From Unitarity to Irreversibility: The Role of Infinite Tensor Products and Nested Wigner's Friends

TL;DR

This paper investigates how infinite tensor products and nested Wigner's friend scenarios explain the transition from reversible quantum processes to irreversible measurements, highlighting the mathematical structures involved.

Contribution

It introduces a novel interpretation of quantum irreversibility using infinite tensor products and nested Wigner's friend models, connecting quantum foundations with advanced mathematical concepts.

Findings

Infinite tensor products can cause sectorization, disrupting unitary equivalence.

Nested Wigner's friend scenarios illustrate the emergence of irreversibility.

Mathematical parallels with real analysis and statistical physics are established.

Abstract

The transition from unitary, reversible von Neumann-Everett quantum processes to non-unitary, irreversible processes and measurements is explored through infinite tensor products interpreted as nested, chained, or iterated Wigner's friend scenarios. Infinite tensor products can disrupt unitary equivalence through sectorization and factorization, drawing parallels to concepts from real analysis, recursive mathematics, and statistical physics.