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Relativity: The Special and General Theory
Albert Einstein: Relativity
Part II: The General Theory of Relativity
The Gravitational Field
"If we pick up a stone and then let it go, why does it fall to the ground ?" The usual answer to this
question is: "Because it is attracted by the earth." Modern physics formulates the answer rather
differently for the following reason. As a result of the more careful study of electromagnetic
phenomena, we have come to regard action at a distance as a process impossible without the
intervention of some intermediary medium. If, for instance, a magnet attracts a piece of iron, we
cannot be content to regard this as meaning that the magnet acts directly on the iron through the
intermediate empty space, but we are constrained to imagine — after the manner of Faraday —
that the magnet always calls into being something physically real in the space around it, that
something being what we call a "magnetic field." In its turn this magnetic field operates on the piece
of iron, so that the latter strives to move towards the magnet. We shall not discuss here the
justification for this incidental conception, which is indeed a somewhat arbitrary one. We shall only
mention that with its aid electromagnetic phenomena can be theoretically represented much more
satisfactorily than without it, and this applies particularly to the transmission of electromagnetic
waves. The effects of gravitation also are regarded in an analogous manner.
The action of the earth on the stone takes place indirectly. The earth produces in its surrounding a
gravitational field, which acts on the stone and produces its motion of fall. As we know from
experience, the intensity of the action on a body dimishes according to a quite definite law, as we
proceed farther and farther away from the earth. From our point of view this means : The law
governing the properties of the gravitational field in space must be a perfectly definite one, in order
correctly to represent the diminution of gravitational action with the distance from operative bodies.
It is something like this: The body (e.g. the earth) produces a field in its immediate neighbourhood
directly; the intensity and direction of the field at points farther removed from the body are thence
determined by the law which governs the properties in space of the gravitational fields themselves.
In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable
property, which is of fundamental importance for what follows. Bodies which are moving under the
sole influence of a gravitational field receive an acceleration, which does not in the least depend
either on the material or on the physical state of the body. For instance, a piece of lead and a piece
of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from
rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a
different form in the light of the following consideration.
According to Newton's law of motion, we have
(Force) = (inertial mass) x (acceleration),
where the "inertial mass" is a characteristic constant of the accelerated body. If now gravitation is
the cause of the acceleration, we then have
(Force) = (gravitational mass) x (intensity of the gravitational field),
where the "gravitational mass" is likewise a characteristic constant for the body. From these two
relations follows: