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)
If we imagine our whole universe, with its observers, planetary
orbits, instruments, and everything else, embedded in a jelly, and
then distort the jelly and contents in any way, the numbers at which
our planetary orbits (or rather their telescopic images) intersect
our scales will be unaltered. Moreover, we could vary, in any manner,
the times at which all objects (including the clock hands) occupied
their distorted positions, and the hand of some clock near the point
where the planetary image crossed the scale would record for this
occurrence the same dial reading as before. An inhabitant of this
distorted universe would be absolutely unconscious of the change. Now
the General Theory of Relativity which expresses itself in slightly
varied forms, amounts to satisfying a certain philosophical craving
of the mind, by asserting that the laws of nature which control our
universe ought to be such that another universe like the above, whose
inhabitants would be unconscious of their change, would also satisfy
these laws, not merely from the standpoint of its own inhabitants,
but also from the standpoint of our measurements. In other words,
this second universe ought to appear possible to us as well as to
its inhabitants.
Einstein decides to make his theory conform to this philosophical
desire, and this greatly limits the modifications of clocks and
scales which he permits himself for the purpose of representing
gravitation. Further, if we express the alterations of the measures
as functions of proximity to matter, velocity and so forth, our
expressions for these alterations will include, as a particular case,
that where matter is absent, although the scales and observer may still
remain. Our alteration of the scales and clocks with velocity must thus
revert, for this case, to that corresponding to the older theory of
relativity, in order to avoid predicting that two observers, in uniform
motion relative to each other in empty space, will measure different
values for the velocity of light. In this way, the velocity of light
comes to play a part in expressing the alterations of the measures.
Even with these restrictions, Einstein was able to do the equivalent
of finding an alteration of scales and clocks in the presence of
matter which would account for our finding that the planetary motions
take place very nearly in accordance with Newton's law. The new law
has accounted with surprising accuracy for certain astronomical
irregularities for which Newton's law failed to account, and has
predicted at least one previously unknown phenomenon which was
immediately verified.
In conclusion, it may be of interest to state how the new law describes
the motion of a particle in the vicinity of a body like the earth. The
law amounts to stating that, if we measure a short distance, radially
as regards the earth's center, we must allow for the peculiarity of
our units by dividing by
$$\sqrt{1-\frac{2mG}{c^2r}}$$
Public-domain text, read in full here on John Shaqi.
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