Time, quantum mechanics, and decoherence

A. Ruschhaupt, Reinhard F. Werner

Rodolfo Gambini, Rafael A. Porto, Jorge A. Pullin

A recently introduced discrete formalism allows to solve the problem of time in quantum gravity in a relational manner. Quantum mechanics formulated with a relational time is not exactly unitary and implies a fundamental mechanism for decoherence of quantum states. The mechanism is strong enough to render the black hole information puzzle unobservable.

Maximilian Schlosshauer, Arthur I. Fine

James M. Yearsley

We extend previous work on the arrival time problem in quantum mechanics, in the framework of decoherent histories, to the case of a particle coupled to an environment. The usual arrival time probabilities are related to the probability current, so we explore the properties of the current for general open systems that can be written in terms of a master equation of the Lindblad form. We specialize to the case of quantum Brownian motion, and show that after a time of order the localization time of the current becomes positive. We show that the arrival time probabilities can then be written in terms of a positive operator-valued measure (POVM), which we compute. We perform a decoherent histories analysis including the effects of the environment and show that time-of-arrival probabilities are decoherent for a generic state after a time much greater than the localization time, but that there is a fundamental limitation on the accuracy $\ensuremath{\delta}t$, with which they can be specified which obeys $E\ensuremath{\delta}t\ensuremath{\gg}\ensuremath{\hbar}$. We confirm that the arrival time probabilities computed in this way agree with those computed via the current, provided there is decoherence. We thus find that the decoherent histories formulation of quantum mechanics provides a consistent explanation for the emergence of the probability current as the classical arrival time distribution, and a systematic rule for deciding when probabilities may be assigned.

Michel Bitbol, Eva Ruhnau

Rafael Eduardo Lorca

Emergent Causality Through Decoherence An imaginary hypothesis, not a theory. What if causality were not fundamental? What if it emerged, like temperature, from the degree of decoherence in a system? This hypothesis proposes that there is no single causality, but three regimes of the same process. The core idea:There is no single causality. There are causalities that emerge according to the degree of decoherence in a system. In other words: causality is not a property of the universe. It is a property of the level of description. The three regimes: Quantum causality (zero or low decoherence). The system is isolated. What exists are pure correlations: entanglement, superposition. There is no causality in the classical sense. There is correlation without direction. There is no defined "before" or "after." Relativistic causality (medium decoherence). The system interacts with the environment, but not completely. There is a causal structure defined by spacetime. There is causality, but it is relative: it depends on the observer. Classical causality (high decoherence). The system is fully coupled to the environment. It is classical. There is absolute, local causality: cause → effect, without ambiguity. The mechanism: decoherence.The more degrees of freedom interact with the system, the more decoherence. More decoherence → more classical → more causal. There is no "line" that is crossed. There is a continuum. Causality emerges gradually, just as temperature emerges from the number of particles. Why this makes the three regimes fit together: They are not separate levels. They are degrees of the same process. Time emerges together with causality. Without decoherence, there is no defined time. With decoherence, irreversibility emerges. And with it, the arrow of time. Relativity is the intermediate regime. What it would resolve: The problem of time: it emerges with decoherence. The arrow of time: it is the irreversibility of decoherence. The relativity–quantum clash: it is not a clash. They are different regimes of the same process. Causality: it is not fundamental. It is emergent. What it does not resolve: What decoherence exactly is. How to quantize gravity. Why there is decoherence. The information paradox. The label (important):This is an imaginary hypothesis, not a theory. It is coherent with what we know, but it is not demonstrated. It lacks mathematics, predictions, and confirmation. It does not say that time does not exist. It says that time could emerge. It does not say that causality does not exist. It says that causality could emerge. All of this, if one takes decoherence seriously, without adding anything else. But no one has demonstrated it. That is why it is a hypothesis, not a theory. A note on the anchor:This hypothesis does not invent its premise. It takes it from established physics: quantum mechanics already treats information as correlation, not as substance. Entanglement is pure correlation. Decoherence is entanglement with the environment. If information is always relational, then causality could be relational too. Related work: "Measure Reinforcement: Emergent Causality From Quantum Interactions" (Zenodo, 2025). Proposes emergent causality from quantum interactions without predefined time. Difference: includes a conscious observer. This hypothesis does not. Here decoherence is the mechanism, without consciousness. "Spacetime as an Emergent Causal Structure: A Quantum Mechanical Perspective" (Preprints.org, 2026). Derives proper time from the degree of decoherence. Difference: focuses on time, not causality as a regime. This hypothesis unifies the three regimes (quantum, relativistic, classical) into a single continuum. "Causal Space-Time: Emergent Physics from Causality" (2010). Proposes that physics emerges from a causal network. Difference: opposite direction. There causality is fundamental; here it emerges from decoherence. "Radial Coherential Dynamics: Emergent Causality" (2025). Proposes collapse as a decoherence front that generates time and causality. Difference: it is radial and has specific predictions. This hypothesis is more general: it describes causality as a regime of description, not as a radial process. The gap: no one has unified the three regimes (quantum, relativistic, classical) into a continuum parametrized by the degree of decoherence, nor has proposed that causality is a property of the level of description, not of the universe. Keywords: decoherence, emergent causality, quantum mechanics, foundations of physics, emergent time, quantum-classical transition.