From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Quantum Cosmological Boundaries and Determinisim?
Keywords: Quantum cosmology
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 22 Jul 92 15:26:46 GMT

In article <jtwamley.711766649@adelphi> jtwamley@physics.adelaide.edu.au (Jason Twamley) writes:
>Question:
>Assume the the while universe can be described by a quantum theory.ie. there
>exists a wave function for the universe. There have been a number of proposals
>for the quantum boundary conditions for this wavefunction at the begining of
>the universe. If one of these boundary conditions succeed in specifiying
>a unique wavefunction what does this say concerning the uncertainty in the
>evolution of the everyday classical world and free will? Frequently the 
>wavefunction of the universe is called on to calculate the characteristics
>of large structures ie. inflation, density perturbations etc. However,
>in principle, how far can the information content of this wavefunction reach?
>Can it (is it suposed to?) describe the milk mixing in my tea? 

I have seen various equations for the wavefunction of the universe
(these are rather speculative proposals of course) and none of them
seems to predict that you decided to have tea yesterday.  I will repeat
Gell-Man's joke to Hartle: "If you know the wavefunction of the
universe, why aren't you rich?"  Alas, the stock prices simply cannot be
derived from the wavefunction of the universe as given by quantum
cosmology, not even in principle.   This of course is not surprising: if
I know that the wavefunction of an electron is spin-up along the z axis,
I know very little about what to expect when I measure it's spin along
the x axis.  Any given wavefunction only gives sharp predictions for
observables for which it is almost an eigenfunction.

But as another poster pinted out, speaking of "the wavefunction of the
universe" is easily misleading.  People are busy trying to come up with
somewhat deeper ways of understanding quantum mechanics.  If I may make
my own suggestion (which I may regret), it would be to regard the
wavefunction (or more generally, density matrix) of a quantum system as
a mathematical model of what we know, or can imagine knowing, about the
state of the system.  From this we can calculate probabilistic answers
to questions.  "The wavefunction of the universe" as given by various
formulas in quantum cosmology is a proposal for what we might be
expected to know about the state of the universe knowing ONLY THE LAWS
OF PHYSICS and not having, say, bothered to take into account the fact that we
know the solar system exists, etc. etc..  Of course, this is rather
tautologous since the wavefunction of the universe as given by these
proposals would BE one of the laws of physics -- the "boundary
conditions" as opposed to the dynamical equations, roughly speaking.  

In any event, asking "what's the chance that Jason will make tea, pour
milk in it, and see the milk mix in the tea just like this, GIVEN the
information contained in the wavefunction of the universe" would be
quite hard to calculate, but we can imagine it would be possible once we made
ourselves much clearer about what counts as a "Jason" in the
language of elementary particle physics, what counts as "tea," "milk,"
"just so" etc..  The narrower we made our definitions of these terms the
lower the probability would be, but in any case, it would hardly be a
useful calculation.  

On the other hand, asking "what's the chance that the milk will mix in
the tea just like this, GIVEN that Jason makes tea and pours milk in it"
can (again throwing the practical difficulties to the winds) be
calculated from a wavefunction which models the situation in which you
make tea and pour in some milk.  The wavefunction, in short, is part of
mathematical formalism closely related to that of CONDITIONAL PROBABILITY in
probability theory.

I probably should have used the example of two electrons colliding,
rather than Jaons pouring milk in his tea, because the latter brings in
all sorts of red-herring issues like whether we can ever define complex
events precisely enough to do sensible calculations about them from
first principles.  So it would be better to ponder "what's the chance
that an atom of gold will form, given this proposal for a wavefunction
of the universe" -- already too hard to answer in practice.




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