A Thought Experiment with RealQM

RealQM is a new form of Quantum Mechanics QM based on non-overlapping electron charge densities in 3d physical space, to be compared with textbook StdQM based on multi-dimensional wave functions over $3N$-dimensional configuration space for a system with $N$ electrons.

I gave chatGPT gives the following prompt:

• Suppose RealQM represents a physically correct model of QM.

chatGPT:

✅ 1. Quantum mechanics as we know it would not be fundamental

If RealQM were literally correct:

• no Hilbert space

• no operators

• no wave-particle duality

• no probabilistic Born postulate

• no intrinsic randomness

• no entanglement as defined in standard QM

• no nonlocality

Quantum mechanics would become an emergent or approximate theory, not fundamental.

This would be the biggest revision of physics since 1926.

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✅ 2. Spin and fermionic statistics would need a classical explanation

RealQM uses a scalar PDE on ℝ³.
But in modern physics:

• electrons require spinor fields

• antisymmetry comes from fermionic statistics

• stability of matter relies on Pauli exclusion

If RealQM truly explained atoms with a scalar PDE, then:

• spin would have to be a geometric or boundary-condition effect

• Pauli exclusion would need a classical continuum mechanism

• the Dyson–Lieb stability theorems would have classical analogs

This would radically change modern atomic theory.

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✅ 3. Quantum field theory would cease to be fundamental

If all matter can be described by a 3D classical PDE:

• no need for quantized electromagnetic fields

• no photons as field excitations

• no creation/annihilation operators

• no vacuum fluctuations

• no Lamb shift or Casimir effect from QED

• no renormalization theory

You would have to re-derive:

• blackbody radiation

• spontaneous emission

• scattering cross-sections

• high-energy processes

all from a classical PDE.

That radically rewrites quantum electrodynamics, particle physics, and even cosmology.

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❗ 4. Bell inequalities, EPR correlations, and quantum nonlocality become impossible

A 3D deterministic PDE is a local, classical, context-free theory unless supplemented with nonlocal terms.

But real experiments violate Bell inequalities.

So if RealQM is exact:

• either the experiments are misinterpreted,

• or the PDE includes hidden nonlocal structure,

• or measurement theory is fundamentally classical and contextual.

Any way you choose, this would overturn 60 years of quantum foundations.

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❗ 5. Multi-electron atoms cannot be in 3D unless the PDE encodes antisymmetry

Hydrogen works in 3D because it has one electron.

But for N electrons:

• the wavefunction must live on ℝ³ᴺ

• antisymmetry under exchange is essential

• no 3D scalar PDE is known to reproduce multi-electron spectra, shells, or chemical bonding

To match real atoms, RealQM would have to:

• generate shell structure,

• produce correct periodic table ordering,

• reproduce Hartree–Fock and post-HF correlation corrections,

• generate Pauli exclusion from a classical PDE.

If it did, chemistry as we know it would be reinterpreted in classical continuum terms.

This is a monumental consequence.

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⭐ 6. If RealQM works, modern physics is not “wrong,” but “emergent”

RealQM would not contradict quantum mechanics but underlie it, in the same way:

• Navier–Stokes underlies turbulence

• kinetic theory underlies thermodynamics

The standard Schrödinger equation would be like a derived or averaged equation.

QM would be a statistical shadow of a deeper classical PDE.

This is the “subquantum mechanics” dream.

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⭐ SUMMARY OF CONSEQUENCES IF RealQM IS ACTUALLY TRUE**

1. Quantum mechanics becomes an emergent statistical theory.

2. No fundamental Hilbert space; no operators; no probabilistic axiom.

3. Spin, Pauli exclusion, and chemical structure get classical PDE explanations.

4. Quantum field theory collapses as a fundamental framework.

5. Nonlocality, entanglement, and Bell-violation experiments require reinterpretation.

6. All of atomic, molecular, and solid-state physics must be rebuilt on classical PDEs.

7. Particle creation/annihilation, photons, vacuum fluctuations, etc. are reinterpreted.

This would be the most radical shift in physics since quantum mechanics itself.