The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell [Int. (...) J. Quantum chem. 155--159, (1980)] appears to suggest that such an interpretation is not possible. Bell’s argument is shown to be based upon a different understanding of the density matrix to that proposed here. (shrink)

This article focuses on two of the main problems raising interpretational issues in quantum mechanics, namely the notorious measurement problem and the equally important but not quite as widely discussed problem of the classical regime. The two problems are distinct, but they are both intimately related to some of the issues arising from entanglement and density operators. The article aims to be fairly non-technical in language, but modern in outlook and covering the chosen topics in more depth than most introductory (...) treatments. (shrink)

The most striking observable feature of our indeterministic quantum universe is the wide range of time, place, and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this domain of classical predictability of every day experience emerges from a quantum theory of the universe’s state and dynamics.

In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: ‘molecular chaos.’ The program of ‘Einselection’ within Everettian approaches faces a similar ‘Loschmidt’s Paradox’: the universe, according to the Everettian picture, is a closed system obeying only unitary dynamics, and it therefore contains no distinguishable environmental subsystems with the necessary ‘phase randomness’ to effect einselection of a pointer observable. The theoretically unjustified assumption of (...) distinguishable environmental subsystems is the hidden premise that makes the derivation of einselection circular. In effect, it presupposes the ‘emergent’ structures from the beginning. Thus the problem of basis ambiguity remains unsolved in Everettian interpretations. (shrink)

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of (...) physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular \ limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits. (shrink)

On the observational equivalence of continuous-time deterministic and indeterministic descriptions Content Type Journal Article Pages 193-225 DOI 10.1007/s13194-010-0011-5 Authors Charlotte Werndl, Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London, WC2A 2AE UK Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

Supporters of the de Broglie-Bohm interpretation of quantum theory argue that because the theory, like classical mechanics, concerns the motions of point particles in 3D space, it is specially suited to recover classical behavior. I offer a novel account of classicality in dBB theory, if only to show that such an account falls out almost trivially from results developed in the largely interpretation-neutral context of decoherence theory. I then argue that this undermines any special claim that dBB theory is purported (...) to have on the unification of the quantum and classical realms. (shrink)

The Ollivier–Poulin–Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition inapplicable within quantum theory. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence (...) suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality. (shrink)

A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called reduction. While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory's laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker "local" form of reduction, (...) which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows the broad prescriptions of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist's" limit-based notion of reduction. (shrink)

It can be shown that certain kinds of classical deterministic and indeterministic descriptions are observationally equivalent. Then the question arises: which description is preferable relative to evidence? This paper looks at the main argument in the literature for the deterministic description by Winnie (The cosmos of science—essays of exploration. Pittsburgh University Press, Pittsburgh, pp 299–324, 1998). It is shown that this argument yields the desired conclusion relative to in principle possible observations where there are no limits, in principle, on observational (...) accuracy. Yet relative to the currently possible observations (of relevance in practice), relative to the actual observations, or relative to in principle observations where there are limits, in principle, on observational accuracy the argument fails. Then Winnie’s analogy between his argument for the deterministic description and his argument against the prevalence of Bernoulli randomness in deterministic descriptions is considered. It is argued that while the arguments are indeed analogous, it is also important to see they are disanalogous in another sense. (shrink)

There are results which show that measure-theoretic deterministic models and stochastic models are observationally equivalent. Thus there is a choice between a deterministic and an indeterministic model and the question arises: Which model is preferable relative to evidence? If the evidence equally supports both models, there is underdetermination. This paper first distinguishes between different kinds of choice and clarifies the possible resulting types of underdetermination. Then a new answer is presented: the focus is on the choice between a Newtonian deterministic (...) model supported by indirect evidence from other Newtonian models which invoke similar additional assumptions about the physical systems and a stochastic model that is not supported by indirect evidence. It is argued that the deterministic model is preferable. The argument against underdetermination is then generalised to a broader class of cases. Finally, the paper criticises the extant philosophical answers in relation to the preferable model. Winnie’s (1998) argument for the deterministic model is shown to deliver the correct conclusion relative to observations which are possible in principle and where there are no limits, in principle, on observational accuracy (the type of choice Winnie was concerned with). However, in practice the argument fails. A further point made is that Hoefer’s (2008) argument for the deterministic model is untenable. (shrink)

I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level model to that of the high-level model that approximately (...) commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity. (shrink)