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Vague identity and quantum indeterminacy: further reflections

Katherine Hawley (1998) makes some interesting points in criticizing my response (Lowe 1997) to an argument by Harold Noonan (1995) against ontic indeterminacy of identity. My proposed example of such indeterminacy, the target of Noonan's objection, was a quantum-mechanical one (Lowe 1994). I envisaged an electron a being absorbed by an atom and becoming entangled with the single electron already present in the atom's outer shell. Subsequently, I said, an electron b is emitted from the atom's outer shell and my claim was that it is ontically (not just epistemically or semantically) indeterminate whether electron a is identical with electron b. One version of the problem raised by Noonan is this. On the hypothesis that it is indeterminate whether electron a is identical with electron b, electron b seems to have a property which electron a lacks, namely, the property of being such that it is indeterminate whether it was absorbed by the atom. But then it turns out that electron a and electron b differ in their properties and consequently that they are determinately not identical, contrary to the hypothesis. Hence, the hypothesis must be false. Now, I concede to Hawley that my response to Noonan (Lowe 1997) was not entirely satisfactory (but see also Lowe 1998: 67ff., for a more considered response). However, I do not agree with her that ontic indeterminacy claims are coherent only in the case of 'particles which exist only during the period of entanglement' and that 'For particles like Lowe's a and b, which are supposed to survive absorption or emission, ontic indeterminacy is ruled out' (Hawley 1998: 106). It is still my contention that quantum particles are such that they can be determinately distinct at one time and yet not at another (later) time. Once entangled, they are not determinately distinct, but this consequence plausibly does not apply retrospectively to a time before their entanglement. So, provided that such particles can persist through the onset of entanglement, which seems not only intelligible but consistent with the way in which many quantum physicists themselves seem to talk, my contention would appear to hold. However, what I think I ought now to acknowledge is that, once particles have become entangled, they can never thereafter become determinately distinct again. Thus, in my absorption/emission example, what I should have said is the following. Prior to absorption, there are two determinately distinct electrons, one (call it a) which is determinately