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)
This may be otherwise stated by going back to our idea of a
four-dimensional world, the points of which represent the positions
and times of events. If we mark in such a space-time the successive
positions of an object we get a line, or curve, which represents the
whole history of the object, inasmuch as it shows us the position
of the object at every time. The reader may imagine that all events
happen in one plane, so that only two perpendicular dimensions
are needed to fix positions in space, with a third perpendicular
dimension for time. He may then conceive, if he may not picture,
an analogous process for four-dimensional space-time. These lines,
"tracks of objects through space-time," were called by Minkowski
"world-lines." We may now say that all the events we observe are the
intersections of world-lines. The temperature at noon was 70°. This
means that if I plot the world-line of the top of the mercury column
and the world-line of a certain mark on the glass they intersect in
a certain point of space-time. All that we know are intersections of
these world-lines. Suppose now we have a large number of them drawn
in our four-dimensional world, satisfying all known intersections,
and let us suppose the whole embedded in a jelly. We may distort
this jelly in any way, changing our coordinates as we please, but we
shall neither destroy nor create intersections of world-lines. It
may be proved that a change from one system of reference, to which
observations are referred, to any other system, moving in any way
with respect to the first system, may be pictured as a distortion of
the four-dimensional jelly. The laws of nature, therefore, being laws
that describe intersections, must be expressible in a form independent
of the reference system chosen.
From these postulates, Einstein was able to show such a formulation
possible. His law may be stated very simply:--All bodies move through
space-time in the straightest possible tracks.
The fact that an easy non-mathematical explanation can not be given,
of how this law is reached, or of just why the straightest track of
Mercury through space-time will give us an ellipse in space after we
have split space-time up into space and time, is no valid objection to
the theory. Newton's law that bodies attract with a force proportional
to their masses and inversely proportional to the square of the
distance is simple, but no one has ever given an easy non-mathematical
proof of how that law requires the path of Mercury to be an ellipse,
with the sun at a focus, instead of some other curve.]182
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