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Relativity: The Special and General Theory

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 diminishes 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),
 
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