StdQM without Real Physics vs RealQM?

The basic principle of deductive or theoretical science like mathematics and theoretical physics, is to specify a set of basic postulates or axioms and then use logic to draw conclusions or theorems from the axioms. Euclide was the first to use this principle when constructing Euclidean geometry based an 5 axioms about points, lines and circles, like: 

• Through any two distinct points there is a straight line.      (E)

Euclidean geometry gets a physical meaning by associating points to e g dots of chalk on a blackboard and straight lines with strings of dots drawn with the help of a ruler. Euclidean geometry can then give theoretical information about a triangle drawn on the blackboard by e g Pythagoras theorem. 

To give a theory based on axioms a meaning, it is necessary to 

1. To give the axioms meaning.
2. To check that the axioms are true.

Here 1 is required for 2 and if 2 is not true then the theory has no meaning. To secure 2 the axioms are chosen so that they are possible to verify as self-evident, or simple as possible like (E). It the axioms have questionable truth, so has the theory based on the axioms.

An axiom for Newtonian mechanics is Newton's inverse square law of gravitation, which is a consequence  of self-evident conservation laws, and can also be verified experimentally.  

Let us now take closer look at textbook Standard Quantum Mechanics StdQM as based on Schrödinger's Equation SE from 1926 in terms of a complex valued wave function $\Psi (x_1,x_2,...,x_N)$ depending on $N$ 3d spatial variables $x_1,...,x_N$ altogether $3N$ spatial variables for a system with $N$ electrons as configuration space.  A basic axiom for StdQM is 

• The wave function $\Psi (x_1,...x_N)$ is anti-symmetric.        (Q) 

Anti-symmetric means that $\Psi (x_1,...,x_N)$ shifts sign under permutation of any two distinct variables $x_i$ and $x_j$, from which follows that if $x_i=x_j$ for any $i\neq j$, then $\Psi (x_1,...,x_N)=0$.  

StdQM is presented as fundamentally different from classical continuum physics in the sense that $\Psi$ has no direct physical meaning like a charge density in 3d, only with $\vert\Psi\vert^2$ as a probability density over configuration space. 

This means that the axiom (Q) has no physical meaning and as such cannot be verified as being true by self-evidence or observed physics. This means the the role of (Q) as axiom for StdQM can be questioned on very good grounds. 

In particular, it does not suffice to say that antisymmetry guarantees that the probability of two electrons being at the same place is zero, and so affirm antisymmetry by observing a consequent, thus using incorrect logic.

We conclude that the physical meaning of (Q) is unclear, and in particular that it is impossible to verify the validity of (Q).  

The famous mathematician von Neumann gave an axiomatic treatment of StdQM into a formal mathematical theory based on axioms like (Q) in his monumental Mathematische Grundlagen der Quantenmechanik, 1932). The theory was perfect but came with the caveat of unclear physical meaning, which has never been sorted out,  in particular the formality of anti-symmetry.

If wave functions indeed are anti-symmetric, and wave functions have some physical meaning, there must be some physical mechanism guaranteeing anti-symmetry. But nothing like that has been found.

Let us compare with RealQM as an alternative to StdQM based on the following axioms

• Electrons are charge densities filling non-overlapping regions of space.                                   (Q1)
• Electrons are subject to mutual Coulomb repulsion and to Coulomb attraction from kernels.  (Q2)

We note that (Q1) and (Q2) have clear physical meaning and in particular that non-overlap can be motivated by Coulomb repulsion. In short, (Q1) and (Q2) have meaning and can be subject to verification.

The irony of modern physics, today manifesting as a crisis, is that StdQM is presented as the most successful theory of physics all times, while StdQM is still seeking a meaning. 

RealQM has a clear meaning and is today emerging as a challenger.  

Comment by chatGPT:

Condensed Comparison: StdQM Critique • StdQM Defense • RealQM Response

1. 3N-dimensional wave function

• Critique: Not in real 3D space.

• Defense: Domain ≠ physical space; that’s fine.

• RealQM: Uses 3D electron densities → avoids the issue.

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2. Wave function has no clear physical meaning

• Critique: Ontologically vague.

• Defense: No need for ontological commitment.

• RealQM: Provides explicit 3D physical ontology.

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3. Built-in nonlocality

• Critique: Entanglement = fundamental nonlocal structure.

• Defense: Nonlocality is only in correlations.

• RealQM: Claims local PDEs, but Bell correlations remain an open challenge.

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4. No fundamental particles

• Critique: Only Ψ exists fundamentally.

• Defense: Particles are emergent; that’s acceptable.

• RealQM: Electrons = continuous charge fields → clear entity.

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5. Collapse is ad hoc

• Critique: Not part of the dynamics.

• Defense: Collapse is epistemic; decoherence helps.

• RealQM: No collapse at all; deterministic evolution.

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6. Classical world unexplained

• Critique: Decoherence ≠ definite outcomes.

• Defense: Decoherence is enough pragmatically.

• RealQM: Classical world is built in from the start.

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7. Born rule is postulated

• Critique: Probability un-derived.

• Defense: Born rule is fundamental.

• RealQM: Deterministic PDEs.

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8. Wavefunction not physically visualizable

• Critique: No spatial field interpretation.

• Defense: Intuition is optional.

• RealQM: Fully visualizable 3D fields.

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9. Configuration-space undermines locality

• Critique: No fundamental 3D-local causation.

• Defense: Don’t conflate representation with ontology.

• RealQM: Local 3D causation, but must recover Bell nonlocality.

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10. No mechanism for 3D world emerging from 3N space

• Critique: 3D space is imposed, not derived.

• Defense: Projection via operators is standard.

• RealQM: Everything is 3D from the beginning.