🚀 go-pugleaf

In article <mcirvin.711851892@husc8> mcirvin@husc8.harvard.edu (Mcirvin) writes:

>Someone recently mentioned that in 
>quantum cosmology, though, there might be such a thing as a truly mixed
>state-- that the universe might be describable only by a density matrix,
>not a single state vector or wave function.  Is this related to the idea
>of degrees of freedom disappearing behind event horizons?  What does
>it mean?  Am I babbling?

No, you're just asking questions in rapid-fire succession.  :-)
I'm not the expert but I note that a recent conference proceedings has a
paper by Hawking entitled "The Density Matrix of the Universe".  (Sorry,
folks, I don't have the reference!)  I wouldn't be surprised if in
Hawking's case there is a relation to degrees of freedom disappearing
behind event horizons, because that's why an observer accelerating at a
constant rate sees the vacuum (a pure state) as blackbody radiation (a
mixed state).  (I always found this odd until I realized that all that
was going on was that since the accelerating observer doesn't get to see
all of Minkowski space his algebra of observables is a subalgebra of the
full algebra of observables; the restriction of a pure state to a
subalgebra can be a mixed state on the subalgebra ONLY IF the algebra in
question is noncommutative (i.e. only in quantum mechanics, not in 
classical mechanics).)  This is the basis of Hawking radiation and his
later predictions that virtual black holes might make time evolution
turn pure states into mixed states -- which he represents by a
"superscattering operator".  This of course would seem to give an arrow
of time.  Confusion reigns, as far as I'm concerned.