Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum mechanics without time: A model

Carlo Rovelli C

Published Oct 15, 1990• 316 citations
Publisher

Abstract

The quantization of a simple dynamical system in which a unitary time evolution appears only within a certain approximation is studied in detail. The probabilistic interpretation of quantum mechanics in the regimes in which time is not defined is discussed and shown to be consistent.
DOI
10.1103/physrevd.42.2638

Related papers

Time as a stochastic process

M. W. Kalinowski

In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider continuous and discrete time.

arXiv:1411.1741•Oct 17, 2014•0 citations

A simple derivation of Born's rule with and without Gleason's theorem

Alexia Auffèves, Philippe Grangier

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual quantum formalism, within a new conceptual framework that is discussed heuristically in details. The structure of Quantum Mechanics, from its probabilistic nature to its mathematical expression, appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities.

arXiv:1505.01369•May 6, 2015•3 citations

Time in Quantum Theory

H. D. Zeh

The concept of time as used in various applications and interpretations of quantum theory is briefly reviewed.

arXiv:0705.4638•May 31, 2007•2 citations

Multiple-event probability in general-relativistic quantum mechanics. II. A discrete model

Mauricio Mondragón, Alejandro Pérez, Carlo Rovelli C

We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution.

arXiv:0705.0006•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 10, 2007•8 citations

THE INTERPRETATION OF QUANTUM MECHANICS. THE CASE OF THE RELATIVISTIC VELOCITY OF A PARTICLE WITHOUT SPIN

A.B. Datzeff

In previous works on probabilistic description of the quantum motion of a micro-particle mu the non-relativistic Schroedinger equation was derived. The idea developed is now used to show that one can find this probabilistic description for mu also for relativistic velocities. (T.R.H.)

Compt. rend.•Jan 1, 1960•0 citations

Recovering the Quantum Formalism from Physically Realist Axioms

Philippe Grangier

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.

•Jan 8, 2018•19 citations
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual quantum formalism, within a new conceptual framework that is discussed heuristically in details. The structure of Quantum Mechanics, from its probabilistic nature to its mathematical expression, appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities.
We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution.
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.