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arXiv:2005.05711 · Frontiers in Physics

Discrete-Event Simulation of an Extended Einstein-Podolsky-Rosen-Bohm Experiment

Hans A. De Raedt, Manpreet Singh Jattana, Dennis Willsch, Madita Willsch, Fengping Jin, Kristel F. L. Michielsen

Published May 12, 2020• 11 citations
arXivHTMLPDF

Abstract

We use discrete-event simulation to construct a subquantum model that can reproduce the quantum-theoretical prediction for the statistics of data produced by the Einstein-Podolsky-Rosen-Bohm experiment and an extension thereof. This model satisfies Einstein's criterion of locality and generates data in an event-by-event and cause-and-effect manner. We show that quantum theory can describe the statistics of the simulation data for a certain range of model parameters only.

DOI
10.3389/fphy.2020.00160

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We use discrete-event simulation to construct a subquantum model that can reproduce the quantum-theoretical prediction for the statistics of data produced by the Einstein-Podolsky-Rosen-Bohm experiment and an extension thereof. This model satisfies Einstein's criterion of locality and generates data in an event-by-event and cause-and-effect manner. We show that quantum theory can describe the statistics of the simulation data for a certain range of model parameters only.
Data produced by laboratory Einstein-Podolsky-Rosen-Bohm (EPRB) experiments is tested against the hypothesis that the statistics of this data is given by quantum theory of this thought experiment. Statistical evidence is presented that the experimental data, while violating Bell inequalities, does not support this hypothesis. It is shown that an event-based simulation model, providing a cause-and-effect description of real EPRB experiments at a level of detail which is not covered by quantum theory, reproduces the results of quantum theory of this thought experiment, indicating that there is no fundamental obstacle for a real EPRB experiment to produce data that can be described by quantum theory.
We construct an event-based computer simulation model of the Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a one-to-one copy of the data gathering and analysis procedures used in real laboratory experiments. We consider two types of experiments, those with a source emitting photons with opposite but otherwise unpredictable polarization and those with a source emitting photons with fixed polarization. In the simulation, the choice of the direction of polarization measurement for each detection event is arbitrary. We use three different procedures to identify pairs of photons and compute the frequency of coincidences by analyzing experimental data and simulation data. The model strictly satisfies Einstein’s criteria of local causality, does not rely on any concept of quantum theory and reproduces the results of quantum theory for both types of experiments. We give a rigorous proof that the probabilistic description of the simulation model yields the quantum theoretical expressions for the single- and two-particle expectation values.
We review an event-based simulation approach which reproduces the statistical distributions of quantum physics experiments by generating detection events one-by-one according to an unknown distribution and without solving a wave equation. Einstein-Podolsky-Rosen-Bohm laboratory experiments are used as an example to illustrate the applicability of this approach. It is shown that computer experiments that employ the same post-selection procedure as the one used in laboratory experiments produce data that is in excellent agreement with quantum theory.
We review the data gathering and analysis procedure used in real Einstein-Podolsky-Rosen-Bohm experiments with photons and we illustrate the procedure by analyzing experimental data. Based on this analysis, we construct event-based computer simulation models in which every essential element in the experiment has a counterpart. The data is analyzed by counting single-particle events and two-particle coincidences, using the same procedure as in experiments. The simulation models strictly satisfy Einstein's criteria of local causality, do not rely on any concept of quantum theory or probability theory, and reproduce all results of quantum theory for a quantum system of two S=1/2S=1/2S=1/2 particles. We present a rigorous analytical treatment of these models and show that they may yield results that are in exact agreement with quantum theory. The apparent conflict with the folklore on Bell's theorem, stating that such models are not supposed to exist, is resolved. Finally, starting from the principles of probable inference, we derive the probability distributions of quantum theory of the Einstein-Podolsky-Rosen-Bohm experiment without invoking concepts of quantum theory.
We take the point of view that building a one-way bridge from experimental data to mathematical models instead of the other way around avoids running into controversies resulting from attaching meaning to the symbols used in the latter. In particular, we show that adopting this view offers new perspectives for constructing mathematical models for and interpreting the results of Einstein–Podolsky–Rosen–Bohm experiments. We first prove new Bell-type inequalities constraining the values of the four correlations obtained by performing Einstein–Podolsky–Rosen–Bohm experiments under four different conditions. The proof is “model-free” in the sense that it does not refer to any mathematical model that one imagines to have produced the data. The constraints only depend on the number of quadruples obtained by reshuffling the data in the four data sets without changing the values of the correlations. These new inequalities reduce to model-free versions of the well-known Bell-type inequalities if the maximum fraction of quadruples is equal to one. Being model-free, a violation of the latter by experimental data implies that not all the data in the four data sets can be reshuffled to form quadruples. Furthermore, being model-free inequalities, a violation of the latter by experimental data only implies that any mathematical model assumed to produce this data does not apply. Starting from the data obtained by performing Einstein–Podolsky–Rosen–Bohm experiments, we construct instead of postulate mathematical models that describe the main features of these data. The mathematical framework of plausible reasoning is applied to reproducible and robust data, yielding without using any concept of quantum theory, the expression of the correlation for a system of two spin-1/2 objects in the singlet state. Next, we apply Bell’s theorem to the Stern–Gerlach experiment and demonstrate how the requirement of separability leads to the quantum-theoretical description of the averages and correlations obtained from an Einstein–Podolsky–Rosen–Bohm experiment. We analyze the data of an Einstein–Podolsky–Rosen–Bohm experiment and debunk the popular statement that Einstein–Podolsky–Rosen–Bohm experiments have vindicated quantum theory. We argue that it is not quantum theory but the processing of data from EPRB experiments that should be questioned. We perform Einstein–Podolsky–Rosen–Bohm experiments on a superconducting quantum information processor to show that the event-by-event generation of discrete data can yield results that are in good agreement with the quantum-theoretical description of the Einstein–Podolsky–Rosen–Bohm thought experiment. We demonstrate that a stochastic and a subquantum model can also produce data that are in excellent agreement with the quantum-theoretical description of the Einstein–Podolsky–Rosen–Bohm thought experiment.
Abstract A discrete‐event simulation approach is reviewed that does not require the knowledge of the solution of the wave equation of the whole system, yet reproduces the statistical distributions of wave theory by generating detection events one‐by‐one. The simulation approach is illustrated by applications to a two‐beam interference experiment and two Bell test experiments, an Einstein‐Podolsky‐Rosen‐Bohm experiment with single photons employing post‐selection for pair identification and a single‐neutron Bell test interferometry experiment with nearly 100 % detection efficiency.