Regarding Glenn's questions (in response to Moorad) of 04/25/98:
> Let me ask what the deficit is in a GR description of the solar system?
Experimentally, none whatsoever. Practically, though, it is theoretical
and mathematical overkill for describing the nature of gravitational
phenomena within the solar system. Newton's theory works just fine for
most practical purposes for intra solar system motions to at least 6
significant figures. It is only if further accuracy is needed that the
much less mathematically tractable GR theory is needed, and even then, the
full apparatus of GR is *not* needed, since for the GR corrections to the
Newtonian predictions involving another 6 significant figures (or so) a
weaker (than Newtonian gravity), slightly less limiting case of GR for
speeds slow compared to c and correspondingly weak gravitational fields,
i.e. the so-called 'Post-Newtonian Approximation' works just fine to the
limits of experimental detectability. GR's only down side here is its
mathematical unwieldliness for problems that can be adequately treated in
practice much more easily with less sophisticated (but wrong in principle
and in detailed experimental fact) theories.
> Considering that GR is probably the most accurately verified theory as far
> as predictions are concerned, exactly what is the evidence that it doesn't
> fit reality?
George Murphy has already commented on this concerning the fact that,
although GR is confirmed to experimental accuracy for all observations so
far, the precision of that confirmation is not nearly so spectacular as for
quantum electrodynamics (QED). The main problem with testing GR with more
rigor is simply that the first 6 to 9 significant figures of agreement
between the predictions of the theory and the observations tend to be just
the overall agreement of Newton's theory with observation, and GR's unique
predictions beyond the Newtonian predictions show up in very tiny (and hard
to measure) discrepancies with the Newtonian predictions. Another problem
is that sometimes other (non-GR) theories predict the same leading order
post-Newtonian corrections as GR does, and the observations are just not
precise or accurate enough to discriminate among various predictions of the
competing theories. The difficulty of generating and detecting a
measurable amount of gravitational radiation is due to the intrinsic
weakness in the coupling of gravity to matter (the gravitational
force between the proton and the electron in a H atom is 2.3 x 10^39 times
weaker than the electric force between them).
Even though there is no experimental evidence (such as it is) that GR
doesn't "fit reality", as Glenn says, this does not mean that physicists
consider GR as the final 'true' theory of gravitation. This is
because, for one thing, GR, as it stands, is mathematically inconsistent
with quantum field theories (such as the well-confirmed QED and the other
field theories of the 'standard model' of particle physics). The
inconsistency shows up in Einstein's field equation(s) of GR when the
non-gravitational aspects of matter are treated quantum mechanically. One
side of this equation is a classical expression (i.e. made up of ordinary
functions) involving certain aspects of the curvature of spacetime, and
the other side of the equation is a quantum expression (i.e. made up of
quantum field operators on an abstract Hilbert/Fock space) involving the
local stress/energy/momentum of the matter present. An operator is really
a set of instructions for how to perform some task (like an algorithm or a
computer program) and a function is really just a shorthand for a table
of numbers (or data). Thus Einstein's equation boils down (in the
presence of quantized fields) to an absurdity sort of analogous to the
identification of the data segment and the code segment of a compiled
computer program with each other (and using the same memory locations
for both).
This inconsistency does not show up for (i.e. have any practical
problematic effect for) gravitational phenomena whose scale is large
enough so that quantum effects on spacetime are not important. It only
becomes important for phenomena which occur over time scales less than
the so-called Planck time of ~10^(-43) s and distances less that the
Planck length of ~10^(-35) m. Since we know GR is not compatible with
quantum mechanics at the deepest level, we know that GR cannot be correct
as it stands and needs to be modified and generalized to be properly
compatible with the quantum nature of nature. It is the hope of
those engaged in the quest for the "Theory of Everything" that a
consistent synthesis between relativity and quantum mechanics is possible
(and preferably unique).
> Is there empirical mis-fits between GR and observation?
None that I know of.
David Bowman
dbowman@gtc.georgetown.ky.us
(after May 1, 1998 new email address: dbowman@georgetowncollege.edu)