We can now begin to interpret the common sense notion of one body
having an “effect” upon another, which we must do if we are really to
understand what is meant by the abolition of “force.” Suppose you come
into a dark room and switch on the electric light: the appearance of
everything in the room is changed. Since everything in the room is
visible because it reflects the electric light, this case is really
analogous to that of the image in the mirror; the electric light is the
center from which all the changes emanate. In this case, the “effect”
is explained by what we have already said. The more important case is
when the effect is a movement. Suppose you let loose a tiger in the
middle of a Bank Holiday crowd: they would all move, and the tiger
would be the center of their various movements. A person who could
see the people but not the tiger would infer that there was something
repulsive at that point. We say in this case that the tiger has an
effect upon the people, and we might describe the tiger’s action upon
them as of the nature of a repulsive force. We know, however, that they
fly because of something which happens to _them_, not merely because
the tiger is where he is. They fly because they can see and hear him,
that is to say, because certain waves reach their eyes and ears. If
these waves could be made to reach them without there being any tiger,
they would fly just as fast, because the neighborhood would seem to
them just as unpleasant.
Let us now apply similar considerations to the sun’s gravitation. The
“force” exerted by the sun only differs from that exerted by the tiger
in being attractive instead of repulsive. Instead of acting through
waves of light or sound, the sun acquires its apparent power through
the fact that there are modifications of space-time all round the sun.
Like the noise of the tiger, they are more intense near their source;
as we travel away they grow less and less. To say that the sun “causes”
these modifications of space-time is to add nothing to our knowledge.
What we know is that the modifications proceed according to a certain
rule, and that they are grouped symmetrically about the sun as center.
The language of cause and effect adds only a number of quite irrelevant
imaginings, connected with will, muscular tension, and such matters.
What we can more or less ascertain is merely the formula according to
which space-time is modified by the presence of gravitating matter.
More correctly: we can ascertain what kind of space-time _is_ the
presence of gravitating matter. When space-time is not accurately
Euclidean in a certain region, but has a non-Euclidean character which
grows more and more marked as we approach a certain center, and when,
further, the departure from Euclid obeys a certain law, we describe
this state of affairs briefly by saying that there is gravitating
matter at the center. But this is only a compendious account of what
we know.
Public-domain text, read in full here on John Shaqi.
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