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RichardS comments on Decoherence as Projection - Less Wrong
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This article has left me confused. I don't see how this notion of phase relates back to a locally-evolving amplitude distribution over a space of configurations, if those configurations are merely the locations of some indistinguishable lumps in a field. How do these phases become manifest in the configuration space? It seems like there must be more to the configuration space than just a set of locations for each type of "particle", but previous articles have claimed otherwise.
This left me totally confused too.
But then, I realized that there is a property of photons that can help with this confusion here: spin. So, the configuration space is not a "a photon here and a photon there...", but a "a photon with a +1 spin here, a photon with -1 spin there..." And then this phase thing arises from the values of the amplitude distribution for the configurations with photons of opposite spins. This makes the math quite a bit easier too.
I might be completely mistaken about this, though.
The configuration space is a field where there's a number at each place. This number is a complex number.
Does that help?