Worm Holes and Warp Drives
Einstein realized that the special theory could not describe gravitation. He generalized Galileo's observation that all objects fall with the same acceleration into the "equivalence principle". The equivalence principle asserts that a "non-inertial" uniformly accelerating frame of reference is locally equivalent (i.e., over a small enough region of space and time) to a frame fixed to a gravitating mass. This principle also asserts that a frame of reference in free fall (also called "free float") in the gravitational field of a mass, is locally equivalent to an inertial frame in empty space far from any significant gravitating mass. In both cases, gravity is eliminated and the occupants of a space craft forming such a frame are weightless. In fact, very precise measurements will show "tidal forces" due to inhomgeneities in the field of an actual gravitating mass. The tidal forces define "spacetime curvature". The freely floating orbit of a space shuttle around the earth with its engines off is called a geodesic motion. A geodesic is the straightest path possible in a warped four-dimensional spacetime. This geodesic can be an elliptical orbit with the earth at a focus when projected into three-dimensional space. In fact Einstein's general theory of relativity reduces to Newton's theory of gravitation when the spacetime curvature is weak and the speeds of the masses are small compared to the speed of light.
Strong curvatures produced by a hypothetical "exotic" phase of matter can produce giant stable wormholes for time travel to the future and the past. It can also produce a warp drive for effective faster-than-light travel to the stars and beyond. All of this assumes that quantum gravity fluctuations do not destroy these time travel and warp drive models. No one knows for sure yet. This is the most important problem in spacetime physics today IMHO.
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