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Einstein's Theory of General Relativity

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In Albert Einstein's 1905 theory (special relativity), he showed that among inertial frames of reference there was no "preferred" frame. The development of general relativity came about, in part, as an attempt to show that this was true among non-inertial (i.e. accelerating) frames of reference as well.

Evolution of General Relativity

In 1907, Einstein published his first article on gravitational effects on light under special relativity. In this paper, Einstein outlined his "equivalence principle," which stated that observing an experiment on the Earth (with gravitational acceleration g) would be identical to observing an experiment in a rocket ship that moved at a speed of g. The equivalence principle can be formulated as:
we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

as Einstein said or, alternately, as one Modern Physics book presents it:

There is no local experiment that can be done to distinguish between the effects of a uniform gravitational field in a nonaccelerating inertial frame and the effects of a uniformly accelerating (noninertial) reference frame.

A second article on the subject appeared in 1911, and by 1912 Einstein was actively working to conceive of a general theory of relativity that would explain special relativity, but would also explain gravitation as a geometric phenomenon.

In 1915, Einstein published a set of differential equations known as the Einstein field equations. Einstein's general relativity depicted the universe as a geometric system of three spatial and one time dimensions. The presence of mass, energy, and momentum (collectively quantified as mass-energy density or stress-energy) resulted in a bending of this space-time coordinate system. Gravity, therefore, was movement along the "simplest" or least-energetic route along this curved space-time.

The Math of General Relativity

In the simplest possible terms, and stripping away the complex mathematics, Einstein found the following relationship between the curvature of space-time and mass-energy density:

(curvature of space-time) = (mass-energy density) * 8 pi G / c4
The equation shows a direct, constant proportion. The gravitational constant, G, comes from Newton's law of gravity, while the dependence upon the speed of light, c, is expected from the theory of special relativity. In a case of zero (or near zero) mass-energy density (i.e. empty space), space-time is flat. Classical gravitation is a special case of gravity's manifestation in a relatively weak gravitational field, where the c4 term (a very big denominator) and G (a very small numerator) make the curvature correction small.

Again, Einstein didn't pull this out of a hat. He worked heavily with Riemannian geometry (a non-Euclidean geometry developed by mathematician Bernhard Riemann years earlier), though the resulting space was a 4-dimensional Lorentzian manifold rather than a strictly Riemannian geometry. Still, Riemann's work was essential for Einstein's own field equations to be complete.

What Does General Relativity Mean?

For an analogy to general relativity, consider that you stretched out a bedsheet or piece of elastic flat, attaching the corners firmly to some secured posts. Now you begin placing things of various weights on the sheet. Where you place something very light, the sheet will curve downward under the weight of it a little bit. If you put something heavy, however, the curvature would be even greater.

Assume there's a heavy object sitting on the sheet and you place a second, lighter, object on the sheet. The curvature created by the heavier object will cause the lighter object to "slip" along the curve toward it, trying to reach a point of equilibrium where it no longer moves. (In this case, of course, there are other considerations -- a ball will roll further than a cube would slide, due to frictional effects and such.)

This is similar to how general relativity explains gravity. The curvature of a light object doesn't affect the heavy object much, but the curvature created by the heavy object is what keeps us from floating off into space. The curvature created by the Earth keeps the moon in orbit, but at the same time the curvature created by the moon is enough to affect the tides.

Proving General Relativity

All of the findings of special relativity also support general relativity, since the theories are consistent. General relativity also explains all of the phenomena of classical mechanics, as they too are consistent. In addition, several findings support the unique predictions of general relativity:

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