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

Journal of Mathematical Physics

A Superposition Principle in Physics

Stanley Gudder

Published Mar 1, 1970• 37 citations
Publisher

Abstract

A superposition principle is considered both in classical mechanics and in the quantum logic approach to quantum mechanics. It is shown, roughly speaking, that in classical mechanics the only type of superposition of states is a mixture and that no pure state is a nontrivial superposition of other pure states. In quantum mechanics it is shown that, if a superposition principle holds, then the quantum logic is a complete atomic lattice.

DOI
10.1063/1.1665193

Related papers

On the Principle of Superposition in Quantum Mechanics

G. F. D. Duff

The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."

Canadian Mathematical Bulletin•Mar 1, 1964•0 citations

Facial aspect of superposition principle in algebraic quantum theory

Etang Chen

A facial version of superposition principle is introduced in algebraic quantum theory; similar to the quantum logic approach it exhibits characteristic features of quantum theory. It is shown that any pair of primary states satisfy the superposition principle if and only if they are quasiequivalent. A coherent sector is then defined as a quasi-equivalent class of primary states, which holds for both pure states in quantum theory and pure thermodynamic phases in quantum statistical mechanics.

Journal of Mathematical Physics•Oct 1, 1973•7 citations

Full Superposition Principle Is Inconsistent with Non-Deterministic Versions of Quantum Physics

Andrés Felipe Ortiz, Владик Крейнович

Many practical systems are non-deterministic, in the sense that available information about the initial states and control values does not uniquely determine the future states. For some such systems, it is important to take quantum effects into account. For that, we need to develop non-deterministic versions of quantum physics. In this paper, we show that for non-deterministic versions of quantum physics, we cannot require superposition principle -- one of the main fundamental principles of modern quantum mechanics. Specifically, while we can consider superpositions of states corresponding to the same version of the future dynamics, it is not consistently possible to consider superpositions of states corresponding to different versions of the future.

•Jan 1, 2013•1 citation

Quantum supervaluationism

Arkady Bolotin

As it is known, neither classical logical conjunction “and” nor classical logical alternative “either…or” can replace “+” representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In this paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind, even granting that their compounds (such as logical alternative “either…or”) can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.

arXiv:1709.01207•Journal of Mathematical Physics•Dec 1, 2017•7 citations

Superposition of states and the structure of quantum logics

Platon C. Deliyannis

A derivation of the classical Hilbert space model of quantum theory is given (including superselection rules) based (i) on various axioms on the behavior of events and (ii) an explicit formula for the superposition of two pure states in terms of transition probabilities.

Journal of Mathematical Physics•Feb 1, 1976•7 citations

Coherence of Superpositions

Qiu-Ling Yue, Chao‐Hua Yu, Feng Liu +3 more

Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of superpositions.

arXiv:1605.04067•May 13, 2016•2 citations
A superposition principle is considered both in classical mechanics and in the quantum logic approach to quantum mechanics. It is shown, roughly speaking, that in classical mechanics the only type of superposition of states is a mixture and that no pure state is a nontrivial superposition of other pure states. In quantum mechanics it is shown that, if a superposition principle holds, then the quantum logic is a complete atomic lattice.
The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."
Many practical systems are non-deterministic, in the sense that available information about the initial states and control values does not uniquely determine the future states. For some such systems, it is important to take quantum effects into account. For that, we need to develop non-deterministic versions of quantum physics. In this paper, we show that for non-deterministic versions of quantum physics, we cannot require superposition principle -- one of the main fundamental principles of modern quantum mechanics. Specifically, while we can consider superpositions of states corresponding to the same version of the future dynamics, it is not consistently possible to consider superpositions of states corresponding to different versions of the future.
As it is known, neither classical logical conjunction “and” nor classical logical alternative “either…or” can replace “+” representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In this paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind, even granting that their compounds (such as logical alternative “either…or”) can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.
Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of superpositions.