Einstein-Podolsky-Rosen-Bohm experiments: a discrete data driven approach

Abstract

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. (truncated here)

Corrected typo's, minor corrections in appendix B.3, major correction in section 11.4.2

References in corpus (39)

• Bell nonlocality
• Violation of Bell's inequality under strict Einstein locality conditions
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Understanding quantum measurement from the solution of dynamical models
• Is the Fair Sampling Assumption supported by EPR Experiments?
• Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
• Bell's theorem: Critique of proofs with and without inequalities
• Benchmarking gate-based quantum computers
• A sub-ensemble theory of ideal quantum measurement processes
• Bell's theorem and the experiments: Increasing empirical support to local realism
• Quantum theory as the most robust description of reproducible experiments
• Where Bell went wrong
• Possible Experience: from Boole to Bell
• Test of the no-signaling principle in the Hensen "loophole-free CHSH experiment"
• Event-by-event simulation of Einstein-Podolsky-Rosen-Bohm experiments
• Violations of locality and free choice are equivalent resources in Bell experiments
• Analysis of assumptions of recent tests of local realism
• Einstein-Podolsky-Rosen-Bohm laboratory experiments: Data analysis and simulation
• Can we close the Bohr-Einstein quantum debate?
• The contextuality loophole is fatal for Bell inequalities: Reply to a comment by I. Schmelzer
• Understanding quantum mechanics: a review and synthesis in precise language
• Bell's inequalities I: An explanation for their experimental violation
• Bell inequalities for random fields
• Quantum theory as a description of robust experiments: derivation of the Pauli equation
• Quantum theory as plausible reasoning applied to data obtained by robust experiments
• Irrelevance of Bell's Theorem for experiments involving correlations in space and time: a specific loophole-free computer-example
• Towards experiments to test violation of the original Bell inequality
• Hertz's viewpoint on quantum theory
• Violation of Bell Inequalities as a Violation of Fair Sampling in Threshold Detectors
• Discrete-event simulation of an extended Einstein-Podolsky-Rosen-Bohm experiment
• Logical inference approach to relativistic quantum mechanics: derivation of the Klein-Gordon equation
• Analysis of Wigner's Set Theoretical Proof for Bell-type inequalities
• Is Bell's theorem relevant to quantum mechanics? On locality and non-commuting observables
• Separation of conditions as a prerequisite for quantum theory
• The GHSZ argument: a gedankenexperiment requiring more denken
• A Mathematician's Viewpoint to Bell's theorem: In Memory of Walter Philipp
• Models for quantum measurement of particles with higher spin
• Model-free inequality for data of Einstein-Podolsky-Rosen-Bohm experiments

Cited by in corpus (6)

• Quantum Nonlocality: how does Nature do it?
• Can foreign exchange rates violate Bell inequalities?
• My discussions of quantum foundations with John Stewart Bell
• Statistical Contextual Explanation of Quantum Paradoxes
• Quantum Monogamy with Predetermined Events
• Does Quantum Information Require Additional Structure?