Re: Is temporal sign ambiguity inherent in Einstein's general relativistic field equation?
- From: "John Bell" <john.bell@xxxxxxxxxxxxxxxxxx>
- Date: Thu, 20 Apr 2006 09:26:18 +0000 (UTC)
Charles Francis pronounced:
Thus spake John Bell <john.bell@xxxxxxxxxxxxxxxxxx>
Charles Francis wrote:
Gravity is a manifestation of geometry, and
More precisely, gravity is -interpreted- as a manifestation of geometry
in the context of classical GR. It is not interpreted as a
manifestation of geometry in, for example, Newtonian physics.
Yes, but I say something a bit stronger. That it is a manifestation of
geometry, not just an interpretation or simply equivalent to geometry.
Even MTW
do not recommend geometry as the appropriate tool for examining the
deeper physics that is indicated by the collapse of geometry at the
beginning of time (Ch. 44, Gravitation), and even Einstein said that
the fact of singularities was indicative of a weakness in the
mathematical apparatus used (The Meaning of Relativity).
That is true. When the very idea of geometry, i.e. the classical idea of
measurement, breaks down we have no valid theory.
If your argument merely boils down to the fact that we need the
concepts of space and time to describe motion and acceleration, then
you could equally well argue that thermodynamics is a manifestation of
geometry too, since we also need these dimensions to describe the
'jiggling' of molecules that is manifested macroscopically as heat.
That is not what people normally mean by the term "manifestation of
geometry"
I am sure the mathematical equation makes both predictions. We often
meet equations with non-physical solutions in applied mathematics and
theoretical physics. When we do we rely on physical considerations to
distinguish the solution.
My reason for asking the question was to test whether our relativistic
field equations and Einstein's are rigorously mathematically synonymous
within their overlapping domain of mutual applicability, despite being
expressed using a radically different form of mathematical apparatus.
Your answers appear to confirm that you have misunderstood the reason
for asking the question, as well as its meaning.
John Bell
2nd discussion moderator at http://global.accelerators.co.uk
(Change John to Liberty to respond)
.
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