A Mathematical Model of Free Will Based on Experience Information in a Quantum Universe

Hans A. De Raedt, Mikhail I. Katsnelson, Manpreet Singh Jattana +5 more

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.

Kathryn Blackmond Laskey

Christopher Thron, Braeden Welsch

The many-worlds interpretation (MWI) of quantum mechanics is currently experiencing a popular resurgence, propelled by such prominent and articulate physicists as Sean Carroll, David Deutsch, Max Tegmark, and Lev Vaidman. The consequences of MWI are mind-boggling: the spacetime universe of our experience is only one branch of an unimaginably fast-multiplying plethora of alternative universes held incommunicado. In this paper, we propose that the mass of Medusa's hair served up by MWI is due to a failure to embed the spacetime universe in the right space: spacetime is a slice of bread, not a splitting strand of pasta. By way of motivation, we first give a very simple presentation of Bell's inequality by comparing it to a ``quantum game show'', followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. We interpret the paradoxical correlation between measurements as resulting from a process outside of spacetime that produces both the original entanglement and the measurements. This is followed by a brief presentation of MWI, and then by a pictorial comparison of the proposed process model and MWI. The final section lists a number of potential consequences of the model related to causality, determinism, free will, and consciousness, and points to further references that give a more in-depth and rigorous presentation of the process dimension model. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.

Robert J. Kane

Rachael Louise Bond

“Pseudodiagnostic" patterns of information search were first classified by Doherty et al. (1979), predicated on their assertion that only the selection of data that allow for the calculation of Bayseian probability ratios may be considered rational. However, with the exception of Crupi et al. (2009), who have argued for an epistemological explanation loosely based on the de Finetti theorem of exchangeable probability assignments (see, eg., Heath and Sudderth, 1972), the Doherty et al. interpretation of information search patterns has gone unchallenged. This thesis seeks to answer three questions: can people make reasonable inferences from probabilistic information; is there an identifiable common approach to information selection; and, if not Bayes' theorem, then what mathematics might underlie human decision-making? A series of experiments demonstrate that people appear to select data not only for their ordinal values, but also to establish the relationships between them. However, since such a holistic approach to decision-making lies beyond the scope of the naïve Bayes' classifier, an alternative expression for the calculation of likelihood ratios is presented. By rejecting the Kolmogorov axioms of classical statistics in favour of the von Neumann mathematical axioms of quantum mechanics, it is shown that not only may probabilistic information be reconceptualised as isomorphic representations of quantised and entangled statistical systems, but that it is only this approach which allows for the assumption free calculation of likelihood ratios. Further, the mathematical derivation demonstrates that Bayes' theorem is a special case of this more general quantum expression, applicable only where the conditional independence of data is guaranteed. Mathematical modelling, combined with the results of another experiment, is used to investigate the plausibility of this expression as an explanation for both information search patterns, and people's estimation of probability. The nature of this “relational information theory" is both discussed and situated within the wider psychological field of mental models.