Some Consequences of the Equivalence Principle
Consider a freely falling elevator near the surface of the earth, and suppose a laser fixed in one
wall of the elevator sends a pulse of light horizontally across to the corresponding point on the
opposite wall of the elevator. Inside the elevator, where there are no fields present, the
environment is that of an inertial frame, and the light will certainly be observed to proceed
directly across the elevator. Imagine now that the elevator has windows, and an outsider at rest
relative to the earth observes the light. As the light crosses the elevator, the elevator is of course
accelerating downwards at
g
, so since the flash of light will hit the opposite elevator wall at
precisely the height relative to the elevator at which it began, the outside observer will conclude
that the flash of light also accelerates downwards at
g
. In fact, the light could have been emitted
at the instant the elevator was released from rest, so we must conclude that light falls in an
initially parabolic path in a constant gravitational field. Of course, the light is traveling very fast,
so the curvature of the path is small! Nevertheless,
the Equivalence Principle forces us to the
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 Fall '10
 DavidJudd
 Physics, General Relativity, Light, Speed of light, Gravitational field, Fundamental physics concepts, Elevator

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