Existence of a Single-World Classical Replacement for Quantum Mechanics

Determine whether there exists a single-world classical theory—deterministic or indeterministic—that replaces quantum mechanics by reproducing its predictions, while overcoming the constraints posed by Bell’s theorem and the Kochen–Specker theorem; or establish that such a replacement is impossible.

Background

The paper proposes a classical many-worlds interpretation in which quantum mechanics is reconstructed from coexisting classical worlds with identity-changing evolution and objective self-location probabilities. In discussing whether one could avoid the apparent extravagance of many worlds, the author directly addresses the prospect of a single-world classical alternative to quantum mechanics.

The author explicitly states that no such method is currently known and highlights fundamental barriers imposed by Bell’s and Kochen–Specker theorems. Settling the existence or impossibility of a single-world classical replacement would clarify whether many-worlds or other nonclassical features are necessary to account for quantum phenomena.

References

There is no known way to replace quantum mechanics by a single-world classical theory (as, for example, in Step 2.1), being it deterministic or not. Any attempt to do so has to overcome very strong restrictions following from Bell’s theorem (Bell, 1964, 2004) and the Kochen-Specker theorem (Kochen and Specker, 1967; Conway and Kochen, 2006). There are still attempts to avoid these restrictions, but I will not discuss them here.

— Classical Many-Worlds Interpretation  (2407.16774 - Stoica, 2024) in Section 5: Can’t we simply cut off the branches?

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible (, p. 780).

— Hidden Variables in Quantum Mechanics: A Journey Into de Broglie-Bohm Pilot-Wave Theory  (2608.18829 - Oldofredi, 19 Aug 2026) in Section 1, Introduction: Hidden Variables and the Completeness of Quantum Mechanics

Although such speculations did not concretize into new results, Bohm's hope to make his theory falsifiable or testable remains open in today's proponents of the pilot-wave theory (for more details, cf. Sections \ref{philo} and \ref{Spin}).

— Hidden Variables in Quantum Mechanics: A Journey Into de Broglie-Bohm Pilot-Wave Theory  (2608.18829 - Oldofredi, 19 Aug 2026) in Section 2.2, “David Bohm’s rediscovery of Pilot-Wave Theory”