🚀 go-pugleaf

matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:

>I fear...correct me if I am mistaken... that when you say that
>the "metric affects where they are going" you are thinking of the metric
>tensor as a thing that lives on Minkowski space: the particle would
>really like to follow the Minkowski geodesics, but the metric compels it
>to go elsewhere.

Not really... my point is that the metric in GR isn't a fixed thing; it
depends on the distribution of masses, stresses, etc., and that where
my test particle eventually ends up depends on that distribution of
masses etcetera, and that the effect is due to the metric.  Whether
you call that an interaction or not is immaterial... we obviously
agree on what's going on.

Now, a remarkable thing is that you *can* start by thinking of the
metric as a thing living in Minkowski space and trying to construct
a workable tensor field theory; you eventually end up with GR.  This
is covered somewhere in Misner, Thorne, and Wheeler.  But the
"underlying Minkowski metric" is obviously artificial, not a thing
essential to the theory. 

>Would you say that the Minkowski metric "interacts"
>with free particles in Minkowski space and "forces" them to move along
>straight lines ["inertons"!]? No? Well, if you do not wish to say it of
>Minkowski space, then don't say it of any other spacetime. "Gravity" was
>all a mistake, resulting from our ignorance of spacetime curvature. How
>does one quantize a mistake?

One doesn't quantize a mistake; one quantizes spacetime geometry.
I don't know much about quantum gravity, but I do know that it
*doesn't* assume gravity to be an effect independent of geometry,
living on Minkowski spacetime.  You *can* go a certain distance in
this way, defining the field to be perturbations of the metric,
expressed as a tensor; using the general relativity Lagrangian,
with nonlinearities treated as self-interaction terms; and trying
to construct a perturbation theory.  However, you immediately
run into extreme trouble from the necessity of renormalizing an
infinity of nonrenormalizable interaction terms, and the whole
program falls in.  Therefore, this approach is *not* considered
fruitful. 

I think that the efforts in quantum gravity currently in progress
have less to do with gravitons than with trying to define a 
functional integral over different geometric configurations of
spacetime, with the scalar curvature giving the action.  This is
essentially the application of Feynman's path-integral technique
to the dynamics of geometry described by general relativity.  All
kinds of problems occur, but they are *not* the result of ignoring
the fact that an object in free fall is simply following a
geodesic. 

If you don't like the world "gravity," you can use MTW's term
and talk about "quantum geometrodynamics."
 
-- 
Matt McIrvin   mcirvin@husc.harvard.edu   Long live short .sigs