RealQM as Foundation of Chemistry?

To make a discussion if RealQM can serve as a foundation of chemistry meaningful, it may be helpful to consider to what extent StdQM fills this role. 

chatGPT says: 

• Standard QM serves as a constraint and calibration framework for chemistry, but it does not serve as its constructive or explanatory foundation.
• That is the maximal defensible claim — anything stronger is false, anything weaker ignores real successes.

We get a clear message from reading all of the literature, which is expanded below, that StdQM does not serve as theoretical foundation of chemistry. 

RealQM offers such a foundation which is now under review for publication in Foundations of Chemistry.

It is possible that RealQM can deliver theoretical support for heuristic rules developed to explain chemical bonding such as in particular Valence Bond VO.

 

Since StdQM apparently does not serve as foundation, hopefully the review can focus on what RealQM can deliver rather than merits of StdQM after 100 years of investigation.

  

chatGPT:

Let’s be explicit about what “foundation” could mean, and which meanings QM satisfies.

---

1. QM as a foundational constraint (YES)

Standard QM does function as a foundation in this limited but important sense:

• It constrains what kinds of matter are possible

• It explains stability of atoms

• It fixes energy scales

• It enforces Pauli exclusion

• It explains periodicity trends

• It provides quantization of spectra

In short:

QM defines the admissible physical regime in which chemistry can exist.

Without QM:

• atoms collapse,

• the periodic table disappears,

• chemistry does not get off the ground.

In this sense, QM is a background foundation, like relativity is for GPS.

---

2. QM as a numerical foundation (PARTIALLY)

QM is also foundational in a computational sense:

• It supplies energies, forces, and spectra

• It constrains models

• It calibrates effective theories

• It bounds errors

But this role is conditional:

• exact for very small systems

• approximate and empirical for real chemistry

• dependent on modeling choices

• reliant on cancellations

So QM is not the numerical foundation, but a reference standard.

---

3. QM as a constructive foundation (NO)

This is where the claim fails.

Standard QM does not:

• define molecules as physical entities

• derive molecular structure

• produce bonds as objects

• explain localization

• generate chemistry from axioms

Instead, chemistry must assume:

• molecular structure,

• nuclear localization,

• effective forces,

• stable bonds,

and then use QM after the fact to evaluate energies and spectra.

So QM does not construct chemistry.

---

4. QM as an explanatory foundation (NO)

Standard QM also fails as a foundation in the explanatory sense:

• It does not explain what a bond is

• It does not explain why molecules have shape

• It does not explain chemical functionality

• It does not explain reaction mechanisms as physical processes in space and time

What it explains instead are:

• allowed energies

• transition probabilities

• selection rules

Explanation of chemistry remains structural, effective, and model-based.

---

5. The clean verdict (no compromise language)

Here is the precise statement that survives scrutiny:

Standard QM is a necessary but not sufficient foundation of chemistry.

Or more sharply:

Standard QM underwrites chemistry but does not ground it.

Or sharpest of all:

Chemistry is not applied quantum mechanics; it is an autonomous physical science constrained by quantum mechanics.

---

6. Why this matters (and why the confusion persisted)

The confusion arose because:

• QM is spectacularly successful numerically

• energies were mistaken for explanations

• “foundation” was redefined as “not contradicted by”

• emergence was used as a placeholder for derivation

Once those moves are undone, the picture becomes coherent:

• QM keeps its genuine achievements

• Chemistry keeps its autonomy

• No magic is required

• No false reductionism is needed

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Final answer (one sentence)

Standard quantum mechanics serves as a limiting, constraining, and calibrating framework for chemistry — but it does not serve as its constructive or explanatory foundation.

That is the honest, stable equilibrium position.

Quantum Chemistry: State of the Art?

As a preparation for the upcoming launch of RealQM I ask chatGPT to summarise the state of the art of quantum chemistry as the essence of theoretical chemistry based on atom physics with key question: 

• Does textbook StdQM form a foundation of chemistry as the physics of molecules formed by chemically bonded atoms?

Does chatGPT give a fair correct assessment? chatGPT reports what is in the literature, but maybe not very explicitly. What would be the reaction from physicists vs chemists? The exponential computational complexity is not brought up, which requires drastic simplifications changing physics and numbers with effects difficult to quantify. 

chatGPT:

What StdQM does deliver (for atoms and molecules)

1. Well-defined mathematical models

StdQM provides:

• A many-body Schrödinger Hamiltonian for electrons and nuclei

• A mathematically precise spectral problem

• Conditions for self-adjointness, stability, and boundedness from below

This means:

The quantum model exists and is internally consistent.

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2. Atomic bound states and spectra

For atoms, StdQM delivers:

• Existence of discrete energy levels

• Correct qualitative and quantitative spectra

• Ionization thresholds and resonances

This is StdQM at its strongest:

Atoms are genuine quantum systems.

---

3. Total energies (in principle)

StdQM determines:

• Ground-state energies

• Excitation energies

• Reaction energies (as differences)

These are global scalar quantities, accessible without spatial interpretation.

---

4. Scattering and asymptotic processes

StdQM describes:

• Scattering cross sections

• Dissociation limits

• Long-time asymptotic behavior

Here again, the output is primarily spectral or asymptotic.

---

5. Justification of approximations

StdQM can:

• Justify Born–Oppenheimer separation in asymptotic limits

• Explain why reduced models work

• Provide error estimates for approximations

Importantly:

StdQM explains why chemists’ models work, not what they mean physically.

---

What StdQM does not deliver

6. Molecular structure

StdQM does not deliver:

• A theorem guaranteeing stable molecular geometry

• Unique equilibrium bond lengths or angles

• Classical molecular shape as a direct consequence of the wave function

Structure enters only via:

• Classical nuclei

• Potential energy surfaces

• Symmetry breaking assumptions

---

7. Chemical bonds

StdQM does not provide:

• A bond operator

• A unique definition of “bond”

• An intrinsic quantum observable corresponding to bonding

Bonds are interpretive constructs, not quantum objects.

---

8. Localization of electrons

StdQM does not deliver:

• Pointwise electron positions

• Intrinsic electron localization

• Distinct electrons occupying definite regions

Localization requires:

• Measurement postulates

• Classical limits

• Additional modeling choices

---

9. Chemical identity

StdQM does not explain:

• Why molecules have persistent identity

• Why functional groups behave similarly across contexts

• Why chemistry is robust under perturbations

These are structural and dynamical facts, not spectral ones.

---

10. Reaction mechanisms

StdQM does not deliver:

• Reaction pathways as physical processes

• Transition states as real entities

• Time-resolved chemical change

Mechanisms are reconstructed from:

• Energy surfaces

• Classical trajectories

• Human interpretation

---

One-sentence summary

Standard quantum mechanics delivers energies, spectra, and asymptotic behavior for atoms and molecules, but it does not deliver molecular structure, bonding, or chemical processes as intrinsic physical facts.

Or, even more compact: StdQM

• predicts numbers; chemistry needs objects,
• is a powerful evaluative tool for chemistry,
• is not a constructive foundation of chemistry,
• can verify chemical models, but it does not create them. 
• is a qualified success in physics, but a failure as a foundation of chemistry. 
•  does not provide is a constructive procedure that starts from its axioms and ends with: molecule, bond, shape, reaction.

If the goal is to “Construct chemistry from first principles” then StdQM fails:

• Molecules are not constructed, only assumed.

• Structure is input, not derived.

• Bonds, shapes, and mechanisms are not quantum objects.

• Classical physics is silently reintroduced to make chemistry possible.

So as a reductionist program —chemistry = applied quantum mechanics —StdQM does not succeed.

 

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

Chemical Bonding: StdQM vs RealQM

The basic problem of chemistry is how molecules as stable composites are formed through chemical bonding between collections of atoms consisting of positively charged nuclei surrounded by negatively charged electrons. The total energy $TE$ of a stable molecule is smaller than the sum of the energies of the atoms involved, with $TE$ the sum of 

• electron-nucleus potential energy $E_{en}$ negative
• electron-electron potential energy $E_{ee}$ positive
• nucleus-nucleus potential energy $E_{nn}$  positive
• electron kinetic energy $E_{ke}$ positive.

Standard Quantum Mechanics StdQM seeks to explains chemical bonding as an effect of: 

1. Localisation of electrons between nuclei giving maximal decrease of $E_{en}$.
2. Delocalisation of electrons over the whole molecule compensating for increases of $E_{ke}$ from localisation.  

We see a combined process of localisation-delocalisation, which is contradictory and requires intricate explanation to make sense forming a vast literature. The need of 2 in StdQM comes from the fact that electron wave functions have global support with a smooth approach to zero which makes $E_{ke}$ scale as $\frac{1}{d^2}$ with $d$ effective width of support, which means that potential energy decrease from localisation is countered by kinetic energy increase. 

In RealQM as an alternative to StdQM electron wave functions have non-overlapping local supports meeting with continuity without need of approaching zero. This means that localisation in RealQM does not come with increase in electron kinetic energy, and so can serve as an explanation of total energy minimisation from 1 alone without need of contradictory 2. For details see these articles.

Connecting to the previous post, recall that the main role of the Periodic Table is to support understanding of chemical bonding.

Can QM explain the Periodic Table?

Chemist Eric Scerri as world authority on the Periodic Table asks in the article Can Quantum Ideas Explain Chemistry's Greatest Icon? (Nature 2019): 

• Does Quantum Mechanics QM explain the Periodic Table PT?  

Scerri recalls that Swedish chemist Löwdin in 1969 presented this as one of chemistry's major theoretical challenges, and adds that it still is. 

To non-expert readers of Nature and also the general public this may sound a bit surprising, since QM in its standard form stdQM based on a linear multi-dimensional Schrödinger Equation SE is viewed as the fundamental mathematical model of modern physics describing in particular the electron configurations of all atoms as the basis of PT. 

But Scerri and Löwdin say that stdQM only gives a partial explanation of PT with a lot missing. Whatever real truth PT may carry, stdQM does not seem to reveal the physics behind, at least in the eye of a chemist. But a physicist would without hesitation say that PT is well explained by stdQM, at least in principle, and that it is the job of chemists to supply the petty details. 

This state of affairs has added to the crisis of modern physics, which largely is a credibility crisis. If stdQM cannot explain such a simple thing as the electron configuration of atoms in ground state, as the basis for all of chemistry, something must be seriously wrong, but what?

One answer may be that solutions to SE denoted by $\Psi$ and named wave functions and supposed to carry all information about the electron configuration of an atom, does not have a direct interpretation in physical terms because of its multi-dimensionality, and so only a vague statistical interpretation is possible. Moreover, computational work to compute wave functions scale exponentially in number of electrons and so SE requires drastic dimensional reduction to be computable with further loss of real physics. The result is that stdQM cannot compute electron configurations without hands-on expert knowledge without theory. It is not surprising that under these conditions it fails to explain PT. 

Real Quantum Mechanics RealQM is based on a different form of Schrödinger's equation, which has a clear physical meaning with an atomic electron configuration described as a set of non-overlapping one-electron charge densities, for which computational work scales linearly with number of electrons. RealQM directly extends to molecules as Real Quantum Chemistry described in these articles. 

It seems possible that RealQM can give a better explanation of PT than stdQM, and maybe even correct PT in some details, because it has direct physical meaning and computation is affordable for all atoms.  

StdQM seeks to explain the electron configuration of an atom with many electrons in terms of the excited states of the Hydrogen atom with just one electron filling s, p, d shells. To make this Aufbau Principle fit with observation various ad hoc rules have been adopted attributed to e g Madelung and Hund. The resulting explanation does not appear to be fully convincing to chemists like Scerri and Löwdin. Something appears to be missing...

RealQM explains the electron configuration in a different way as an electron packing problem, which has a clear physical meaning and so at least has the potential to offer an explanation of PT on physical grounds or suggest corrections. Preliminary studies show promise and further studies are on the way. 

 

Why No Unified Atom-Nucleus Model?

The previous post presented RealQM = RealAtom + RealNucleus appearing to be the first computable unified model of an atom including nucleus with full quantum mechanical representation in the form of non-overlapping charge densities of both electrons and protons interacting by Coulomb potentials. 

Is this really the first full quantum mechanical model of an atom + nucleus? What have theoretical physicists been doing during the 100 years since the advent of quantum mechanics in 1925? 

Yes, at least according to chatGPT, telling that there is QED for atoms = electrons+point-wise nuclei and QCD for nuclei = quarks and gluons, but QED and QCD represent different "sectors" and cannot be unified:

• There is currently no fully computable, unified quantum mechanical model of an , "atom that includes both the electrons and the atomic nucleus in full quantum detail and that is tractable for general-purpose computation.

How can this be? Is this the concrete meaning of the "crisis of modern physics" proclaimed by leading theoretical physicists? Is it a consequence of all the unresolved contradictions present in the mathematical foundations of quantum mechanics including "wave-particle duality", "complementary principle", "collapse of the wave function", "measurement problem", "statistical interpretation", "uncertainty principle", "exclusion principle", "anti-symmetry", "Born rule", "exchange energy", "indistinguishability of identical particles", "electron orbitals", "superposition", "entanglement", "decoherence", "spin-orbit coupling" + all the wonders of QCD…? 

When I ask if the lack of a unified atom-nucleus model is a sign of failure/crisis of modern physics, chatGPT explains:

• The lack of a unified, computable atomic-nuclear theory is not a failure — it's a reflection of the extraordinary success and specialization of the theories we already have (QED and QCD).  

This is the tragedy of modern physics: Too successful to fail. Like a Big Bank or Great Empire. If you find chatGPT's argument convincing, you have a position at a department of fundamental physics (about to collapse from missing unified theory).

Does Quantum Mechanics Explain Chemistry?

There is an extensive literature seeking to come to grips with the following Question: Is chemistry explained by the physics of the Schrödinger Equation SE as basis of Quantum Mechanics QM? Physicists in general claim that this is so, without supplying much detail of any QM explanation, while chemists wanting to see the details in general resort to their own explanations with only vague connection to QM. 

The basic trouble is that solutions to SE are uncomputable for multi-electron molecules and so cannot be inspected to reveal the physics of chemical bonding as the central aspect of the Question. What is available are other equations supposedly motivated by SE for which solutions can be omputed, but then with unclear status as approximate solutions to SE. In practice this works to accept approximate solutions which fit with observation and reject those who do not. This can result in ad hoc fitting of model to data missing the predictive first principle power of SE, then taken for granted. 

Here is an illuminating discussion with chatGPT showing how the scientific community grapples with the Question.

My own grapple has resulted in RealQM as Real Quantum Chemistry. 

    

RealQM for Nucleus

Here is a new article in the series on RealQM: 

• RealQM: Nucleus

The idea is to view an atomic nucleus to be composed in the same way as an atom with a switch of roles between electron and proton, thus with a collection of protons as charge densities around a pointlike negative charge. Such a nucleus is held together by Coulomb attraction from the negative charge overcoming Coulomb repulsion between protons. 

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? 

RealQM: Helium and Orthohelium

Here is a new article about RealQM:

• Helium and Orthohelium

added to a list of articles.

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.

 

RealQM: Shell Structure and Periodic Table

Here is a next article in the series on RealQM posted in recent posts:

• RealQM: Shell Structure and Periodic Table

World expert on the Periodic Table Eric Scerri has investigated to what extent the Periodic Table can be explained by StdQM and seems to say that there are pieces missing in this puzzle. The article gives a first hint into explanations based on RealQM to be complemented with more details.

 

RealQM: First Molecule

 Here is a new article in a series about RealQM

• RealQM: First Molecule He+H

The article presents a RealQM simulation of the formation from a Helium atom He and a proton H+ the molecule He+H  from a transfer of one electron from He to H+ thus combing He+ and H into the first molecule formed after Big Bang, from which H could form from dissociation of He+H. Altogether a process to form H from He with He by its stronger kernel attraction forming before H in a sea of electrons.  

RealQM models this process as endothermic requiring input of energy (from Big Bang) to position H+ close to He with the distance determined so as to arrive at a ground state energy of He+H lower than -2.500 Hartree allowing He+H to dissociate into He+ of energy -2.000 and H of -0.5. 

StdQM gives a different perspective with instead a molecule HeH+ formed in a weakly exothermic reaction with a He atom incorporating a H+ proton. 

He+H can thus serve as a test of validity of StdQM vs RealQM since they give radically different messages.

Download article and open in Acrobat to get active hyperlinks.

See also earlier post1 and post2.

Quantum Mechanics All Wrong

In the above interview of Tim Maudlin by Brian Green we hear a message that Quantum Mechanics QM  is filled with mysteries and paradoxes. That QM does not make sense. We also hear that despite this undeniable fact, QM is a theory about atomic physics with a wave function describing in principle everything that can be known about a world built from atoms although the connection between the wave function and the real world is hidden to inspection by humans. So we've gotten a lot wrong a lot about QM but Maudlin gives no hint to a more correct theory. This is a report about a theory in stagnation since 100 years. As a possible way out of stagnation take a look at RealQM.

Weak Reactivity of Gold by RealQM

 Here is a new article to the series about RealQM as an alternative to StdQM:

• Real Quantum Mechanics: Weak Reactivity of Gold

RealQM explains why Au with electron shell configuration 2+8+18+32+18+1 with 1 valence electron in a last shell outside a sphere of radius R containing all other shells, does not form a molecule Au2 by covalent bonding as a geometric effect of large R preventing electron accumulation between kernels.

RealQM explains covalent bonding of H into H2 and non-bonding of He2 in this earlier article in the series:

• Real Quantum Mechanics: Covalent Bonding. 

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Computational vs Theoretical Mathematics in Physics

The mathematical models of physics take the form of partial differential equations like Euler's Equations for incompressible inviscid fluid flow EE, corresponding Navier-Stokes equation for viscous flow NSE and Schrödinger's equations for atoms and molecules SE. 

The task of a theoretical mathematician has been to prove by symbolic analytical techniques (i) existence, (ii) uniqueness and (ii) regularity of solutions to a given equation with data given in some large class of possible data with data including initial data, forcing and parameters like viscosity in NSE. 

The task of a computational mathematician has been to compute solutions for specific choices of data which in each specific case can answer (i)-(iii) by inspection of the computed solution. 

It has been argued that computation is not enough, even if for each specific choice of data (i)-(iii) can be answered, because only a limited number of specific choices can be inspected. The possibly very large class of data can thus never be exhausted by computation, which gives analytical symbolic mathematics a role to play by covering a large class of data.

It is natural to ask if there are examples of equations for which the class of relevant data is so small that it can be exhausted by computation. This means first that the equation cannot contain any parameter like viscosity. Are there any models of interest which are parameter free? Inspection of EE and SE shows that they are both parameter free, and so meet the requirement of Einstein of an ideal mathematical model opening to say something about the world without measuring anything. This is like learning the area of a circular disc by computation with unit radius as only input.

Solving EE computationally thus delivers the drag of a body moving through a slightly viscous fluid such as air and water at a subsonic speed with the only data being the shape of the body and not any viscosity as parameter. This limits the class of data to shapes of bodies with a limited range of shapes of interest to be covered by computation. This is all described here.

The case of SE is in its traditional form of Standard Quantum Mechanics StdQM troubled by the fact SE by its multi-dimension nature is uncomputable and so needs dimensional compression which introduces parameters. 

RealQM is different realisation of the same parameter-free Hamiltonian as StdQM into computable form without introduction of any parameter. RealQM thus expresses SE in parameter-free computable form and so opens the possibility of saying something about the atomic world without experimental input. RealQM thus computes the ground state of an atom with the only input being the number of electrons and so can exhaust the Periodic Table.      

An analytical estimate of ground state energy as the result of a longer or shorter sequence of successive bounds, can be seen as a form of symbolic computation, while a numerical computation can be seen as very long arithmetic proof.

Computation with a parameter-free mathematical model can produce a rich set of outputs from very limited structural input, which can serve as data for AI in need of rich data. Computation is then used both to produce data and to learn from data. Symbolic mathematics has an important role to set up computation.

The Clay Institute Millennium Problem on (i)-(iii) for NSE is still open in the form of symbolic mathematics with no progress reported over 25 years. Can computation get the million dollar Prize?

Covalent Bonding by RealQM

Here is the next article in a sequence of articles exhibiting the capabilities of RealQM as an alternative to StdQM as the canon of modern physics: 

• RealQM: Covalent Bonding

with earlier articles in recent posts. Download article and open in Acrobat to get hyperlinks to essential codes to run, inspect and modify.

Shut up and Calculate vs Compute, Learn and Speak

Here is a reflection connecting to the previous post on RealQM as a computable model of atoms and molecules and Mearmin's Shut up and Calculate desperate reaction to the difficulty of making sense of the theory of Standard Quantum Mechanics StdQM. 

Let us recall the following views on the divide between StdQM as the theoretical foundation of chemistry according to physicists and the theoretical chemistry actually used by chemists. 

Eberhardt 2012:

• Chemistry is a discipline of two faces, one applied and the other theoretical. The applied face focuses on the design and synthesis of molecules and solids, while the theoretical face looks for explanations of a molecule or solid’s properties.

Bader 2011:

• ....the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or bent to suit preconceived ideas.

Dirac 1929:

• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

Dirac identifies the root cause of the divide as the impossibility of solving Schrödinger's equation of StdQM for the complex atomic systems of chemistry. If computational solution was possible there would be no divide and the whole of chemistry would be like an open book to read by computation. 

RealQM is an alternative to StdQM which is ab initio computable for the complex atomic systems of chemistry and is also understandable in the same sense as classical continuum mechanics. If RealQM indeed shows to models physics, then there is no longer any reason for a divide between theory and practice. The Shut up and Calculate can then be replaced by Compute, Learn and Speak. 

 

RealQM Article to Submit

I am now now preparing to submit a sequence of articles about Real Quantum Mechanics to relevant journals and here is a first test to check out reaction:

• Real Quantum Mechanics

Take a look and give a comment.