Introduction to Geometrodynamics

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http://new.math.uiuc.edu/optiverse/img/rs11-107.jpeg

Bubble eversions


An Introduction to Geometrodynamics

The existence of gravitational waves is a prediction of the General Theory of Relativity which is Einstein's explanation of the gravitational interaction (1915). The basic idea is:

Gravity is no force but an aspect of the geometry of spacetime.

Space is not an absolute invariant entity, but is influenced by the distribution of mass and energy in the Universe. The basic principle is:

Matter tells space how to curve, and space tells matter how to move.

Large masses introduce a strong curvature in spacetime. Light and matter are forced to move according to this metric. Since all the matter is in motion, the geometry of space is constantly changing. Hence Geometrodynamics is a better name for Einstein's theory of gravitation. In order to derive the basic field equation, one has to relate the curvature of space to the mass/energy density:

G = k T

http://www.physics.gla.ac.uk/gwg/geodynamics.html

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The Elegant Universe, by Brian Greene, pg 231 and Pg 232


"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of genral relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called quantum geometry.