Re: New version of a relativity FAQ


"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote in message
news:g40evl01via@xxxxxxxxxxxxxxxxxx
Pmb says...

GR is not a geometrical formulation of gravity. It merely uses geometrical
language. But then again so does electrodynamics.

That is not correct. GR doesn't just *use* geometry. The principle
"field" in GR is the metric, and the metric *determines* the geometry
of spacetime.

Please define what you mean by "determines the geometry"? Do you mean that
it determines the metrical connection? If so then that's obvious. However
the geometry can also be determined by the affine connection.

That's very different from E&M.

The metric is considered to a set of gravitational potentials. It just
happens to be the same geometrical object that is used in geometry to
determine a norm of a vector and for that reason also determines the
structure of the spacetime manifold. This is what Einstein meant when he
said
----------------------------------
The notion probably comes from the fact that the mathematical origin of the
is the Gaussian-Riemann theory of the metrical continuum which we are wont
to look at as part of a geometry.
----------------------------------

All the usual geometric quantities, the length of an object,
the volume and surface area of a closed region of space, you
have to use the metric in order to compute these things. That's
very different from electromagnetism.

I never said that gravity is identical to electromagnetism in every single
way. That'd be silly because then they'd be the same thing and not different
phenomena. The mathematics which is used to describe electrodynamics is
geometry. In fact geometry is considered to be a branch of physics rather
than a branch of geometry.

In electromagnetism the metric still determines the norm of 4-vectors and
the definition of the spacetime interval which in tern determines proper
time. The proper time is used to define other 4-vectors. The operations on
tensors in EM are also geometric quantities and have a geometric meaning.

Please prove that Einstein was wrong in his letter to Lincoln Barnett.

Pete


.

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