Geometrodynamics

In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. It was enthusiastically promoted by John Wheeler in the 1960s, and work on it continues in the 21st century.

The term geometrodynamics is as a synonym for general relativity. More properly, some authors use the phrase Einstein's geometrodynamics to denote the initial value formulation of general relativity, introduced by Arnowitt, Deser, and Misner (ADM formalism) around 1960. In this reformulation, spacetimes are sliced up into spatial hyperslices in a rather arbitrary fashion, and the vacuum Einstein field equation is reformulated as an evolution equation describing how, given the geometry of an initial hyperslice (the "initial value"), the geometry evolves over "time". This requires giving constraint equations which must be satisfied by the original hyperslice. It also involves some "choice of gauge"; specifically, choices about how the coordinate system used to describe the hyperslice geometry evolves.

Wheeler wanted to reduce physics to geometry in an even more fundamental way than the ADM reformulation of general relativity with a dynamic geometry whose curvature changes with time. It attempts to realize three concepts:

He wanted to lay the foundation for quantum gravity and unify gravitation with electromagnetism (the strong and weak interactions were not yet sufficiently well understood in 1960 to be included).

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