Irreversibility and the Foundations of Quantum Mechanics

Giulia Marcucci, Maria Chiara Braidotti, Silvia Gentilini +1 more

Abstract The description of irreversible phenomena is a still debated topic in quantum mechanics. Still nowadays, there is no clear procedure to distinguish the coupling with external baths from the intrinsic irreversibility in isolated systems. In 1928 Gamow introduced states with exponentially decaying observables not belonging to the conventional Hilbert space. These states are named Gamow vectors, and they belong to rigged Hilbert spaces. This review summarizes the contemporary approach using Gamow vectors and rigged Hilbert space formalism as foundations of a generalized “time asymmetric” quantum mechanics. We study the irreversible propagation of specific wave packets and show that the topic is surprisingly related to the problem of irreversibility of shock waves in classical nonlinear evolution. We specifically consider the applications in the field of nonlinear optics. We show that it is possible to emulate irreversible quantum mechanical process by the nonlinear evolution of a laser beam and we provide experimental tests by the generation of dispersive shock waves in highly nonlocal regimes. We demonstrate experimentally the quantization of decay rates predicted by the time‐asymmetric quantum mechanics. This work furnishes support to the idea of intrinsically irreversible wave propagation, and to novel tests of the foundations of quantum mechanics.

N. V. Lunin, Vladimir I Kogan

Boris B. Kadomtsev

Darren Cudd

Quantum Incompleteness presents an ontological interpretation of quantum mechanics in which physical systems are objectively under-specified prior to irreversible interaction. The theory rejects hidden variables, parallel worlds, and observer-dependent collapse, proposing instead that definite outcomes emerge through irreversible information-theoretic constraints that physically exclude alternatives. The wavefunction is treated as a real but non-material structural entity that defines the space of admissible outcomes rather than pre-existing values. Measurement, entanglement, classical definiteness, and the arrow of time are unified under a single completion mechanism grounded in thermodynamic irreversibility, while preserving the standard mathematical formalism of quantum mechanics. This work is empirically equivalent to standard quantum theory and is intended as a foundational clarification of what quantum mechanics describes rather than a modification of how it computes predictions.

Kenneth Searcy

If these constraints hold, physical theories must take the form they do. This paper evaluates how established physical theories relate to a set of foundational constraints derived without physical assumptions. Building on prior work that establishes the necessity of transition, irreversibility, probabilistic constraint, temporal order, and entropy as logical requirements for nontrivial describable ontology, it examines whether classical mechanics, thermodynamics, quantum mechanics, and relativity instantiate, approximate, or presuppose these structures. Rather than proposing new physics or modifying existing theories, the paper adopts an explicitly evaluative stance. Each theory is assessed according to whether it supports irreversible transition, structured possibility, ordered asymmetry, and monotonic entropy understood as irreversible constraint accumulation. Particular attention is given to quantum mechanics as a stress test, showing that probabilistic transition and irreversible measurement instantiate the derived constraints independently of interpretive commitments. The analysis demonstrates that successful physical theories do not escape these foundational constraints, and that apparent tensions arise only from idealized formalisms or interpretive abstractions. The framework thus serves as a diagnostic lens for understanding why physical theories must take the forms they do, rather than as a replacement for empirical physics.

A. Pérez-Madrid