniqueness, stability, and convergence of the boundary evolution are largely unaddressed. These issues are critical if RealQM is to be regarded as a well-posed physical theory rather than a numerical construction.

5. Polemic tone
   While the historical critique of StdQM is understandable, the repeated framing in terms of “brainwashing” and “non-physics” may alienate readers who would otherwise engage seriously with the model. A more neutral tone would strengthen the paper’s reception in the broader community.

Overall assessment

The article is bold, unconventional, and intellectually rich. It challenges deeply entrenched assumptions in quantum chemistry and offers a coherent alternative grounded in real-space physics and computability. Whether RealQM can ultimately replace or complement StdQM remains an open question, but the work deserves careful scrutiny rather than dismissal. At minimum, it functions as a valuable thought experiment that forces reconsideration of what is essential—and what may be contingent—in the quantum-mechanical description of chemistry.

If developed further with clearer empirical benchmarks, mathematical analysis of the free-boundary problem, and a more systematic treatment of excited-state phenomena, RealQM could stimulate productive debate well beyond its immediate claims.

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?