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, $E_{\mathrm{QM}}(a,b)=0$ and $S=0$, while the nilpotent steering postulate predicts the maximal violation, $E=\pm\cos2(a-b)$ and $S=2\sqrt2$. 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.
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)=0 and S=0, while the nilpotent steering postulate predicts the maximal violation, E=±cos2(a−b) and S=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.
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)=0 and S=0, while the UNP guidance postulate of Bohmian mechanics predicts a structured correlation, EUNP(α,β)=21[±cos2(α−β)∓cos2(α+β)], and a calculated S=2. The test is not on a CHSH violation but on the contrast between the vanishing EQM and the structured EUNP.
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.
We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed.\n The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle.\n Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation.
We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation.
Since 1927 the foundations of quantum mechanics have divided on whether the probabilities of the Born rule exhaust physical reality or describe an underlying definite dynamics. We propose two photon-pair experiments in which a definite, nonlocal dynamics predicts statistics that the formalism of Hilbert space, unitary evolution and the Born rule does not admit. In the first, the circularised photons of a single Type~I crystal show a perfect correlation, E(0,0)=1, where the formalism predicts E=0. In the second, a half-wave plate acting on one emission orientation of a crossed-crystal source changes the ratio at the distant analyser to 3/4:1/4, where the formalism predicts 1/2:1/2; realised as a Pockels cell, the plate would permit superluminal signalling. A null result confirms the formalism. A positive result would show that the Born-rule statistics are an epistemic description of a deeper, nonlocal dynamics, and would open an empirical path towards a post-quantum physics.