I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast-even though quantum dynamics is unitary, hence, reversible-reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss-rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that the observer's friend-an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result-can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast-even though quantum dynamics is unitary, hence, reversible-reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss-rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that the observer's friend-an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result-can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This has led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of mixing quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit in quantum statistical mechanics and quantum gravity. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.
We present a unified operational framework for the arrow of time grounded in irreversible information loss. While microscopic physical laws are time-reversal invariant, macroscopic irreversibility arises when systems overwrite metastable records. We show that recent reversible quantum-control experiments do not reverse time, but instead operate in regimes where no logically irreversible record is created. To formalize this, we introduce the **forgetting rate** (Ξcr), a coarse-grained rate defined on physically selected metastable record states (e.g., pointer states, memory registers, or macroscopic configurations). Unlike standard entropy production, which is expressed in terms of microscopic transition asymmetry, (Ξcr) captures the **rate of irreversible record overwriting**. In this formulation, entropy production obeys the lower boundS˙irr≥kBΞcr,consistent with Landauer's principle but expressed at the level of record dynamics. Within this framework, thermodynamic, quantum-measurement, psychological, and cosmological arrows emerge as substrate-dependent manifestations of Ξcr>0. Temporal asymmetry is therefore not a single global property, but a distributed feature of physical information-processing systems. The approach naturally explains the decoupling of arrows in composite systems and identifies experimentally accessible regimes where irreversibility can be locally suppressed. This work does not introduce a new microscopic law but provides a unifying, operational reformulation that connects information thermodynamics, decoherence theory, and memory dynamics through a single coarse-grained rate.
Quantum mechanics lacks a physical definition of measurement, observer, probability, and experienced time. These notions are instead treated as primitive or interpretation-dependent, leading to persistent foundational problems including the measurement problem, the origin of the Born rule, observer disagreement in Wigner’s Friend scenarios, the arrow of time, and apparent information loss in black hole evaporation. In this work, we show that these problems share a single missing ingredient: the absence of an operational definition of observers as bounded physical systems. We define observers as physically realizable systems capable of forming irreversible internal records under unitary dynamics. Measurement is identified with record formation, probability with record redundancy, experienced time with record accumulation, and irreversibility with computational inaccessibility rather than non-unitarity. Using decoherence and quantum Darwinism, we show that the number of accessible, decoherence-stable records associated with an outcome scales with the squared amplitude, yielding the Born rule from record counting without invoking collapse, subjective probability, or additional axioms. Observer-relative paradoxes dissolve once outcome definiteness is indexed to record formation rather than to the global quantum state. Reconstruction of global quantum information is shown to require exponential resources, rendering measurement and black hole evaporation operationally irreversible despite global unitarity. The resulting framework closes quantum mechanics conceptually by eliminating undefined primitives, without modifying its mathematical structure or introducing new dynamical postulates.
The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information gathering which can be considered, one characterizing the information provided about the initial preparation, useful in communication, and the other characterizing the information about the final state, useful in state-preparation and control. Here we are interested in understanding the properties of these measures, and the information gathering capacities of quantum and classical measurements. We provide a partial answer to the question `in what sense does information gain increase with initial uncertainty?' by showing that, for classical and quantum measurements which are symmetric with respect to reversible transformations of the state space, the information gain regarding the initial state always increases with the observer's initial uncertainty. In addition, we calculate the capacity of all unitarily covariant and commutative permutation-symmetric measurements for obtaining classical information. While it is the von Neumann entropy of the effects which appears in the latter capacity, it is the subentropy which appears in the expression for the former.
There is a constraining relation between the reliability of a quantum measurement and the extent to which the measurement process is, in principle, reversible. The greater the information that is gained, the less reversible the measurement dynamics become. To illustrate this relation, we develop a simple physical model for quantum measurement, as well as a hypothetical scheme by which the experimenters can determine the reliability and reversibility. We derive an "uncertainty" (constraining) relation between reliability and reversibility, which holds even when there is no interaction with any external environment other than the fundamental information recording device.
The quantum measurement problem is traditionally framed as a conflict between unitary dynamics and the emergence of definite outcomes. A wide range of quantum paradoxes—including Schrödinger’s Cat, Wigner’s Friend, Bell nonlocality, delayed-choice experiments, and the Quantum Zeno effect—are commonly interpreted as manifestations of this conflict. This paper argues that these paradoxes share a common origin: the assumption that quantum states represent observer-independent physical reality. Building on an Observer-First Interpretation (OFI), quantum states are instead treated as observer-relative informational constructs constrained by evidence accessibility and record stability. Within this unified framework, definite outcomes, nonlocal correlations, temporal ordering, and measurement-induced stabilization emerge consistently without modifying quantum mechanics or introducing additional dynamics. The quantum measurement problem is thus reformulated as an informational consistency condition rather than a physical inconsistency.