From Physics to Information Theory and Back

Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified

Modal Interpretations and Relativity

A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.Comment: 14 pages, to appear in Foundations of Physics Letter

Nonseparability, Classical and Quantum

This paper examines the implications of the holonomy interpretation of classical electromagnetism. As has been argued by Richard Healey and Gordon Belot, classical electromagnetism on this interpretation evinces a form of nonseparability, something that otherwise might have been thought of as confined to non-classical physics. Consideration of the differences between this classical nonseparability and quantum nonseparability shows that the nonseparability exhibited by classical electromagnetism on the holonomy interpretation is closer to separability than might at first appear

Probabilities in Statistical Mechanics: What are they?

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely ontic, or purely epistemic. I will propose a third alternative: they are almost objective probabilities, or epistemic chances. The definition of such probabilities involves an interweaving of epistemic and physical considerations, and thus they cannot be classified as either purely epistemic or purely ontic. This conception, it will be argued, resolves some of the puzzles associated with statistical mechanical probabilities: it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it

From Physics to Information Theory and Back

Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified

Boltzmann's H-theorem, its limitations, and the birth of (fully) statistical mechanics

A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests' 1912 wind-tree model. The little-cited 1896 (pre-recurrence) objection of Zermelo (similar to an 1889 argument due to Poincare) is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give particular emphasis to the radical nature of Poincare's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to the objections as a whole.Comment: 40 page

On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting 'not completely positive' evolution, but as linear extensions, to a system's entire state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.Comment: To be presented at the 2012 biennial meeting of the Philosophy of Science Association (PSA), San Diego, Californi

The Science of ΘΔcs\Theta \Delta^{cs}

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics (or even a candidate theory of fundamental physics), but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This view has been dismissed by many philosophers of physics, in my opinion too hastily. This paper is a sketch and defense of a science of manipulations and their effects on physical systems. This is, I claim, the best way to make sense of thermodynamics as it is found in textbooks and as it is practiced. I call this science thermo-dynamics (with hyphen), or $\Theta \Delta^{cs}$, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. Even if one is not convinced that it is the best way to make sense of thermodynamics as it is practiced, it should be non-controversial that $\Theta \Delta^{cs}$ is a legitimate science. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Given the definition of statistical thermo-dynamic entropy, it can be proven that, under the assumption of availability of thermodynamically reversible processes, these functions are the unique (up to an additive constant) functions that represent thermo-dynamic entropy. Light is also shed on the use of coarse-grained entropies.

What is a Wavefunction?

Much of the the discussion of the metaphysics of quantum mechanics focusses on the status of wavefunctions. This paper is about how to think about wavefunctions, when we bear in mind that quantum mechanics—that is, the nonrelativistic quantum theory of systems of a fixed, finite number of degrees of freedom—is not a fundamental theory, but arises, in a certain approximation, valid in a limited regime, from a relativistic quantum field theory. We will explicitly show how the wavefunctions of quantum mechanics, and the configuration spaces on which they are defined, are constructed from a relativistic quantum field theory. Two lessons will be drawn from this. The first is that configuration spaces are not fundamental, but rather are derivative of structures defined on ordinary spacetime. The second is that wavefunctions are not as much like classical fields as might first appear, in that, on the most natural way of constructing wavefunctions from quantum-field theoretic quantities, the value assigned to a point in configuration space is not a local fact about that point, but rather, depends on the global state

Ontology of Relativistic Collapse Theories

If some sort of dynamical collapse theory is correct, what might the world be like? Can a theory of that sort be a quantum state monist theory, or must such theories supplement the quantum state ontology with additional beables? In a previous work (Myrvold 2018), I defended quantum state monism, with a distributional ontology along the lines advocated by Philip Pearle. In this chapter the account is extended to collapse theories in relativistic spacetimes