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

Zhur. Eksptl'. i Teoret. Fiz.

QUANTUM MECHANICAL PROBABILITIES AS SUMS OVER TRAJECTORIES

G. V. Ryazanov

Published Jul 1, 1958• 0 citations
OpenAlex

Abstract

A new formulation of nonrelativistic quantum mechanics, that is, a general definition of the probability for any event is proposed. The physical content of quantum mechanics reduces to a single principle which is similar to the Gibbs principle and permits one to solve problems without making recourse to wave functions and operators. (tr-auth)

Related papers

On the Measurement Problem

Raed M. Shaiia

In this paper, we will see that we can reformulate the purely classical probability theory, using similar language to the one used in quantum mechanics. This leads us to reformulate quantum mechanics itself using this different way of understanding probability theory, which in turn will yield a new interpretation of quantum mechanics. In this reformulation, we still prove the existence of none classical phenomena of quantum mechanics, such as quantum superposition, quantum entanglement, the uncertainty principle and the collapse of the wave packet. But, here, we provide a different interpretation of these phenomena of how it is used to be understood in quantum physics. The advantages of this formulation and interpretation are that it induces the same experimental results, solves the measurement problem, and reduces the number of axioms in quantum mechanics. Besides, it suggests that we can use new types of Q-bits which are more easily to manipulate.

International Journal of Theoretical and Mathematical Physics•Oct 1, 2014•0 citations

Quantum Mechanics

Jørgen Rammer

This chapter introduces the quantum mechanics. It explores the formulation in terms of the operator calculus. The chapter shows how nonrelativistic quantum kinematics emerges from the general theory. It discusses how physical quantities are related to symmetries through unitary transformations, and consider translations. The chapter also introduces the statistical operator and the density matrix. It introduces the consistent history interpretation of quantum mechanics. The true core of quantum mechanics is the rule for assigning the amplitude to an event that can be effected in indistinguishable ways. The chapter examines the presentation of Feynman's space-time approach since it offers the most intuitive formulation of quantum mechanics. A physical quantity is said to be conserved if it for any state of the system stays constant in time. In quantum mechanics this therefore means that its probability distribution in any state is independent of time.

CRC Press eBooks•May 4, 2018•0 citations

Quantum Mechanics as Generalised Theory of Probabilities

Michel Bitbol

It is argued that quantum mechanics does not have merely a predictive function like other physical theories; it consists in a formalisation of the conditions of possibility of any prediction bearing upon phenomena whose circumstances of detection are also conditions of production. This is enough to explain its probabilistic status and theoretical structure.

•Jan 1, 2014•1 citation

Multiple-event probability in general-relativistic quantum mechanics

Frank Hellmann, Mauricio Mondragón, Alejandro Pérez +1 more

We discuss the definition of quantum probability in the context of ``timeless'' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse'' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

arXiv:gr-qc/0610140•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Apr 19, 2007•29 citations

The New Probabilistic Approach to the Quantum Mechanics

Jiří Souček

Quantum Mechanics (QM) is primarily a probabilistic theory. The standard Kolmogorov probability theory is not suitable for this goal since it does not offer the possibility of the reversible time evolution. This implies the need to construct a new probability theory which is able to model the reversible time evolution. I have proposed such an Extended probability theory. The main goal of this project is to understand what QM is. In this note I shall describe the program of the research which is already partially realized.

•Jul 1, 2015•0 citations

The Montevideo Interpretation: How the Inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem

Rodolfo Gambini, Jorge A. Pullin

We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.

arXiv:2010.14519•Universe•Dec 11, 2020•12 citations
A new formulation of nonrelativistic quantum mechanics, that is, a general definition of the probability for any event is proposed. The physical content of quantum mechanics reduces to a single principle which is similar to the Gibbs principle and permits one to solve problems without making recourse to wave functions and operators. (tr-auth)
In this paper, we will see that we can reformulate the purely classical probability theory, using similar language to the one used in quantum mechanics. This leads us to reformulate quantum mechanics itself using this different way of understanding probability theory, which in turn will yield a new interpretation of quantum mechanics. In this reformulation, we still prove the existence of none classical phenomena of quantum mechanics, such as quantum superposition, quantum entanglement, the uncertainty principle and the collapse of the wave packet. But, here, we provide a different interpretation of these phenomena of how it is used to be understood in quantum physics. The advantages of this formulation and interpretation are that it induces the same experimental results, solves the measurement problem, and reduces the number of axioms in quantum mechanics. Besides, it suggests that we can use new types of Q-bits which are more easily to manipulate.
This chapter introduces the quantum mechanics. It explores the formulation in terms of the operator calculus. The chapter shows how nonrelativistic quantum kinematics emerges from the general theory. It discusses how physical quantities are related to symmetries through unitary transformations, and consider translations. The chapter also introduces the statistical operator and the density matrix. It introduces the consistent history interpretation of quantum mechanics. The true core of quantum mechanics is the rule for assigning the amplitude to an event that can be effected in indistinguishable ways. The chapter examines the presentation of Feynman's space-time approach since it offers the most intuitive formulation of quantum mechanics. A physical quantity is said to be conserved if it for any state of the system stays constant in time. In quantum mechanics this therefore means that its probability distribution in any state is independent of time.
We discuss the definition of quantum probability in the context of ``timeless'' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse'' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.
Quantum Mechanics (QM) is primarily a probabilistic theory. The standard Kolmogorov probability theory is not suitable for this goal since it does not offer the possibility of the reversible time evolution. This implies the need to construct a new probability theory which is able to model the reversible time evolution. I have proposed such an Extended probability theory. The main goal of this project is to understand what QM is. In this note I shall describe the program of the research which is already partially realized.
We review the Montevideo Interpretation of quantum mechanics, which is based on the use of real clocks to describe physics, using the framework that was recently introduced by Höhn, Smith, and Lock to treat the problem of time in generally covariant systems. These new methods, which solve several problems in the introduction of a notion of time in such systems, do not change the main results of the Montevideo Interpretation. The use of the new formalism makes the construction more general and valid for any system in a quantum generally covariant theory. We find that, as in the original formulation, a fundamental mechanism of decoherence emerges that allows for supplementing ordinary environmental decoherence and avoiding its criticisms. The recent results on quantum complexity provide additional support to the type of global protocols that are used to prove that within ordinary—unitary—quantum mechanics, no definite event—an outcome to which a probability can be associated—occurs. In lieu of this, states that start in a coherent superposition of possible outcomes always remain as a superposition. We show that, if one takes into account fundamental inescapable uncertainties in measuring length and time intervals due to general relativity and quantum mechanics, the previously mentioned global protocols no longer allow for distinguishing whether the state is in a superposition or not. One is left with a formulation of quantum mechanics purely defined in quantum mechanical terms without any reference to the classical world and with an intrinsic operational definition of quantum events that does not need external observers.