p-adic probability prediction of correlations between particles in the two-slit and neutron interferometry experiments

TL;DR

This paper introduces p-adic probability models to explain quantum interference experiments, predicting particle correlations that can be tested experimentally, offering a novel approach beyond standard probability theory.

Contribution

It develops a class of non-Kolmogorovian p-adic probability models to explain quantum interference phenomena and predicts measurable correlations between particles.

Findings

Predicted correlations between particles in interference experiments.

Established a framework using p-adic probabilities for quantum phenomena.

Proposed specific neutron interferometry experiments for validation.

Abstract

We start from Feynman`s idea to use negative probabilities to describe the two slit experiment and other quantum interfernce experiments. Formally by using negative probability distributions we can explain the results of the two slit experiment on the basis of the pure corpuscular picture of quantum mechnanics. However, negative probabilities are absurd objects in the framework of the standard Kolmogorov theory of probability. We present a large class of non-Kolmogorovean probability models where negative probabilities are well defined on the frequency basis. These are models with probabilities which belong to the so-called field of $p$-adic numbers. However, these models are characterized by correlations between trails. Therefore, we predict correlations between particles in interference experiments. In fact, our predictions are similar to the predictions of the so-called nonergodic interpretation of quantum mechanics, which was proposed by V. Buonomano. We propose the concrete experiments (in particular, in the framework of the neutron interferometry) to verify our predictions on the correlations.