| “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. |
1 |
| The action of the earth on the stone takes place indirectly.
The earth produces in its surroundings 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. |
2 |
| 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. |
3 |
According to Newton’s law of motion, we have
| (Force) = (inertial mass) × (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) × (intensity of the gravitational
field), |
where the “gravitational mass” is likewise a characteristic constant for
the body. From these two relations follows: |
4 |
| If now, as we find from experience, the acceleration is to be
independent of the nature and the condition of the body and always the
same for a given gravitational field, then the
ratio of the gravitational to the inertial mass must likewise be the same
for all bodies. By a suitable choice of units we can thus make this ratio
equal to unity. We then have the following law: The gravitational
mass of a body is equal to its inertial mass. |
5 |
| It is true that this important law had hitherto been recorded
in mechanics, but it had not been interpreted. A satisfactory interpretation
can be obtained only if we recognise the following fact: The same
quality of a body manifests itself according to circumstances as “inertia”
or as “weight” (lit. “heaviness”). In the following section we shall show
to what extent this is actually the case, and how this question is connected
with the general postulate of relativity. |
6 |