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The Physics and Metaphysics of Identity and Individuality Steven French and De´Cio Krause: Identity in Physics: a Historical, Philosophical, and Formal Analysis

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The Physics and Metaphysics of Identity and Individuality Steven French and De´Cio Krause: Identity in Physics: a Historical, Philosophical, and Formal Analysis Metascience (2011) 20:225–251 DOI 10.1007/s11016-010-9463-7 BOOK SYMPOSIUM The physics and metaphysics of identity and individuality Steven French and De´cio Krause: Identity in physics: A historical, philosophical, and formal analysis. Oxford: Clarendon Press, 2006, 440 pp, £68.00 HB Don Howard • Bas C. van Fraassen • Ota´vio Bueno • Elena Castellani • Laura Crosilla • Steven French • De´cio Krause Published online: 3 November 2010 Ó Springer Science+Business Media B.V. 2010 Don Howard Steven French and De´cio Krause have written what bids fair to be, for years to come, the definitive philosophical treatment of the problem of the individuality of elementary particles in quantum mechanics (QM) and quantum-field theory (QFT). The book begins with a long and dense argument for the view that elementary particles are most helpfully regarded as non-individuals, and it concludes with an earnest attempt to develop a formal apparatus for describing such non-individual entities better suited to the task than our customary set theory. D. Howard (&) Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA e-mail: [email protected] B. C. van Fraassen Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA e-mail: [email protected] O. Bueno Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA e-mail: [email protected] E. Castellani Department of Philosophy, University of Florence, Via Bolognese 52, 50139 Florence, Italy e-mail: elena.castellani@unifi.it L. Crosilla Department of Pure Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK e-mail: [email protected] 123 226 Metascience (2011) 20:225–251 Are elementary particles individuals? I do not know. It depends on what one means by ‘individuals’. This much is certain—elementary particles as described by QM and QFT are not individuals in the same sense in which classical mechanical systems, the molecules constituting a Boltzmann gas, or Daltonian atoms are individuals. The elementary particles of QM obey either bosonic or fermionic statistics. The molecules of a Boltzmann gas do not. An individual elementary particle can find itself in a state that is a superposition of eigenstates of some observable. Dalton’s atoms cannot. On the standard interpretation of QM, interacting quantum systems are described by an entangled joint state that is not fixed completely by any possible separate states of those systems. Not so the interacting systems described by Newtonian mechanics and gravitation theory. In QFT, there might be states of indefinite or indeterminate particle number. In classical physics, a given region of space during a given time always contains a determinate number of atoms. In QFT, particle number is frame dependent, mutually accelerated observers feeling or seeing different numbers of photons in one and the same region of space. In classical physics, particle number is frame independent. You and I must detect the same number of atoms or molecules regardless of our relative states of motion. So, are elementary particles individuals? The philosopher’s customary way of approaching the question is via the Principle of the Identity of Indiscernibles (PII), which asserts the identity—hence the lack of individuality—of two things that share all of the same properties. The strength of PII depends upon what one takes to be the relevant individuating properties. French and Krause distinguish three versions, in order of increasing strength. The weakest, PII(1), includes all properties. Slightly stronger is PII(2), which excludes spatio-temporal properties. Stronger still is PII(3), which excludes all relational properties. Some version of PII seems to be relevant in the case of at least some kinds of elementary particles. Consider the more straightforward case of bosons. Photons are massless, spin-1 systems obeying Bose–Einstein statistics. Hence, on the standard interpretation, QM does not regard as physically different two configurations that one might think describable as involving merely the switch of physical location of two otherwise identical photons. Not even a difference in spatial situation suffices to endow two such photons with discernible or distinct identities of a kind sufficient to mark the two configurations as physically different. Two such photons being, thus, indiscernible, in spite of a difference in spatial situation, one is tempted to conclude by way of PII(2), that they are identical, and, for that reason, not individuals. S. French Department of Philosophy, University of Leeds, Leeds, UK e-mail: [email protected] D. Krause Department of Philosophy, Federal University of Santa Catarina, 88040-900 Campus Trindade, Floriano´polis, SC, Brazil e-mail: [email protected] 123 Metascience (2011) 20:225–251 227 This metaphysical state of affairs has definite, testable, physical consequences. There being only one way of arraying two bosons in two different locations, that configuration receives a statistical weight equal to that attaching to each of the two different ways of arraying the two bosons in one or another of the same locations. When, then, we ask what is the probability of the two bosons being together in the same place, the answer is 2/3, significantly higher than the ‘classical’ value of 1/2, which was computed by applying equiprobability to what were, classically, four different configurations. As noted, this difference between quantum and classical statistics has testable consequences, most famously in the form of Einstein’s 1925 prediction of the phenomenon of Bose–Einstein condensation, wherein, at sufficiently low temperatures the atoms of a bosonic gas all condense into the same lowest quantum state. So, again, one is tempted to conclude that two (or more) indiscernible bosons are not individuals. This conclusion can be resisted in various ways. Thus, one might choose a non-standard interpretation of QM, such as the Bohmian interpretation, which ascribes determinate trajectories to all elementary particles, endowing those particles with in-principle distinguishing identities, and locating all of the quantum weirdness elsewhere, mainly in the quantum potential. Or one can assume that, in spite of their seeming indiscernibility, two such indiscernible bosons are neverthe- less rendered metaphysically distinct by virtue of their each possessing some form of transcendental individuality, primitive ‘thisness’, or, in the language of the Scholastics, haecceitas. One recovers the standard quantum statistics by applying the appropriate probabilities—1/6—to what are, on this view, distinct configurations differing only by particle exchange. A price must be paid for one’s resisting the conclusion that bosons are not individuals. Going the Bohmian route requires lots of extra apparatus, including the quantum potential, quantum ergodicity, and relativistic non-localities at the level of the hidden variables. Choose the route of haecceitas and one requires a seemingly ad hoc weighting of configurations, a weighting for which there is no plausible physical explanation beyond the ex post facto argument that those are the weightings needed to get the predictions to turn out right. But if one is willing to pay some such price, neither logic nor empirical evidence can debar one’s taking one of these routes. Are we asking the right question? While it is clear, as I said above, that elementary particles as described by QM are not individuals in the same sense as the molecules of a Boltzmann gas, what it means positively to say that they are non-individuals is less clear. The second major goal of French and Krause’s book is to develop formal tools in the form of quasi-set theory to make easier our speaking and thinking clearly about non-individuals. But space is wanting in this essay for a proper appreciation of that effort. Instead here, like French and Krause—but for slightly different reasons—I want to suggest that some of the preliminary unclarity about the sense in which elementary particles are non-individuals derives from our having chosen to approach the question in the first instance via PII. That PII is the philosophers’ favourite tool does not imply that it is the most helpful tool for the physicist to employ. 123 228 Metascience (2011) 20:225–251 Two considerations suggest that there is something odd about deploying PII in assaying the individuality of bosons. Firstly, even if one accepts the conclusion that, owing to their indiscernibility, two bosons are not individuals, in spite of their difference in spatial situation, this lack of individuality does not come in the form of the bosons’ being numerically identical. That is to say, that this variety of indiscernibility does not imply that we have just one boson, rather than two. One cannot tell which boson is which, perhaps not just because of a lack of epistemic access to that which might constitute the ‘whichness’ of the bosons, but because they lack such ‘whichness’ from the start. But that there are two bosons, not one, is a fact. Secondly, in thinking about Bose–Einstein statistics, what are more helpfully regarded as being indiscernible in the sense relevant for the applicability of PII are not the bosons themselves, but rather the configurations classically distinguished by particle exchange. This is because the indiscernibility of the configurations does, as noted, imply the strict numerical identity of those configurations. In bosonic quantum statistics, there is, literally, only one configuration in which there is exactly one boson in each of two cells of phase space. The point towards which I mean now to be tending in so querying the helpfulness of PII is that, in making all of this out to be an argument about the individuality of elementary particles, we might be asking the wrong question or a question that is not well posed.
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