General Relativity

General Relativity was formulated by Einstein in 1915. There are four basic principles that it is founded on:

1. Freely falling frames move on geodesics (force free frames travel the shortest route through spacetime)
2. Principle of Equivalence (inertial mass = gravitational mass)
3. Principle of General Covariance (use tensors which are mathematical objects that are invariant under transformation)
4. Einstein's Field Equations: (Spacetime Curvature = Matter Content)

The most important of these principles to our discussion is (4). It states that the shape, and thereby the metric equation, of spacetime is determined by matter content of the spacetime. Simply put, matter warps spacetime through its gravity. This can be visualized in what is known as an embedding diagram (figure 1). In the diagram the four dimensions of spacetime are reduced to a two dimensional sheet. If you imagine this sheet as being made of rubber and stretched taut then any mass, say a marble, placed on the sheet will warp it. This warping effect will cause gravity to bend and focus light like a lens. This effect has been observed during solar eclipses. When the sun's photosphere is blocked by the moon, background stars are visible. The stars' apparent positions are shifted near the sun from their positions when the sun is not in the field. There have been many experimental verifications of general relativity over the past 70 years and the theory is now generally accepted. This is very promising for us aspiring time travelers as not only will general relativity allow us to visit the future but we may also be able to journey to the past.

Figure 1: An Embedding Diagram of the spacetime curvature about a mass

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