From: phfrom@nyx.uni-konstanz.de (Hartmut Frommert)
Subject: Re: BAEZZIAN physics and astronomy [was: Space-time IS a semi-Riemannian manifold (?)
Organization: Dept. of Physics, University of Constance
Date: Mon, 5 Oct 1992 18:51:53 GMT

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

>jbaez@riesz.mit.edu (John C. Baez) writes:
>: 
>: I am awed by your certainty.  Many of the best researchers in quantum
>: gravity would dearly like to know whether spacetime is a
>: semi-riemannian manifold.  What info do you have that they don't? 
>: Barring seances with Einstein's ghost, I would prefer to say
>: "spacetime is well modelled 
              ^^ should (perhaps) better read: "can be"
>: by a semi-riemannian manifold on
        ^^^^ ^^^^^^^^^^-- you mean "metric" and "torsion-free" ?
        ^^^^ This refers only to the signature of the metric, right ?
>: sufficiently large distance scales."  

Such a model is more or less good if you consider matter as composed of
structureless point particles and "classical" light (i.e. structureless
massless point particles). Then you can "derive" a conformal structure
by observing free fall and lightrays, just obtaining timelike and null
geodesics. This was outlined by Ehlers, Pirani, and Schild [1]. You thereby
obtain a "matter-conformal" structure, which can be claimed to be coincident
with that of the underlying manifold. If this statement is true is subject to
experiment, of course.

Since structureless point particles do not exist, this procedure needs 
modification. Unfortunately it is then no more easy or trivial to separate
the effects of gravity and (posibly i.e.) geometry from that by other
"internal" forces.

>Two points. First, nobody in that discussion mentioned quantum effects.
>So naturally what I meant was that CLASSICAL spacetime IS a
>semi-riemannian manifold. 

The rigorous absense of torsion and/or nonmetricity is also subject to
observation and experiment. If you relax the rigor, then there may be
a small amount of both, and you need to find out why this is so small
compared to the third geometrical field strength, curvature (or in some
limit Newtonian gravity). This may all be important also in the classical
limit, and might become modified long before you approach distances as short
as Planck length.

[stuff deleted]

>ON THE OTHER HAND I am extremely sceptical of statements such as "at
>sufficiently small length [huh? what's that?] scales, spacetime is
>replaced by [wormholes, worms, knots ,loops, strings, etc]. Spacetime is
>the set of all events. What does it mean to say that events are
>"replaced" by anything? 

Completely agreed. I sometimes wonder why most physicists take those rather 
strange things as real possibilities, while on the other hand they take
UN-modified GR, i.e. Einstein-Hilbert action, as granted: How about
scalar-tensor, squared curvature (R^2), or non-Riemannian (torsion, 
nonmetricity) modifications ? The experiments are not too restrictive for 
all these.

References:

[1] J. Ehlers, F.A.E. Pirani, and A. Schild. The Geometry of Free Fall and
    Light Propagation, in General Relativity, Papers in Honor of L. Synge,
    ed. L. O'Raifeartaigh, Claredon, Oxford 1972.
--
 Hartmut Frommert                 <phfrom@nyx.uni-konstanz.de>
 Dept of Physics, Univ of Constance, P.O.Box 55 60, D-W-7750 Konstanz, Germany
                                           -- Eat whale killers, not whales --