🚀 go-pugleaf

In article <17584@ucdavis.ucdavis.edu> carlip@landau.ucdavis.edu (Steve Carlip) writes:
>In article <19tid9INNo1h@agate.berkeley.edu> ted@physics.Berkeley.EDU (Emory F. Bunn) writes:
>>[much deleted...]
[more deleted...]
>> What bothers me about
>>this is that there is no natural measure one can impose on the set
>>of possible initial conditions for Universes in order to make that
>>statement meaningful.
>>[...]
[more deleted...]
>
>If I understand you correctly, you are claiming that there is no
>possible measure on the space of three-geometries (or maybe
>three-geometries plus initial configurations of matter fields).
>This seems unlikely to me; do you have a proof or a reference?
>Would you argue that a path integral is impossible in principle
>in general relativity, for instance?
>

I was making the assertion you attribute to me, and I made it with
more confidence than I probably should have.  I believe, based on my
admittedly limited understanding of measure theory, that the space
of 3-geometries is simply "too big" to admit a well-behaved measure
that would allow one to talk about probabilites.  (I have formed
some vague arguments in my mind in support of this position,
but they're far from being rigorous enough to convince anyone else.)

I hope that I am wrong about this, as I think it would be very nice 
to have such a measure.  Is there anyone out there who can be more 
definitive about this than I can?

-Ted

(By the way, I think that path integrals are pretty ill-founded
in ordinary quantum field theory, so I am not too sanguine
about applying them in GR.  That's another story, though.)