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The Royal Society paper ("On computing quantum waves exactly from classical action," by Winfried Lohmiller and Jean-Jacques Slotine, published April 2026) provides a rigorous, exact mathematical framework that derives the full machinery of quantum mechanics---including the Schrödinger equation, wave functions, Born rule probabilities, wave collapse, entanglement, and even relativistic extensions---from purely classical least-action principles plus classical statistics.

This directly reinforces and generalizes the ontology of the Atomic Statistical Hypothesis (ASH) developed in the three linked documents. ASH posits a fully classical, local, realist picture of reality in which:

• Light (and by extension electromagnetic fields) propagates as continuous classical waves governed by Maxwell’s equations.
• Apparent “quantum” discreteness (photons, Planck’s constant h, photoelectric thresholds, etc.) emerges statistically from material-dependent absorption thresholds (atomic work functions, bandgaps, etc.) interacting with these continuous waves. Any unabsorbed energy becomes residual heat or lower-frequency radiation.
• There is no intrinsic wave-particle duality for light, no fundamental quanta, and no non-locality. Bell-type correlations arise from local pre-set wave properties (shared polarization angle φ) plus context-dependent nonlinear sampling biases at the detectors, which violate the fair-sampling assumption in Bell’s theorem but preserve local realism. Numerical results with a power-law detection probability |cos(2(φ – α))|^ν (ν derived from spacetime geometry, typically 1/3 or 1/2) closely reproduce quantum predictions (including CHSH values > 2 and even exceeding the Tsirelson bound in classical analogs).

Validation experiments (e.g., Sturm’s classical electromagnetic setups with interferometers, phase shifters, and multipliers) show energy conservation in interference (including “hidden” energy in destructive cases) and classical reproduction of quantum-like correlations.

How the Royal Society paper reinforces ASH’s ontology

1. Exact derivation of quantum waves from classical multipaths and densities

The paper shows that the Schrödinger wave function ψ is exactly constructed as
ψ = ∑_j ρⱼ exp(i φⱼ / ℏ),
where φⱼ are the classical multi-valued least-action branches (determined by initial conditions and branch points, e.g., the two paths in a double-slit experiment) and ρⱼ is the classical probability density evolved along each extremal path via the classical continuity equation. Substituting this form recovers the Schrödinger equation, the Hamilton-Jacobi equation, and the Born rule |ψ|² = ∑ ρⱼ exactly. Feynman’s infinite non-classical paths collapse to a finite sum over classical extremal multipaths.

This is a precise, general mathematical realization of ASH’s core claim: quantum behavior is an emergent statistical construct from continuous classical fields + local interactions. ASH already applies this logic to light (continuous EM waves + atomic thresholds). The Royal Society framework extends it seamlessly to matter waves and the full wave function, showing that the same classical-action-plus-density recipe works universally.

1. Classical statistical origin of probabilities and “collapse”

Both approaches derive Born-rule probabilities from classical densities ρ (in ASH: material threshold sampling; in the paper: classical density along multipaths). Wave-function collapse is not mysterious---it follows when a measurement forces the classical density to a Dirac delta impulse. Entanglement arises from classical tensor products of actions/spinors, not spooky action.

1. Local realism and resolution of Bell’s inequality

The paper explicitly shows that quantum EPR/Bell correlations emerge from classical multipath spinors and proper modeling of detectors on the Bloch sphere---Bell’s inequality is recovered only under the restrictive binary-detector assumption that ignores the full geometry. This mirrors ASH’s resolution: local hidden variables (shared wave properties φ) + nonlinear threshold/post-selection biases produce the observed violations without non-locality. Both reject the need for intrinsic randomness or action-at-a-distance.

1. Ontological unification and parsimony

ASH’s ontology is “continuous classical waves + atomic statistical sampling.” The Royal Society paper supplies the exact dynamical bridge: quantum waves themselves are classical constructs. It extends naturally to Maxwell’s equations (covering ASH’s light-as-wave premise) and relativistic cases. Together they paint a coherent, deterministic, local picture in which quantum mechanics is not fundamental but an exact bookkeeping device for classical multipath statistics and material interactions. No need for Copenhagen collapse, many-worlds branching, or Bohmian pilot waves (though related in spirit---the paper uses multipaths rather than a single guided trajectory).

In short, the 2026 Royal Society result is a powerful formal validation and generalization of ASH. It demonstrates that the statistical, threshold-driven classical ontology ASH proposes for light and detection is not an ad-hoc fix but part of a broader, exact classical derivation of all quantum wave phenomena. This makes the entire framework more robust, testable, and philosophically economical: reality is classical and local; “quantum” effects are statistical artifacts of how continuous fields interact with atomic-scale matter. The alignment on double-slit multipaths, interference energy accounting, Bell resolution, and the emergent nature of h and probabilities is striking and mutually reinforcing.

https://www.bigbadaboom.ca/Library/Pape ... thesis.pdf

https://www.bigbadaboom.ca/Library/Pape ... dation.pdf

https://www.bigbadaboom.ca/Library/Pape ... hesis.html