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Analysis

Weak discernibility

Katherine Hawley

Published Sep 14, 2006• 16 citations

Abstract

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).

DOI: 10.1093/analys/66.4.300

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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 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.

Muller and Saunders ([2008]) purport to demonstrate that, surprisingly, bosons and fermions are discernible; this article disputes their arguments, then derives a similar conclusion in a more satisfactory fashion. After briefly explicating their proof and indicating how it escapes earlier indiscernibility results, we note that the observables which Muller and Saunders argue discern particles are (i) non-symmetric in the case of bosons and (ii) trivial multiples of the identity in the case of fermions. Both problems undermine the claim that they have shown particles to be physically discernible. We then prove two results concerning observables that are truly physical: one showing when particles are discernible and one showing when they are not (categorically) discernible. Along the way we clarify some frequently misunderstood issues concerning the interpretation of quantum observables. 1 Background2 Criticisms 2.1 Bosons 2.2 Fermions3 Reformulating the Insight 3.1 What weakly discerns? 3.2 General results4 Conclusion

In a series of recent papers, Simon Saunders, Fred Muller, and Michael Seevinck have collectively argued, against the folklore, that some nontrivial 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 nonsymmetric, that is, permutation-noninvariant, 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.

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.