This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the role played by the concept of 'world'. The view presented is that we are entitled to use 'many-worlds' terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an 'instant' or moment of time in relativity, with the lack of (...) a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed. (shrink)

The life of Niels Bohr spanned times of revolutionary change in science itself as well as its impact on society. Along with Albert Einstein, Bohr can be considered to be this century's major driving force behind the new philosophical and mathematical descriptions of the structure of the atom and the nucleus. Abraham Pais, the acclaimed biogrpaher of Albert Einstein, here traces Bohr's progress from his well-to-do origins in late nineteenth-century Denmark to his position at centre stage in the world political (...) scene, particularly during the Second World War and the development of atomic weapons. Pais' description moves through the science as it was before Bohr, as it became because of Bohr, and thence to Bohr's scientific and philosophical legacy. That legacy is contained both in theory as it is now universally enshrined, as well as in its practice in such great Danish institutions as Riso. But more than that, Pais captures the essence of Bohr, the intensely private family figure who, despite appalling personal tragedy, became one of the most loved cultural figures of recent times. (shrink)

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.

It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, (...) we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence. (shrink)

THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

These articles and speeches by the Nobel Prize-winning physicist date from 1934 to 1958. Rather than expositions on quantum physics, the papers are philosophical in nature, exploring the relevance of atomic physics to many areas of human endeavor. Includes an essay in which Bohr and Einstein discuss quantum and_wave equation theories. 1961 edition.

The classic, influential essay in 'descriptive metaphysics' by the distinguished English philosopher.

Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...

Presents German physicist Werner Heisenberg's 1958 text in which he discusses the philosophical implications and social consequences of quantum mechanics and other physical theories.

Of all the developments in twentieth century physics, none has given rise to more heated debates than the changes in our understanding of science precipitated by the quantum revolution''. In this revolution, Niels Bohr's dramatically non-classical theory of the atom proved to be the springboard from which the new atomic physics drew it's momentum. Furthermore, Bohr's contribution was crucial not only because his interpretation of quantum mechanics became the most widely accepted view but also because in his role as educator (...) and spokesman for atomic physics Bohr was very much the patron spirit of the entire quantum revolution. The conceptual framework which he proposed to provide a new viewpoint for understanding the quantum theoretical description of atomic systems became for most of this century the dominant outlook of countless productive experimental and theoretical physicists. He called this new framework complementarity''. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, (...) we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

This essay is a discussion of the philosophical and foundational issues that arise in non-relativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and non-locality. In each case, the main point is to give the reader some introductory understanding of some of the major issues and recent ideas.

What is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr's complementarity interpretation, which does not employ wave packet collapse in its account of measurement and does not accord the subjective observer any privileged role in measurement. It is argued that the Copenhagen interpretation is an invention of the mid‐1950s, for which Heisenberg is chiefly responsible, various other physicists and philosophers, including Bohm, Feyerabend, Hanson, and Popper, having (...) further promoted the invention in the service of their own philosophical agendas. (shrink)

Quantum mechanics has raised in an acute form three problems which go to the heart of man's relationship with nature through experimental science: (r) the public objectivity of science, that is, its value as a universal science for all investigators; (2) the empirical objectivity of scientific objects, that is, man's ability to construct a precise or causal spatio-temporal model of microscopic systems; and finally (3), the formal objectivity of science, that is, its value as an expression of what nature is (...) independently of its being an object of human knowledge. These are three aspects of what is generally called the "crisis of objec tivity" or the "crisis of realism" in modern physics. This crisis is. studied in the light of Werner Heisenberg's work. Heisenberg was one of the architects of quantum mechanics, and we have chosen his writings as the principal source-material for this study. Among physicists of the microscopic domain, no one except perhaps Bohr has expressed himself so abundantly and so profoundly on the philosophy of science as Heisenberg. His writings, both technical and non-technical, show an awareness of the mysterious element in scientific knowledge, far from the facile positivism of Bohr and others of his contemporaries. The mystery of human knowledge and human SUbjectivity is for him an abiding source of wonder. (shrink)

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

My contribution will focus on only one question, which I would like to state in the simplest possible way. This question will be: why do we find Bohr obscure? Or, alternatively, why is there so much — and ever renewed — complaint in the literature over Bohr ‘being unintelligible’?

Is the correspondence principle valid for quantum systems whose classical counterparts are chaotic? This question has been at the center of a debate that has taken place in recent years within the community of scientists interested in quantum chaos [4,17–20,33]. In this paper we will argue that the apparent failure of the correspondence principle is cured by decoherence, which is an essential ingredient to properly define a classical limit. We shall begin by schematically presenting the problem. Subsequently, we shall sketch (...) the solution provided by decoherence. (shrink)

A solution to the measurement problem of quantum mechanics is proposed within the framework of an intepretation according to which only quantum systems with an infinite number of degrees of freedom have determinate properties, i.e., determinate values for (some) observables of the theory. The important feature of the infinite case is the existence of many inequivalent irreducible Hilbert space representations of the algebra of observables, which leads, in effect, to a restriction on the superposition principle, and hence the possibility of (...) defining (macro-) observables which commute with every observable. Such observables have determinate values which are not subject to quantum interference effects. A measurement process is schematized as an interaction between a microsystem and a macrosystem, idealized as an infinite quantum system, and it is shown that there exists a unitary transformation which transforms the initial pure state of the composite system in a finite time (the duration of the interaction) into the required mixture of disjoint states. (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)

The contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg.

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)

The centerpiece of Jeffrey Bub's book Interpreting the Quantum World is a theorem (Bub and Clifton 1996) which correlates each member of a large class of no-collapse interpretations with some 'privileged observable'. In particular, the Bub-Clifton theorem determines the unique maximal sublattice L(R,e) of propositions such that (a) elements of L(R,e) can be simultaneously determinate in state e, (b) L(R,e) contains the spectral projections of the privileged observable R, and (c) L(R,e) is picked out by R and e alone. In (...) this paper, we explore the issue of maximal determinate sets of observables using the tools provided by the algebraic approach to quantum theory; and we call the resulting algebras of determinate observables, "maximal *beable* subalgebras". The capstone of our exploration is a generalized version of Bub and Clifton's theorem that applies to arbitrary (i.e., both mixed and pure) quantum states, to Hilbert spaces of arbitrary (i.e., both finite and infinite) dimension, and to arbitrary observables (including those with a continuous spectrum). Moreover, in the special case covered by the original Bub-Clifton theorem, our theorem reproduces their result under strictly weaker assumptions. This added level of generality permits us to treat several topics that were beyond the reach of the original Bub-Clifton result. In particular: (a) We show explicitly that a (non-dynamical) version of the Bohm theory can be obtained by granting privileged status to the position observable. (b) We show that Clifton's (1995) characterization of the Kochen-Dieks modal interpretation is a corollary of our theorem in the special case when the density operator is taken as the privileged observable. (c) We show that the 'uniqueness' demonstrated by Bub and Clifton is only guaranteed in certain special cases -- viz., when the quantum state is pure, or if the privileged observable is compatible with the density operator. We also use our results to articulate a solid mathematical foundation for certain tenets of the orthodox Copenhagen interpretation of quantum theory. For example, the uncertainty principle asserts that there are strict limits on the precision with which we can know, simultaneously, the position and momentum of a quantum-mechanical particle. However, the Copenhagen interpretation of this fact is not simply that a precision momentum measurement necessarily and uncontrollably disturbs the value of position, and vice-versa; but that position and momentum can never in reality be thought of as simultaneously determinate. We provide warrant for this stronger 'indeterminacy principle' by showing that there is no quantum state that assigns a sharp value to both position and momentum; and, a fortiori, that it is mathematically impossible to construct a beable algebra that contains both the position observable and the momentum observable. We also prove a generalized version of the Bub-Clifton theorem that applies to "singular" states (i.e., states that arise from non-countably-additive probability measures, such as Dirac delta functions). This result allows us to provide a mathematically rigorous reconstruction of Bohr's response to the original EPR argument -- which makes use of a singular state. In particular, we show that if the position of the first particle is privileged (e.g., as Bohr would do in a position measuring context), the position of the second particle acquires a definite value by virtue of lying in the corresponding maximal beable subalgebra. But then (by the indeterminacy principle) the momentum of the second particle is not a beable; and EPR's argument for the simultaneous reality of both position and momentum is undercut. (shrink)

We study the process of observation (measurement), within the framework of a “perspectival” (“relational,” “relative state”) version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the object system (...) itself (as opposed to the observational system) is needed for the emergence of classicality. Decoherence is an essential element in the mechanism of observation that we assume, but it turns out that in our approach no environment-induced decoherence on the level of the object system is required for the emergence of classical properties. (shrink)

A vast amount of ink has been spilled in both the physics and the philosophy literature on the measurement problem in quantum mechanics. Important as it is, this problem is but one aspect of the more general issue of how, if at all, classical properties can emerge from the quantum descriptions of physical systems. In this paper we will study another aspect of the more general issue-the emergence of classical chaos-which has been receiving increasing attention from physicists but which has (...) largely been neglected by philosophers of science. (shrink)

By questioning the validity of some of our basic concepts, such as space, object, and causality, quantum physics contributes quite decisively to the dramatic changes now taking place in our world picture. Veiled Reality provides a detailed view of the reasons why such a questioning arises, a survey of the corresponding conceptual and theoretical problems, and a comprehensive, up-to-date account, useful to scientists and epistemologists alike, of the various ways present-day physicists tackle these problems.The book deals with the E.P.R. reality (...) criterion, local causality, and quantum measurement including relativistic quantum collapse, decoherence theories, consistent histories approaches, and ontologically interpretable theories. Questions bearing on the connection between counterfactuality and realism, intersubjective agreement, and limits of the bearing of the verbs “to have” and “to be,” follow naturally from the analysis and are thoroughly examined. Finally, distinguishing between empirical reality and a veiled independent reality whose only knowable features are structural yields a clue to a plausible interpretation of current physics.Accessible to readers with only very elementary background in modern physics, Veiled Reality offers nonspecialists, including students in physics and philosophy, easy access to basic problems in the foundation of physics. (shrink)

The current status of localization and related concepts, especially localized statevectors and position operators, within Lorentz-invariant Quantum Theory (LIQT) is ambiguous and controversial.1 Ever since the early work of Newton & Wigner (1949), and the subsequent extensions of their work, particularly by Hegerfeldt (1974, 1985), it has seemed impossible to identify localized statevectors or position operators in LIQT that were not counterintuitive—strange—in one way or another; the most striking strange property being the superluminal propagation of the localized states. The ambiguous (...) and controversial status of these concepts arises from the varied reactions that workers have to the strange properties. Some regard them, particularly the superluminal propagation, as utterly unacceptable, and conclude that no precise concepts of localized statevectors and position operators exist in LIQT (Wigner 1973, p. 325-327; 1983, pp. 310-313; Malament 1996). Others downplay the whole issue, on the grounds that current theoretical and experimental practice has no need of sharply formulated concepts of localization, localized states etc. (Birrell & Davies 1984, pp. 48-59; Haag 1992, p. 34). Still others, including ourselves, believe that the superluminal propagation does not lead to causal contradictions, and is not in conflict with available empirical data: so that it should not be ruled out. We also believe that the other strange properties are merely unfamiliar novelties of LIQT which we must simply learn to accept. (Like the superluminal propagation, they do not lead to causal contradictions, nor conflict with available data.) So in this paper, we aim to help remove the ambiguous and controversial status of localization concepts in LIQT. Overall, our strategy will be to assess a number of localization concepts, and thereby clarify the often complex relationships among them. (shrink)

Since the Niels Bohr centenary of 1985 there has been an astonishing international surge of scholarly analyses of Bohr's philosophy. Now for the first time in Niels Bohr and Contemporary Philosophy Jan Faye and Henry Folse have brought together sixteen of today's leading authors who have helped mould this new round of discussions on Bohr's philosophy. In fifteen entirely new, previously unpublished essays we discover a surprising variety of the different facets of Bohr as the natural philosopher whose `framework of (...) complementarity' shaped the final phase of the quantum revolution and influenced two generations of the century's leading physicists. There is much on which the authors included here agree; but there are also polar disagreements, which assure us that the philosophical questions revolving around Bohr's `new viewpoint' will continue to be a subject of scholarly interest and discussion for years to come. This collection will interest all serious students of history and philosophy of science, and foundations of physics. (shrink)

In the first comprehensive biography of Erwin Schrödinger--a brilliant and charming Austrian, a great scientist, and a man with a passionate interest in people and ideas--the author draws upon recollections of Schrödinger's friends, family and colleagues, and on contemporary records, letters and diaries. Schrödinger led a very intense life, both in his research and in the personal realm. This book portrays his life against the backdrop of Europe at a time of change and unrest. His best known scientific work was (...) the discovery of wave mechanics, for which he was awarded the Nobel Prize in 1933. In Dublin, he wrote his most famous and influential book What is Life?, which attracted some of the brightest minds of his generation into molecular biology. This highly readable biography of a fascinating and complex man will appeal to anyone interested in the history of our times, and in the life and thought of one of the great men of twentieth-century science. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, describes an observer-independent reality. In (...) this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics. (shrink)