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Klao comments on Decoherence as Projection - Less Wrong
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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.