(The fact that it is greater, not less, is due to the fact that the
sort of interval we are considering is more analogous to time than to
distance.) For example, if a person could leave the earth and travel
about for a time and then return, the time between his departure and
return would be less by his clocks than by those on the earth: the
earth, in its journey round the sun, chooses the route which makes
the time of any bit of its course by its clocks longer than the time
as judged by clocks which move by a different route. This is what is
meant by saying that bodies left to themselves move in geodesics in
space-time.
We assume that the body considered is not acted upon by electromagnetic
forces. We are concerned at present with the law of gravitation, not
with the effects of electromagnetism. These effects have been brought
into the framework of the general theory of relativity by Weyl,[5] but
for the present we will ignore his work. The planets, in any case,
are not subject, as wholes, to appreciable electromagnetic forces; it
is only gravitation that has to be considered in accounting for their
motions, with which we are concerned in this chapter.
[5] See his _Space, Time, Matter_, Methuen, 1922.
Our second postulate, that a light ray travels so that the interval
between two parts of it is zero, has the advantage that it does not
have to be stated only for _small_ distances. If each little bit of
interval is zero, the sum of them all is zero, and so even distant
parts of the same light ray have a zero interval. The course of a light
ray is also a geodesic according to the definition. Thus we now have
two empirical ways of discovering what are the geodesics in space-time,
namely light rays and bodies moving freely. Among freely-moving
bodies are included all which are not subject to constraints or to
electromagnetic forces, that is to say, the sun, stars, planets and
satellites, and also falling bodies on the earth, at least when they
are falling in a vacuum. When you are standing on the earth, you are
subject to electromagnetic forces: the electrons and protons in the
neighborhood of your feet exert a repulsion on your feet which is just
enough to overcome the earth’s gravitation. This is what prevents you
from falling through the earth, which, solid as it looks, is mostly
empty space.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account