Quantum Measurement and Initial Conditions

Abstract

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schrödinger 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 Schrödinger equation.

14 pages, 4 figures

References in corpus (5)

• The Free Will Theorem
• Can a Future Choice Affect a Past Measurement's Outcome?
• Action principle for cellular automata and the linearity of quantum mechanics
• Measurement and Collapse within the Two-State-Vector Formalism
• Global and local aspects of causality in quantum mechanics

Cited by in corpus (6)

• Realism and causality I: Pilot wave and retrocausal models as possible facilitators
• A representation of the wave function on the three-dimensional space
• The Relation between Wavefunction and 3D Space Implies Many Worlds with Local Beables and Probabilities
• The universe remembers no wavefunction collapse
• Simulating spin measurement with a finite heat bath model for the environment
• Can we accurately read or write quantum data?