Gravitation
Newton explained how the Earth,Moon and the Sun moved about in space
by the influence of a gravitational force. Einstein showed that space
(and time) is connected with matter and gravitation in a much more complex
manner defined by non-euclidean geometry.
Einstens field equations are described by a 2'nd order differential equation
of the spacetime metric and its first and second derivatives.
To formulate a quantum version of general relativity requires a 2-step procedure.
- i) The first step is to replace the metric that measures infinitesmal surface elements
- with a more general connection that measures infinitesmal line elements.
- ( technically the ds^2 metric is split into two ds^1 objects called the 'Astekhar connection' and
- the 'frame field' )
- ii) The second step is to introduce loop observables in spacetime and express the
- quantum theory as path integrals on these loops. The curvature of classical spacetime is
- thus a dynamic effect caused by the way such microscopic loops link into each other.
One may presume that these loops would correspond to some basic entity of the quantum world
such as the strings that has been postulated by particle physics.