QM is Uncomputable + Unphysical but Still Fundamental?

Let me confront chatGPT with the following prompt:

• The basic model of Quantum Mechanics is Schrödinger's Equation SE.
• Solutions to SE as wave functions are uncomputable for multi-electron systems.
• SE is not derived from physical principles and so has unclear physical meaning.
• Wave functions have unclear physical meaning.
• Why is SE chosen as basic model when it is both uncomputable and unphysical?  

Below you get the response by chatGPT, which essentially says that SE was adopted as a basic model because this was the only alternative, not because it expressed any profound insight. I then inform about RealQM as an alternative and get the response that it sounds interesting, but will have to fight a tough match against QM as being the only alternative. I add that uncomputable and unphysical go together: A physical model is computable because physics is a form of computation.  

chatGPT:

You ask why physics chose a model that is “uncomputable” and “unphysical” as fundamental.The answer is simply this:

• Because nature forced it on us.

The Schrödinger equation was not adopted because it was philosophically clear or computationally convenient. It was adopted because no other model reproduced the observed facts: atomic spectra, electron diffraction, tunneling, chemical bonding, semiconductor behavior, and so on. Classical and semi-classical theories failed; the Schrödinger framework succeeded.

Regarding “uncomputable”:
Many-body equations in physics are frequently analytically intractable (Navier–Stokes, Einstein’s equations, turbulence). This does not disqualify a theory as fundamental. It only reflects the complexity of nature.

Regarding “unphysical”:
The wave function’s ontology is indeed unsettled, but conceptual ambiguity is historically common in fundamental physics. Maxwell’s fields and Newton’s gravity were both considered “unphysical” when introduced; their meaning became clearer only later. A theory can be empirically correct long before it is philosophically understood.

So the reason quantum mechanics is treated as fundamental is not because it is simple or fully interpreted, but because:

• It remains the only framework that correctly predicts the phenomena it describes, and no alternative “computable and physical” model has matched its empirical success.

Until such an alternative exists, Schrödinger’s equation stays fundamental by necessity, not by choice.

My prompt: 

• What about the alternative to QM in the from of RealQM by Claes Johnson?

ChatGPT:

RealQM is an interesting and ambitious alternative proposition. It addresses one of your original concerns: it offers a model that aims to be computable and physically interpretable, in contrast to how you characterised standard QM (uncomputable + unclear). If RealQM could be shown to reproduce all phenomena of standard QM (and beyond) while being simpler/clearer, it would warrant serious attention.

However, the burden of proof is high. Until RealQM demonstrates equivalence (or superiority) to standard QM across the full range of quantum phenomena, and is subjected to robust peer review and empirical tests (especially in areas where standard QM shines, like entanglement, quantum statistics, quantum field effects), we should treat it as a speculative alternative—not as yet a replacement of standard QM.

• RealQM is a model of atoms/molecules formulated as a deterministic continuum system in 3-dimensional physical space (plus time) with one-electron charge densities that occupy non-overlapping spatial regions, subject to Coulomb interactions, rather than a high-dimensional wave-function over configuration space. claesjohnson.blogspot.com+3Real Quantum Mechanics+3claesjohnson.blogspot.com+3

• In RealQM, the wave functions (or densities) live in ordinary 3-D space and satisfy boundary conditions (such as homogeneous Neumann conditions at boundaries between regions), thereby avoiding global support overlap and thereby avoiding the need for the Pauli Exclusion Principle (PEP) in the usual form. claesjohnson.blogspot.com+1

• Johnson argues that RealQM is “computable” in the same sense as classical continuum PDE models (like Maxwell, Navier–Stokes) and avoids what he calls the “curse of dimensionality” of the conventional many-body Schrödinger equation (which depends on 3N spatial coordinates for N electrons). claesjohnson.blogspot.com+1

• He claims RealQM has a clearer “physical meaning” (ontology) than standard quantum mechanics (StdQM) because the densities are spatially localised in 3D space rather than residing in abstract configuration space. claesjohnson.blogspot.com

• He extends the model even to nuclei (treating nuclei as analogous to atoms with a kernel and surrounding positive charge densities) under purely Coulomb interactions, in an attempt to bypass conventional nuclear/strong‐force models. claesjohnson.blogspot.com+1

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What RealQM tries to solve

Johnson presents RealQM as a response to several identified problems with conventional QM (StdQM):

• The interpretational problem: what is the wave function? What is the physical meaning of Ψ in 3N-dimensional space? (He argues that StdQM lacks a clear ontology) claesjohnson.blogspot.com

• The computational problem: the standard many-body Schrödinger equation has dimensionality scaling as 3N for N electrons (leading to “exponential complexity”). Johnson views this as effectively uncomputable in practice. claesjohnson.blogspot.com+1

• The foundational “mystery” of quantum mechanics: measurement, superposition, indistinguishability, and the need for postulates like PEP are seen as symptoms of the model’s conceptual opacity. RealQM claims to provide a more “physical” classical-type description. claesjohnson.blogspot.com

• The incompatibility between quantum mechanics and relativity/gravity – Johnson argues RealQM as a 3D continuum system may align more easily with deterministic classical physics and therefore may provide a path toward unification. claesjohnson.blogspot.com

Strengths

• It is commendable that Johnson tries to bring clarity to the ontology: locating electronic densities in real 3D space is intuitively more “visualisable” than wave functions in 3N-dimensional space. That addresses a genuine foundational discomfort many have with standard QM.

• The motivation of reducing computational complexity and seeking a 3D spatial model rather than a configuration‐space model is interesting and resonates with efforts in quantum chemistry to develop tractable approximations (though RealQM claims much more than just an approximation).

• The attempt to build a unified view of atoms and nuclei within a continuum Coulomb‐only framework is bold and invites further exploration.

Challenges / Issues

• Empirical validation: Does RealQM reproduce all known empirical results of quantum mechanics (atomic spectra, scattering, entanglement, quantisation, exchange symmetry, spin, Bell inequalities, quantum nonlocality, quantum field effects)? Johnson makes claims for atoms/shell structure, but I haven’t found peer‐reviewed comprehensive studies showing full equivalence to the standard model of atoms, molecules, and quantum phenomena.

• Exchange symmetry, spin, entanglement: In standard QM, many phenomena (e.g., Pauli exclusion, spin‐statistics, entanglement, Bell inequality violations) rely on the full formalism of indistinguishable particles and multi‐particle Hilbert spaces. RealQM claims to bypass PEP by spatial non‐overlap of densities—but does it fully reproduce fermionic statistics/spinor structure? That is unclear.

• Quantum field effects / relativistic effects / many‐body quantum phenomena: Conventional QM (and quantum field theory) handles things like particle creation/annihilation, relativistic corrections, virtual particles, scattering amplitudes, quantum electrodynamics etc. RealQM appears focused on Coulomb‐bound atoms rather than full relativistic field theory – so how it handles high‐energy phenomena, quantum fields, and relativity is not clear.

• Justification of new boundary conditions and structure: RealQM introduces perhaps ad‐hoc conditions (non-overlapping densities, free boundaries, kernel radius, Neumann/Robin conditions) that need independent justification, and need to show why nature uses those particular structures rather than the standard formalism.

• Community acceptance / peer review: New fundamental models require extensive scrutiny, competing predictions (or at least matched predictions) and peer‐review. The mainstream physics community does not appear (at least so far) to have broadly adopted RealQM; that doesn’t invalidate it per se but means it has yet to demonstrate convincing superiority or broad explanatory range.

• Computability claims: While RealQM proposes “computable in principle” within 3D space, actual many‐electron quantum systems remain extremely challenging even for continuum models; the claim of linear or manageable scaling may be optimistic unless substantial computational evidence is provided for large N.

• Compatibility with known quantum phenomena: Many experiments verify non-classical features (superposition, interference, nonlocality, Bell violations). It is not clear how RealQM accounts for those in full generality. For example: how do non-local correlations or EPR‐type phenomena appear in a local continuum‐density model

Your conclusion?