Continuous Observations and the Wave Function Collapse

TL;DR

This paper introduces a continuous collapse model for quantum wave functions, replacing the traditional instantaneous collapse with a finite-time process, aiming to eliminate unphysical artifacts and better describe quantum measurements.

Contribution

It proposes the Continuous Collapse Axiom (CCA), a novel framework for modeling wave function collapse as a finite-time process in quantum measurement theory.

Findings

CCA applies to all cases exhibiting the Zeno effect.

It removes unphysical artifacts caused by instantaneous collapse.

The post-measurement wave function is obtained by solving Schrödinger's equation with specific boundary conditions.

Abstract

We propose to modify the collapse axiom of quantum measurement theory by replacing the instantaneous with a continuous collapse of the wave function in finite time $\tau$. We apply it to coordinate measurement of a free quantum particle that is initially confined to a domain $D\subset\rR^d$ and is observed continuously by illuminating $\rR^d-D$. The continuous collapse axiom (CCA) defines the post-measurement wave function (PMWF)in $D$ after a negative measurement as the solution of Schr\"odinger's equation at time $\tau$ with instantaneously collapsed initial condition and homogeneous Dirichlet condition on the boundary of $D$. The CCA applies to all cases that exhibit the Zeno effect. It rids quantum mechanics of the unphysical artifacts caused by instantaneous collapse and introduces no new artifacts.