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From Interpretation to Experiment: Is Nature Deterministic or Probabilistic?

Anton Lorenz Vrba

Published Aug 5, 2026• 0 citations
Publisher

Abstract

We propose an optical experiment to distinguish orthodox quantum mechanics from a deterministic Bohmian framework, using standard, laboratory-proven photonics. In a single-pass Type-I parametric down-conversion source with a quarter-wave plate in each arm --- an arrangement standard to modern photonic state tomography --- circularizing the photon pair at π⁄4 leaves it separable on the orthodox account, predicting a vanishing correlation, EQM(α,β) and S=0, at the fixed CHSH angles used throughout. Under the hypothesis of a global constraint on Bohmian guidance --- Universal Nilpotency (UNP), a zero-totality condition under which a photon pair is entangled at its creation event rather than by the subsequent optical arrangement --- the same configuration is instead predicted to yield a structured correlation, EUNP(α,β)= 1/2 ±cos2(α−β)∓cos2(α+β), and S = √2.. The test is not designed to search for a CHSH violation or to corroborate the UNP hypothesis, but to provide a direct contrast, at fixed measurement settings, between a vanishing and a structured correlation. Because Bohmian mechanics otherwise reproduces every orthodox prediction, this previously untested configuration bears directly on whether the statistical character of quantum mechanics is fundamental or describes an underlying deterministic dynamics.

DOI
10.1364/opticaopen.33156188.v1

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From Interpretation to Experiment: Is Nature Deterministic or Probabilistic?

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We propose an optical experiment to distinguish orthodox quantum mechanics from a deterministic Bohmian framework, using standard, laboratory-proven photonics. In a single-pass Type-I parametric down-conversion source with a quarter-wave plate in each arm --- an arrangement standard to modern photonic state tomography --- circularizing the photon pair at π⁄4 leaves it separable on the orthodox account, predicting a vanishing correlation, EQM(α,β) and S=0, at the fixed CHSH angles used throughout. Under the hypothesis of a global constraint on Bohmian guidance --- Universal Nilpotency (UNP), a zero-totality condition under which a photon pair is entangled at its creation event rather than by the subsequent optical arrangement --- the same configuration is instead predicted to yield a structured correlation, EUNP(α,β)= 1/2 ±cos2(α−β)∓cos2(α+β), and S = √2.. The test is not designed to search for a CHSH violation or to corroborate the UNP hypothesis, but to provide a direct contrast, at fixed measurement settings, between a vanishing and a structured correlation. Because Bohmian mechanics otherwise reproduces every orthodox prediction, this previously untested configuration bears directly on whether the statistical character of quantum mechanics is fundamental or describes an underlying deterministic dynamics.

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Physics Letters A•May 11, 2026•0 citations
We propose an optical experiment to distinguish orthodox quantum mechanics from a deterministic Bohmian framework, using standard, laboratory-proven photonics. In a single-pass Type-I parametric down-conversion source with a quarter-wave plate in each arm --- an arrangement standard to modern photonic state tomography --- circularizing the photon pair at π⁄4 leaves it separable on the orthodox account, predicting a vanishing correlation, EQM(α,β) and S=0, at the fixed CHSH angles used throughout. Under the hypothesis of a global constraint on Bohmian guidance --- Universal Nilpotency (UNP), a zero-totality condition under which a photon pair is entangled at its creation event rather than by the subsequent optical arrangement --- the same configuration is instead predicted to yield a structured correlation, EUNP(α,β)= 1/2 ±cos2(α−β)∓cos2(α+β), and S = √2.. The test is not designed to search for a CHSH violation or to corroborate the UNP hypothesis, but to provide a direct contrast, at fixed measurement settings, between a vanishing and a structured correlation. Because Bohmian mechanics otherwise reproduces every orthodox prediction, this previously untested configuration bears directly on whether the statistical character of quantum mechanics is fundamental or describes an underlying deterministic dynamics.
We propose an optical experiment to distinguish orthodox quantum mechanics from a deterministic Bohmian framework, using standard, laboratory-proven photonics. In a single-pass Type-I parametric down-conversion source with a quarter-wave plate in each arm --- an arrangement standard to modern photonic state tomography --- circularizing the photon pair at π⁄4 leaves it separable on the orthodox account, predicting a vanishing correlation, EQM(α,β) and S=0, at the fixed CHSH angles used throughout. Under the hypothesis of a global constraint on Bohmian guidance --- Universal Nilpotency (UNP), a zero-totality condition under which a photon pair is entangled at its creation event rather than by the subsequent optical arrangement --- the same configuration is instead predicted to yield a structured correlation, EUNP(α,β)= 1/2 ±cos2(α−β)∓cos2(α+β), and S = √2.. The test is not designed to search for a CHSH violation or to corroborate the UNP hypothesis, but to provide a direct contrast, at fixed measurement settings, between a vanishing and a structured correlation. Because Bohmian mechanics otherwise reproduces every orthodox prediction, this previously untested configuration bears directly on whether the statistical character of quantum mechanics is fundamental or describes an underlying deterministic dynamics.
Whether Nature is deterministic or probabilistic has stood outside the reach of experiment since 1926 --- a gap this paper proposes to close. Bohmian mechanics reproduces the predictions of quantum mechanics without residue, so the choice between chance and determinism has so far been one of interpretation, not of measurement; we identify a regime in which the two can be told apart experimentally, using a modified version of the Kwiat et al.\ (1995) configuration, with a quarter-wave plate (QWP) in each arm, as in modern photonic state tomography. The paper's premise is that Bohmian mechanics requires a global constraint --- a zero-totality principle called the nilpotent condition --- under which every photon pair is entangled at its creation event, so that Bohmian guidance is supplemented by a postulate we call Universal Nilpotency (UNP). What the celebrated source arrangements of the Bell literature manufacture is not entanglement but the condition for its expression: we identify this condition as a circular state, supplied natively by the atomic-cascade source of the first Bell test and constructed after creation by the beam-splitter, crossed-crystal, and cone-intersection arrangements of the down-conversion era. This reading admits a configuration the record leaves untested: a single-pass Type-I source whose pair, separable on the orthodox account, is converted to circular guidance by a quarter-wave plate in each arm. There quantum mechanics predicts a vanishing correlation, EQM(α,β)=0E_{\mathrm{QM}}(\alpha,\beta)=0EQM​(α,β)=0 and S=0S=0S=0, while the UNP guidance postulate of Bohmian mechanics predicts a structured correlation, EUNP(α,β)=12[±cos⁡2(α−β)∓cos⁡2(α+β)]E_{\mathrm{UNP}}(\alpha,\beta)=\tfrac12\bigl[\pm\cos2(\alpha -\beta)\mp\cos2(\alpha +\beta)\bigr]EUNP​(α,β)=21​[±cos2(α−β)∓cos2(α+β)], and a calculated S=2S=\sqrt2S=2​. The test is not on a CHSH violation but on the contrast between the vanishing EQME_{\mathrm{QM}}EQM​ and the structured EUNPE_{\mathrm{UNP}}EUNP​.
Whether Nature is deterministic or probabilistic has stood outside the reach of experiment since 1926: Bohmian mechanics reproduces the predictions of quantum mechanics without residue, so the choice between chance and determinism has been one of interpretation, not of measurement. This paper constructs a nilpotent steering theory --- definite corpuscles guided by physically real waves, under a global conservation constraint --- that is empirically equivalent to quantum mechanics save in one experimental arrangement, stated here. The theory treats the conservation laws as primitive ontological constraints --- a zero-totality principle called the nilpotent condition --- under which every photon pair is entangled at its creation event, carrying its conserved content as a single ledger entry. What the celebrated source arrangements of the Bell literature manufacture is not entanglement but the condition for its expression: a circularly structured pilot wave, supplied natively by the atomic-cascade source of the first Bell test and constructed after creation by the beam-splitter, crossed-crystal, and cone-intersection arrangements of the down-conversion era. This reading admits a configuration the record leaves untested: a single-pass Type-I source whose pair, separable on the orthodox account, is converted to circular guidance by a quarter-wave plate in each arm. There quantum mechanics, under any interpretation, predicts a vanishing correlation and no Bell--CHSH violation, EQM(a,b)=0E_{\mathrm{QM}}(a,b)=0EQM​(a,b)=0 and S=0S=0S=0, while the nilpotent steering postulate predicts the maximal violation, E=±cos⁡2(a−b)E=\pm\cos2(a-b)E=±cos2(a−b) and S=22S=2\sqrt2S=22​. A violation would point to globally constrained dynamics (interpreted here as deterministic); a null result rejects the theory proposed here while leaving orthodox de~Broglie--Bohm mechanics untouched. The ledger accounting offered here is bookkeeping, not yet dynamics; its completion --- a formalism in which the bookkeeping becomes the evolution of physical fields --- is stated as the theory's principal debt. Either outcome of the experiment is informative, and the enabling conditions are stated in advance.
We propose the Modal-Disconnection Collapse (MDC) hypothesis: coherence between optical modes persists only while the physical coupling structure establishing their modal relation remains intact; removing that structure after photon(s) have passed triggers objective collapse without which-path measurement or decoherence. Standard quantum mechanics deems such post-departure manipulations irrelevant. To our knowledge, no experiment has directly tested this specific intervention. We propose two decisive tests. Experiment A: a single-photon polarization interferometer whose input beam splitter is removed after splitting but before detection. Experiment B: an entangled-photon Bell test where the source region is blocked after emission but before detection, spacelike-separated from detections. MDC predicts vanishing interference visibility (A) and reduction of the Bell-CHSH parameter to separable-state values (B); standard quantum mechanics predicts no change. These experiments close a basic empirical gap, exemplifying a core norm: seemingly obvious claims should remain provisional until directly verified.
Quantum mechanics is a pillar of modern physics, confirmed by a huge number of experiments. Nevertheless, it presents many unintuitive properties, strongly differing from classical mechanics due to its intrinsic non-epistemic probabilistic nature. Many attempts have been devoted to building a deterministic theory reproducing all the results of standard quantum mechanics (SQM). One of the most successful attempts, in this sense, is de Broglie–Bohm (dBB) theory. This theory is built in order to reproduce almost all SQM predictions. However, it has recently been suggested that different coincidence patterns are predicted by SQM and dBB when a double-slit experiment is realized under specific conditions. In this paper we present the first realization of such a double-slit experiment with correlated photons produced in type I parametric down-conversion. We observe a perfect agreement with SQM prediction, whilst our result is almost eight standard deviations from the dBB prediction.
We propose the Modal-Disconnection Collapse (MDC) hypothesis: coherence between optical modes persists only while the physical coupling structure establishing their modal relation remains intact; functionally disconnecting that structure after photon(s) have passed triggers objective collapse without which-path measurement or decoherence. Standard quantum mechanics deems such post-departure manipulations irrelevant. To our knowledge, no experiment has directly tested this specific intervention. We propose two decisive tests. Experiment A: a single-photon polarization interferometer whose input beam splitter is functionally disconnected after splitting but before detection. Experiment B: an entangled-photon Bell test where the source region is blocked after emission but before detection, spacelike-separated from detections. MDC predicts vanishing interference visibility (A) and reduction of the Bell-CHSH parameter to separable-state values (B); standard quantum mechanics predicts no change. These experiments close a basic empirical gap, exemplifying a core norm: seemingly obvious claims should remain provisional until directly verified.