Negative probabilities and Counterfactual Reasoning on the doubleslit 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 doubleslit 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 doubleslit experiment in terms of the MachZehnder interferometer, and show that the main features of quantum systems relevant to the doubleslit are present also in the MachZehnder. This converts the problem from a continuous to a discrete random variable representation. We then show that, for the MachZehnder interferometer, negative probabilities do not exist that are consistent with interference and whichpath 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 MachZehnder experiment.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 DOI:
 10.48550/arXiv.1412.4888
 arXiv:
 arXiv:1412.4888
 Bibcode:
 2014arXiv1412.4888A
 Keywords:

 Quantum Physics
 EPrint:
 24 pages, 4 figures, submitted to a volume in honor of Patrick Suppes edited by JeanYves Beziau and Decio Krause