The General Theory of Relativity
The Principle of Equivilance
The theory of special relativity was necessary because it solved two important problems left over from the nineteenth century: the apparent constancy of the speed of light regardless of an observer's velocity relative to the beam of light and peculiarities in Maxwell's equations of electrodynamics that gave contradictory results concerning the induction of magnetic and electric fields between a moving magnet and a coil of wire (in fact, the title of Einstein's famous paper on special relativity is "On the Electrodynamics of Moving Bodies").
Special relativity shows there is no absolute answer to the question "Who is moving?" When two people pass each other at constant velocity, each with equal validity can claim to be at rest. Einstein wanted to believe that all motion is relative, however. Even those situations involving acceleration (a change in velocity). Inconsistencies arising from forces felt during acceleration troubled him since the claim of rest or motion at constant velocity could not be legitimately claimed for both observers.
A breakthrough came in 1907, however, when Einstein had what he later described as "the happiest thought" of his life: that whenever weight is felt, it can equally be attributed to the effects of acceleration or gravity. The Principle of Equivalence (see Figure 1) states that the effects of gravity are indistinguishable from those of accelerated motion.
Figure 1. Copyright ©Addison-Wesley
Indeed, scientists as far back as Newton knew of the similarities between the force of gravity and the forces of accelerated motion, but they believed them to be merely coincidental. Einstein imagined an inextricable connection. Stated more simply, the Principle of Equivalence says that a person isolated from the outside world can not tell if she is at rest in a gravitational field that results in a measurable weight or if she is out in space and accelerating.
No experiment can be performed, such as swinging a pendulum or dropping weights, to determine which state the woman is in since the experiments would yield the same results as if she were standing on Earth the entire time.
It's All Relative
Figure 2. Copyright ©Addison-Wesley
Consider a situation where Ginger and Marianne are in separate shuttlecrafts and Ginger sees Marianne moving away with ever greater velocity (see Figure 2.) In other words, she believes Marianne is accelerating away and her own shuttle is at rest.
Marianne might claim that she is at rest and Ginger is the one receding into the distance (see Figure 3), but the force felt by Marianne causes a problem. Ginger can look back at Marianne and say, "If I'm moving, why are you the one feeling a force? You have to be accelerating away from me!"
Figure 3. Copyright ©Addison-Wesley
The equivalence principle allows the women to truly claim that all motion is indeed relative as Einstein had believed. When Ginger observes Marianne feel a force, she can claim that Marianne is accelerating away from her. Marianne, however, can claim with equal validity that both shuttlecrafts are in the presence of a gravitational field resulting in Marianne having a measurable weight. The only reason she isn't moving is because her rocket engines are allowing her to hover over the ground (See Figure 4.)
Figure 4. Copyright ©Addison-Wesley
If she is in fact hovering over the ground, Marianne can then reason that Ginger is truly the one accelerating and the only reason she does not feel any force is or detect any acceleration with her instruments is because Ginger is in free-fall just like a skydiver would be after jumping out of an airplane but before the parachute is opened. It does, in fact, appear to be true that no experiment or measurement can be performed that would give absolute proof that an observer in stationary within a gravitational field or moving with constant acceleration in a zero-gravity (or more accurately, a micro-gravity) environment such as space.