How Quantum is the Classical World

Background: Experiment has confirmed that quantum phenomena can violate the Information Bell Inequalities. A violation of the one or the other of these inequalites is equivaent to a violation of local realism meaning that either objectivity or locality, or both, do not hold for the phenomena under investigation. Main idea: Test suspected classical violations of local realism for statistical significance by determining whether or not a data set – which displays a well-defined, built-in complementarity structure – is “classically random”. Problem: Design an experiment which mocks up ontological complementarity in a set of classical measurements, thus providing epistemologically complementary (pseudocomplementary) data which can be analysed with the same information theoretic algebra normally used to detect an information deficit in quantum physical results. Method & Analysis: Test for violations of local realism in classical measurements in the absence of ontological complementarity using inference statistics to reject stochastic and/or suspected violations of local realism in such data. Results: Local realism can be violated stochastically in the case of classical measurements using an experimental design mocking complementarity. The probability that local realism is violated by chance increases (1) the more outcomes a given experiment encompasses and (2) in accord with the (anti)correlation of results between the outcomes of a given experiment. The degree to which local realism is violated by chance is relatively independent of the number of outcomes and the correlation of results between the outcomes of a given experiment. A measure for the statistical significance of violations of local realism is presented. Conclusions: Pseudocomplementary data collected from a classical experiment in the way suggested here can be tested for the statistical significance of an initially hypothesized synchronicity between the (dichotomous) values of two physical quantities measured in two isolated, classical systems.