The Evans Equations of Unified Field Theory - Alpha Institute for ...

A metric is a formal map from one point in a spacetime to another.
Newton’s space was nothing; it was an empty 3-dimensional background upon
which matter moved and one could measure distances. Our everyday idea of
spacetime is much like Newton’s and unless one deals in the very small or large,
or in high velocities, it is a good enough. It is a 3-dimensional concept and time
is outside its definition. The speed of electromagnetism and gravitation were
assumed to be instantaneous in Newtonian physics.
Einstein’s special relativistic metric is called Minkowski spacetime. It is flat
without gravitational curvature, however it has 4-dimensional distance defined. It
is a combination of space and time into one inseparable 4-dimensional
spacetime. In addition, that spacetime can compress due to velocity. The
distinction between spacetime and the matter within it starts to blur. We will deal
with it in a bit of detail in Chapter 2.
. Einstein’s general relativistic metric is that of Riemann geometry.
Spacetime has four dimensions and gravity is geometry with curvature. Special
relativity can be derived from general relativity when there is no curvature. Time
can be treated like a fourth spatial dimension.
The development of general relativity indicated that spacetime is a
mathematical analytical, fully differentiable manifold. That is, it was an active,
real existence that had points that connected smoothly. The physical description
starts to becomes mathematical. We do not have the necessary experience or
the mechanical concepts to describe spacetime any other way than
mathematically. One will hear physicists say physics is mathematics or general
relativity is geometry. There is no doubt truth in this and until our engineering
skills can look at the vacuum itself, it must be the way we think.
Special relativity used flat four dimensional geometry. Time was included
in the metric.
General relativity used the curved four dimensional geometry developed
by Riemann. It had four dimensional distances however specifically had no
spinning of the metric.
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