Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

Salim Yasmineh

doi:10.3389/fphy.2021.770764

Abstract

All the arguments of a wavefunction are defined at the same instant, implying the notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts contradict the special relativity. We propose defining the wavefunction with respect to the invariant proper time of special relativity instead of the standard time. Moreover, we shall adopt the original idea of Schrodinger, suggesting that the wavefunction represents an ontological cloud-like object that we shall call “individual fabric” that has a finite density amplitude vanishing at infinity. Consequently, the action of measurement can be assimilated to the introduction of a confining potential that triggers an inherent nonlocal mechanism within the individual fabric. This mechanism is formalised by multiplying the wavefunction with a localising Gaussian, as in the GRW theory, but in a deterministic manner.

Highlights

As clearly explained by Travis Norsen in his book “Foundations of Quantum Mechanics” [1] there are three main interconnected problems in Quantum Mechanics: measurement, relativity and ontology of a wavefunction.Quantum measurements can be highlighted by measuring the physical properties of a microscopic system using a measuring instrument
The first property is that all the arguments of the invariant wavefunction are associated with the points (τ, x) of a corresponding slice Sτ, and are defined at a specific proper time instant τ which is invariant for all observers
The quantum state of a physical system can be described by an invariant wavefunction φ(τ, x) corresponding to a single quantum event at a specific proper time τ which is invariant for all observers

Summary

INTRODUCTION

As clearly explained by Travis Norsen in his book “Foundations of Quantum Mechanics” [1] there are three main interconnected problems in Quantum Mechanics: measurement, relativity (nonlocality and simultaneity) and ontology of a wavefunction. The invariant wavefunction φ(τ, x) representing a free particle corresponds to an individual fabric that evolves according to the invariant equation of motion (3.14) as an indivisible holistic bloc within the upper (or lower) light cone; its evolution is local and consistent with special relativity. During this evolution, the invariant wavefunction spreads out in the standard space in a smooth manner as a consequence of its passage from one slice Sτ1 into a subsequent slice Sτ2. The interaction between the different particles confines the dense part of each fabric (represented by its wavefunction) within the confining potential; a macroscopic object is always in a localised state

DISCUSSION

CONCLUSION