In this paper, we discuss the general significance of order in physics, as a first step toward the development of new notions of order. We begin with a brief historical discussion of the notions of order underlying ancient Greek views, and then go on to show how these changed in key ways with the rise of classical physics. This leads to a broader view of the significance of order, which helps to indicate what is to be meant by a change (...) of our general notions of order in physics. We then go into relativity and quantum theory, showing how these developments actually did bring in further new notions of order, which are however inconsistent and otherwise inadequate in certain ways. Finally, using these inconsistencies and inadequacies as clues or indications for yet a further new concept of order, we make some proposals for novel directions of inquiry (to be discussed in some detail in later papers) which could lead to theories as different from relativity and quantum theory as these are from classical physics. (shrink)

A sophisticated and original introduction to the philosophy of quantum mechanics from one of the world’s leading philosophers of physics In this book, Tim Maudlin, one of the world’s leading philosophers of physics, offers a sophisticated, original introduction to the philosophy of quantum mechanics. The briefest, clearest, and most refined account of his influential approach to the subject, the book will be invaluable to all students of philosophy and physics. Quantum mechanics holds a unique place in the (...) history of physics. It has produced the most accurate predictions of any scientific theory, but, more astonishing, there has never been any agreement about what the theory implies about physical reality. Maudlin argues that the very term “quantum theory” is a misnomer. A proper physical theory should clearly describe what is there and what it does—yet standard textbooks present quantum mechanics as a predictive recipe in search of a physical theory. In contrast, Maudlin explores three proper theories that recover the quantum predictions: the indeterministic wavefunction collapse theory of Ghirardi, Rimini, and Weber; the deterministic particle theory of deBroglie and Bohm; and the conceptually challenging Many Worlds theory of Everett. Each offers a radically different proposal for the nature of physical reality, but Maudlin shows that none of them are what they are generally taken to be. (shrink)

The 1927 Solvay conference was perhaps the most important meeting in the history of quantum theory. Contrary to popular belief, the interpretation of quantum theory was not settled at this conference, and no consensus was reached. Instead, a range of sharply conflicting views were presented and extensively discussed, including de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schrödinger's wave mechanics. Today, there is no longer an established or dominant interpretation of (...) class='Hi'>quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. This book contains a complete translation of the original proceedings, with background essays on the three main interpretations of quantum theory presented at the conference, and an extensive analysis of the lectures and discussions in the light of current research in the foundations of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a theory of 'quantum mechanics' apparently lacking in wave function collapse or fundamental time evolution. This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory. (shrink)

Tous les mots, phrases et expressions avec leur prononciation pour pouvoir communiquer en toute situation.

In this paper I am concerned with analyzing in detail how ideas and expectations regarding the role of time in quantum theory arose and evolved in the early years of quantum mechanics. The general theme is that expectations which seemed reasonable from the point of view of matrix mechanics and Dirac's q-number formalism became implausible in light of Dirac-Jordan transformation theory, and were dashed by von Neumann's Hilbert space formalism which came to replace it. Nonetheless, I (...) will identify two concerns that remain relevant today, and which blunt the force of Hilgevoord's claim that the demand that time feature as an observable arose as the result of a simple conceptual error. (shrink)

This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of (...) a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quantum foundations. The book is directed at researchers in physics, computer science, and mathematics and would be appropriate as the basis of a graduate course in Quantum Foundations. (shrink)

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed (...) in defending the claim that QT is about quantum information. First of all, I argue that Bub’s interpretation of QT as a principle theory fails to fully explain quantum non-locality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories. (shrink)

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a (...) primitive ingredient of any quantum theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive “logic”). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems. (shrink)

​This book summarizes the results of research the authors have pursued in the past years on the problem of implementing Bell's notion of local causality in local physical theories and relating it to other important concepts and principles in the foundations of physics such as the Common Cause Principle, Bell's inequalities, the EPR scenario, and various other locality and causality concepts. The book is intended for philosophers of science with an interest in the formal background of sciences, philosophers of physics (...) and physicists working in foundation of physics. (shrink)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as (...) mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced (...) by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

The answer to the question 'what is money?' has changed throughout history. During the Gold Standard era, money was seen as gold or silver (the theory known as bullionism). In the early 20th century, the alternative theory known as chartalism proposed that money was a token chosen by the state for payment of taxes. Today, many economists take an agnostic line, and argue that money is best defined in terms of its function, e.g. as a neutral medium (...) of exchange. This paper argues that none of these approaches adequately describes the nature of money, and proposes a new theory, inspired by non-Newtonian physics, which takes into account the dualistic real/virtual properties and complex nature of money. The theory is applied to the example of the emergence of cybercurrencies. (shrink)

SummaryThe history of quantum physics has been deeply conditioned by the change in scientific practice as a social activity during the past fifty years. As a result the theory has not been allowed full maturing; both its formal and empirical advances have not resulted in a comparable conceptual progress. The recasting of quantum theory thus appears as an epistemological necessity. One of the main aspects of this process is to clear quantum theory from (...) its persisting classical connections in order to endow it with an autonomous and intrinsic status. Problems related to the foundations, description, interpretation and approximations of quantum theory are considered in turn, and various recent works are reviewed which contribute to the proposed endeavour.RésuméL'histoire de la théorie quantique a été fortement conditionnée par les changements intervenus au cours des cinquante dernières années dans la pratique scientifique en tant qu'activité sociale. La théorie en conséquence n'a pu atteindre sa pleine maturité et ses développements à la fois formels et empiriques n'ont pas conduit à des progrès conceptuels comparables. La refonte de la théorie quantique apparaît ainsi comme une nécessitéépistémologique. L'un des principaux aspects de ce processus consiste à débarrasser la théorie quantique de ses persistantes attaches classiques, de façon à lui conférer un statut autonome et intrinsèque. On considère ici tour à tour les problèmes de fondements, de terminologie, d'interprétation et de limites, de la théorie quantique, tout en passant en revue divers travaux récents contribuant à l'entreprise proposée.ZusammenfassungDie Geschichte der Quantenphysik ist in entscheidender Weise durch die Veränderungen, die in den letzten fünfzig Jahren in der wissenschaftlichen Praxis als einer sozialen Tätigkeit eingetreten sind, bestimmt worden. Die Theorie hat deshalb ihre volle Reife nicht erlangen können; ihre zugleich formalen und empirischen Entfaltungen haben nicht zu einem entsprechenden begrifflichen Fortschritt geführt. Eine Umgestaltung der Quantentheorie muss daher als ein erkenntnistheoretisches Desiderat betrachtet werden. Einer der wichtigsten Aspekte eines derartigen Unterfangens wird darin bestehen, die Theorie von ihren hartnäckigen Bindungen an klassische Begriffe zu befreien, um ihr einen eigenständigen und autonomen Status zu verleihen. Es werden die Probleme der Begründung, der Terminologie, der Interpretation und der Grenzen der Quantentheorie diskutiert, indem auch verschiedene kürzlich erschienene Arbeiten, die sich auf das vorgeschlagene Unternehmen beziehen, berücksichtigt werden. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link (...) these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924–1925. Although it failed to attract the attention of Einstein’s contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein’s quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein’s (...) confusion with his initial success in extending Bose’s results and in realizing the consequences of what later came to be called Bose–Einstein statistics. We discuss Einstein’s motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein’s belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well known to Einstein from earlier work on Wien’s displacement law, Planck’s radiation theory and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory. (shrink)

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that “strange” weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of (...) Lüders’ Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

The book considers foundational thinking in quantum theory, focusing on the role the fundamental principles and principle thinking there, including thinking that leads to the invention of new principles, which is, the book contends, one of the ultimate achievements of theoretical thinking in physics and beyond. The focus on principles, prominent during the rise and in the immediate aftermath of quantum theory, has been uncommon in more recent discussions and debates concerning it. The book argues, however, (...) that exploring the fundamental principles and principle thinking is exceptionally helpful in addressing the key issues at stake in quantum foundations and the seemingly interminable debates concerning them. Principle thinking led to major breakthroughs throughout the history of quantum theory, beginning with the old quantum theory and quantum mechanics, the first definitive quantum theory, which it remains within its proper (nonrelativistic) scope. It has, the book also argues, been equally important in quantum field theory, which has been the frontier of quantum theory for quite a while now, and more recently, in quantum information theory, where principle thinking was given new prominence. The approach allows the book to develop a new understanding of both the history and philosophy of quantum theory, from Planck's quantum to the Higgs boson, and beyond, and of the thinking the key founding figures, such as Einstein, Bohr, Heisenberg, Schrödinger, and Dirac, as well as some among more recent theorists. The book also extensively considers the nature of quantum probability, and contains a new interpretation of quantum mechanics, "the statistical Copenhagen interpretation." Overall, the book's argument is guided by what Heisenberg called "the spirit of Copenhagen," which is defined by three great divorces from the preceding foundational thinking in physics-reality from realism, probability from causality, and locality from relativity-and defined the fundamental principles of quantum theory accordingly. (shrink)

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's (...) principle of least time, the principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that “strange” weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of (...) Lüders’ Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis (...) for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

ABSTRACT: A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application (...) of Luders' Rule. It is argued that an assumption of reverse causality implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions. (shrink)

Quantum probability is used to provide a new organization of basic quantum theory in a logical, axiomatic way. The principal thesis is that there is one fundamental time evolution equation in quantum theory, and this is given by a new version of Born’s Rule, which now includes both consecutive and conditional probability as it must, since science is based on correlations. A major modification of one of the standard axioms of quantum theory allows (...) the implementation of various mathematically distinct models (commonly called ‘pictures’) of them. A natural definition of isomorphism of models is presented next. For a given Hamiltonian the standard ‘pictures’ of quantum theory (e.g., Schrödinger, Heisenberg, interaction) are isomorphic models, whose probabilities are nonetheless model independent. The Schrödinger equation remains valid in one model of the axioms, even though it is no longer the fundamental equation of time evolution. All the usual calculations of standard, textbook quantum theory remain valid, but they are put in a new light. For example, the ‘collapse’ of the state is now viewed in the Schrödinger model as _one_ step in a _two_ step algorithm for calculating _one_ conditional probability. In the isomorphic Heisenberg model, where states are constant in time, one has the same conditional probability given by the same formula. Also, entanglement is defined in a new, more general model independent way as an aspect of quantum probability without using ‘collapse’ or tensor products. (shrink)

This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics. Drawing on original publications and letters written by the main protagonists of that time, it shows that Einstein's contributions from 1905 (...) to 1924 laid the essential foundations for the development of Quantum Theory. Einstein introduced quantization of the radiation field; Born added quantized mechanical behavior. In addition, Born recognized that Quantum Mechanics necessarily required Quantum Optics; his radical concept of truly discontinuous and statistical quantum transitions ("quantum leaps") was directly based on Einstein's physical concepts. (shrink)

In November of 1925 Born, Heisenberg and Jordan wrote an article together in which they demonstrated that Einstein's energy fluctuation formula could be derived from quantum mechanics. They remark that the equations are subject to reinterpretation. Specifically, the states of radiation oscillators can be reinterpreted as numbers of quanta of radiation. They also connected this latter idea up with Bose-Einstein statistics. Heisenberg wrote to Pauli that it was Jordan who contributed the idea of reinterpreting the terms. This was the (...) first step toward quantum field theory. In August of the following year Dirac derived Einstein's A and B coefficients for induced transitions between states but on the assumption that the electromagnetic field could be treated classically (Dirac 1927). In 1927 Dirac lay the mathematical foundations for quantum electrodynamics. Early that year he combined quantum mechanics, special relativity, and radiation theory in treating the electromagnetic field as if it were an infinite collection of oscillators. (shrink)

After a brief survey of arguments for a unitary particle theory of matter, offered by the writer in previous publications, the following new items are discussed. (1) The wave part of the dual aspect of matter, resting on the translation formula λ=h/p, is not covariant in the nonrelativistic domain. And relativistically, it is untenable not only on methodological grounds, but because it leads to obvious contradictions to elementary experience, e.g., in the equilibrium between a material oscillator and radiation. (2) (...) The photon story as usually presented is rectified historically and factually. (3) The previous derivation by the writer of quantum mechanical theory from a nonquantal background is supplemented, in order to be conclusive, by the postulate that the general probability relation is to become the ordinary addition law in the average. (4) Quotations from the writings of prominant dualists, intended by the latter to support their ideology, disclose a fantastic disarray of pseudophilosophical standpoints which can be cleared up only by repudiating the alleged dual nature of matter and of light and by ceasing to constantly mix up the contrast between particles and fields with that between particles and waves, and by returning to a strictly unitary aspect. (shrink)

Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule of time-symmetrised quantum theory. I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrised counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the (...) objections, except in a limited special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price's concept of 'advanced action', which further supports the special case discussed. (shrink)

Gathering 115 entries written by 101 internationally renowned experts in their fields, the Handbook of Whiteheadian Process Thought aims at canvassing the current state of knowledge in Whiteheadian scholarship and at identifying promising directions for future investigations through (internal) cross-elucidation and (external) interdisciplinary development. Two kinds of entries are weaved together in order to interpret Whitehead secundum Whitehead and to read him from the vantage point of interdisciplinary and crossdisciplinary research. The “thematic ” entries provide (i) a broad contextualisation of (...) the issue at stake; (ii) a focus on Whitehead's treatment (if any) or of a possible Whiteheadian treatment of the issue; (iii) a history of relevant scholarship; (iv) a personal assessment by the Author. The “biographical ” entries provide (i) a brief vita of the targeted thinker; (ii) a sketch of his/her categories relevant to the Whiteheadian scholarship; (iii) a personal assessment of the actual (or possible) Whiteheadian semantic transfer to or from the thinker. (shrink)

The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed (...) with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect, and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra. (shrink)

Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such (...) students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study. (shrink)

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable to be measured is multiplied by some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their principal and practical feasibility. A brief historical review (...) of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics. (shrink)

Early in 1926 Erwin Schrodinger presented his famous theory of wave mechanics to account for atomic phenomena. It is often assumed that Schrodinger’s work reflected a realist philosophy. In this article, I will argue that this assumption is incorrect.

This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool (...) during the 1920s. It provides new insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the ‟skillful guessing” that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory. (shrink)

A geometro-differential quantum theory of extended particles is presented. The geometrical selling is that of Hilbert fiber bundles whose base manifolds are pseudo-Riemannian space-times of points χ which are interpreted as partial aspects of physical reality (the extended particle). The fibers are carrier spaces of induced (internal configuration and momentum) representations of the structural group (the de Sitter group here). Sections of these bundles are seen as physical representations of the particle, and their values in the fibers are (...) interpreted as states of internally localized modes composing the particle. This geometrical structure is “analogous” to that of a geometro-stochastic quantization developed in recent years. The physical interpretation is a combination of those of an old functional quantum theory and of an induced representation scheme based on an interpretation of intertwining, between configuration and momentum representations, as localization, materialization, and propagation of particles. Our model is applied in two cases: (1) Induced representation is applied in both space-time and internal space: both have de Sitter symmetry whose connection is ignored. Intertwining is considered in both spaces in a composed fashion. (2) For generic spacetimes and when the connection is taken into account, intertwining is applied only in the internal space. Parallel transport is combined with intertwining for a redefinition of localization, materialization, and propagation (the latter in a path integral context inspired from geometro-stochastic quantization). (shrink)