The General Theory of Relativity 141
If the observer dropped two objects, let us say, an iron ball and a
wooden ball, in the elevator car on Earth, these two balls would fall at
exactly the same rate because of the equality of their gravitational and
inertial masses. If our observer were to drop the balls in the accelerating
elevator car in outer space, she would experience the two balls
accelerating towards the floor at exactly the same rate as they did in the
elevator car on Earth. The reason for this is as follows: as the observer,
releases the two balls from her hands, the balls will no longer be
accelerated upwards. They will remain at rest in a frame of reference,
which was moving at the same speed as the elevator at precisely the time
the two balls were released. The elevator continues to be accelerated,
however, and hence, the floor of the elevator will accelerate up at the
rate, g, towards the balls, until the floor hits the balls. To an observer in
the elevator, however, it appears as though the balls had fallen to the
floor with the acceleration, g. In other words to an observer in the
accelerating elevator, the masses behave exactly as they would in the
elevator at rest on the surface of the Earth. The acceleration of his
elevator car, therefore, exactly duplicates a gravitational field.
If the direction in which the elevator car was being accelerated
changed direction so that the elevator was being pulled down with an
acceleration, g, then there would be an effective gravitational field
pulling things towards the ceiling of the elevator instead of towards the
floor. If such an elevator were placed near the surface of the Earth, then
the effects of the gravitational field produced by its acceleration down
would exactly cancel the gravitational field of the Earth. This is exactly
what happens in an aircraft, which is experiencing free fall. The effective
gravitational field created as a result of its being accelerated down by the
Earth, exactly cancels the gravitational field of the Earth and hence,
observers in the free falling craft experience no gravity. Objects will float
around inside the aircraft just as they do when an astronaut travels to the
Moon and is no longer within the influence of the Earth’s gravitational
field.
Following Einstein, we have established that the laws of physics
describing the motion of massive particles are the same in the elevator
car sitting in the Earth’s gravitational field at rest and in the elevator car
being constantly accelerated upwards with an acceleration, g. Einstein
concluded that, on the basis of this demonstration, all the laws of physics
would be identical in these two frames of reference. He expressed his
hypothesis in terms of the equivalence principle, which states the