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Remarks on General Relativity
Michael Fowler
University of Virginia
Einstein’s Parable
In Einstein’s little book
Relativity: the Special and the General Theory
, he introduces general relativity
with a parable. He imagines going into deep space, far away from gravitational fields, where any body
moving at steady speed in a straight line will continue in that state for a very long time. He imagines
building a space station out there—in his words, “a spacious chest resembling a room with an observer
inside who is equipped with apparatus.” Einstein points out that there will be no gravity, the observer
will tend to float around inside the room.
But now a rope is attached to a hook in the middle of the lid of this “chest” and an unspecified “being”
pulls on the rope with a constant force. The chest and its contents, including the observer, accelerate
“upwards” at a constant rate. How does all this look to the man in the room? He finds himself moving
towards what is now the “floor” and needs to use his leg muscles to stand. If he releases anything, it
accelerates towards the floor, and in fact all bodies accelerate at the same rate. If he were a normal
human being, he would assume the room to be in a gravitational field, and might wonder why the room
itself didn’t fall. Just then he would discover the hook and rope, and conclude that the room was
suspended by the rope.
Einstein asks: should we just smile at this misguided soul? His answer is no—the observer in the chest’s
point of view is just as valid as an outsider’s. In other words,
being inside
the (from an outside
perspective)
uniformly accelerating room is physically equivalent to being in a uniform gravitational
field
. This is the basic postulate of general relativity. Special relativity said that all inertial frames were
equivalent. General relativity extends this to accelerating frames, and states their equivalence to frames
in which there is a gravitational field. This is called the
Equivalence Principle
.
The acceleration could also be used to cancel an existing gravitational field—for example, inside a freely
falling elevator passengers are weightless, conditions are equivalent to those in the unaccelerated space
station in outer space.
It is important to realize that this equivalence between a gravitational field and acceleration is only
possible because the gravitational mass is exactly equal to the inertial mass. There is no way to cancel
out electric fields, for example, by going to an accelerated frame, since many different charge to mass
ratios are possible.
As physics has developed, the concept of fields has been very valuable in understanding how bodies
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 Fall '07
 MichaelFowler
 General Relativity, Gravitational field

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