🚀 go-pugleaf

In article <1dhvm2INN6e5@gap.caltech.edu> brahm@cco.caltech.edu (David E. Brahm) writes:

> For the universe, one can consider a sum of "histories," which are 4D
> manifolds with metrics (modulo diffeomorphisms).  Hartle and Hawking
> proposed very simple boundary conditions, restrictions on the histories
> analogous to restricting the baseball to start at the pitcher and ending at
> the catcher: "This class consisted of curved spaces, without singularities,
> and which were of finite size, but which did not have boundaries or edges."
> This is called the "No Boundary" proposal.
> 
> Once again, the sum over all histories is dominated by a small subset, and
> the task of quantum cosmology is to show that this dominant path is in fact
> the 4D macroscopic universe we call home.

Um, not to get offensive about this, but...

Even ordinary path integrals make me a bit nervous sometimes; I
occasionally have trouble keeping myself under control so that I don't
jump up, screaming "What's the measure?"  I can usually manage to do
this by telling myself comforting lies about how the path integral is
really the limit of a well-defined integral on a lattice as the
lattice spacing is taken to zero, and by ignoring the fact that the
measure diverges in this limit.

I have even more trouble, though, when people talk about doing path
integrals in quantum cosmology.  It doesn't seem at all clear to me
that there is any sensible measure for an integral over the space of
all possible four-dimensional manifolds.
--
Matthew Austern                   Just keep yelling until you attract a
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