Quantum Measurement and Initial Conditions

TL;DR

This paper proves a no-go theorem showing that under pure unitary evolution, only very restricted initial conditions can lead to definite measurement outcomes, challenging the idea that wavefunction collapse can be fully explained by unitary processes.

Contribution

It provides a mathematical restriction on initial conditions for measurements with unitary evolution, even considering environmental effects.

Findings

Unitary evolution alone cannot generally produce definite measurement outcomes.

The restrictions on initial conditions are consistent with a four-dimensional block universe perspective.

The theorem applies even when environmental interactions are included.

Abstract

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schr\"odinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schr\"odinger equation.