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%%% Primary Title: The Gravitational Field
%%% Primary Category Code: 04.20.-q
%%% Filename: GravitationalField.tex
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\begin{document}
\subsection{The Gravitational Field}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}
``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 ({\it 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
\begin{center}
(Force) = (inertial mass) $\times$ (acceleration),
\end{center}
\noindent where the ``inertial mass" is a characteristic constant of the
accelerated body. If now gravitation is the cause of the acceleration,
we then have
\begin{center}
(Force) = (gravitational mass) $\times$ (intensity of the gravitational
field),
\end{center}
\noindent where the ``gravitational mass" is likewise a characteristic constant
for the body. From these two relations follows:
$$\mbox{(acceleration)} = \frac{\mbox{gravitational mass}}{\mbox{inertial mass}}
\times \mbox{intensity of the gravitational field}$$
~
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 law.
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 \htmladdnormallink{section}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} we shall show to what extent this is actually
the case, and how this question is connected with the general
postulate of relativity.
\subsection{References}
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.
\end{document}
