Depending on the outcome of the triphoton experiment now underway, it is possible that the new local realistic Markov Random Field (MRF) models will be the only models now available to correctly predict both that experiment and Bell’s Theorem experiments. The MRF models represent the experiments as graphs of discrete events over space-time. This paper extends the MRF approach to continuous time, by defining a new class of realistic model, the stochastic path model, and showing how it can be applied to ideal polaroid type polarizers in such experiments. The final section discusses possibilities for future research, ranging from uses in other experiments or novel quantum communication systems, to extensions involving stochastic paths in the space of functions over continuous space. As part of this, it derives a new Boltzmann-like density operator over Fock space, which predicts the emergent statistical equilibria of nonlinear Hamiltonian field theories, based on our previous work extending the Glauber-Sudarshan P mapping from the case of classical systems described by a complex state variable α to the case of classical continuous fields.
Depending on the outcome of the triphoton experiment now underway, it is possible that the new local realistic Markov Random Field (MRF) models will be the only models now available to correctly predict both that experiment and Bell’s Theorem experiments. The MRF models represent the experiments as graphs of discrete events over space-time. This paper extends the MRF approach to continuous time, by defining a new class of realistic model, the stochastic path model, and showing how it can be applied to ideal polaroid type polarizers in such experiments. The final section discusses possibilities for future research, ranging from uses in other experiments or novel quantum communication systems, to extensions involving stochastic paths in the space of functions over continuous space. As part of this, it derives a new Boltzmann-like density operator over Fock space, which predicts the emergent statistical equilibria of nonlinear Hamiltonian field theories, based on our previous work extending the Glauber-Sudarshan P mapping from the case of classical systems described by a complex state variable α to the case of classical continuous fields.
Depending on the outcome of the triphoton experiment now underway, it is possible that the new local realistic Markov Random Field (MRF) models will be the only models now available to correctly predict both that experiment and Bell's theorem experiments. The MRF models represent the experiments as graphs of discrete events over space-time. This paper extends the MRF approach to continuous time, by defining a new class of realistic model, the stochastic path model, and showing how it can be applied to ideal polaroid type polarizers in such experiments. The final section discusses possibilities for future research, ranging from uses in other experiments or novel quantum communication systems, to extensions involving stochastic paths in the space of functions over continuous space. As part of this, it derives a new Boltzmann-like density operator over Fock space, which predicts the emergent statistical equilibria of nonlinear Hamiltonian field theories, based on our previous work of extending the Glauber–Sudarshan P mapping from the case of classical systems described by a complex state variable α to the case of classical continuous fields. This extension may explain the stochastic aspects of quantum theory as the emergent outcome of nonlinear PDE in a time-symmetric universe.
A previous paper demonstrated that two local, realistic models based on Markov Random Fields (MRF) across space time do replicate the correct, tested predictions of quantum mechanics for simple Bell Theorem experiments. This paper demonstrates a third such model, MRF3, which is more plausible physically, making contact with the physics of polarizers. It shows how to translate that type of model into an equivalent quantum mechanical model, which requires an augmentation to the usual measurement operator now used to represent polarizers in such experiments. The validity of that augmentation may be testable in experiments involving three or four photons, with relevance to quantum computing and communication.
Is it possible for a simple lumped parameter model of a circuit to yield correct quantum mechanical predictions of its behavior, when there is quantum entanglement between components of that circuit? This paper shows that it is possible in a simple but important example – the circuit of the original Bell’s Theorem experiments, for ideal polarizers. Correct predictions emerge from two alternative simple models, based on classical Markov Random Fields (MRF) across spacetime. Exact agreement with quantum mechanics does not violate Bell’s Theorem itself, because the interplay between initial and final outcomes in these calculations does not meet the classical definition of time-forwards causality. Both models raise interesting questions for future research. The final section discusses several possible directions for following up on these results, both in lumped system modeling and in more formal and general approaches. It describes how a new triphoton experiment, not yet performed, may be able to discriminate between MRF models and the usual measurement formalism of Copenhagen quantum mechanics.
One of the three laboratories which has previously produced three entangled photons (the asymmetric GHz state) has performed the triphoton equivalent of the Bell’s Theorem experiment. The results so far are inconsistent with the traditional operator projection model of polarizers, which was previously used in mainstream explanations of Bell’s Theorem experiments, but consistent with simple local realistic models previously shown to be consistent with Bell’s Theorem results and developed by implementing the form of time-symmetric physics which we previously developed [1]. This paper gives a more detailed proposal (MQED1) for a Markovian version of Quantum Electrodynamics (MQED), which it defines as the minimal modification of traditional versions of QED needed to fit the new results, to resolve disagreements between the four mainstream variants of QED used to predict experiments today, and to be consistent with the program of stochastic realism, albeit not a local model. The paper also discusses how MQED1 might be derived as the emergent outcome of a more fundamental local model fulfilling earlier direct discussions between this author and Louis De Broglie, using new statistical distribution functions extending the Glauber-Sudarshan P mapping essential to quantum optics.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.
The famous “Bell’s Theorem” proved by Clauser, Horne, Shimony, and Holt [1] rules out all “local causal hidden variable” theories of the universe. However, as demonstrated by Werbos [2], the word “causal” strictly implies an asymmetric, time-forwards model of measurement; this leaves open the reality that local realistic physics can be preserved by adopting a time-symmetric model of measurement. Three distinct, highly rigorous sets of experiments—exploring modified versions of the traditional Bell configuration—demonstrate empirical outcomes that are structurally inconsistent with the classical, time-forwards Copenhagen model of quantum measurement. Crucially, these disparate datasets consistently agree with each other and with the alternative time-symmetric model presented here. The new model of quantum measurement in a previous version of this paper was already able to fit solid new experiments with two entangled photons[3,4], experiments which strongly violated the Copenhagen theory of measurement and collapse. The new model, based on an early form of a new proposed Lagrangian for fundamental physics {5}, also improved the fit to puzzling triphoton experiments involving three entangled photons.[6]. This paper reports an upgrade of that new measurement model, based on an upgrade of that Lagrangian [5] f=giving substantial improvements on three tests on solid nuclear data carried further here This upgraded model exploits new findings in quantitative validation of the continuous-time Markov Random Field (CMRFp) model of time-symmetric quantum measurement against two independent triphoton experiments [6,7] spanning distinct entanglement types and coupling regimes. When tested on polarization GHZ data from the Shih laboratory, CMRFp achieves a 51.4% root-mean-square improvement over the standard Copenhagen collapse model, with characterized experimental asymmetries — including detector imbalance and angular misalignments of −2.4° and −6.1° — accounting for a substantial fraction of the residual error. On time-energy W-state triphoton data from Feng et al., CMRFp fits the conditional two-photon correlations with 3.0% RMS error in the weak-coupling regime and 4.5% RMS error in the strong-coupling regime. The transition from anti-bunching to damped Rabi oscillations across the exceptional point is captured by a single functional form varying only two physically motivated parameters, with the extracted oscillation frequency (0.195 rad/ns, corresponding to ~31 MHz) matching the independently reported dressed-state splitting. A new extraction of the J-field coupling constant from Sawada's published anomalous scattering strengths yields g_J = 0.0054 per nucleon, constant to within 2% from calcium to lead, confirming the mass-number (A) scaling that is the central prediction of the Ouroboros+Eli Lagrangian. The CMRFp framework, grounded in the Ouroboros+Eli Lagrangian, replaces the non-unitary collapse postulate with local, time-symmetric boundary conditions imposed by the macroscopic measurement apparatus. These results establish CMRFp as a unified, quantitatively accurate, and experimentally validated description of multiphoton entanglement, with direct implications for quantum sensor design, nuclear detection, and next-generation quantum architectures.