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General Relativity

Special relativity is generalised to accommodate non-inertial reference frames. This is done via the principle of relativity, illustrated in figure 15 and stated below.

It is not possible to distinguish (in a closed system) between the effects produced by a gravitational field and those produced by an acceleration of the closed system

Figure 15: Graphic depiction of the principle of equivalence.
\includegraphics[width=0.9\textwidth]{equiv.ps}

This principle allows one to replace the effects of gravity by equivalent effects based on the geometry of space-time. Once gravity is ``abolished'' in this way, and there is no ``force of gravity'' then all (gravitating) objects will have motions described by Newton's First Law. That is, those in motion will continue in a straight line at constant velocity. However, ``straight line'' now means only locally straight (locally parallel to a co-ordinate axis in space). However, the geometry of space is now ``warped'' (no longer Euclidean) in such a way that the objects actual trajectory is ``similar'' to that calculated in the classical way. Einstein wrote down a Field Equation which allowed the warping of the geometry of space-time to be calculated given a certain mass distribution.

The trajectory of the moon around the earth is locally straight in a space-time region warped by the presence of the earth's mass. Such ``straight lines'' are called geodesics, defined as the shortest distance between two points in a curved space. This is illustrated in figure 16.

Figure 16: In General Relativity, the warping of the geometry of space-time due to mass distributions accounts for the effects of ``gravitational attraction''.
\includegraphics[width=1.0\textwidth]{warp.ps}

This is not simply an alternative but equivalent way of looking at gravity. It would not be such a disturbing idea if that were so ! It is easy to see that dramatic new ``gravitational'' effects may be predicted.

General Relativity is now widely accepted, following three major experimental verifications :

Black holes have not yet been definitely verified, although there are many strong candidates in the cosmos, and further compelling theoretical evidences.


next up previous
Next: The Global Positioning System Up: Relativistic Mechanics [8 lectures] Previous: Massless particles
Simon Connell 2006-02-21