Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument (...) as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

In discussion of the interpretation of quantum mechanics the terms ‘ontic’ and ‘epistemic’ are often used in the sense of pertaining to what exists, and pertaining to cognition or knowledge respectively. The terms are also often associated with the formal definitions given by Harrigan and Spekkens for the wavefunction in quantum mechanics to be ψ-ontic or ψ-epistemic in the context of the ontological models framework. The formal definitions are contradictories, so that the wavefunction can be either ψ-epistemic or ψ-ontic but (...) not both. However, we argue, nothing about the informal ideas of epistemic and ontic interpretations rules out wavefunctions representing both reality and knowledge. The implications of the Pusey–Barrett–Rudolph theorem and many other issues may be rethought in the light of our analysis. (shrink)

I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...) the ontology-first approach, whereas the Gibbsian framework should assume the theory-first approach. -/- . (shrink)

Statistical mechanics is often taken to be the paradigm of a successful inter-theoretic reduction, which explains the high-level phenomena (primarily those described by thermodynamics) by using the fundamental theories of physics together with some auxiliary hypotheses. In my view, the scope of statistical mechanics is wider since it is the type-identity physicalist account of all the special sciences. But in this chapter, I focus on the more traditional and less controversial domain of this theory, namely, that of explaining the thermodynamic (...) phenomena.What are the fundamental theories that are taken to explain the thermodynamic phenomena? The lively research into the foundations of classical statistical mechanics suggests that using classical mechanics to explain the thermodynamic phenomena is fruitful. Strictly speaking, in contemporary physics, classical mechanics is considered to be false. Since classical mechanics preserves certain explanatory and predictive aspects of the true fundamental theories, it can be successfully applied in certain cases. In other circumstances, classical mechanics has to be replaced by quantum mechanics. In this chapter I ask the following two questions: I) How does quantum statistical mechanics differ from classical statistical mechanics? How are the well-known differences between the two fundamental theories reflected in the statistical mechanical account of high-level phenomena? II) How does quantum statistical mechanics differ from quantum mechanics simpliciter? To make our main points I need to only consider non-relativistic quantum mechanics. Most of the ideas described and addressed in this chapter hold irrespective of the choice of a (so-called) interpretation of quantum mechanics, and so I will mention interpretations only when the differences between them are important to the matter discussed. (shrink)

In discussions of the foundations of statistical mechanics, it is widely held that the Gibbsian and Boltzmannian approaches are incompatible but empirically equivalent; the Gibbsian approach may be calculationally preferable but only the Boltzmannian approach is conceptually satisfactory. I argue against both assumptions. Gibbsian statistical mechanics is applicable to a wide variety of problems and systems, such as the calculation of transport coefficients and the statistical mechanics and thermodynamics of mesoscopic systems, in which the Boltzmannian approach is inapplicable. And the (...) supposed conceptual problems with the Gibbsian approach are either misconceived, or apply only to certain versions of the Gibbsian approach, or apply with equal force to both approaches. I conclude that Boltzmannian statistical mechanics is best seen as a special case of, and not an alternatve to, Gibbsian statistical mechanics. (shrink)

I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; the central role of Hawking radiation in permitting (...) black holes to be in thermal contact with one another; the wide range of routes by which Hawking radiation can be derived and its back-reaction on the black hole calculated; the interpretation of Hawking radiation close to the black hole as a gravitationally bound thermal atmosphere. In an appendix I discuss recent criticisms of black hole thermodynamics by Dougherty and Callender. This paper confines its attention to the thermodynamics of black holes; a sequel will consider their statistical mechanics. (shrink)

It is well-known that the invocation of `equilibrium processes' in thermodynamics is oxymoronic. However, their prevalence and utility, particularly in elementary accounts, presents a problem. We consider a way in which their role can be played by sets of sequences of processes demarcated by curves carrying the property of accessibility. We also examine the vexed question of whether equilibrium processes are necessarily reversible and the revision of this property in relation to sets of sequences of such processes.

There is a long tradition of thinking of thermodynamics, not as a 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 article is a sketch and defense of a science of manipulations and their effects on physical (...) systems. I call this science thermo-dynamics, or ΘΔcs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta \Delta }^{\text{cs}}$$\end{document}, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Light is also shed on the use of coarse-grained entropies. (shrink)

Foundational puzzles surround gravitational thermal physics—a realm in which stars are treated as akin to molecules in a gas. Whether such an enterprise is successful and the domain of thermal physics extends beyond our terrestrial sphere is disputed. There are successes and paradoxical features. Callender :960–981, 2011) advocates reconciling the two sides of the dispute by taking a broader view of thermodynamics. Here I argue for an alternative position: if we are careful in distinguishing statistical mechanics and thermodynamics, then no (...) reconciliation is required. Both sides can live in harmony because whilst statistical mechanics applies, thermodynamics does not. This state of affairs—the applicability of statistical mechanics without the emergence of thermodynamic behaviour—can be explained in terms of an infamous infinite idealisation: the thermodynamic limit. (shrink)

Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) classical algorithm. Shor’s algorithm was soon followed by several (...) other algorithms that aimed to solve combinatorial and algebraic problems, and in the years since theoretical study of quantum systems serving as computational devices has achieved tremendous progress. Common belief has it that the implementation of Shor’s algorithm on a large scale quantum computer would have devastating consequences for current cryptography protocols which rely on the premise that all known classical worst-case algorithms for factoring take time exponential in the length of their input (see, e.g., Preskill 2005). Consequently, experimentalists around the world are engaged in attempts to tackle the technological difficulties that prevent the realisation of a large scale quantum computer. But regardless whether these technological problems can be overcome (Unruh 1995; Ekert and Jozsa 1996; Haroche and Raimond 1996), it is noteworthy that no proof exists yet for the general superiority of quantum computers over their classical counterparts. -/- The philosophical interest in quantum computing is manifold. From a social-historical perspective, quantum computing is a domain where experimentalists find themselves ahead of their fellow theorists. Indeed, quantum mysteries such as entanglement and nonlocality were historically considered a philosophical quibble, until physicists discovered that these mysteries might be harnessed to devise new efficient algorithms. But while the technology for harnessing the power of 50–100 qubits (the basic unit of information in the quantum computer) is now within reach (Preskill 2018), only a handful of quantum algorithms exist, and the question of whether these can truly outperform any conceivable classical alternative is still open. From a more philosophical perspective, advances in quantum computing may yield foundational benefits. For example, it may turn out that the technological capabilities that allow us to isolate quantum systems by shielding them from the effects of decoherence for a period of time long enough to manipulate them will also allow us to make progress in some fundamental problems in the foundations of quantum theory itself. Indeed, the development and the implementation of efficient quantum algorithms may help us understand better the border between classical and quantum physics (Cuffaro 2017, 2018a; cf. Pitowsky 1994, 100), and perhaps even illuminate fundamental concepts such as measurement and causality. Finally, the idea that abstract mathematical concepts such as computability and complexity may not only be translated into physics, but also re-written by physics bears directly on the autonomous character of computer science and the status of its theoretical entities—the so-called “computational kinds”. As such it is also relevant to the long-standing philosophical debate on the relationship between mathematics and the physical world. (shrink)

The principle of 'information causality' can be used to derive an upper bound---known as the 'Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. In this paper, however, I argue that the principle has not to date been sufficiently motivated to play this role; the motivations that have so far been given are either unsatisfactorily vague or else amount to little more than an appeal to intuition. I then consider how (...) one might begin to successfully motivate the principle. I argue that a compelling way of so doing is to understand it as a generalisation of Einstein's principle of the mutually independent existence---the 'being-thus'---of spatially distant things, interpreted as a special methodological principle. More specifically: I describe an argument, due to Demopoulos, to the effect that the quantum-mechanical no-signalling condition can be viewed as a generalisation, appropriate to an irreducibly statistical theory such as quantum mechanics, of the Einsteinian principle. And I then argue that a compelling way to motivate information causality is to in turn consider it as a further generalisation of the Einsteinian principle that is appropriate to a theory of communication. I nevertheless describe important obstacles that must yet be overcome if the project of establishing information causality as a foundational principle of nature is to succeed. (shrink)