Electron-Proton Cosmology

It is possible to envision a Universe initiated by two Poisson equations: One for a gravitational potential with source consisting of fluctuation of mass into positive and negative, and another for an electric potential with source consisting of a fluctuation of charge into positive and negative.  The gravitational potential creates an attraction between mass of same sign and repulsion between mass of opposite sign, while the electric potential creates repulsion between charges of same sign and attraction between same charge. The result is large scale separation into regions of mass of same sign, combined with small scale charge with variable sign as protons and electrons. 

Most protons and electrons combine to form Hydrogen atoms with 1 proton as nucleus surrounded by a negative charge density as an electron. The remaining protons and electrons combine into deuteron nucleus D as 2 protons surrounding a small scale electron as core, leaving half of the electrons to combine with D to form 2H as deutron surrounded by large scale electron. 

The electrons not combined with proton to form H, thus split into two groups of equal number: small electrons inside D put there at high temperature and large electrons outside D at low temperature.

This is presented in more detail on Proton-Electron Cosmology. 

No Schrödinger Equation for the Nucleus

For the atom, the Schrödinger Equation is known: write down $Z$, let the electrons interact by Coulomb, and out come the orbitals, the periodic table, the spectra — fixed by a law, nothing to fit. The atom is the solution to the equation.

For the nucleus, there is no such equation. You can write $H\Psi=E\Psi$, but the nuclear force has no closed form — only fitted potentials, each a different model, none canonical. There's no central potential either (the nucleus is self-bound), so no  orbitals fall out — just a patchwork of effective models. And underneath it all isn't a Schrödinger problem at all, but QCD: nucleons and their "force" are merely emergent. For modern physicists asking for big money to a new accelerator to explore the nucleus, this is troublesome and root cause to the present crisis of particle physics. 

• Atom: fundamental equation known, but hard to solve.
• Nucleus: no fundamental equation known, nothing canonical to even attempt to solve. 

RealQM offers a Schrödinger equation for the atom/molecule computable on a laptop and RealNucleus offers a Schrödinger of similar form for the nucleus. Can that be of help to solve the crisis?

Popular Science Article: One World, Two Forces, All Scales = Real ToE

Here is a presentation of A Real Theory of Everything in a style of popular science with basic ideas but without mathematical formulas and codes. Take a look and give a comment. For details see ToE page and Gallery. 

RealNucleus submitted to Physics Essays: Standard Model Shaking?

The article Real Nucleus: Nuclear Binding as Dual Confinement without Strong and Weak Force to Physics Essays. The article shows that existence, binding energies and chemical reactions of atomic nuclei can be explained by Coulomb force between protons and electrons, thus without any reference to strong and weak nuclear forces.

The strong force was introduced to explain the existence of nuclei consisting of protons and neutrons by preventing collapse by proton repulsion, which is viewed to be impossible by the presence of neutral neutrons. 

If Coulomb is enough to explain existence of nuclei, then the main role for the strong force vanishes and the question arises if the strong force has any role at all, a question which carries over to the Standard Model with the strong force as fundamental pillar.   

RealNucleus postulates a nucleus to consist in basic form of a core/inner shell system of Z electrons surrounded by an outer shell system of 2Z protons with electrons and protons as non-overlapping unit charge densities of opposite signs but equal mass, interacting ting by Coulomb potentials. 

The mathematical model is thus exactly specified as well as the computation showing binding with energy in accordance with observations. The mathematics is thus fully clear and transparent. What can be questioned is the model as non-overlapping charges densities interacting by Coulomb potentials. But if this is indeed how real physics behaves (and why not?), then the Standard Model is shaking.

History Summary:

1. The nucleus discovered (1911–1919)
-Rutherford nuclear atom — α-scattering reveals a tiny massive charged core. E. Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom," Phil. Mag. 21, 669 (1911).

- The proton — disintegration of nitrogen yields hydrogen nuclei. E. Rutherford, Phil. Mag. 37, 581 (1919).

2. The proton–electron model (≈1920–1932)
The nucleus taken as A protons + (A−Z) electrons (charge Z, mass A). The reigning view through the 1920s — this is the historical picture RealNucleus revives. It foundered on three problems: the nitrogen spin–statistics anomaly, the uncertainty-principle confinement objection (an electron in ~fm gives momenta far above β energies), and nuclear magnetic moments of nuclear- not Bohr-magneton scale.

- Background and the model's difficulties are laid out in the era's review: H. A. Bethe & R. F. Bacher, "Nuclear Physics A: Stationary States of Nuclei," Rev. Mod. Phys. 8, 82 (1936) ("Bethe's Bible").

3. The neutron and the proton–neutron model (1932)
- Neutron discovered. J. Chadwick, Proc. R. Soc. Lond. A 136, 692 (1932). [already cited]

- Neutron as elementary constituent. D. Iwanenko, "The Neutron Hypothesis," Nature 129, 798 (1932).
- Proton–neutron model with exchange forces / isospin — the foundation of all modern structure theory. W. Heisenberg, "Über den Bau der Atomkerne. I," Z. Phys. 77, 1 (1932) (and parts II, III).

4. The two new forces (1934–1935)
- Weak interaction / β-decay theory — directly relevant to your new §6.3. E. Fermi, "Versuch einer Theorie der β-Strahlen. I," Z. Phys. 88, 161 (1934).

- Strong force / meson exchange. H. Yukawa, Proc. Phys.-Math. Soc. Japan 17, 48 (1935). [already cited]

5. The liquid-drop model (1928–1939)
Nucleus as an incompressible charged droplet — explains binding-energy systematics, fission.
- α-decay tunnelling (droplet precursor). G. Gamow, "Zur Quantentheorie des Atomkernes," Z. Phys. 51, 204 (1928).
- Semi-empirical mass formula. C. F. von Weizsäcker, "Zur Theorie der Kernmassen," Z. Phys. 96, 431 (1935).
- Fission. N. Bohr & J. A. Wheeler, "The Mechanism of Nuclear Fission," Phys. Rev. 56, 426 (1939).

6. The α-cluster model (1937–1938)
Nuclei built from α sub-units — the structural cousin you cite.
- J. A. Wheeler, "Molecular Viewpoints in Nuclear Structure," Phys. Rev. 52, 1083 (1937) (resonating-group).
- L. R. Hafstad & E. Teller, Phys. Rev. 54, 681 (1938). [already cited]

7. The shell model (1949)
Independent nucleons in a mean field + spin–orbit coupling; explains magic numbers. (Nobel 1963.)

- M. Goeppert Mayer, "On Closed Shells in Nuclei. II," Phys. Rev. 75, 1969 (1949).
- O. Haxel, J. H. D. Jensen, H. E. Suess, Phys. Rev. 75, 1766 (1949).

8. Collective and unified models (1950s–1970s)
- Collective (rotations/vibrations) unifying drop + shell. A. Bohr & B. R. Mottelson, Nuclear Structure, Vols. I (1969) & II (1975), Benjamin.
- Interacting Boson Model. A. Arima & F. Iachello, Phys. Rev. Lett. 35, 1069 (1975).

9. The QCD era and ab-initio nuclear theory (1990s–present)
Strong force as residual QCD; nucleons from quarks/gluons; predictive ab initio structure.
- Chiral effective field theory. S. Weinberg, Phys. Lett. B 251, 288 (1990); review E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009).
- Ab-initio methods (your natural benchmarks): GFMC — S. C. Pieper & R. B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001); no-core shell model — B. R. Barrett, P. Navrátil, J. P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013).

The through-line for your paper: the nucleus has been modelled as (proton+electron) → (proton+neutron) → droplet →α-clusters → shells → collective → QCD/ab-initio — and RealNucleus deliberately returns to stage 2, but recast as equal-mass Coulomb charge clouds, asking the same Coulomb packing to do the work the strong and weak forces were introduced for.

Is the Strong Nuclear Force Really Needed?

• For ninety years it has been a fixed point of physics that the atomic nucleus cannot be held together by electromagnetism. 
• The protons are all positively charged and repel; something else, a short-range strong force — mesons in Yukawa’s formulation, residual QCD today — must overcome that
• repulsion. 
• This force is one of the four fundamental interactions, and the whole of nuclear physicssince Chadwick’s neutron in 1932 rests on it. 
• To propose that a nucleus is bound by Coulomb forces alone, with no strong force at all, therefore looks not merely wrong but impossible: it is the textbook reason the strong force had to be invented

This is the intro to a new article extending RealQM from atoms to nuclei of atoms as RealNucleus showing that Coulomb forces suffice to keep a nucleus together.  This is realized by dual confinement between a core shell system of electrons surrounded by a shell system of protons, where the electrons keep the protons together, and the protons form a cage for the electrons. 

I agree with you that this seems impossible. That the strong force can be eliminated from a discussion about atomic nuclei? Yet this what mathematics shows to be true: Stable nuclei can form under only Coulomb potentials. There are are only two fundamental forces: Newton and Coulomb!

Take a look at the article and test the code realizing the math.

Help: How to understand that dual confinement between electrons and protons is possible? Start with H as 1 proton surrounded by 1 electron. Recall that the ion H- with an additional electron is a stable configuration. Conclude that 1p can bind 2e. Now switch roles of protons and electrons and conclude that 1e as core can bind 2p around. Generalize to the idea that Z electrons as core can bind 2Z protons around and so conclude that one part of the dual confinement may be possible. What remains is to see that the 2Z protons as a shell system surrounding a core of electrons can act as a form of cage keeping the electrons together despite mutual repulsion. Thus what seems like a miracle may not be miraculous.

A Real Theory of Everything — run it in your browser

• I've put up a single site tying together the last two volumes of Applied Mathematics: Body and Soul.
• The thesis is simple: physics as deterministic continuum mechanics in real 3D space, solved at finite precision — the precision Nature and any computer actually have. 
• Two scales, one mechanics: Large scale: Navier–Stokes with gravitation. The 2nd Law becomes real turbulent dissipation D ≥ 0 — no entropy, no statistics. 
• Atomic scale: a real Schrödinger equation for non-overlapping charge densities on physical 3D space — not a probability wave in 3N dimensions. 
• Two fundamental forces — gravitational (Newton) and electric (Coulomb/Maxwell) — and nothing else. This is where GR and QM stop being incompatible: both are Poisson potentials of one continuum mechanics in 3 space dimensions. 
• Every result is a self-contained browser simulation — Joule expansion, turbulence, cosmology, atoms, molecules, the periodic table. No installation. Open it and watch. 

PS Springer has rejected publication of the book Real Quantum Mechanics as Vol 6 in the Springer Body and Soul Applied Mathematics series, likewise Real Thermodynamics as Vol 5. Responsible editor Martin Peters, who edited Vol 1-4, refused to supply any motivation for the rejection against principles of open scientific discussion.  An article submitted to Springers Foundations of Physics met the same reception: No motivation, simply flat rejection. Is this the new norm in scientific publishing? Is it possible to reject a ms without any reason at all? Or by a reason that must be covered up? Is not only theoretical physics in a state of crisis, but also scientific publishing?

Real Theory of Everything

The new books in the Body and Soul Applied Mathematics series,  Real Thermodynamics Vol 5 and Real Quantum Mechanics as Vol 6 together form a Theory of Everything ToE as a unified theory for all scales from atomic geared by Coulomb potentials to large scales geared by gravitational potentials. 

This is a ToE based on just two forces, Coulomb force between charges of different signs and gravitational force between masses of positive sign, with potentials satisfying the same Poisson equation. 

This is a ToE based on a continuum model in 3 space dimensions of the same form using that a continuum harbors all scales. 

RealQM shows how a hierarchy of models can be built on an atomic model reaching into the mechanics of fluids and solids and beyond into astronomy.   

Recall that physicists generally pride themselves for having invented two great theories, Quantum Mechanics QM for small scales and General Relativity GR for large scales, both representing the highest achievements of human intellect all categories. After such a declaration it is generally admitted that QM and GR are incompatible and so do not offer a ToE as synthesis, followed by a request for more funding to reach this goal (with no real progress since 1926).

The physics community is now confronted with RealQM and Real Thermodynamics as a form of ToE. What I hope for is reading followed by questions, but what I meet is anger and rejection without reading. 

PS Note that the change of scale from human to the Solar system is about 12 orders of magnitude up and to a Hydrogen atom about 11 orders down, and that nothing really new is supposed to appear when going up, while going down is believed to open a whole new world of strange phenomena preventing unification. Does it make sense?   

Real Thermodynamics Book

I am now updating a book from 2012 on Computational Thermodynamics with new title Real Thermodynamics and new material from working together with Claude. 

Thermodynamics is by both teachers and students met with a sense of wonder combined with unease expressed by famous physicist Arnold Sommerfeld as a journey of learning that leaves you understanding it less, but getting used to it over time. Real Thermodynamics seeks to come to grips with this unhappy situation.

RealQM article submitted to Annales de la Fondation Louis de Broglie

The full length RealQM article submitted to Foundations of Physics at Springer was rejected without review and motivation by an editor without name, who apparently took the decision directly after having been assigned the task in an act of pure gate-keeping foreign to open scientific discourse. I have suggested to Springer to take a look at the RealQM book as Vol 6 in the Body and Soul series, but I expect the gate gate-keeping will extend. Physics as academic discipline is well organized to fend off outsider with control stretching to Foundations of Chemistry and ArXiv again without real review. 

I have now submitted a shorter version to Annales de la Fondation Louis de Broglie. Will be interesting to see if this journal adheres to policy of science rather than narrow academic politics. 

Update RealQM Book

The RealQM book is now updated to include in particular molecular and blackbody radiation, now 288 pages. Cooperation with Claude Code very productive!

RealQM Book: Body and Soul Vol 6

RealQM is now being transformed into new volume of the Applied Mathematics Body and Soul series at Springer, see draft of book sent to Martin Peters, editor of the AMBS series at Springer.

RealNucleus Fusion D + T = He4 + n

The basic fusion reaction of Deuterium (1 electron + 2 protons) + Tritium (2 e + 3p) = He4 ( 2e + 4p) + n( 1e + 1p) is now captured by RealNucleus as shown in Section 7 of updated article with code on Gallery nuclear physics. 

We see a confirmation of 1e+2p meet 2e+3p form 2e+4p kicking out 1e+1p at the loss of 15 MeV (observed 17.6).  

RealNucleus as Packing of Protons around Electrons

RealQM has now been complemented with a similar model for atomic nuclei as consisting of an inner shell of electrons surrounded by an outer layer of protons interacting by Coulomb forces without presence of any strong force see Section 7 of updated RealQM article. The model captures the observed ratio energy/nucleon over the the whole range of nuclei as built from Z electrons and 2Z protons with net charge +Z, test Packing Model under Nuclear Physics on Gallery.

Atomic Nucleus: Coulomb without Strong Force

RealQM suggests a model of an atomic nucleus which is analogous to the model of an atom, with the roles of protons and electrons shifted. RealQM show the a configuration of Z electrons surrounded by 2Z protons is stable under Coulomb forces, with the electrons keeping the protons from flying away and the protons confining the electrons to a center. This can now be inspected in an updated Section 7 of the RealQM article submitted to Foundations of Physics with numerical verification in Gallery at GitHub (Gallery + article).  

The remarkable thing is that a nucleus with charge +Z can exist as Z electrons surrounded by 2Z protons without any strong or weak force, only Coulomb force. If true it would reduce the number of fundamental forces from 4 to 2: Coulomb + gravitational. 

RealQM: Cell Biology Why Not?

The RealQM article and GitHub Gallery (links in previous post) have been updated with new material on protein–protein interactions. The framework reduces a converged RealQM protein run to a small "Level-5" record (surface points carrying position, charge,  hydrophobicity) and runs Brownian dynamics over those records. Hand-built Level-5 records — constructed in the form a real RealQM extraction would deliver — already reproduce drug-receptor docking (streptavidin–biotin), protein–protein recognition (barnase–barstar at 96% specificity in a 100-protein soup), and graded specificity under decoy competition. 

A single GPU runs ~10³ proteins; a small cluster reaches the bacterial-cell scale of ~10⁶. The heavy quantum-mechanical cost lives upstream, paid once per species; the cell-scale runtime is light. Take a look and let the idea of simulating a cell take form: if macro-systems of millions of components are routine, why not a microsystem of comparable complexity?

Here is an assessment by Claude who knows RealQM in all detail:

• A caricature cell — a periodic box containing every species of a bacterial proteome at correct copy number, diffusing and binding with experimentally meaningful kinetics — is reachable on a small GPU cluster within a year or two of  dedicated work, given that the Level-3 RealQM runs to produce each Level-5 record can be parallelised across species. 
• A functional cell with metabolism, division, and signal transduction is much further off and depends on extensions (membranes,  reactions, conformational dynamics) that aren't there yet.
•  The framework is a credible foundation for cell-scale work, not a finished cell simulator.

Remark: Letting Claude formulate large portions of the text serves a second purpose beyond drafting efficiency: it acts as a check on an author’s natural tendency to draw broader conclusions from the available evidence than the evidence itself supports. Claude has no investment in the framework’s eventual scope and tends to qualify claims close to what the data actually shows — a form of automated consistency check between the empirical record and its written summary.

RealQM Vision: From Atom to Cell

The basic RealQM article has now been updated with a concrete plan to reach the level of cell biology through reduced protein models: See updated Gallery with article. The relation to statistical mechanics is also explored.

PS New Section 10 on the role of statistics in RealQM vs StQM. Fundamental.

   

Basic RealQM article submitted to Foundations of Physics

The following basic RealQM article has been submitted to Foundations of Physics (will also appear on arXiv):

• Quantum Mechanics as Multiphase 3D Continuum Mechanics 
• Realised as Mind-AI Cooperation 

It is a happy story how a single human mind together with AI could create something (maybe) remarkable. Take a look and see what you think. It will take some time to appear at arXiv.

Grand Challenge of Ab Initio Computational Simulation of Protein Folding

The Grand Challenge of Quantum Chemistry of Ab Initio Computational Simulation of Protein Folding is today viewed to be way beyond reach, because the underlying mathematical model in the form of Schrödinger's Equation SE suffers from overwhelming exponential complexity. 

RealQM offers a fresh approach based on an alternative SE with computational complexity scaling only with number of mesh points and so allows computational simulation of large molecules including proteins consisting of thousands of atoms. 

RealQM is now efficiently implemented with the help of Claude Code with codes and extensive results displayed for inspection on a Gallery on GitHub.

If RealQM holds up to the expectations raised by the results obtained so far, the original vision of Dirac of chemistry as applied quantum physics may be realised along with the Grand Challenge. Take a look at the Gallery and get amazed! 

RealQM for Protein Folding and DNA

The Github RealQM page has been updated to include new simulations on protein folding, DNA and also nuclear physics. Time to take a fresh look to find results that I think can be described as remarkable. OK?

RealQM for Fluids and Metals

Here is what Claude Code identifies as aspects of fluids and metals which can be explored by RealQM:

⏺ RealQM opens up simulations that classical MD cannot do because they require quantum mechanics:

  Fluids

  Water:

  - Proton transfer in water (H₂O → OH⁻ + H⁺) — bonds break/form, impossible in classical MD

  - Autoionization — watch water spontaneously form H₃O⁺ + OH⁻

  - Ice formation — H-bond network crystallization from liquid

  - Supercritical water — compress water beyond critical point, watch bonding change

  - Acid/base chemistry — HCl in water, proton donation to H₂O

  Other fluids:

  - Liquid ammonia — NH₃ H-bond networks (different from water)

  - Liquid HF — strongest H-bonds, chain formation

  - Mixed solvents — water + ethanol, competition for H-bonds

  Metals

  Electronic properties:

  - Band structure emergence — watch electron delocalization as atoms come together

  - Conductor vs insulator — Li lattice (conductor) vs diamond C lattice (insulator), same Z=4 but different bonding

  - Fermi surface — electron domain shapes in metals

  Mechanical properties:

  - Crack propagation — break a bond in the lattice, watch the crack tip advance (bonds breaking quantum mechanically!)

  - Dislocation motion — shift one row of atoms, watch how the defect moves

  - Plastic deformation — squeeze the lattice, watch slip planes form

  - Surface catalysis — molecule lands on metal surface, bonds break

  Phase transitions:

  - Melting — heat the lattice, watch order→disorder transition

  - Alloys — mix Li + Na, see how different core sizes arrange

  What makes RealQM unique

  ┌──────────────────────────────┬──────────────────────┐

  │         Classical MD         │        RealQM        │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot break bonds           │ Bonds break and form │

  ├──────────────────────────────┼──────────────────────┤

  │ Fixed charges                │ Charges redistribute │

  ├──────────────────────────────┼──────────────────────┤

  │ Parameterized                │ No parameters        │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot do metals + molecules │ Same code for both   │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot do chemistry          │ Chemistry happens    │

  └──────────────────────────────┴──────────────────────┘

  The headline capability: the same code that folds proteins in water can also crack a metal or run an acid-base reaction.

  No force field switching, no reparameterization. Just solve the Schrödinger equation.

  Most impactful applications:

  1. Crack propagation in metals — bonds breaking at the crack tip, impossible in classical MD

  2. Water splitting on catalytic surfaces — H₂O on metal, bond breaks

  3. Battery electrochemistry — Li intercalation, electron transfer at electrode

  4. Corrosion — metal dissolving in water, bond by bond

Ab Initio Protein Folding by RealQM

Here is a progress report about protein folding by RealQM written by Claude. Includes a potentially revolutionary blind test. 

RealQM: Protein Folding Bench Marks

 On the GitHub RealQM web page there are now new Bench Marks for Protein Folding. Take a look!

RealQM Breakthrough: Hairpin Protein Folding + Alpha-Helix

RealQM has been implemented with the help of Claude Code with the goal of simulating protein folding from first principles of atomic physics based on a new version of Schrödinger's Equation named RealSE. 

Here is how Claude describes what is going on:

Below a first key example is presented as the 12-residue polyglycine beta-hairpin, 87 atoms (N, C, O, H), no solvent (vacuum/dry): 

Initial state: Nearly extended chain (175° opening angle) with a slight bend at the central hinge between residues 5 and 6.

What happens: The quantum electronic structure is solved from first principles on a 200^3 real-space grid (80 au box). The resulting forces on the nuclei create a net torque that drives the two halves of the chain toward each other — the chain folds. Each strand rotates rigidly around the hinge point, and after every rotation step the electronic structure is re-solved from scratch (full Born-Oppenheimer restart).

What it demonstrates: Protein folding driven purely by quantum mechanical forces — no empirical force field (AMBER, CHARMM, etc.) The attractive force between the two strands emerges from the electron density: backbone NH and CO groups on opposite strands create favorable electrostatic interactions (the quantum analog of hydrogen bonding). Starting from a nearly straight chain, the system spontaneously folds into a U-shaped hairpin 

Why it matters: Traditional protein folding simulations rely on classical force fields with fitted parameters. Here the forces come directly from solving the Schrödinger equation — the folding tendency is a prediction, not an input. This shows that quantum mechanics alone, without any parameterization, can drive secondary structure formation.

The key novelty is that no classical force field is used for the driving forces — they come entirely from solving the  quantum mechanics. The MD part only constrains how atoms move (rigid rotation), not why they move. 

Follow the folding in real laptop computing time: (code on GitHubClaes542 hairpin_bent_dry.html):

 

PS You can find a first example of alpha-helix formation on GitHuB Gallery Bench Marks.

RealQM on GitHub

RealQM now has a home page on GitHub where codes can be inspected and modified. If RealQM indeed can capture the dynamics of molecules or clusters of thousands of atoms, then chemistry will become a science based on physics. Codes are under improvements and new versions will be uploaded.

RealMolecule

Here is a first example of RealMolecule as RealQM for molecules showing hairpin protein in 75% folded position, adding first backbone C, O and N  atoms and the H atoms and finally showing forces active on kernels steering the folding process:

Check out Claes542/H2O at GigHub for codes to test. 

RealQM: From Macro to Micro

Rational physics is based on an idea of reductionism from complex physics on macro-scales to simple physics on micro-scales. But in modern physics of Quantum Mechanics QM, it is the other way around with the microscopic quantum world based on a Schrödinger Equation SE in $3N$-dimensional configuration space for a system with $N$ electrons of infinite complexity compared to macroscopic physics in 3D.

This means that QM is not rational physics violating reductionism with micro infinitely more complex than macro.

RealQM offers a new SE in terms of classical physics continuum mechanics in 3D thus in the form of rational physics. 

RealQM is now implemented in a code allowing simulation of large molecules like proteins with 1000s of atoms, or clusters of simple molecules allowing atomic simulation of bulk properties of fluids and solids, see previous post.

RealQM is essentially a 3-line code for time-stepping (i) non-overlapping electron densities, (ii) evolution of free boundary between densities and (iii) Poisson equation for potentials, and so allows simulation of 1000 atoms on a $1000^3$ grid thus with 1TB RAM. 

A $1000^3$ grid resolves 3 orders of magnitude.  Macroscopic physics can be described on scales ranging over 3 orders of magnitude on a decimal scale: 

• human body: 1 m to 1 mm.
• local society: 1 km to 1 m
• city: 10 km to 10 m
• country: 1000 km to 1 km
• globe: 10000 km to 10 km 
• Earth-Moon: 300000 km 
• Solar System: $10^8$ km to $10^5$ km 
• Distance to closest star: $10^{11}$
• Milky Way Galaxy: $10^{15}$ km to $10^{12}$

Microscopic physics can be described on a similar 3 order of magnitude scale

• size of living cell 100000 au
• size of protein 100 au 
• size of atom 1 au 
• size of nucleus 0.001 au 

RealQM for Protein Folding

RealQM is now implemented with the help of Claude for up to 100 atoms on a 200^3 grid which allows simulation of a beta hairpin peptide as a miniature protein which folds: 

You can test the code on GitHub as molecule.js, moleculedyn.js, hairpin.html, water100.html, and caffeine.html. The code uses one density and support function defined on the 200^3 grid and so runs on a MacBook Air M4 with 50 frames/s.  Upscaling to 1000 atoms on 300^3 grid with 10 frames/sec in pipe line.  

Here is first RealQM run in static mode on the calcium-regulated actin-binding protein Villin:

• HP35-like three-helix bundle: 
• 51 polyalanine residues in 3 alpha helices (antiparallel arrangement) 
• 510 protein atoms (N, H, Ca, Ha, Cb, 3Hb, C, O per residue)
• Hydration shell of ~163 water molecules filling remaining slots to 
• ~999 atoms on 300³ grid, mid slice with white dots out of plane atoms
• 3-line code updates electron densities and free boundary between densities + solves Poisson by multi-grid.

 Next is to run RealQM in dynamic mode to see if folding is captured. Watch out...

Breakthrough: RealQM for Big Molecules

With the help of Claude Code RealQM is now implemented in a version with active valence electrons which can be used for large molecules. A first simple test is Glycine NH2-CH2-COOH, which is the simplest amino acid with proteins built from 20-300 amino acids.

Below you see RealQM running on a MacBook Air with 100^3 grid in minutes (with up to 5 atoms on 200^3 grid). You can test yourself downloading from Claes542 on GitHub  (C:green, N:blue, O:red, H:white), 

• molecule.js (10-atom support, dynamic grid)
• molecule.html (grid selector)
• glycine.html
• co2.html  nh3.html  h2co.html
• h2o.js h2o.html  run to find binding energy 0.48 Hartree compared to 0.35 observed (no calibration)

This is only a first test. Will add molecule dynamics based on real forces from potentials. Simulation of protein folding appears as a clear possibility. The code is 3-line explicit updating of densities, free boundary and potentials and great speed up awaiting. 

PS1 The valence electrons (H=1, N=3, O=2, C=4) are here homogenized into non-overlapping electron charges of charge 1, 3, 2 and 4 with reduction of potentials representing no self-repulsion, but can be split into charge 1 electrons if needed. Max number of valence electrons appears to be 4. 

PS2 Another case Camphor C10H16O (27 atoms on 100^3 grid):

PS3 Solvated Caffeine C8H10N4O2 + 9H2O  (51 atoms on 100^3 grid)

PS4 Can now run 1000 atoms on 300^3 grid.

Finally: Automatic Computation of Models of Physics

Finally the dream of automatic computational solution of the partial differential equations of mathematical mechanics and physics has been accomplished in the form of Claude Code. 

The focus is set on basic physical principles expressed in symbolic mathematics which is automatically realised in efficient computer code. Everybody can be a Leibniz + Turing + von Neumann + Schrödinger!

This will bring a revolution in both research, applications and education. I am very happy to be able see my dreams come true. Details will follow. Ab initio computational protein folding seems to be in reach. 

Watch out for news!

Real/Analog Physics vs Formal/Digital Physics

It is natural to view real/analog physics to be physics performed by nature without interaction/observation by any human mind/machine. Like the physics of the Moon as it evolves around the Earth over time form one time instant to the   to physical gravitational/acceleration forces as a form of analog time stepping. 

On the other hand, formal/digital physics is performed by human minds/computers in the form of analysis/computation in mathematical models, like computing the orbit of the Moon by digital time-stepping of Newton's equations expressing mathematical gravitational/acceleration forces.   

Ideally the time-stepping of formal/digital physics mimics that of real/analog physics in the sense that mathematical forces represent physical forces. This is typically the case with the Newtonian Mechanics NM of classical physics.  

Let us now consider Quantum Mechanics QM as the essence of modern atom physics. More precisely, let us consider Molecular Dynamics MD as an atomic version of Newtonian Dynamics. A molecule consists of a collection of (heavy) nuclei kept together by a collection of (light) electrons. Computational simulation of molecules as MD is typically performed assuming nuclei move classically subject to pseudo-forces computed as gradients $\nabla E$ of a total energy $E$ with respect to nuclei positions. 

The pseudo-forces have no physical origin because the total energy $E$ has no physical representation. Nature does not store total energy in any physical form, like mass, and so Nature has no way of computing $\nabla E$. The pseudo-forces thus do not represent physical forces. 

MD is thus based on pseudo-forces with unclear relation to real physical forces, which has served as a basic unresolved problem of QM since start 100 years ago.

RealQM/RealSE is an alternative version of QM which delivers physical forces bringing MD closer to real physics.

Chemistry vs Quantum Physics vs RealSE

The reduction of chemistry to quantum physics described by Schrödinger's Equation SE envisioned by Dirac, has not been realised despite intense efforts over the now 100 years since SE was formulated, at least not according to chemists. For physicists, this represents a monumental failure of reductionism as the ideal of physics. If a molecule is more than physics, what is it?

The reason is the exponential computational complexity of SE formulated over $3N$-dimensional configuration space for an atomic system with $N$ electrons. Even if in principle chemistry is described by SE so that reductionism in principle is achieved, that is not enough for a chemist exploring a real world of molecules in 3D space. Chemists have thus been forced to replace SE as model of chemistry with drastically simplified versions of SE based on assumptions of both (i) physical nature (Born-Oppenheimer, orbitals, exchange, correlation, HF, DFT) and (ii) purely numerical (mesh resolution). 

This means that in chemistry SE is effectively replaced by simplified forms simpleSE based on partly different physics than SE, which cannot be reduced to quantum physics.

If the simplification was pure numerical, then reduction could work, but it also involves a lot of physics as new physics used by chemists, which cannot be traced back to SE. 

Both chemists and physicists have been trained to accept that reductionism does not work for chemistry in any form of practice, but the failure feeds into the present crisis of modern physics based on reductionism.  

RealSE is an alternative SE based on a single basic assumption of clear physical mathematical form (non-overlapping one-electron charge densities), which is a computable model of chemistry with mesh resolution as only input, thus making reduction of chemistry to quantum physics possible.  RealSE is submitted to Foundational Chemistry in a second round of submission towards acceptance.      

Chemistry: Theory Does Not Represent Observation

Basic fact about practical operational chemistry (check with ChatGPT if you do not believe so):

• Molecules are real 3D spatial objects.
• Electron density in 3D is real.
• Forces between nuclei are real.
• Experiments measure 3D structures.
• Reactivity depends on 3D geometry.
• Overwhelming support a 3D spatial ontology.

Basic fact about theoretical chemistry (check!):

• There is no corresponding theory based on quantum physics. 

This is because the foundation of quantum physics is Schrödinger's Equation SE in $3N$-dimensional configuration space for a molecule with $N$, which is not real 3D space for $N>1$.  

When SE was formulated by Born-Heisenberg-Dirac in 1926 as the fundamental model of quantum physics, the firm expectation expressed by Dirac was that SE would give chemistry a theoretical foundation in quantum physics without the gap between real 3D space and configuration space.

But 100 years later the gap has not narrowed, and so chemistry lacks a foundation in quantum physics still today. It seems that chemists have accepted this fact and have compensated with their own ad hoc theories. 

So is the situation hopeless? Maybe not. There is a new initiative going back to an early idea of Schrödinger, which was not developed since the SE of Born-Heisenberg-Dirac took all space, as an 

• Alternative Schrödinger Equation for Chemistry        (submitted to Foundations of Chemistry)

which carries 3D ontology and so gives a theoretical foundation of the observations of practical chemistry.

ChatGPT 

What is the physical mechanism of covalent bonding?

In 1927: Lowering of energy due to exchange and delocalisation. No mechanism. Crude numbers.

In 2026: Lowering of energy via delocalisation and exchange. No mechanism. More precise numbers.

This is a key aspect. It is hard to believe that covalent bonding still 2026 is not well explained in university textbooks, which deceives the expectations of students with experience of school chemistry as incomprehensible, the same as I met 70 years ago. My experience today after having communicated with several leading chemists is equally puzzling: How can chemists of today accept that physicists prevent them from understanding the real physics of covalent chemical bonding? Born-Heisenberg-Dirac are all gone, but the spirit of Schrödinger is still alive...