I. Introductory Remarks. The Copenhagen Era. II. The Psychology of the 1925 Revolution. III. Reassessing Copenhagen. IV. Copenhagen versus Copenhagen. V. Von Neumann, Popper-EPR, Bohm, Bell, Aspect. A Sommerfeld-de Rham View of Single Systems. VI. Period Integrals: A Universal Tool of Physics. VII. Larmor and Cyclotron Aspects of Flux Quanta. VIII. Fitting Period Integrals to Physics. IX. Implications of Cooperative Behavior. X. A Tale of Fine Structure Coincidences. XI. Classical Nonclassical Asymptotics. An Attempt at Cohomological Synthesis. XII. Arrowed Time and Cyclic Time. XIII. Quantum Cohomology. XIV. Optimizing Reduction to Familiar Concepts. Ramifications of the Two-Tier View of Q.M. XV. Compatibility of Quantum Mechanics and Relativity. XVI. Quantum Understanding in Global Perspective. XVII. Absolute versus Relative Indeterminism. XVIII. The Diffeo-4 Mandate of Michelson-Sagnac. Epilogue for Extrapolating a Favor of Fortune. Notes and References. Index.
I. Introductory Remarks. The Copenhagen Era. II. The Psychology of the 1925 Revolution. III. Reassessing Copenhagen. IV. Copenhagen versus Copenhagen. V. Von Neumann, Popper-EPR, Bohm, Bell, Aspect. A Sommerfeld-de Rham View of Single Systems. VI. Period Integrals: A Universal Tool of Physics. VII. Larmor and Cyclotron Aspects of Flux Quanta. VIII. Fitting Period Integrals to Physics. IX. Implications of Cooperative Behavior. X. A Tale of Fine Structure Coincidences. XI. Classical Nonclassical Asymptotics. An Attempt at Cohomological Synthesis. XII. Arrowed Time and Cyclic Time. XIII. Quantum Cohomology. XIV. Optimizing Reduction to Familiar Concepts. Ramifications of the Two-Tier View of Q.M. XV. Compatibility of Quantum Mechanics and Relativity. XVI. Quantum Understanding in Global Perspective. XVII. Absolute versus Relative Indeterminism. XVIII. The Diffeo-4 Mandate of Michelson-Sagnac. Epilogue for Extrapolating a Favor of Fortune. Notes and References. Index.
List of participants Preface Part I. Introduction: 1. The function of the colloquium - editorial 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsacker 4. On Bohr's views concerning the quantum theory D. Bohm Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman 9. Measurement theory and complex systems M. A. Garstens Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose 15. A note on discreteness, phase space and cohomology theory B. J. Hiley 16. Cohomology of observations R. H. Atkin 17. The origin of half-integral spin in a discrete physical space Ted Bastin Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsacker 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post 21. How does a particle get from A to B? Ted Bastin 22. Informational generalization of entropy in physics Jerome Rothstein 23. Can life explain quantum mechanics? H. H. Pattee 24. Discussion: phenomena and sense data in quantum theory D. S. Linney and C. F. von Weizsacker Index of persons Index of subjects.
In previous chapters we presented and discussed the standard, generally accepted Copenhagen interpretation of quantum mechanics according to which there exists in nature at the most fundamental level an irreducible and ineliminable indeterminism. Although we saw that what historically constituted the Copenhagen interpretation of quantum mechanics is difficult to specify with precision, three central commitments do characterize it. (1) In general, no particle trajectories can exist in a space–time background. (2) No deterministic description of fundamental physical phenomena is possible. (3) There exists in the laws of the fundamental physical phenomena of nature an essential and ineliminable indeterminism or probability (unlike the probability of classical physics, that there reflects our ignorance of the finer details of complex physical phenomena). A flavor of these features of the Copenhagen interpretation of quantum mechanics can be gotten from the quotations at the beginning of Part VIII ( Some philosophical lessons from quantum mechanics ). On this view, it is in principle impossible to predict, say, the exact future behavior of an electron (that is, to give its position and velocity as functions of the time). According to the Copenhagen school, there can be no causal description of microphenomena in terms of a continuous space–time background (as there is in classical physics). It is generally believed that a causal interpretation of quantum mechanics is impossible, although no proof of this exists.
In this monograph I present the basic structure of an interpretation of quantum mechanics. Chapter 1 outlines the central ideas behind the interpretation and illustrates them by means of examples: Subsequent chapters fill in the details of the interpretation. But it is important to begin by explaining what I take an interpretation of quantum mechanics to be, and why any further interpretation needs to be offered. After all, quantum mechanics (in some form) is by now both a foundation for much of contemporary physics and a veteran of more than sixty years of intermittent but sometimes intense reflection on its content and meaning. What more can be, or should be, said about the interpretation of this theory? Many physicists believe that no more needs to be said: that there is basically only one way of understanding quantum mechanics, due to Bohr, Heisenberg, Pauli, and others, and that the only remaining interpretative task is that of the physics teacher, who seeks to perfect ways of conveying this understanding to new generations of students. Sir Rudolf Peierls, one of the more lucid and distinguished of these physicists, even objects to the use of the familiar term ‘Copenhagen interpretation’ to refer to the way of understanding quantum mechanics due to Bohr, Heisenberg, Pauli, and others. Because this sounds as if there were several interpretations of quantum mechanics. There is only one. There is only one way in which you can understand quantum mechanics.[…]
This essay is essentially a plea for recognizing the Aharonov–Bohm (AB) integral as part of a quantum superstructure of Maxwell theory counting units of flux. The Gauss–Ampère (GA) integral then is added as a counter of net charge as well as an exterior product of the two, suggested by Kiehn, as counter of units of action. De facto, the AB integral already has this status, yet how its prestatistical nature relates to standard statistics-based quantum mechanics needs delineation. For electromagnetism to claim this quantum superstructure as a legitimate member of its family it is unavoidable to take issue with the Copenhagen view of quantum mechanics as stated in the introductory paragraph of this article. The limiting mathematical traditions that have been standing in the way of such developments are briefly reviewed here. They pertain to the relations between local and global procedures as delineated in de Rham theory as well as recognizing certain metric-free aspects of electromagnetism as a requirement sine qua non for counting in the micro-domain. For extended discussions, references, and proofs pertaining to the ensuing Quantum Reprogramming of the Copenhagen interpretation, readers are invited to consult the monograph of that title, by the present author.
For many years the physical interpretation of quantum theory has been dominated by the “wave-particle duality” attitude of the “Copenhagen school.” This point of view is eloquently described in Bohr's collection of essays on the subject. Despite persistent concerns with apparent paradoxes and limitations to this interpretation (as exemplified by Schrodinger's cat, the paradox of Einstein, Podolsky and Rosen, among others), the Copenhagen view persists de facto in the daily life of the modern physicist. Traditional quantum theory has so successfully explained such a vast amount of data in atomic and molecular physics, solid state physics (and to a lesser extent, elementary particle physics) that little doubt can exist concerning its essential validity. As a consequence of the overwhelming practical success of the “Copenhagen interpretation, ” the latter has acquired the status of dogma. For many years, therefore, most physicists have found it expedient to relegate the puzzling aspects of the theory to philosophers, and mathematicians. Nevertheless, a persistent interest in this subject has produced a significant and fascinating literature, reviewed by Jammer. In recent years, concerns over the proper meaning to be ascribed to quantum theory have produced an increasingly deep and incisive series of investigations. These investigations fall generally into two categories: either (1) discussion of the philosophical content of the theory, or (2) analyses of the mathematical variants of the theory and their connection with differing interpretational schemes. Physicists tend to be detached from a commitment to philosophical issues, because of their realization of the transient character of the meanings attached to theories of the day. As a simple illustration of this we can mention the profound differences between nonrelativistic and relativistic quantum mechanics.
This book is intended to serve as an approachable starting point for scholars, students, and enthusiasts who are keen to learn more about this cutting-edge field. Although quantum computing is based on complex mathematics and abstract physics, its fundamental concepts such as superposition, entanglement, and quantum gates, can be easily comprehended. This study attempts to close the gap between curiosity and comprehension by gradually and clearly presenting these concepts. Chapter I, II, III was prepared by Mr.P.Sathish. This chapter clearly focused on Introduction to Quantum Computing, History and Evolution of Quantum Computing, Classical vs Quantum Computing. Chapter IV, V, VI, VII was prepared by Mr.L.Dinesh. This Chapter introduces the concept of Quantum Mechanics Fundamentals, Qubits: The Building Blocks of Quantum Computing, Quantum Gates and Circuits and Quantum Algorithms. Chapter VIII, IX, X was prepared by Mr.S.Alaguganesan. This chapter clearly focused on Domain-Specific Quantum Algorithms, Quantum Hardware Technologies and Quantum Error Correction (QEC). Chapter XI, XII, XIII, XIV was prepared by Mr.P.Muthamil Selavan. This Chapter introduces the concept of Quantum Cryptography, Applications of Quantum Computing, Challenges in Quantum Computing and Future of Quantum Computing.