John Earman

Schrödinger averred that entanglement is the characteristic trait of quantum mechanics. The first part of this paper is simultaneously an exploration of Schrödinger’s claim and an investigation into the distinction between mere entanglement and genuine quantum entanglement. The typical discussion of these matters in the philosophical literature neglects the structure of the algebra of observables, implicitly assuming a tensor product structure of the simple Type I factor algebras used in ordinary Quantum Mechanics . This limitation is overcome by adopting the algebraic approach to quantum physics, which allows a uniform treatment of ordinary QM, relativistic quantum field theory, and quantum statistical mechanics. The algebraic apparatus helps to distinguish several different criteria of quantum entanglement and to prove results about the relation of quantum entanglement to two additional ways of characterizing the classical versus quantum divide, viz. abelian versus non-abelian algebras of observables, and the ability versus inability to interrogate the system without disturbing it. Schrödinger’s claim is reassessed in the light of this discussion. The second part of the paper deals with the relativity-to-ambiguity threat: the entanglement of a state on a system algebra is entanglement of the state relative to a decomposition of the system algebra into subsystem algebras; a state may be entangled with respect to one decomposition but not another; hence, unless there is some principled way to choose a decomposition, entanglement is a radically ambiguous notion. The problem is illustrated in terms a Realist versus Pragmatist debate, the former claiming that the decomposition must correspond to real as opposed to virtual subsystems, while the latter claims that the real versus virtual distinction is bogus and that practical considerations can steer the choice of decomposition. This debate is applied to the fraught problem of measuring entanglement for indistinguishable particles. The paper ends with some remarks about claims in the philosophical literature that entanglement undermines the separability or independence of subsystems while promoting holism

Stephen Hawking has argued that universes containing evaporating black holes can evolve from pure initial states to mixed final ones. Such evolution is non-unitary and so contravenes fundamental quantum principles on which Hawking's analysis was based. It disables the retrodiction of the universe's initial state from its final one, and portends the time-asymmetry of quantum gravity. Small wonder that Hawking's paradox has met with considerable resistance. Here we use a simple result for C*-algebras to offer an argument for pure-to-mixed state evolution in black hole evaporation, and review responses to the Hawking paradox with respect to how effectively they rebut this argument.

In a recent article in this journal, Barbara Lariviere offers a very useful distinction between two ways of understanding the claims that Leibniz, or relational theorists in general, might wish to make about the nature of motion and the structure of space and time; viz., There is no real inertial structure to space-time.and There is a real inertial structure to space-time, but it is dynamical rather than absolute.Citing the authority of Weyl, the author argues that L1 is untenable; indeed, the argument purports to show that if L1 were true, then there would be no coherent basis for a theory of motion, not even a relational theory. My main goal in this note is to point out why this argument is mistaken while at the same time sketching the real reason why the relational conception of motion is untenable. In addition I will offer a few remarks about the relevance of L2 to the absolute-relational controvery.

We discuss the intertwined topics of Fulling non-uniqueness and the Unruh effect. The Fulling quantization, which is in some sense the natural one for an observer uniformly accelerated through Minkowski spacetime to adopt, is often heralded as a quantization of the Klein-Gordon field which is both physically relevant and unitarily inequivalent to the standard Minkowski quantization. We argue that the Fulling and Minkowski quantizations do not constitute a satisfactory example of physically relevant, unitarily inequivalent quantizations, and indicate what it would take to settle the open question of whether a satisfactory example exists. A popular gloss on the Unruh effect has it that an observer uniformly accelerated through the Minkowski vacuum experiences a thermal flux of Rindler quanta. Taking the Unruh effect, so glossed, to establish that the notion of particle must be relativized to a reference frame, some would use it to demote the particle concept from fundamental status. We explain why technical results do not support the popular gloss and why the attempted demotion of the particle concept is both unsuccessful and unnecessary. Fulling non-uniqueness and the Unruh effect merit attention despite these negative verdicts because they provide excellent vehicles for illustrating key concepts of quantum field theory and for probing foundational issues of considerable philosophical interest.

Recent years have seen a growing consensus in the philosophical community that the grandfather paradox and similar logical puzzles do not preclude the possibility of time travel scenarios that utilize spacetimes containing closed timelike curves. At the same time, physicists, who for half a century acknowledged that the general theory of relativity is compatible with such spacetimes, have intensely studied the question whether the operation of a time machine would be admissible in the context of the same theory and of its quantum cousins. A time machine is a device which brings about closed timelike curves—and thus enables time travel—where none would have existed otherwise. The physics literature contains various no-go theorems for time machines, i.e., theorems which purport to establish that, under physically plausible assumptions, the operation of a time machine is impossible. We conclude that for the time being there exists no conclusive no-go theorem against time machines. The character of the material covered in this article makes it inevitable that its content is of a rather technical nature. We contend, however, that philosophers should nevertheless be interested in this literature for at least two reasons. First, the topic of time machines leads to a number of interesting foundations issues in classical and quantum theories of gravity; and second, philosophers can contribute to the topic by clarifying what it means for a device to count as a time machine, by relating the debate to other concerns such as Penrose's cosmic censorship conjecture and the fate of determinism in general relativity theory, and by eliminating a number of confusions regarding the status of the paradoxes of time travel. The present article addresses these ambitions in as non-technical a manner as possible, and the reader is referred to the relevant physics literature for details.

In this first part of a two-part paper, we describe efforts in the early decades of this century to restrict the extent of violations of the Second Law of thermodynamics that were brought to light by the rise of the kinetic theory and the identification of fluctuation phenomena. We show how these efforts mutated into Szilard’s proposal that Maxwell’s Demon is exorcised by proper attention to the entropy costs associated with the Demon’s memory and information acquisition. In the second part we will argue that the information theoretic exorcisms of the Demon provide largely illusory benefits. According to the case, they either return a presupposition that can be had without information theoretic consideration or they postulate a broader connection between information and entropy than can be sustained.

It is generally acknowledged that the requirement that the laws of a spacetime theory be covariant under a general coordinate transformation is a restriction on the form but not the content of the theory. The prevalent view in the physics community holds that the substantive version of general covariance – exhibited, for example, by Einstein’s general theory of relativity – consists in the requirement that diffeomorphism invariance is a gauge symmetry of the theory. This conception of general covariance is explained and confronted by two challenges. One challenge claims, in effect, that substantive general covariance is not deserving of the name since, just as it is possible to rewrite any spacetime so that it satisfies formal general covariance, so it is also possible to rewrite the theory so that it satisfies the proffered version of substantive general covariance. The other challenge claims that the proffered version of substantive general covariance is not strong enough to guarantee the intended meaning of general covariance. Both challenges are discussed in terms of concrete examples. It is argued that both challenges fail but, at the same time, that they help to clarify what is at stake on the seemingly never ending dispute over the nature and status of general covariance.

Much of the literature on "ceteris paribus" laws is based on a misguided egalitarianism about the sciences. For example, it is commonly held that the special sciences are riddled with ceteris paribus laws; from this many commentators conclude that if the special sciences are not to be accorded a second class status, it must be ceteris paribus all the way down to fundamental physics. We argue that the (purported) laws of fundamental physics are not hedged by ceteris paribus clauses and provisos. Furthermore, we show that not only is there no persuasive analysis of the truth conditions for ceteris paribus laws, there is not even an acceptable account of how they are to be saved from triviality or how they are to be melded with standard scientific methodology. Our way out of this unsatisfactory situation to reject the widespread notion that the achievements and the scientific status of the special sciences must be understood in terms of ceteris paribus laws

Hume defined ‘cause’ three times over. The two principal definitions (constant conjunction, felt determination) provide the anchors for the two main strands of the modem empiricist accounts of laws of nature 1 while the third (the counter factual definition 2) may be seen as the inspiration of the nonHumean necessitarian analyses. Corresponding to the felt determination definition is the account of laws that emphasizes human attitudes, beliefs, and actions. Latter day weavers of this strand include Nelson Goodman, A. J. Ayer, and Nicholas Rescher. In Fact, Fiction and Forecast Goodman writes: “I want to emphasize the Humean idea that rather than a sentence being used for prediction because it is a law, it is called a law because it is used for prediction” (1955, p. 62). In “What is a law of nature?”, Ayer explains that the difference between ‘generalizations of fact’ and ‘generalizations of law’ “lies not so much on the side of facts which make them true, as in the attitude of those who put them forward” (1956, p. 162). And in a similar vein, Rescher maintains that lawfulness is “mind-dependent”; it is not something which is discovered but which is supplied: “Lawfulness is not found in or extracted from the evidence but superadded to it. Lawfulness is a matter of imputation” (1970, p. 107). By contrast, the constant conjunction definition promotes the view that laws are to be analyzed in terms of the de re characteristics of regularities, independently of the attitudes and actions of actual or potential knowers.

Newton's Principia introduced conceptions of space and time that launched one of themost famous and sustained debates in the history of physics, a controversy that involves fundamentalconcerns in the foundations of physics, metaphysics, and scientific epistemology.This bookintroduces and clarifies the historical and philosophical development of the clash between Newton'sabsolute conception of space and Leibniz's relational one. It separates the issues and provides newperspectives on absolute relational accounts of motion and relational-substantival accounts of theontology of space time.Earman's sustained treatment and imaginative insights raise to a new levelthe debate on these important issues at the boundary of philosophy and physics. He surveys thehistory of the controversy from Newton to Einstein develops the mathematics and physics needed topose the issues in sharp form and provides a persuasive assessment of the philosophical problemsinvolved.Most importantly, Earman revitalizes the connection of the debate to contemporary science.He shows, for example, how concerns raised by Leibniz form the core of ongoing debate on thefoundations of general theory of relativity, moving the discussion into a new and vital arena andintroducing arguments that will be discussed for years to come.John Earman is Professor of Historyand Philosophy of Science at the University of Pittsburgh. A Bradford Book.