From Unitarity to Irreversibility: The Role of Infinite Tensor Products and Nested Wigner's Friends
Karl Svozil
TL;DR
The paper addresses how irreversible quantum measurement may emerge from strictly unitary dynamics by modeling an infinite regression of measurements as infinite tensor products. It develops a framework of sectorization and factorization within this infinite-limit setting, showing that unitary equivalence can break down across sectors and between certain von Neumann algebra types. Through this formalism, coherence is lost between sectors, yielding non-unitary irreversibility in the thermodynamic limit, distinct from but related to conventional decoherence. The work provides a mathematically rigorous route to irreversibility at macroscopic scales, with implications for quantum foundations and the interpretation of measurement outcomes.
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.