Foundations Of Quantum Theory Research Articles

Readers Elaborate on Fashion and Truth, Fact and Theory

Igreatly enjoyed Michael Riordan’s Opinion piece criticizing the Platonic aspects of contemporary theoretical physics. He is right that several of today’s research areas—superstrings, wormholes, and extra dimensions, for example—have cut loose almost completely from experimental reality.Unfortunately, though, Riordan’s arguments were undercut by his appeals to Charles Sanders Peirce and the pragmatist definition of truth. Although I believe Riordan is right to be proud of physicists’ discovery of quarks, that feeling would not be justified if the reality of quarks meant merely that experienced practitioners agree that quarks are a “convenient rubric,” as Riordan called it, for mocking up the observable consequences of certain experiments. That was also true of Ptolemy’s epicycles, phlogiston, and Lamarckian evolution—not to mention young-Earth creationism. No, the discovery of quarks is impressive because they are more than a useful fiction; as proved by experiment, they really do exist outside our imaginations.The pragmatist notion of truth is based on radical philosophical skepticism and leads logically to outright subjectivism—the claim that all scientific theories are mere “fanciful ideas and constructs.” And like the Platonism that Riordan criticizes, that kind of error has done real damage to physics.Consider, for example, Andreas Osiander’s plea that Copernicus didn’t really mean it, Ernst Mach’s bizarre and influential refusal to believe that atoms represented more than a useful rubric for organizing experience, and the ongoing refusal to face and fix what John Bell called the “unprofessionally vague and ambiguous” foundations of quantum theory. 1 1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (1987), p. 173. This refusal is usually based on the claim that the wavefunction is merely a mental construct, and does not refer to physical reality (see the Opinion piece by Christopher Fuchs and Asher Peres, Physics Today, March 2000, page 70).Consider also the contemporary attacks on science from the social-construction crowd; as those attackers point out, the pragmatist conception of truth gives scientists the same claim to know reality as any other group: none.Pitting science against Platonism tells only half the story. What makes the scientific method unique is that it rejects both Platonism and skeptical subjectivism. Unlike Platonism, science demands that its conclusions be based on hard, empirical evidence. But science also rejects the idea that we are cut off from true reality, forever confined to superficial appearances, subjective constructs, and useful fictions.At its best, science neither rejects empirical evidence in favor of rationalist flights of fancy nor dismisses as impossible the task of uncovering deep truths about the external world. Instead, it demonstrates, in the face of both traditional philosophical approaches, that hidden realities can be reliably grasped by means of empirical evidence. And that is an achievement all physicists can be proud of.REFERENCESection:ChooseTop of pageREFERENCE <<1. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge U. Press, New York (1987), p. 173. Google Scholar© 2003 American Institute of Physics.

Quantum optics and quantum entanglement

This Special Issue of Journal of Optics B: Quantum and Semiclassical Optics brings together contributions of various researchers working on theoretical and experimental aspects of quantum optics and quantum entanglement. The physics of quantum entangled states, an interdisciplinary field of research involving quantum optics, physics of quantum information and foundations of quantum theory, has been intensively exploited over the last decade in connection with quantum information processing, quantum communication and quantum computing. It was shown that the use of entangled states opens new horizons in such practical fields as cryptography, computing, information transmission, quantum imaging and precision measurements. Essential progress has also been achieved in the area of photon squeezing, generation of nonclassical states, including Schrodinger cats, trapped ions, Bose–Einstein condensates, cavity quantum electrodynamics, the Casimir effect, etc. These results have initiated applications in quantum information and communication, quantum imaging and quantum computing. This special issue is published in connection with the International Conference on Quantum Electronics (IQEC 2002) held on 26 June–1 July 2002, in Moscow, Russia, where the topics of quantum optics, generation and characterization of the entangled states and their applications were discussed in the framework of regular sections on quantum optics, quantum information and quantum computing, and during the special symposium on entangled states. We would like to express our gratitude to both authors and reviewers, for their efforts in preparing and ensuring the high scientific quality of the papers in this special issue. While the issue was in preparation for publication, one of the guest editors, Professor Anatoly Oraevski, suddenly passed away. He was a great scientist, recognized worldwide for his numerous important contributions to nonlinear and quantum optics, and to laser physics. Anatoly was always an enthusiastic advisor, mentor and collaborator. All of us remember numerous positive interactions with him, not only while organizing IQEC 2002 in Moscow last summer, but also throughout the years. He will be missed both for his scientific insight and because he was a good, kind and gentle man. Editing this special issue of Journal of Optics B: Quantum and Semiclassical Optics together with Professor Oraevski was our last joint effort and we would like to pay a tribute to him by dedicating this issue to his memory.

Counting Marbles: A Reply to Critics

Previous article No AccessDiscussionCounting Marbles: A Reply to CriticsPeter J. LewisPeter J. Lewis Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The British Journal for the Philosophy of Science Volume 54, Number 1March 2003 Society: The British Society for the Philosophy of Science Views: 2Total views on this site Citations: 2Citations are reported from Crossref Views: 2Total views on this site Citations: 2Citations are reported from Crossref Article DOIhttps://doi.org/10.1093/bjps/54.1.165 Views: 2Total views on this site Citations: 2Citations are reported from Crossref © 2003 by The Author. All rights reserved.PDF download Crossref reports the following articles citing this article:E. B. Davies Some Remarks on the Foundations of Quantum Theory, The British Journal for the Philosophy of Science 56, no.33 (Dec 2020): 521–539.https://doi.org/10.1093/bjps/axi129 Stephen P. Weldon Current Bibliography of the History of Science and Its Cultural Influences 2005, Isis 96 (Oct 2015): 1–242.https://doi.org/10.1086/isis.96.3652364

On the role of quantum structures in the foundations of quantum theory

On the role of quantum structures in the foundations of quantum theory

IDENTITY AND THE FOUNDATIONS OF QUANTUM THEORY

The foundations of quantum theory can be understood as a consequence of a fundamental concept of identity. Intuitive arguments motivate a mathematical formulation of identicality (the indistinguishability and equality of identical particles). Using a theorem of Fivel, this form of identicality leads to standard quantum theory.

Über zwei Formen von Realismus in der Quantentheorie

On Two Types of Realism in Quantum Theory. Current realist approaches to the foundations of quantum theory emphasize the dichotomy between (Copenhagen) positivism and ‘beable’-realism. Recently it was even attempted to turn this picture into two (equally possible) histories in order to legitimate Bohmian Mechanics as a viable alternative. This paper argues that this dichotomy is philosophically inadequate and historically questionable by embedding it into the philosophical discussion on positivism and realism that has taken place since the 1920s. Logical Empiricists back then advocated empirical realism and contrasted it to absolutistic metaphysical realism. From this viewpoint David Bohm's ‘beable’-realism combines elements of Mach's sensualism with a pre-Kantian metaphysics. As Wesley Salmon's position shows, empirical realism can become quite pronounced without relapsing into Bohmian philosophy. Instead it arrives close to the GRWP-interpretation. Hence, when Bernard d'Espagnat binds both together as ‘ontological interpretations’, he blurs the borderline between empirical and metaphysical realism that his Veiled Reality has set out to draw, quite in concordance with Logical Empiricism.

David Joseph Bohm: 1917?1992

David Bohm, Emeritus Professor of Theoretical Physics at Birkbeck College of the University of London and Fellow of the Royal Society, died of a heart attack on October 29, 1992 at the age of 74. Professor Bohm had been one of the world’s leading authorities on quantum theory and its interpretation for more than four decades. His contributions have been critical to all aspects of the field. He also made seminal contributions to plasma physics. His name appears prominently in the modern physics literature, through the AharonovBohm effect , the Bohm-EPR experiment , the Bohm-Pines collective description of particle interactions (random phase approximation), Bohm diffusion and the Bohm causal interpretation of quantum mechanics, also sometimes called the de Broglie-Bohm pilot wave theory . David Bohm was born in Wilkes-Barre, Pennsylvania on December 20, 1917. A student of J. Robert Oppenheimer, Bohm received his Ph.D. from the University of California at Berkeley in 1943. In 1950 he completed the first of his six books, Quantum Theory , which became the definitive exposition of the orthodox (Copenhagen) interpretation of quantum mechanics. Here Bohm presented his reformulation of the paradox of Einstein, Podolsky, and Rosen. It is this Bohm version of EPR which has provided the basis for the enormous expansion of research on the foundations of quantum theory, focusing on nonlocality and the possible incompleteness of the quantum description (the question of “hidden variables”), which has occurred during the past several decades. 1Fakultat fur Mathematik, Universitat Munchen, Theresienstrasse 39, 8000 Munchen 2, Germany. Supported in part by DFG. 2Department of Mathematics, Rutgers University, New Brunswick, NJ 08903. Supported in part by NSF Grant No. DMS–9105661. 3Istituto di Fisica, Universita di Genova, INFN, Via Dodecaneso 33, 16146 Genova, Italy. Supported in part by INFN.

The principle of identicality and the foundations of quantum theory. II. The role of identicality in the formation of quantum theory

The place of the concept of indistinguishability in the formation of quantum theory is examined, including particularly Planck’s earliest formulations of the quantum hypothesis, as well as the use of this concept in the developments surrounding the new quantum theory.

The principle of identicality and the foundations of quantum theory. I. The Gibbs paradox

The development of the concept of indistinguishability in the writings of Gibbs is traced, leading from the ‘‘Gibbs paradox’’ to his definition of generic phase.

Symmetry at the foundations of quantum theory

Symmetry in its essence is the possibility of making a change that leaves some aspect of the situation unchanged, or, most succinctly, symmetry is immunity to possible change. This is the conceptual formulation of symmetry. It might also be called the qualitative formulation of symmetry, in contrast to the group-theoretical formulation, which might be called the quantitative formulation of symmetry, in contrast to the group-theoretical formulation, which might be called the quantitative formulation of symmetry. The latter is expressed in terms of transformations (or operations), transformation groups, equivalence relations, equivalence classes, symmetry transformations (or symmetry operations), and symmetry groups, and can be developed from the conceptual formulation. For the description and treatment of many applications of symmetry in physics the group-theoretical formulation is the appropriate one. But for the account of the fundamental manifestations of symmetry in physics it is the conceptual formulation that is the more suitable. Symmetry implications of the postulates of quantum theory are investigated.

The foundation of quantum theory and noncommutative spectral theory: Part II

The present paper comprises Sects. 5–8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having layed down the foundations in the first part of this work (which appeared in the last issue of this journal and comprises Sects. 0–4), we arrived at a dual pair 〈Y, M〉 consisting of abase norm space Y and anorder unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. (2,3) In this part we add to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and enable us to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9).

The foundation of quantum theory and noncommutative spectral theory. Part I

The foundation of quantum theory and noncommutative spectral theory. Part I

A Rich Differential Equation for Computer Demonstrations

Born and raised in England, Bernard Banks immigrated to the United States in 1958. He received his B.S. and M.S. degrees in mathematics from California State University, San Diego. In 1975 he received his Ph.D. in mathematics from Oregon State University. His main interest is in the mathematical foundations of quantum theory. His hobbies include travel and ocean racing. Currently he is on the faculty of Cal Poly Pomona.

Spacetime and future quantum theory

The purpose of this article is to describe the arguments leading to the apparent conflict between EPR locality and predictions of quantum theory, and to discuss the impact of this result both upon future developments of quantum theory and upon some questions at issue in the foundations of quantum theory.

Time delay in tunneling: Transmission and reflection time delays.

The problem of time delay in one-dimensional quantum-mechanical scattering by a potential barrier is studied in the framework of time-dependent scattering theory. It is shown how the concept of sojourn time can be used to define three separate time delays: the time delay for transmission through the barrier, the time delay for reflection, and the total time delay (i.e., averaged over transmission and reflection). In addition to the anticipated dependence on the S matrix and its energy derivative, the time delays depend on certain parameters which can be interpreted as describing positions of detectors in a gedanken-experiment measurement. The problem of defining separate time delays for transmission and reflection appears to be rooted in the foundations of quantum theory and its interpretation.

Physical Foundations of Quantum Theory: Stochastic Formulation and Proposed Experimental Test?Addendum and Erratum

The Addendum of this note presents a brief perspective and an additional development pertaining to a previous paper. The even forceKn as well as the odd forceK0 of the time-inversion-covariant (TIC) equation of motion in the presence of a magnetic field are derived from the results of the previous paper by a hint of generalization in classical physics. Then, by following identical steps as in the previous paper, the Addendum completes the derivation of the stochastic Hamilton-Jacobi and the Schrodinger equations in the electromagnetic field. The Erratum of our note points out minor typographical errors plus one clarification of a definition.

Ergodic properties of one-parameter automorphism groups of operator algebras

We shall consider the following two types of dynamical systems employed in the foundations of quantum theory, C*-systems and W*-systems. It is widely believed that quantum dynamics is suitably described by one of the two types of systems (C* for quantum spin systems with “short range” interaction, and W* for “long range”) [5, 8, 17, 25, 27, 301. A C*-system is a pair (@, a,), where G! is a C*-algebra (always assumed to contain an identity), and (x, is a strongly continuous one-parameter group of *automorphism. The continuity requirement is 11 a,(a) a II+ 0 for t + 0, a E 0. A W*-system is a pair (M, yI), where M is a W*-algebra, and yI is a point-ultraweakly continuous one-parameter group of *-automorphisms of M. The continuity requirement here is 01, y,(x) x) + 0 for t + 0, x E M and ,u E M, are the a(M, M,)-continuous (=ultraweakly) linear functionals on M. The cone of positive elements in M, is denoted by Mf, and consists of the normal positive functionals on M (states when normalized). Both of the stated continuity requirements are well known to be natural for the respective systems, from the point of view of both mathematics [4, 14, 231, and physics [l, 5, 27, 291. A mathematical scattering theory for the two types of abstract quantum systems does not exist. The closest such seems to be rigorous conditions for return to equilibrium [28]. In this paper we look into some of the foundational problems associated to such a non-commutative scattering theory. Related results have earlier been obtained by Arveson [3,4], Muhly and co-workers [20,22], Kawamura and Tomiyama 1151, and Zsido [37]. Common to these results is the focus on finite systems (i.e., the special case where traces are present). In applications [ 10, 12, 131 it is known, however. that the actual systems are type III, and in this paper we therefore turn to the infinite case. 354 0022-247X/82/060354-19$02.00/0

Nonlinear wave mechanics and particulate self-focusing

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship connecting coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called “effective” and “tired” photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest.

Physical foundations of quantum theory: Stochastic formulation and proposed experimental test

The time-dependent Schrodinger equation has been derived from three assumptions within the domain of classical and stochastic mechanics. The continuity equation isnot used in deriving the basic equations of the stochastic theory as in the literature. They are obtained by representing Newton's second law in a time-inversion consistent equation. Integrating the latter, we obtain the stochastic Hamilton-Jacobi equation. The Schrodinger equation is a result of a transformation of the Hamilton-Jacobi equation and linearization by assigning the arbitrary constant ħ=2mD. An experiment is proposed to determine ħ and to test a hypothesis of the theory directly. A mathematical apparatus is formulated from the Jacobian formalism to derive physical parameters from ψ(x, t) and to obtain operators for the boundary cases of the theory. The operator formalisms are compared by means of a well-known solution in the quantum theory.

On geometric ideas which lie at the foundation of quantum theory

Part I advances the hypothesis that between any two events on the world-line of a particle there can be at most finitely many intermediate events. From this it draws the conclusion that the space-time coordinates of events do not have precise meanings. Part II modifies the Feynman integral in a way which is analogous to the replacement of white noise by Gaussian noise. It thereby obtains a version of the quantum mechanics for a nonrelativistic particle in a potential. In the new discrete quantum theory, space coordinates have probabilistic rather than precise meanings; the energy of a free particle is a bounded operator; and the potential energy is a compact operator. It is argued that the differential scattering cross section for elastic scattering is unchanged when taken in the Born approximation.