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.
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.
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.
John Bell’s theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell’s inequalities. Employing modifications of Bell’s inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.
Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. Moreover, it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell's theorem and its supporting experiments. By contrast, we provide a strictly local, deterministic, and realistic explanation for the correlations observed in two such supporting experiments, performed independently at Orsay and Innsbruck. To this end, a pair of local variables is constructed to simulate detections of photon polarizations at various angles, chosen freely by Alice and Bob. These generate purely random outcomes, A = +1 or -1 and B = +1 or -1, occurring within a parallelized 3-sphere. These outcomes do not depend on the contexts of measurements, but are determined entirely by the randomly chosen initial orientation of the 3-sphere. When they are compared, however, the correlation between them turn out to be exactly equal to -cos2(alpha - beta), with the corresponding CHSH inequality violated for the polarization angles alpha, alpha', beta, and beta' in precisely the manner predicted by quantum mechanics. The key ingredient in our explanation is the topology of the 3-sphere, which remains closed under multiplication, thus preserving the locality condition of Bell. It allows us to model the physical space as a 3-sphere, and reveals that the illusion of quantum nonlocality in the present case stems from a twist in the Hopf fibration of the 3-sphere.
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.
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.
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.