Negative probabilities and Counterfactual Reasoning on the double-slit Experiment
Abstract
In this paper we attempt to establish a theory of negative (quasi) probability distributions from fundamental principles and apply it to the study of the double-slit experiment in quantum mechanics. We do so in a way that preserves the main conceptual issues intact but allow for a clearer analysis, by representing the double-slit experiment in terms of the Mach-Zehnder interferometer, and show that the main features of quantum systems relevant to the double-slit are present also in the Mach-Zehnder. This converts the problem from a continuous to a discrete random variable representation. We then show that, for the Mach-Zehnder interferometer, negative probabilities do not exist that are consistent with interference and which-path information, contrary to what Feynman believed. However, consistent with Scully et al.'s experiment, if we reduce the amount of experimental information about the system and rely on counterfactual reasoning, a joint negative probability distribution can be constructed for the Mach-Zehnder experiment.
Keywords
Cite
@article{arxiv.1412.4888,
title = {Negative probabilities and Counterfactual Reasoning on the double-slit Experiment},
author = {J. Acacio de Barros and Gary Oas and Patrick Suppes},
journal= {arXiv preprint arXiv:1412.4888},
year = {2014}
}
Comments
24 pages, 4 figures, submitted to a volume in honor of Patrick Suppes edited by Jean-Yves Beziau and Decio Krause