The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its principal (...) predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

The status of the vacuum in relativistic quantum field theory is examined. A sharp distinction arises between the global vacuum and the local vacuum. The concept of local number density is critically assessed. The global vacuum state implies fluctuations for all local observables. Correlations between such fluctuations in space-like separated regions of space-time are discussed and the existence of correlations which are maximal in a certain sense is remarked on, independently of how far apart those regions may be. The analogy (...) with the mirror-image correlations in the singlet state of two spin-1/2 particles is explained. The connection between these maximal correlations and the well-known violation of the Bell inequality in the vacuum state is discussed, together with the way in which the existence of these correlations might be exploited in developing a vacuum version of the Einstein-Podolsky-Rosen argument. The recent relativistic formulation of the Einstein-Podolsky-Rosen argument by Ghirardi and Grassi is critically assessed with particular reference to the vacuum case. (shrink)

First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.

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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)

Many of the "counterintuitive" features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled "Reeh-Schlieder meets Newton-Wigner") have proposed an alternative "Newton-Wigner" localization scheme that avoids the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner localization scheme and (...) clarify the <em>limited</em> extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation. (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 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)

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to (...) perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard non-relativistic quantum theory and classical relativistic field theory. (shrink)