To see how the equivalence principle led Einstein to devise his theory of
general relativity, let’s begin with a thought experiment of the sort Einstein
would devise. Suppose you wake up one morning to find that you have been sealed up (bed and all) within an opaque, soundproof, hermetically sealed
box. “Oh no!” you say. “This is what I’ve always feared would happen.
I’ve been abducted by space aliens who are taking me away to their home
planet.” So startled are you by this realization, you drop your teddy bear.
Observing the falling bear, you find that it falls toward the floor of the box
with an acceleration a = 9.8 m s −2 . “Whew!” you say, with some relief. “At
least I am still on the Earth’s surface; they haven’t taken me away in their
spaceship yet.” At that moment, a window in the side of the box opens to
reveal (much to your horror) that you are inside an alien spaceship which is
being accelerated at 9.8 m s −2 by a rocket engine. When you drop a teddy
bear, or any other object, within a sealed box, the equivalence principle
permits two possible interpretations, with no way of distinguishing between
them. (1) The box is static, or moving with a constant velocity, and the
bear is being accelerated downward by a constant gravitational force. (2)
The bear is moving at a constant velocity, and the box is being accelerated
upward at a constant rate. The behavior of the bear in each case (Figure 3.1)
is identical. In each case, a big bear falls at the same rate as a little bear; in
each case, a bear stuffed with cotton falls at the same rate as a bear stuffed
with lead; and in each case, a sentient anglophone bear would say, “Oh,
bother. I’m weightless.” during the interval before it collides with the floor
of the box. 1