Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000Bird, J. Malcolm (James Malcolm)
Philosophy
Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000
Bird, J. Malcolm (James Malcolm)
Relativity (Physics)
Einstein flatly denies Newton's hypothesis that there is an absolute
system (and, indeed, many others before him had found it difficult
to admit that so insignificant a part of the universe as our fixed
star system should have such a privileged position as that accorded
to it in the Newtonian Mechanics). In any system, he says, we have no
reason to distinguish between the so-called real gravitational force
and the so-called fictitious centrifugal forces--if we wish so to
express it gravitational force is fictitious force. [10] A particle
moving in the neighborhood of material bodies moves according to a law
of inertia--a physical law expressible, therefore, in a manner quite
independent of the choice of coordinates. The law of inertia is that
a particle left to itself moves along the geodesics or shortest lines
in the space. If the particle is remote from other bodies the space
has the Euclidean character and we have Newton's law of inertia;
otherwise the particle is in a space of a non-Euclidean character
(the space being always the four-dimensional space) and the path of
the particle is along a geodesic in that space. Einstein, in order
to make the theory more concrete, makes a certain stipulation as to
the nature of the gravitational space which stipulation is expressed,
as are all physical laws, by means of a tensor equation--and this is
sometimes called his law of gravitation.
Perhaps it will be well, in exemplification, to explain why light
rays, which pass close to the sun, should be bent according to the new
theory. It is assumed that light rays travel along certain geodesics
known as minimal geodesics. The sun has an intense gravitational field
near it--or, as we now say, the departure of the four-dimensional
space from the Euclidean is very marked for points near the sun--but
for points so remote as the earth this departure is so small as
to be negligible. Hence the form of the geodesics near the sun is
different from that near the earth. If the space surrounding the
sun were Euclidean the actual paths of the light rays would appear
different from geodesics or straight-lines. Hence Einstein speaks
of the curvature of the light rays due to the gravitational field of
the sun; but we must not be misled by a phrase. Light always travels
along geodesics (or straight lines--the only definition we have of a
straight line is that it is a geodesic); but, owing to the "distortion"
of the space they traverse, due to the sun, these geodesics reach us
with a direction different from that they would have if they did not
pass through the markedly non-Euclidean space near the sun.
Public-domain text, read in full here on John Shaqi.
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