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 Chemical Education

Particles, waves, and the interpretation of quantum mechanics

N. D. Christoudouleas

Published Sep 1, 1975• 2 citations
Publisher

Abstract

A brief description of the conceptual basis of quantum mechanics and the Copenhagen interpretation.
DOI
10.1021/ed052p573

Related papers

Bohm's realist interpretation of Quantum mechanics

Virendra Singh

A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.

arXiv:0805.1779•May 13, 2008•2 citations

Summary of interpretations of quantum mechanics

Václav Profant

•Jan 1, 2006•0 citations

OUTLINE OF AN INTERPRETATION OF QUANTUM MECHANICS

WORLD SCIENTIFIC eBooks•Jun 1, 2000•0 citations

Je kodaňská interpretace kvantové mechaniky tabu?

Jan Fikatchek

This article analyzes the Copenhagen interpretation of quantum mechanics with regard to its historical role, logical consistency, and ontological assumptions. It argues that the Copenhagen interpretation has been extraordinarily successful as a practical framework connecting the mathematical formalism of quantum mechanics with experimental results, but that its positivist restriction to observable quantities does not provide a complete physical explanation of quantum wave behaviour. The analysis of other interpretations suggests that no interpretation of quantum mechanics, including the Copenhagen interpretation, can avoid some form of hidden entity. The central argument is based on the double-slit experiment: probability or mere possibility cannot by themselves physically cause interference, and therefore some real wave-like entity must exist whose effect is only probabilistically described by the wave function. The wave function is therefore not understood as a physical wave itself, but as an epistemic description of the interaction between a particle and a deeper hidden wave structure. The Copenhagen interpretation need not be simply rejected; rather, it can be understood as a successful simplification of a deeper interpretation. It accurately describes measurable results, but it does not explain the real mechanism that produces them. The article suggests that inspiration for such a deeper view can be found in quantum field theory: particles are perturbations of fields, and quantum entanglement may indicate the existence of a deeper nonlocal field of entanglement.

•Jun 24, 2026•0 citations

A Brief Survey of Main Interpretations of Quantum Mechanics

Jarosław Pykacz

SpringerBriefs in physics•Jan 1, 2015•7 citations

Quantum mechanical reality according to Copenhagen 2.0

A.M. Din

The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is sufficiently incremental so as to be appropriately characterized as Copenhagen 2.0.

International Journal of Modern Physics A•May 26, 2016•0 citations
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
This article analyzes the Copenhagen interpretation of quantum mechanics with regard to its historical role, logical consistency, and ontological assumptions. It argues that the Copenhagen interpretation has been extraordinarily successful as a practical framework connecting the mathematical formalism of quantum mechanics with experimental results, but that its positivist restriction to observable quantities does not provide a complete physical explanation of quantum wave behaviour. The analysis of other interpretations suggests that no interpretation of quantum mechanics, including the Copenhagen interpretation, can avoid some form of hidden entity. The central argument is based on the double-slit experiment: probability or mere possibility cannot by themselves physically cause interference, and therefore some real wave-like entity must exist whose effect is only probabilistically described by the wave function. The wave function is therefore not understood as a physical wave itself, but as an epistemic description of the interaction between a particle and a deeper hidden wave structure. The Copenhagen interpretation need not be simply rejected; rather, it can be understood as a successful simplification of a deeper interpretation. It accurately describes measurable results, but it does not explain the real mechanism that produces them. The article suggests that inspiration for such a deeper view can be found in quantum field theory: particles are perturbations of fields, and quantum entanglement may indicate the existence of a deeper nonlocal field of entanglement.
The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is sufficiently incremental so as to be appropriately characterized as Copenhagen 2.0.