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 14 April 2008 09:29:30AM 1 point [-]

A configuration-centric way to put it might be as follows. Consider a particular association of amplitudes with all possible two-particle configurations. If one assumes indiscernibility, then the configuration space is not R^3 x R^3, it's that divided in half, by an equivalence relation which equates (x0,x1) with (x1,x0) (the xs are three-vectors). So working the other way, if you start in that truncated configuration space as the real configuration space, and expand out to R^3 x R^3, you end up with a symmetrical function (since you've just copied the amplitudes across). This is the overall wavefunction one normally encounters in descriptions of multi-particle states, a symmetrized sum of tensor products of single-particle wavefunctions. One can then de-symmetrize this, treat it as an entangled state of individually existing particles, and in particular construct relative states. So Dirac is sort of saying that the branches in a relative state of one particle don't interfere with branches in a relative state of another particle.

Apologies to readers who don't know what the hell I'm talking about, but I think Eliezer will get the gist.