arXiv subjects

Adam Caulton

Publications and source records attributed to Adam Caulton.

8 recordsLinked to original sources

arXiv2024

Is a particle an irreducible representation of the Poincar\'e group?

The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it is often taken as, or claimed to be, a definition. My aims in this paper are to: (i) clarify, and partially defend, the guiding ideas behind this identification; (ii) raise objections to its being an adequate definition; and (iii) offer a rival characterisation of particles. My main objections to Wigner's identification appeal to the problem of interacting particles, and to alternative spacetimes. I argue that the link implied in Wigner's identification, between a spacetime's symmetries and the generator of a particle's space of states, is at best misleading, and that there is no good reason to link the generator of a particle's space of states to symmetries of any kind. I propose an alternative characterisation of particles, which captures both the relativistic and non-relativistic setting. I further defend this proposal by appeal to a theorem which links the decomposition of Poincar\'e generators into purely orbital and spin components with canonical algebraic relations between position, momentum and spin.

quant-ph↗

arXiv2024

Hume's dictum as a guide to ontology

In this paper I aim to defend one version at least of Hume's dictum: roughly, the idea that possibility is determined by ontology through something like independent variation. My defence is broadly pragmatic, in the sense that adherence to something like Hume's dictum delivers at least three benefits. The first benefit is that, through Hume's dictum, a physical theory's ontology delimits a range of possibilities, that I call \emph{kinematical possibilities}, which serves as a sufficiently permissive notion of possibility to sustain something like an intensional semantics for its claims, and a sufficiently demanding notion of supervenience to sustain plausible claims of inter-theoretic reduction and theoretical equivalence. The second benefit is that Hume's dictum allows us to work backwards from a range of kinematical possibilities to an ontology. This is especially useful when aiming to glean an interpretation of a physical theory, since often we are more confident that we have arrived at the right space of possibilities than that we have arrived at the right ontology. The third benefit is that Hume's dictum -- at least the version I aim to defend here -- may be applied to physical theories more or less as we find them, and therefore we can practice something resembling ontology without having to force our theories into some Procrustean bed, such as a first-order language.

physics.hist-ph↗

arXiv2014

Is mereology empirical? Composition for fermions

How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation invariance reflects a representational redundancy in the formalism. Under such a proposal, it is far from obvious how a constituent quantum system is represented. Consequently, it is also far from obvious how quantum systems compose to form assemblies, i.e. what is the formal structure of their relations of parthood, overlap and fusion. In this paper, I explore one proposal for the case of fermions and their assemblies. According to this proposal, fermionic assemblies which are not entangled -- in some heterodox, but natural sense of 'entangled' -- provide a prima facie counterexample to classical mereology. This result is puzzling; but, I argue, no more intolerable than any other available interpretative option.

quant-ph↗

arXiv2014

Physical entanglement in permutation-invariant quantum mechanics

The purpose of this short article is to build on the work of Ghirardi, Marinatto and Weber (Ghirardi, Marinatto & Weber 2002; Ghirardi & Marinatto 2003, 2004, 2005) and Ladyman, Linnebo and Bigaj (2013), in supporting a redefinition of entanglement for "indistinguishable" systems, particularly fermions. According to the proposal, non-separability of the joint state is insufficient for entanglement. The re-definition is justified by its physical significance, as enshrined in three biconditionals whose analogues hold of "distinguishable" systems.

quant-ph↗

arXiv2014

Qualitative individuation in permutation-invariant quantum mechanics

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understanding has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The most striking of the heterodox consequences are: (i) that fermionic states ought not always to be considered entangled; (ii) it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that (iii) fermions (but not bosons) may always be so discerned.

quant-ph↗

arXiv2014

Discerning "indistinguishable" quantum systems

In a series of recent papers, Simon Saunders, Fred Muller and Michael Seevinck have collectively argued, against the philosophy of quantum mechanics folklore, that some non-trivial version of Leibniz's principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles -- fermions, paraparticles, anyons, even bosons -- may be weakly discerned by some physical relation. Here I show that their arguments make illegitimate appeal to non-symmetric, i.e. permutation-non-invariant, quantities, and that therefore their conclusions do not go through. However, I show that alternative, symmetric quantities may be found to do the required work. I conclude that the Saunders-Muller-Seevinck heterodoxy can be saved after all.

quant-ph↗

arXiv2011

On Kinds of Indiscernibility in Logic and Metaphysics

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions made by Quine and Saunders.) Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles (which will come in two versions), and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity (i.e. non-identity) weaker than what we will call individuality (being an individual): two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory.

physics.hist-ph↗

arXiv2010

Symmetries and Paraparticles as a Motivation for Structuralism

This paper develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature--a theory's `not caring which point, or particle, is which'--supported a structuralist ontology. Pooley criticizes this analogy: in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of symmetry, in which states (vectors, rays or density operators) are not fixed by all permutations (called `paraparticle states'). Thus Stachel's analogy is revived.

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