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Luke_A_Somers comments on No Individual Particles - Less Wrong
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An attempt at translation: each point in the quantum configuration space corresponds to a particular configuration of every field (e.g. electromagnetic, gluon, electron etc.), and the regularities in these fields tell us how many particles of each species do we have and where they are. Is this even approximately correct?
So... how many dimensions does the real quantum configuration space then have? Uncountably infinite?
Yes, that is correct. The fields that physicists actually use (Fock spaces or Hilbert spaces) are considerably more general than the configuration spaces Eliezer has been using. In Eliezer's case, each position in configuration space corresponds to a particular number of point excitations in each field, and you need to integrate these to reach a full quantum configuration.
A single point in the Hilbert/Fock spaces that physicists use correspond to a complete quantum state; Eliezer's configuration spaces are each just a choice of basis vectors in that space. When you add them up to get the full quantum state, it's adding up the basis vectors to get the full vector. That's how you get from a full distribution in Eliezer's configuration spaces corresponding to a single point in a Hilbert/Fock space.