Gauge Theory Gravity with Geometric Calculus
Short Description
to a geometric calculus (GC) that includes the tools of differential geometry. needed for Einstein’s theory of general relativity (GR) on flat spacetime. My …
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Content
Gauge Theory Gravity with Geometric
Calculus
David Hestenes1
Department of Physics and Astronomy
Arizona State University, Tempe, Arizona 85287-1504
A new gauge theory of gravity on flat spacetime has recently been developed
by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general
relativity are replaced by gauge principles asserting, respectively, local rotation
and global displacement gauge invariance. A new unitary formulation of
Einstein’s tensor illuminates long-standing problems with energy-momentum
conservation in general relativity. Geometric calculus provides many simplifications
and fresh insights in theoretical formulation and physical applications
of the theory.
I. Introduction
More than a decade before the advent of Einstein’s general theory of relativity
(GR), and after a lengthy and profound analysis of the relation between physics
and geometry [1], Henri Poincar’e concluded that:
“One geometry cannot be more true than another; it can only
be more convenient. Now, Euclidean geometry is and will remain,
the most convenient. . . . What we call a straight line in astronomy
is simply the path of a ray of light. If, therefore, we were to discover
negative parallaxes, or to prove that all parallaxes are higher than a
certain limit, we should…
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