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arXiv:quant-ph/0703021 · Foundations of Physics

Identical Quantum Particles and Weak Discernibility

Dennis Dieks, Marijn A. M. Versteegh

Published Oct 1, 2008• 78 citations
arXivHTMLPDF

Abstract

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects , just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.

DOI
10.1007/s10701-008-9243-z

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Identical Particles and Weak Discernibility

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Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects , just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.
Saunders has recently claimed that ``identical quantum particles'' with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black's spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz's principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black's spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.
Some authors (Muller and Saunders, Huggett and Norton) have attempted to defend Leibniz’s Identity of Indiscernibles through weak discernibility. The idea is that if there is a symmetric, nonreflexive physical relation that holds between two particles, then those particles cannot be identical. In this article I focus only on Muller and Saunders’s account and argue that the means by which they achieve weak discernibility is not through a quantum mechanical observable but an alternate mathematical construction that is both unorthodox and incomplete.
Simon Saunders argues that, although distinct objects must be discernible, they need only be weakly discernible (Saunders 2003, 2006a). I will argue that this combination of views is unmotivated: if there can be objects which differ only weakly, there can be objects which don’t differ at all. Objects are weakly discernible if they stand in some irreflexive relation (Quine 1976). Max Black’s two spheres are weakly discernible: each is one mile from the other, but not one mile from itself (Black 1952). As Saunders points out, some entangled fermions seem to exhibit mere weak discernibility. Two maximally entangled fermions (electrons in the singlet state, for example) are indiscernible in some straightforward respects: same mass, same charge. They are indiscernible in less straightforward respects too: neither has a determinate location or momentum, but they are indeterminate in just the same ways. What about spin? Pick any line, say that running between your ears right now. For each electron in the pair, it is indeterminate whether it is spinning clockwise or anti-clockwise around that axis. Crucially, however, it is determinate that each is spinning in the opposite direction to the other: their collective state is anti-symmetric. Thus they are weakly discernible: each electron spins in the opposite direction to the other, but not in the opposite direction to itself (despite the fact that neither spins in any determinate direction at all).
Saunders' recent arguments in favour of the weak discernibility of (certain) quantum particles seem to be grounded in the 'generalist' view that science only provides general descriptions of the worlIn this paper, I introduce the ‘generalist’ perspective and consider its possible justification and philosophical basis; and then look at the notion of weak discernibility. I expand on the criticisms formulated by Hawley (2006) and Dieks and Veerstegh (2008) and explain what I take to be the basic problem: that the properties invoked by Saunders cannot be pointed to as ‘individuators’ of otherwise indiscernible (and thus numerically identical) entities because their ontological status remains underdetermined by the evidence and the established interpretation of the theory. In addition to to this, I suggest that Saunders does not deal adequately with bosons, and cannot do so exactly because he subscribes to PII and the generalist picture. The last part of the paper contains a critical examination of the claim (or at least implicit assumption) that the generalist picture should be regarded as obviously compelling by the modern-day empiricist.
We maximally extend the quantum-mechanical results of Muller and Saunders (2008) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite-dimensional Hilbert spaces. This confutes the currently dominant view that (A) the quantum-mechanical description of similar particles conflicts with Leibniz's Principle of the Identity of Indiscernibles (PII); and that (B) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We take sides with Muller and Saunders (2008) against this currently dominant view, which has been expounded and defended by many.
In this paper I argue that the focus of much contemporary discussion concerning the proper role and philosophical significance of weak discernibility in the context of quantum mechanics (and other physical theories) is misplaced.In particular, I claim that metaphysicians' criticism of weak discernibility on the basis of its alleged inability to ground objects' numerical distinctness is orthogonal to Saunders's (2003a) main concern in his original paper, which is to use the notion of weak discernibility as part of a broader "logical aid" for interpreting physical theories.How exactly this "methodological" (as opposed to "metaphysical") construal of weak discernibility is supposed to work, however, is not immediately transparent.This paper therefore serves both as an attempt to gain a better understanding of Saunders's interpretational program, and also seeks to encourage a renewed emphasis on the set of issues and questions that such a program-at least on my understanding of it-would appear to raise.