22.5. General Theory of Relativity http://www.ck12.org
22.5 General Theory of Relativity
Objectives
The student will:
- Understand the twin paradox.
- Understand the equivalence of mass and energy.
Vocabulary
- principle of equivalence:An accelerating frame of reference is indistinguishable from the acceleration due
to gravity.
The general theory of relativity
The general theory of relativity, as mentioned earlier, deals with frames of reference undergoing acceleration.
Einstein published this theory in 1916, eleven years after special relativity. The mathematics needed to under-
stand general relativity is well beyond the level of this book, so we will mention just one of the most important
consequences of the theory, the principle of equivalence.
The principle of equivalence
The principle of equivalence states that an accelerating frame of reference is indistinguishable from the acceleration
due to gravity.
For example, imagine a person in an elevator in deep space far from any gravitational fields. If the elevator is
accelerating at 9. (^81) sm 2 , every experiment conducted in the elevator would produce the same results as that same
experiment would on Earth. If the person was not aware of the location of the elevator, they could reasonably
assume they were standing stationary on Earth. Additionally, if the elevator were not accelerating, but just floating
in deep space with no appreciable gravitational fields and a person held an object and released it, the object would
remain floating in front of them. The same event would occur if the elevator was freely falling on the Earth. Again,
the occupants of the elevator could not determine if they were accelerating (falling freely) due to a gravitational field,
or motionless in deep space.
The general theory of relativity can be thought of as a theory of gravity. Einstein was able to explain the nature of
gravity without resorting to action at a distance. The general theory explained gravity as a curvature in space-time
produced by mass. The more massive the body, the greater the curvature. The sun, for example, “warps” the space
around it, and the planets follow paths along this warped space as shown inFigure22.10. There is no invisible
force reaching out and holding the planets in their orbit. The difference between Newton’s conception of gravity and
Einstein’s has been compared to observing a child rolling a ball upon the ground.
Newton is pictured on a tall building observing the child from far away. He notices that when the child rolls the ball,
it always moves toward the center of the pavement. Naturally, Newton assumes that a force must be pulling the ball