how we should regard the size of some part of the configuration space compared to some other part, the L^2 norm is the blindingly obvious mathematical answer because of the properties of the wavefunction.
Does “part of the configuration space” refer to a single state vector, or a whole region that a state vector might belong to? My impression is that measuring the latter sort of thing is problematic from a rigorous mathematical standpoint. Is this correct, and does it have consequences for your discussion?
I say the former; people scared of continuous densities might prefer the latter, at which point they have the traditional sorites paradox of how large an epsilon-neighborhood to draw; but in practical terms, this isn’t so bad because (if we start with low entropy) decoherence rapidly separates the wavefunction into thin wisps with almost-zero values taken between them.
Does “part of the configuration space” refer to a single state vector, or a whole region that a state vector might belong to? My impression is that measuring the latter sort of thing is problematic from a rigorous mathematical standpoint. Is this correct, and does it have consequences for your discussion?
I say the former; people scared of continuous densities might prefer the latter, at which point they have the traditional sorites paradox of how large an epsilon-neighborhood to draw; but in practical terms, this isn’t so bad because (if we start with low entropy) decoherence rapidly separates the wavefunction into thin wisps with almost-zero values taken between them.