Volume 5, Issue 4, pages 115-133
James L. Beck is the George W. Housner Professor of Engineering and Applied Science, Emeritus, at the California Institute of Technology (Caltech). He is a native of New Zealand, which is a seismically active country. As a result, while working for the New Zealand government’s Physics and Engineering Laboratory after completing his BSc in Mathematics and Physics and his MSc in Mathematics at the University of Auckland, he became interested in models to predict the dynamic response of novel civil structures under earthquakes. He then joined the PhD program in earthquake engineering at Caltech where he received his PhD in Civil Engineering in 1978. He has been a professor in Caltech’s Division of Engineering and Applied Science since 1981. Much of Prof. Beck’s research over the last two decades has focused on the development of theory and algorithms, and their application, to utilizing sensor data from complex dynamical systems in order to improve models for predicting their dynamic response and their state of health. For this, he developed a Bayesian probabilistic framework for treating the uncertainty in the modeling of both the dynamic behavior of complex real systems and the future excitation that they might experience. This work dove-tailed well with his long interest in probability and its philosophical foundations. Despite his university training in probability and statistics being exclusively based on a frequentist interpretation of probability, his studies led Prof. Beck to favor a specific Bayesian interpretation of the axioms of probability where it is viewed as a multi-valued conditional logic for quantitative plausible reasoning. This probability logic interpretation builds on the seminal work of the physicists Richard T. Cox and Edwin T. Jaynes. Since his undergraduate days, Prof. Beck has been intrigued by puzzling features of quantum mechanics, despite understanding the mathematics of it. A few years ago he decided to focus some of his research efforts on the foundations of quantum mechanics. His belief is that some of its perceived strangeness, such as quantum nonlocality, is not intrinsic to it but is a result of the wide-spread use of the frequentist interpretation of the probability distributions produced by quantum theory. This thesis is evident in the current paper on the invalidity of the standard probabilistic locality condition for hidden-variable models for the spin outcomes in the EPR-Bohm experiments. The arguments in this paper demonstrate that how probability is interpreted is critical for understanding quantum entanglement and locality, as well as breaking the logical connection between hidden-variable models and Bell inequalities, which has non-trivial implications.
John Bell and others used a locality condition to establish inequalities that they believe must be satisfied by any local hidden-variable model for the spin probability distribution for two entangled particles in an EPR-Bohm experiment. We show that this condition is invalid because it contradicts the product rule of probability theory for any model that exhibits the quantum theory property of perfect correlation. This breaks the connection between Bell inequalities and the existence of any local hidden-variable model of interest. As already known, these inequalities give necessary conditions for the existence of third/fourth-order joint probability distributions for the spin outcomes from three/four separate EPR-Bohm experimental set-ups that are consistent with the second-order joint spin distributions for each experiment after marginalization. If a Bell inequality is violated, as quantum mechanics theory predicts and experiments show can happen, then at least one third-order joint probability is negative. However, this does not imply anything about the existence of local hidden-variable models for the second-order joint probability distributions for the spin outcomes of a single experiment. The locality condition does seem reasonable under the widely-applied frequentist interpretation of the spin probability distributions that views them as real properties of a random process that are manifested through their relative frequency of occurrence, which gives conditioning in the probabilities for the spin outcomes a causal role. In contrast, under the Bayesian interpretation of probability, probabilistic conditioning on one particle’s spin outcome in the product rule is viewed as information to make probabilistic predictions of the other particle’s spin outcome. There is nothing causal and so no reason to develop a locality condition. Thus, how probability is to be interpreted is critical to understanding quantum entanglement and locality.