Online research in philosophy

Both physicists and philosophers claim that quantum mechanics reduces to classical mechanics as 0, that classical mechanics is a limiting case of quantum mechanics. If so, several formal and non-formal conditions must be satisfied. These conditions are satisfied in a reduction using the Wigner transformation to map quantum mechanics onto the classical phase plane. This reduction does not, however, assist in providing an adequate metaphysical interpretation of quantum theory.

There is no question that the theory of quantum mechanics is empirically successful. What the formalism of the theory says about the world, however, remains controversial. In this class, we will look at different theories of quantum mechanics. We will examine a range of philosophical issues that arise for the different theories, including the measurement problem, non-locality, the ontological status of the wavefunction and configuration space, the nature of probability, causation, and the compatibility of quantum mechanics with relativity.

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM.

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed.

Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as expressing the net of relations connecting all different physical systems.

Standard Quantum mechanics (SQM) deals with observers, frames of reference (apparatus) and systems under observation (SUOs). Heisenberg based his approach to quantum mechanics on a desire to avoid metaphysical (i.e. unobservable) concepts, dealing only in terms of experimentally observable quantities. Following this idea, we describe an approach to quantum mechanics which deals only with labstates, which represent the observer'’s quantum information about the apparatus. This approach is compatible and consistent with Hume’'s philosophy known as empiricism. We show that conventional ideas do not work without modification when we consider certain quantum experiments involving classical special relativistic transformations. We discuss the appearance of quantum horizons, which present a barrier to information transmission between initial and final state apparatus whenever these are in relative motion.

The problem of the failure of value definiteness (VD) for the idea of quantity in quantum mechanics is stated, and what VD is and how it fails is explained. An account of quantity, called BP, is outlined and used as a basis for discussing the problem. Several proposals are canvassed in view of, respectively, Forrest's indeterminate particle speculation, the "standard" interpretation of quantum mechanics and Bub's modal interpretation.

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.