mitchell_porter2 comments on Can You Prove Two Particles Are Identical? - Less Wrong

32 Post author: Eliezer_Yudkowsky 14 April 2008 07:06AM

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Comment author: mitchell_porter2 15 April 2008 08:18:23AM 4 points [-]

On the idea that there might be extra properties, presently unknown, which make identical particles distinguishable:

First of all we need to be clear on what 'indistinguishability' means here. In a configuration with one particle at x0 and another particle at x1, the particles are indeed distinguishable in a sense: they have different positions. One is over here, the other is over there.

The essence of indistinguishability is this: that if you were to get the two particles and move them around so that they occupied the other position, that would count as the same configuration, quantum mechanically. Whereas, if the particles each had an extra property that could serve as an individuating label, this would be a new configuration: there would still be particles in the same positions as before, but now the labels would have swapped. And this would mean that there is no constructive interference (summing of amplitude flows) in situations where it does in fact occur.

It might be objected that in swapping the particles, even if they are unlabelled, they can still be individuated by reference to their histories: the particle at x1 now is the particle that was formerly at x0, and vice versa.

However, quantum dynamics does not consist of a single history. It consists of amplitude flows in configuration space. There is one flow through all the configurations corresponding to a particle swap, but there is another flow where the particles stay in place - and both flows end at the same configuration. So with respect to a particular pseudoclassical history - a particular trajectory through configuration space - particles have identity over time - they can be individuated by reference to their individual trajectories; but when the sum over all histories is considered, as is required, that option disappears.