The paper defends a view of structural realism similar to that of French and Ladyman, although it differs from theirs in an important respect: I do not take indistinguishabiity of particles in quantum mechanics to have the significance they think it has. It also differs from Cao's view of structural realism, criticized in my "Critical Notice: Cao's `The Conceptual Development of 20th Century Field Theories".

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. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there are primitive (...) restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

There has been considerable recent philosophical debate over the implications of many particle quantum mechanics for the metaphysics of individuality (cf. Huggett [1997]). In this paper I look at things from a rather different perspective: by investigating the significance of permutation symmetry. I consider how various philosophical positions link up to the physical postulate of the indistinguishability of permuted states-permutation invariance-and how this postulate is used to explain quantum statistics. I offer an explanation of the statistics that relies on the (...) neglected parallel between permutations and covariant spatial transformation. And I explore the parallel, showing that a further kind of symmetry explains why permutations are invariant when spatial symmetries are not. (shrink)

Using Riemann’s Rearrangement Theorem, Øystein Linnebo (2020) argues that, if it were possible to apply an infinite positive weight and an infinite negative weight to a working scale, the resulting net weight could end up being any real number, depending on the procedure by which these weights are applied. Appealing to the First Postulate of Archimedes’ treatise on balance, I argue instead that the scale would always read 0 kg. Along the way, we stop to consider an infinitely jittery flea, (...) an infinitely protracted border conflict, and an infinitely electric glass rod. (shrink)

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation (...) symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)

Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical partition (...) functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics. (shrink)

ABSTRACT. Two arguments have recently been advanced that Maxwell-Boltzmann particles are indistinguishable just like Bose-Einstein and Fermi-Dirac particles. Bringing modal metaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow. The first argument, resting on symmetry in the occupation representation for all three cases, fails since peculiar correlations exist in the quantum (BE and FD) context as harbingers of ontic indistinguishability, while the indistinguishability of classical particles remains purely epistemic. The second argument, deriving (...) from the classical limits of quantum statistical partition functions, embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a third argument is considered that attempts to deflate metaphysical concerns altogether by showing that the phase-space and distribution-space representations of MB-statistics have contrary haecceitistic import. Careful analysis shows this argument to fail as well, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantum statistics. (shrink)

Ontic structural realism (OSR) claims that all there is to the world is structure. But how can this slogan be turned into a worked-out metaphysics? Here I consider one potential answer: a metaphysical framework known as generalism (Dasgupta, 2009, 2016). According to the generalist, the most fundamental description of the world is not given in terms of individuals bearing properties, but rather, general facts about which states of affairs obtain. However, I contend that despite several apparent similarities between the positions, (...) generalism is unable to capture the two main motivations for OSR. I suggest instead that OSR should be construed as a meta-metaphysical position. (shrink)

Ontic structural realism claims that all there is to the world is structure. But how can this slogan be turned into a worked-out metaphysics? Here I consider one potential answer: a metaphysical framework known as ‘generalism’. According to the generalist, the most fundamental description of the world is not given in terms of individuals bearing properties, but rather, general facts about which states of affairs obtain. However, I contend that despite several apparent similarities between the positions, generalism is unable to (...) capture the two main motivations for OSR. I suggest instead that OSR should be construed as a meta-metaphysical position. 1Introduction 2Motivations 2.1Theory change 2.2Permutation invariance 3Metaphysics 4Generalism 4.1Quantifier generalism 4.2Algebraic generalism 5Why Generalism Is Not Ontic Structural Realism 6Ontic Structural Realism as Meta-metaphysics 7Conclusion. (shrink)

Most philosophical discussion of the particle concept that is afforded by quantum field theory has focused on free systems. This paper is devoted to a systematic investigation of whether the particle concept for free systems can be extended to interacting systems. The possible methods of accomplishing this are considered and all are found unsatisfactory. Therefore, an interacting system cannot be interpreted in terms of particles. As a consequence, quantum field theory does not support the inclusion of particles in our ontology. (...) In contrast to much of the recent discussion on the particle concept derived from quantum field theory, this argument does not rely on the assumption that a particulate entity be localizable. (shrink)

Fermi-Dirac statistics are one of two kinds of statistics exhibited by !identical quantum particles, the other being !Bose-Einstein statistics. Such particles are called fermions and bosons respectively (the terminology is due to Dirac [1902-1984] [1]). In the light of the !spin-statistics theorem, and consistent with observation, fermions are invariably spinors (of half-integral spin), whilst bosons are invariably scalar or vector particles (of integral spin). See !spin.

This is an extensive review of recent work on the foundations of statistical mechanics.

According to conventional wisdom, local gauge symmetry is not a symmetry of nature, but an artifact of how our theories represent nature. But a study of the so-called theta-vacuum appears to refute this view. The ground state of a quantized non-Abelian Yang-Mills gauge theory is characterized by a real-valued, dimensionless parameter theta—a fundamental new constant of nature. The structure of this vacuum state is often said to arise from a degeneracy of the vacuum of the corresponding classical theory, which degeneracy (...) allegedly arises from the fact that “large” (but not “small”) local gauge transformations connect physically distinct states of zero field energy. If that is right, then some local gauge transformations do generate empirical symmetries. In defending conventional wisdom against this challenge I hope to clarify the meaning of empirical symmetry while deepening our understanding of gauge transformations. I distinguish empirical from theoretical symmetries. Using Galileo’s ship and Faraday’s cube as illustrations, I say when an empirical symmetry is implied by a theoretical symmetry. I explain how the theta-vacuum arises, and how “large” gauge transformations differ from “small” ones. I then present two analogies from elementary quantum mechanics. By applying my analysis of the relation between empirical and theoretical symmetries, I show which analogy faithfully portrays the character of the vacuum state of a classical non-Abelian Yang-Mills gauge theory. The upshot is that “large” as well as “small” gauge transformations are purely formal symmetries of non-Abelian Yang-Mills gauge theories, whether classical or quantized. It is still worth distinguishing between these kinds of symmetries. An analysis of gauge within the constrained-Hamiltonian formalism yields the result that “large” gauge transformations should not be classified as gauge transformations; indeed, nor should “global” gauge transformations. In a theory in which boundary conditions are modeled dynamically, “global” gauge transformations may be associated with physical symmetries, corresponding to translations of these extra dynamical variables. Such translations are symmetries if and only if charge is conserved. But it is hard to argue that these symmetries are empirical, and in any case they do not correspond to any constant phase change in a quantum state. (shrink)

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, (...) classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

This is a systematic review of the concept of indistinguishability, in both classical and quantum mechanics, with particular attention to Gibbs paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of classical indistinguishability, notwithstanding the widely-held view, that classical particles can always be distinguished by their trajectories. The last section is about the notion of object more generally, and on whether indistinguishables should be thought of as objects at all.

Although there have been several attempts to resist this conclusion, it is commonly held that the peculiar statistical behaviour of quantum particles is due to their non-individuality. In this paper, a new suggestion is put forward: quantum particles are individuals, and the distinctive features of quantum statistics are determined by the fact that all the state-dependent properties described by quantum statistics are emergent relations.