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Photon Exclusivity and Bell Correlations from Bistable Threshold Dynamics

Paul Monforton, Sarah Monforton

Published Mar 29, 2026• 0 citations
Publisher

Abstract

Single-event exclusivity—the fact that one photon emission produces exactly one detection—is confirmed by anti-bunching experiments but lacks a dynamical explanation. Standard quantum mechanics postulates it; we derive it. The source is modeled as a bistable system: excited and ground configurations separated by a potential barrier, coupled bidirectionally to the electromagnetic mode. The mode exerts a force on the source that stabilizes the excited configuration. Absorbers compete stochastically; when one crosses threshold and switches to strong coupling, it rapidly drains the mode. The vanishing mode amplitude removes the force stabilizing the source, triggering its snap transition and delivering all of the source's energy ΔE to the winner. The framework extends to entangled photon pairs by treating the two-photon state as a joint mode in configuration space. The joint mode drains globally when any absorber pair triggers, producing correlations that violate Bell inequalities. The derivation uses bistable dynamics and threshold physics; nonlocality enters through the configuration-space mode structure, not through any modification of the dynamics.

DOI
10.5281/zenodo.19322708

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Single-event exclusivity—the fact that one photon emission produces exactly one detection—is confirmed by anti-bunching experiments but lacks a dynamical explanation. Standard quantum mechanics postulates it; we derive it. The source is modeled as a bistable system: excited and ground configurations separated by a potential barrier, coupled bidirectionally to the electromagnetic mode. The mode exerts a force on the source that stabilizes the excited configuration. Absorbers compete stochastically; when one crosses threshold and switches to strong coupling, it rapidly drains the mode. The vanishing mode amplitude removes the force stabilizing the source, triggering its snap transition and delivering all of the source's energy ΔE to the winner. The framework extends to entangled photon pairs by treating the two-photon state as a joint mode in configuration space. The joint mode drains globally when any absorber pair triggers, producing correlations that violate Bell inequalities. The derivation uses bistable dynamics and threshold physics; nonlocality enters through the configuration-space mode structure, not through any modification of the dynamics.
We extend the electromagnetic mode competition framework to entangled photon pairs. The framework derives the Born rule from classical electromagnetism plus a single empirical input: each emission produces exactly one detection (single-event exclusivity). Here we show that the same postulates, applied to the joint mode structure of spontaneous parametric down-conversion, reproduce the quantum predictions for polarisation-entangled pairs: the sin²(θ₁ − θ₂) coincidence probability and the maximal CHSH violation S = 2√2. We also derive GHZ correlations and the Hong–Ou–Mandel dip. The framework dissolves the mystery of Bell correlations: there are not two photons coordinating across space, but one extended electromagnetic mode undergoing one detection event. Alice and Bob are endpoints of a single structure; their correlation is built in from the moment of emission and enforced by energy conservation. No action at a distance occurs—one detector absorbs the energy, and the shared pool is depleted. Bell's inequality is violated not because of nonlocality, but because Bell's factorisation assumption does not apply to measurements on a single extended object.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed
This paper extends the stochastic electrodynamic framework of Paper 1 [3] to multiparticle systems, providing a physical derivation of quantum entanglement. When a highenergy gamma ray creates an electron-positron pair, both particles emerge from the same spacetime point and share a common electromagnetic quantum field. We propose that the electromagnetic vacuum retains a cross-correlation component S(12)E (x1, x2, ω) in their joint electromagnetic quantum field, arising from the common creation event. The spatial dependence of this cross-correlation—a sinc(ωr12/c) factor—is derived from the known two-point vacuum correlation function of the electromagnetic field, not postulated. This cross-correlation is identified as the physical carrier of quantum entanglement. The two particles undergo correlated Brownian motion in six-dimensional configuration space, each with diffusion coefficient D = ℏ/2m derived in [3]. Nelson’s stochastic mechanics in configuration space gives the two-particle Schrödinger equation. The foundational ergodicity assumption underlying Papers 1 and 2—that the coupled electron-vacuum system admits a unique stationary ergodic measure—is proved in the companion Paper 3 [5] via the Caldeira–Leggett model and the Ford–Kac–Mazur theorem. The EPR paradox is resolved: the instantaneous correlation upon measurement is a consequence of conditional probability applied to a joint stochastic process, not a physical signal. Bell inequality violations are derived explicitly: the cross-correlation is nonlocal in configuration space, bypassing Bell’s locality assumption while satisfying the no-signalling theorem. Decoherence arises naturally as disruption of S(12)E by environmental electromagnetic noise. Fermi and Bose statistics emerge as boundary conditions on the joint stochastic process in configuration space.
Published experimental results and analytic developments indicate the possibility of achieving stronger correlations of physical events with independent photons rather than with entangled ones. The probability of coincident detections of quantum events should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr's or Bell's nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed.
Maximal quantum correlations of unity do not violate the CSHS-Bell inequalities because the remaining two correlations vanish. The probability of coincident detections should not be confused with the correlation of mixed states. The theoretical requirements for implementing the quantum nonlocality theory are not present in the experimental configurations purporting to prove Bohr’s or Bell’s nonlocality because of the quantum Rayleigh scattering of single photons. By means of a normalization factor corresponding to the total number of initiated events, the detection probabilities obtained experimentally are too small to enable any violation of a Bell inequality. Correlations between independent states of qubits can easily outperform those calculated with entangled photons. Additionally, the quantum joint probability for a Bell state can be factorized enabling a local detection of the alleged quantum nonlocality, if it existed.