OK. Well, here's a different perspective.

Suppose we start with quantum mechanics. What is the argument that particles don't have identity? If you start with particles in positions A and B, and end with particles in positions C and D, and you want to calculate the probability amplitude for this transition, you count histories where A goes to C and B goes to D, and histories where A goes to D and B goes to C. Furthermore, these histories can interfere destructively (e.g. this happens with fermions), which implies that the two endpoints really are the same place in configuration space, and not just outcomes that look the same.

From this it is concluded that the particles have no identity across time. According to this view, if you end up in the situation with particles at C and D, and ask if the particle at C started at A or started at B, there is simply no answer, because both types of history will have contributed to the outcome.

However, it is a curious fact that although the evolving superposition contains histories of both types, within any individual history, there is identity across time! Within an individual history in the sum over histories, A does go to strictly one of C or D.

Now I'm going to examine whether the idea of persistent particle-identity makes sense, first in single-world interpretations, then in many-world interpretations.

What do physicists actually think is the reality of a quantum particle? If we put aside the systematic attempts to think about the problem, and just ask what attitudes are implicitly at work from day to day, I see three attitudes. One is the positivistic attitude that it is pointless to talk or think about things you can't observe. Another is the ignorance interpretation of quantum uncertainty; the particle always has definite properties, just like a classical particle, but it moves around randomly, in a way that adds up to quantum statistics. Finally, you have wavefunction realism: particles really are spread out in space or in superpositions. (The thinking of an individual physicist may combine several of these attitudes.)

The positivistic attitude is likely to dismiss the question of 'which path the electron took' or even 'did the electron take a definite path' as metaphysics and unanswerable, so it's irrelevant to the present discussion. Wavefunction realism, pursued systematically, usually becomes a many-worlds philosophy, so I'll save that option for the second part. So if we are asking whether electrons persist over time and follow definite paths in a single-world interpretation, we are really asking whether that is the case under an ignorance interpretation of quantum uncertainty.

I think it is obviously so. This way of thinking says that particles are just like classical particles - they always have a definite location, they always execute definite motions - except that they act randomly. If we have two particles apparently just sitting there, and we want to know whether they changed places or not, the real answer will be yes or no, even if we can never know which is right.

(A remark on the legitimacy of this way of thinking. Bell's theorem evidently rattled a lot of people because it showed that a naive conception of how these random motions worked could not give rise to quantum mechanics - it could not produce sufficiently strong correlations at a distance. Nonetheless, it is possible to derive quantum probabilities from local random behavior, just as you can get a diffusion probability distribution from Brownian motion. The punchline is that it has to be local random motion in configuration space. In configuration space you treat the whole classical configuration as a single point in an infinite-dimensional abstract space, so "motion" in that abstract space will involve simultaneous changes to physical properties all across real space. This may sound like cheating; it means that when you go back to thinking in terms of real space, if your random motions are going to produce quantum statistics, then the randomness has to be correlated at a distance, without further cause. But some people are prepared to bite that bullet; that's just how reality is, they'll tell you.)

Now to many worlds. Here we are saying that superpositions are real; so the history where the particles stay where they are, and the history where they swap places, are both real, and they flow into the same world at the end. Now, surely, we cannot speak of a particle's identity persisting over time. We started out with a world containing a particle at A and a particle at B; it evolved into a world that was a superposition (or was it a superposition of worlds?), each element of the superposition still containing two particles, but now in other positions; and it terminated in a world with a particle at C and a particle at D. Each final particle inherited a bit of amplitude from multiple predecessors, and for each there are paths heading back to A and to B. So we simply can't say that the particle at C is the sole heir of either original particle.

However, perhaps we can say that these two particles were entangled, and that this entangled duo had a persistent identity across time! Certainly, as described, there were only ever two particles in the picture. You might object that in the real world, there would be other particles, and they would also interact with the duo, and even trade places with them in some histories, and so this notion of a locally encapsulated entanglement is false. Everything is entangled with everything else, indirectly if not directly, and so all I could say is that the universe as a whole has identity across time.

My response to that is that developing a coherent many-worlds interpretation is a lot more difficult than you might think. Many worlds has been presented here as the economical, no-collapse alternative to theories arbitrarily postulating a collapse process; but to actually find individual worlds in a universal wavefunction, you have to break it up somehow (break it up conceptually), and that is a project with a lot of hidden difficulties (significant example). The arbitrariness of the collapse postulate has its counterpart in the arbitrariness of how the worlds are defined. If a natural, non-arbitrary definition exists, it is going to have to find natural structures, such as temporarily localized entanglements; and I note Eliezer's comment in the original article, "I'm calling you a factored subspace". If that is so - if the idea can even make sense - then it will be that subspace which has continuity of identity across time.

So, whether you adopt a single-world or a many-world perspective, a nonpatternist theory of physical identity is viable.

We are actually talking about personal identity here, not physical identity, and that raises further issues. But if physical identity is a viable concept after all, then so too may be a concept of personal identity grounded in temporal persistence of physical identity.