A Reponse to the Sheldon Goldstein Objection to a Series of Covariant Relativistic Bohmian Models

Abstract

In this work we try to answer a very important objection to the Covariant Bohmian Models type Nikolić and Hernández-Zapata that was formulated by the american physicist Sheldon Goldstein (private communication, 2010) about the imposibility to interpret the configuration space-time density found by the authors of these models like a probability density. The problem is that it is very dificult to show that the N space-time configuration density has a finite integral. That is very important in order to normalize the density to produce a PDF (probability density function). All the steps in the demonstrations seemed complete but this objection must be resolved imperatively before to continue using this kind of models with full confidence. Since the aim of Bohmian Mechanics (also known as the De Broglie-Bohm Mechanics) is to provide a precise and objective formulation of Quantum Mechanics free from vagueness and obscurity (Bell point of view at least), addressing this issue is crucial. In this article, we set out to tackle this by employing a specific type of function that we call an "Arrangement Function".