Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information

TL;DR

This paper demonstrates that quantum jumps and the discreteness of measurement outcomes emerge from unitarity and repeatability principles, even in macroscopic, open systems, challenging the notion of wave-packet collapse.

Contribution

It shows that the discreteness underlying quantum jumps arises from core quantum postulates combined with measurement repeatability in macroscopic systems.

Findings

Repeatability of measurements implies orthogonal subspaces for macroscopic states.

Discreteness and wave-packet collapse are derived from unitarity and repeatability, not literal collapse.

Symmetry breaking singles out preferred subspaces, contradicting superposition principle.

Abstract

An unknown quantum state of a single system cannot be discovered, as a measured system is reprepare: it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of a macroscopic, open system (such as an apparatus), and we allow its microscopic state to change when, e.g., measured by an observer, provided that its salient features remain unchanged and that observers regard macroscopic state of the pointer as representing the same record. We conclude that repeatably accessible states of macroscopic systems (such as the states of the apparatus pointer) must correspond to orthogonal subspaces in the Hilbert space. The symmetry breaking we exhibit defies the egalitarian quantum superposition principle and unitary symmetry of the Hilbert space, as it singles out preferred subspaces. We conclude that the resulting discreteness (which underlies quantum jumps) emerges from the continuity of the core quantum postulates plus repeatability also in macroscopic and open, but ultimately quantum systems such as measuring devices accessed by observers, where (in contrast with pure states of microsystems) repeatability is paramount.