The prime example of a field theory is Einstein's general relativity, according to which the acceleration due to gravity is a purely geometric consequence of the properties of space-time in the neighbourhood of attracting masses. (As will be seen below, general relativity makes certain specific predictions that are borne out well by observation.) In a whole class of more general theories, these and other effects not predicted by simple Newtonian theory are characterized by free parameters; such formulations are called parameterized post-Newtonian (PPN) theories. There is now considerable experimental and observational evidence for limits to the parameters. So far, no deviation from general relativity has been demonstrated convincingly.
Field theories of gravity predict specific corrections to the
Newtonian force law, the corrections taking two basic forms:
(1) When matter is in motion, additional gravitational fields
(analogous to the magnetic fields produced by moving electric
charges) are produced; also, moving bodies interact with gravitational
fields in a motion-dependent way. (2) Unlike electromagnetic
field theory, in which two or more electric or magnetic fields
superimpose by simple addition to give the total fields, in
gravitational field theory nonlinear fields proportional to
the second and higher power of the source masses are generated,
and gravitational fields proportional to the product of different
masses are created. Gravitational fields themselves become sources
for additional gravitational fields. Examples of some of these
effects are shown below. The acceleration, A, of a moving
particle of negligible mass that interacts with a mass, M,
which is at rest, is given in the following formula, derived
from Einstein's gravitational theory. The expression for A
now has, as well as the Newtonian expression from equation
(1), further terms in higher
powers of GM/R
--that is, in G
M/
R
. As
elsewhere, V is the particle's velocity vector, A
is its acceleration vector, R is the vector from the
mass M, and c is the speed of light. When written
out, the sum is
This expression gives only the first post-Newtonian corrections;
terms of higher power in 1/c are neglected. For planetary
motion in the solar system the 1/c
terms are smaller than Newton's acceleration term by at least
a factor of 10{sup -}
, but some of the consequences of these correction terms are
measurable and important tests of Einstein's theory. It should
be pointed out that prediction of new observable gravitational
effects requires particular care; Einstein's pioneer work in
gravity has shown that gravitational fields affect the basic
measuring instruments of experimental physics--clocks, rulers,
light rays--with which any experimental result in physics is
established. Some of these effects are listed below:
1. The rate at which clocks run is reduced by proximity of massive bodies; i.e., clocks near the Sun will run slowly compared with identical clocks farther away from it.
2. In the presence of gravitational fields the spatial structure
of physical objects is no longer describable precisely by Euclidean
geometry; for example, in the arrangement of three rigid rulers
to form a triangle, the sum of the subtended angles will not
equal 180
. A more general
type of geometry,
Riemannian geometry, seems
required to describe the spatial structure of matter in the
presence of gravitational fields.
3. Light rays do not travel in straight lines, the rays being deflected by gravitational fields. To distant observers the light-propagation speed is observed to be reduced near massive bodies.
