THE
PRINCIPLE OF EQUIVALENCE AND SPACE-TIME CURVATURE The exact Minkowski space-time of special relativity is incompatible
with the existence of gravity. A frame chosen to be inertial for a particle far from the Earth where the
gravitational field is negligible will not be inertial for a particle near the Earth. An approximate compatibility between the two, however, can be achieved through a remarkable property of gravitation called the weak equivalence
principle (WEP): all modest-sized bodies fall in a given external gravitational field with the same acceleration regardless of their mass, composition, or structure. The principle's validity has been checked experimentally by Galileo, Newton, and Friedrich Bessel, and in the early 20th century by Baron Roland von Eotvos (after whom such experiments are named). If an observer were to ride in an elevator falling freely in a gravitational field, then all bodies inside the elevator, because they are falling at the same rate, would consequently move uniformly in straight lines as if gravity had vanished. Conversely, in an accelerated elevator in free space, bodies would fall with the same acceleration (because of their inertia), just as if there were a gravitational field. Einstein's great insight was to postulate that this "vanishing" of gravity in free-fall applied not only to mechanical motion but to all the laws of physics, such as electromagnetism. In any freely falling frame, therefore, the laws of physics should (at least locally) take on their special relativistic forms. This postulate is called the Einstein equivalence principle (EEP). One consequence is the gravitational red shift, a shift in frequency f for a light ray that climbs through a height h in a gravitational field, given by Æf/f = gh/c6 where g is the gravitational acceleration and c is the velocity of light. (If the light ray descends, it is blueshifted.) Equivalently, this effect can be viewed as a relative shift in the rates of identical clocks at two heights. A second consequence of EEP is that space-time must be curved. Although this is a highly technical issue, consider the example of two frames falling freely, but on opposite sides of the Earth. According to EEP, Minkowski space-time is valid locally in each frame; however, because the frames are accelerating toward each other, the two Minkowski space-times cannot be extended until they meet in an attempt to mesh them into one. In the presence of gravity, space-time is flat only locally but must be curved globally. Any theory of gravity that fulfills EEP is called a "metric" theory (from the geometrical, curved-space-time view of gravity). Because the equivalence principle is a crucial foundation for this view, it has been well tested. Versions of the Eotvos experiment performed in Princeton in 1964 and in Moscow in 1971 verified EEP to 1 part in 10x6. Gravitational red shift measurements using gamma rays climbing a tower on the Harvard University campus (1965), using light emitted from the surface of the Sun (1965), and using atomic clocks flown in aircraft and rockets (1976) have verified that effect to precisions of better than 1 percent.