Previous research in the history of physics has led us to believe that Yoshio Nishina (1890–1951) virtually single‐handedly imported quantum physics into Japan. However, there are first‐hand accounts that Yoshikatsu Sugiura (1895–1960) also played an important role. Sugiura made his name in quantum chemistry with his contribution to the Heitler‐London theory of the chemical bond. Yet, historians of physics have paid scant attention to him. This paper brings forward information on Sugiura from his letters, his scientific papers, (...) and his own recollections until ca. 1930. By examining this material, the present paper studies Sugiura's accomplishments in Europe and his contributions to the development of quantum physics in Japan. We conclude that Sugiura was one of the most important physicists when it comes to the arrival of quantum physics in Japan. In addition, we assess why he has been under‐appreciated in the history of physics in Japan. Our historical study on Sugiura suggests that, in addition to the position Nishina and his students rightfully occupy, there still are important unexplored aspects in the history of Japanese quantum physics. (shrink)

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s. We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect (...) measurement, which influenced his discussion of the "reduction of the wave packet" and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical measurement. (shrink)

This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The (...) book is self-contained in that it presents the necessary parts of the mathematical formalism of quantum mechanics and also covers other interpretative topics, such as the problem of measurement and the uncertainty relations. A considerable portion of the book is based on original arguments presented by the author in lectures and research papers over the past ten years. However, this material is integrated with a broad coverage of most of the recent research in the field, so as to provide a balanced introduction to the whole subject. (shrink)

Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is a collection of 33 selected papers from the scientific contributions presented at the 16th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI), held at Ishikawa Prefecture Museum of Art in Kanazawa, Japan, from September 11th to 17th, 2011. The volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a (...) wide range of problems in physics, chemistry, and biology. The breadth and depth of the scientific topics discussed during QSCP-XVI appears in the classification of the contributions in six parts: I. Fundamental Theory II. Molecular Processes III. Molecular Structure IV. Molecular Properties V. Condensed Matter VI. Biosystems. Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is written for advanced graduate students as well as for professionals in theoretical chemical physics and physical chemistry. The book covers current scientific topics in molecular, nano, material, and bio sciences and provides insights into methodological developments and applications of quantum theory in physics, chemistry, and biology that have become feasible at end of 2011. (shrink)

This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950's for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger's published papers and books of the same period. However, they were (...) likely to be misinterpreted out of their context. The problem was that current scholarship could not help very much the reader of these writings to figure out their significance. The few available studies about SchrOdinger's interpretation of quantum mechanics are generally excellent, but almost entirely restricted to the initial period 1925-1927. Very little work has been done on Schrodinger's late views on the theory he contributed to create and develop. The generally accepted view is that he never really recovered from his interpretative failure of 1926-1927, and that his late reflections are little more than an expression of his rising nostalgia for the lost ideal of picturing the world, not to say for some favourite traditional picture. But the content and style of Schrodinger's texts of the 1950's do not agree at all with this melancholic appraisal; they rather set the stage for a thorough renewal of accepted representations. In order to elucidate this paradox, I adopted several strategies. (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast (...) to Wave Function Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The "standard" formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the (...) other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the "quantum logic" approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics. (shrink)

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of (...) Quantum Mechanics are depending on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

In this paper we discuss and outline a version of non-relativistic quantum mechanics based on a new non-reflexive logic, where the basic entities (elementary particles) lack identity conditions. Some relationships with quantum field theories are also sketched.

As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of (...) Quantum Mechanics are depending on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

This entry reviews Carnap's philosophical views on the quantum mechanics of his time. It also offers some thoughts on how he might have reacted to some recent developments in the foundations of quantum mechanics.

Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich (...) with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles ; to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original. Quantum Mechanics in a Nutshell expertly addresses traditional and modern topics, including perturbation theory, WKBJ, variational methods, angular momentum, the Dirac equation, many-particle wave functions, Casimir Force, and Bell's Theorem. And it treats many topics--such as the interactions between photons and electrons, scattering theory, and density functional theory--in exceptional depth. A valuable addition to the teaching literature, Quantum Mechanics in a Nutshell is ideally suited for a two-semester course. The most concise, up-to-date, and accessible graduate textbook on the subject Contains the ideal amount of material for a two-semester course Focuses on the description of actual quantum systems, including a range of applications Covers traditional topics, as well as those at the frontiers of research Treats in unprecedented detail topics such as photon-electron interaction, scattering theory, and density functional theory Includes numerous homework problems at the end of each chapter. (shrink)

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the (...) manifested world and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations. (shrink)

We explicitly compute, following the method of Weyl, the commutator [Q, P] of the position operatorQ and the momentum operatorP of a particle when the dimension of the space on which they act is finite with a discrete spectrum; and we show that in the limit of a continuous spectrum with the dimension going to infinity this reduces to the usual relation of Heisenberg.

The paper aims to show how Japanese theoretical physics groups emerged between the First and Second World Wars. First, it will be argued that by the early 1930s the Japanese physics community had been predominantly inclined towards experimental physics and that several academic, cultural, and social factors had worked for the maintenance of this status quo. Next, how the situation slowly changed during the early 1930s, and how the young theoretical physicists successfully established a bridgehead during the mid-1930s will be (...) analysed. Four different elements are suggested: the dazzling success of quantum mechanics and its spread in the West; the dominance of experimental physics and its effect on the university system; cultural/social influence; and the emergence of the research network. (shrink)

Merleau-Ponty’s remarks on quantum mechanics offer a unique perspective on the relationship between scientific results and their interpretation. This article elaborates Merleau-Ponty’s phenomenological perspective on quantum mechanics by considering the main texts in which he explicitly attends to this topic: namely, La Nature: notes cours du Collège de France and The Visible and the Invisible.

During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining (...) articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to Mrs. Lillian O'Toole, Mrs. Dianne Kanerva, and Mrs. Marguerite Shaw, for their extensive assistance. (shrink)

The goal of the dissertation is, first, to develop in the tradition of conventional quantum mechanics what I call a propensity view of quantum properties, and to examine its coherence. Conventional quantum mechanics assumes the completeness of quantum mechanics. Taking the ontic version of the completeness assumption, which says that a state vector completely describes an individual quantum system as it is, I argue that the propensity view of quantum properties, i.e., (...) the attribution of certain irreducible propensities to a quantum system, is not only demanded but also can be coherently maintained. ;Second, I evaluate the relation between a propensity view of quantum properties and the demands of Einstein's program of realism, the backbone of which is the requirement that physical systems, as described by a theory, have properties independently of measurement. In doing so, I argue for a non-relational version of the quantum propensity view, which amounts to attributions propensities to individual quantum systems, and claim that conventional quantum mechanics together with the non-relational propensity view of quantum properties realizes physical realism, which is a particular version of Einstein's realist thesis and which reads that a physical system, as described by a theory, has at least some of its extrinsic properties independently of measurement. ;Third, quantum mechanics, in spite of its empirical success, has suffered from certain well-known conceptual puzzles, viz., the measurement problem and the problem of nonlocality as it arises in the Einstein-Podolsky-Rosen paradox. So we ask whether the propensity view of quantum properties can help us the resolve these problems. I argue that the so-called reduction of the wave packet is the source of both problems and suggest that there is a sense in which the propensity view of quantum properties explains the reduction of the wave packet and its nonlocal nature. On the other hand, the propensity view by itself fails to resolve the question of when or in what circumstances the reduction of the wave packet occurs, indicating that we do not as yet possess a complete understanding of quantum propensities. (shrink)

The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is (...) the ergodic demand what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)

Este artigo destina-se a introduzir a conferência de Heisenberg "A doutrina goethiana e newtoniana das cores à luz da física moderna", proferida em 1941, cuja tradução é aqui publicada. Analisa-se primeiramente o projeto filosófico de uma ordenação da realidade, desenvolvido pelo físico no início da década de 1940, o qual subjaz à discussão sobre as doutrinas das cores em Goethe e Newton. No segundo momento, faz-se uma exposição de algumas das implicações filosóficas da teoria quântica, com ênfase na interpretação da (...) assim denominada escola de Copenhague. Por fim, procura-se mostrar como a querela entre Goethe e Newton é utilizada para defender as abstrações da física teórica dos ataques da assim denominada "física ariana" e, ao mesmo tempo, preservar o valor das considerações intuitivas de Goethe. This paper aims at exposing the Heisenberg's conference "The teachings of Goethe and Newton on colors in the light of modern physics", presented in 1941, whose translation is presented here. In the first place the paper analyzes the philosophical project of an ordination of the reality, developed by the physicist in the early 1940s and which is the basis for the discussion of the "Teachings of Goethe and Newton on colors". Secondly it exposes some philosophical implications of the quantum theory by emphasizing the point of view of the Copenhagen school. Finally, it shows how the dispute between Goethe and Newton is exploited to defend the abstractions of the theoretical physics against the attacks of the so called "German physicists" and, at the same time, to preserve the worth of the Goethe's intuitive analysis. (shrink)

The Ozawa’s intersubjectivity theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. But from OIT viewpoint postulate’s formulation should be completed by the assumption of probability reproducibility. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theoretical statement, QBism is challenged by OIT.

If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and final boundary conditions in non-relativistic quantum mechanics leads to the idea that the properties of macroscopic quantum systems, relevantly measuring instruments, are uniquely determined by the boundary conditions. An important element in reaching that conclusion is that preparations and measurements (...) belong in a special class because they involve many subsystems, at least some of which do not form superpositions of their physical properties before the boundary conditions are imposed. It is suggested that the primary role of the formalism of standard quantum mechanics is to provide the consistency condition on the boundary conditions rather than the properties of quantum systems. Expressions are proposed for assigning a set of (unmeasured) physical properties to a quantum system at all times. The physical properties avoid the logical inconsistencies implied by the no-go theorems because they are assigned differently from standard quantum mechanics. Since measurement outcomes are determined by the boundary conditions, they help determine, rather than are determined by, the physical properties of quantum systems. (shrink)

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced (...) to define the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. In the momentum representation, the same method can be applied to obtain the Schrödinger equation for a free particle while further investigation is still needed for a particle with an external potential. Furthermore, the principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool. It can be applied to derive other quantum formalisms such as quantum scalar field theory. (shrink)

Quantum mechanics is currently being tried to be used as a probe to unravel the mysteries of consciousness. Present paper deals with this probe, quantum mechanics and its usefulness in getting an insight of working of human consciousness. The formation of quantum mechanics based on certain axioms, its development to study the dynamical behavior and motions of fundamental particles and quantum energy particles moving with the velocity of light, its insistence on wave functions, (...) its probability approach, its dependence on uncertainty principles will all be critically discussed. The result of this discussion will be presented. Its limitations in unraveling the form, function and biological nature of consciousness will be presented. The alternative probe available and being used – the translation of Upanishadic insight and Advaita philosophy into cognitive science elements in delineating the definition, form and function of Consciousness will be given. The usefulness of this modeling and analysis in understanding the consciousness, mind and its functions in cognitive science and theory of human language acquisition and communication will also be presented. The physic-chemical nature of ideas, senses, thoughts, feelings, utterances will be grossly dealt with. The functions of consciousness and mind, in knowledge and language acquisition and communication will be dealt with. (shrink)

Why does one theory "succeed" while another, possibly clearer interpretation, fails? By exploring two observationally equivalent yet conceptually incompatible views of quantum mechanics, James T. Cushing shows how historical contingency can be crucial to determining a theory's construction and its position among competing views. Since the late 1920s, the theory formulated by Niels Bohr and his colleagues at Copenhagen has been the dominant interpretation of quantum mechanics. Yet an alternative interpretation, rooted in the work of Louis (...) de Broglie in the early 1920s and reformulated and extended by David Bohm in the 1950s, equally well explains the observational data. Through a detailed historical and sociological study of the physicists who developed different theories of quantum mechanics, the debates within and between opposing camps, and the receptions given to each theory, Cushing shows that despite the preeminence of the Copenhagen view, the Bohm interpretation cannot be ignored. Cushing contends that the Copenhagen interpretation became widely accepted not because it is a better explanation of subatomic phenomena than is Bohm's, but because it happened to appear first. Focusing on the philosophical, social, and cultural forces that shaped one of the most important developments in modern physics, this provocative book examines the role that timing can play in the establishment of theory and explanation. (shrink)

Ernest Nagel once remarked that it is fortunately not necessary to be clear about scientific philosophy and methodology in order to practice good science. He went on to say, "Even eminent scientists can make unholy spectacles of themselves when they don the mantle of philosophy and attempt to discuss the broad implications of their specialized labors." Feynman's recent venture into the philosophy of science is, unfortunately, a lucid illustration of the validity of Nagel's observations. The book is a rather literal (...) transcription of seven semi-popular lectures delivered by Feynman at Cornell in November of 1964. Feynman is a wonderful iconoclast, a legendary virtuoso of the bongo drums and—by the way—a Nobel laureate and one of the great theoretical physicists. But this is all the more reason to expect something a little more intellectually solid than is offered in this volume. It was obviously Feynman's intent to discuss some compelling problems which lie on the borderline of physics and philosophy with an intelligent lay audience. But few will be enlightened by Feynman's clever, if uninformative, discourse about such issues as the relation of mathematics to physics, symmetry and conservation laws, and probability and uncertainty. Feynman's finest hour undoubtedly comes in the lecture on quantum mechanics, in which some aspects of the wave-particle duality are presented. But the value of much of the rest of the book is severely qualified by the author's penchant for imprecise and confusing statements and, in some cases, outright mystery-mongering. This is a great pity because theoretical physics, especially in the hands of Richard Feynman, is a source of ideas which are most worth discussing.—H. P. K. (shrink)

The classical Hamiltonian in generalized coordinates is given asH=1/2 Σ i.k p i g ik p k . We show that there is no operator of the formP i= −iA(qi) (∂/∂qi)+Gi(qi) (note that the Hermitian momentum operatorP i H is of this form) such that the quantum Hamiltonian operatorH Q is given asH Q =1/2 Σ i,k P i g ik P k or1/2 Σ i,k g ik P i P k , etc. In order to maintain a direct (...) transition of this sort from classical to quantum theory, using the classical Hamiltonian as a starting point, we must rely on our previous prescriptions, writing the quantum Hamiltonian asH Q =1/2 Σ i,k P i + g ik P k , whereP i + denotes the adjoint of the operatorP i=−ih ∂/∂qi. (shrink)

This document is a set of notes I took on QFT as a graduate student at the University of Pennsylvania, mainly inspired in lectures by Burt Ovrut, but also working through Peskin and Schroeder (1995), as well as David Tong’s lecture notes available online. They take a slow pedagogical approach to introducing classical field theory, Noether’s theorem, the principles of quantum mechanics, scattering theory, and culminating in the derivation of Feynman diagrams.

After a quick historical account of the introduction of the group-theoretical description of quantum mechanics in terms of symmetries, as proposed by Weyl, we examine some unpublished papers by Ettore Majorana. Remarkable results achieved by him in frontier research topics as well as in physics teaching point out that the Italian physicist can be well considered as a follower of Weyl in his reformulation of quantum mechanics.

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 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)

The following article by Grete Hermann arguably occupies an important place in the history of the philosophical interpretation of of quantum mechanics. The purpose of Hermann's writing on natural philosophy is to examine the revision of the law of causality which quantum mechanics seems to require at a fundamental level of theoretical description in physics. It is Hermann's declared intention to show that quantum mechanics does not disprove the concept of causality, "yet has clarified (...) [it] and has removed from it other principles which are not necessarily connected to it." She attempts to show that this most "obvious" counter-example to the aprioricity of causality, quantum theory, is in fact not a counter-example at all. (shrink)

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing ‘‘surrealistic trajectories’’ proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.

Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles — or, at least, of the measuring instruments we use to explore those behaviors — and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, (...) and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically ; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.[1.. (shrink)

This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie–Bohm–Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie–Bohm–Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make (...) the ad-hoc assumption that the initial distribution of particle locations has to be identical to the initial probability distribution prescribed by the system’s initial wave function. The results presented in this paper moreover suggest that the intrinsically stochastic nature of Bell’s formulation, which is arguable most naturally formulated on an underlying discrete space-time, is sufficient to ensure dynamical relaxation to quantum equilibrium for a large class of quantum systems without the need to introduce coarse-graining or any other modification in the formulation. (shrink)

The textbook presentation of quantum mechanics, in a nutshell, is this. The physical state of any isolated system evolves deterministically in accordance with Schrödinger's equation until a "measurement" of some physical magnitude M (e.g. position, energy, spin) is made. Restricting attention to the case where the values of M are discrete, the system's pre-measurement state-vector f is a linear combination, or "superposition", of vectors f1, f2,... that individually represent states that..

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements (...) in this framework. (shrink)

This paper aims to show that the development of Feyerabend’s philosophical ideas in the 1950s and 1960s largely took place in the context of debates on quantum mechanics. In particular, he developed his influential arguments for pluralism in science in discussions with the quantum physicist David Bohm, who had developed an alternative approach to quantum physics which (in Feyerabend’s perception) was met with a dogmatic dismissal by some of the leading quantum physicists. I argue that (...) Feyerabend’s arguments for theoretical pluralism and for challenging established theories were connected to his objections to the dogmatism and conservatism he observed in quantum physics. However, as Feyerabend gained insight into the physical details and historical complexities which led to the development of quantum mechanics, he gradually became more modest in his criticisms. His writings on quantum mechanics especially engaged with Niels Bohr; initially, he was critical of Bohr’s work in quantum mechanics, but in the late 1960s, he completely withdrew his criticism and even praised Bohr as a model scientist. He became convinced that however puzzling quantum mechanics seemed, it was methodologically unobjectionable – and this was crucial for his move towards ‘anarchism’ in philosophy of science. (shrink)

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller, have thought that the answer to this question is No - that the status of individual continuous quantities is very different in quantum (...) class='Hi'>mechanics than in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics. (shrink)

The aim of this paper is two-fold. Recently, Lewis has presented an argument, now known as the `counting anomaly', that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof (...) of the fact that the composition principle, which holds true in Standard Quantum Mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of collapse interpretations. Once this flaw is uncovered, the anomaly vanishes. (shrink)

ion turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as “superposition (...) events” in addition to the ordinary events. The goal is to use the second notion of abstraction to shed some light on the notion of an indefinite superposition in quantum mechanics. (shrink)

Bohr’s work in quantum mechanics posed a challenge to philosophers of science, who struggled with the question of whether and to what degree his theories and methods could be considered rational. This paper focuses on Popper, Feyerabend, Lakatos and Kuhn, all of whom recognized some irrational, dogmatic, paradoxical or even inconsistent features in Bohr’s work. Popper, Feyerabend, and Lakatos expressed strong criticism of Bohr’s approach to quantum physics, while Kuhn argued that such criticism was unlikely to be (...) fruitful: progress in science is generally not made through philosophical reflection. Feyerabend’s criticism of Bohr gradually weakened, as he gained a more detailed understanding of the development of Bohr’s views on quantum mechanics, and this went together with an increasingly critical view of normative philosophy of science and was instrumental to his conversion to ‘anarchism’. This paper aims to show that quantum mechanics played a central role in their debates and disagreements on the rationality of science and the possibility of a normative philosophy of science. (shrink)

Quantum mechanics has recently indicated that temporal order is not always fixed, a finding that has far-reaching philosophical and theological implications. The phenomena, termed “indefinite causal order,” shows that events can be in a superposition with regard to their order. In the experimental setting with which this article is concerned, two events, A and B, were shown to be in the ordering relations “A before B” and “B before A” at the same time. This article introduces an ongoing (...) project that seeks to make sense of this result, with a particular focus on the methodology by which this research will be undertaken. Specific research questions, particularly regarding what indefinite causal order might mean for the metaphysics of time and the doctrine of salvation, are introduced. The collaborative approach detailed brings together the disciplinary skills of a working scientist and a working theologian. What is offered is a collaborative methodology for interaction between science and religion that is more than the sum of its parts. Alister McGrath’s idea of multiple rationalities is employed as an epistemological framework within which this research takes place. Within an epistemologically pluralistic model, collaborative efforts are not only encouraged but necessary. Complex reality requires an equally complex, usually interdisciplinary, explanation. I argue that such dialogue is both theologically justified and culturally valuable and indicates the direction in which this research will be taken. (shrink)

_Sonoran Desert, Stuart Hameroff and Alwyn Scott awoke from their_ _siestas to take margaritas in the shade of a ramada. On a nearby_ _table, a tape recorder had accidentally been left on and the following_ _is an unedited transcript of their conversation._.