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)
Imagine the path taken by a particle moving solely under the influence
of gravitation. This being the simplest possible motion of an actual
particle in the real world, it is natural to guess that its path
will be such that the particle moves from one point of time-space to
another by the most direct route. This in fact is verified by forming
the equations of the free particle's motion, which turn out to be
precisely those that specify a geodesic (most direct line) joining
the two points. On the (two-dimensional) surface of a sphere such a
line is the position taken by a string stretched between two points
on the surface, and this is the shortest distance on the surface
between them. But in the time-space geometry we find a remarkable
distinction: the interval between any two points of the path taken is
the longest possible, and between any two points there is only one
longest path. Translated into ordinary space and time this merely
asserts that the time taken between any two points on the natural
path is the longest possible.
Recall now that when the line-formula for any kind of space is known
all the metrical properties of that space are completely determined,
and combine with this what we have just found, namely, the equations
of motion of a particle subject only to gravitation are the same
equations as those which fix the line-formula for the four-dimensional
time-space. Since gravitation alone determines the motion of the
particle, and since this motion is completely described by the very
equations which fix all the metrical properties of time-space, it
follows that the metrical (experimentally determinable) properties
of time-space are equivalent to those of gravitation, in the sense
that each set of properties implies the other.
THE UNIVERSE OF SPACE-TIME
We have found the thing in nature which is independent of all
observers, and it turns out to be the very structure of time-space
itself. The motion of the free particle obviously is a thing
unconditioned by accidents of observation; the particle under the
influence of gravitation alone must go a way of its own. And if some
observer in an artificial field of force produced by the acceleration
of his reference framework describes the path as knotted, he merely is
foisting eccentricities of his own motion upon the direct path of the
particle. The conclusion is rational, for we believe that time-space
exists independently of any man's way of perceiving it.
Incidentally note that this space is that of the physical world. For
only by measurements of distances and times can we become aware of
our extension in time and space. If beyond this time-space geometry
of measurements there is some "absolute geometry," science can have
no concern with it, for never can it be revealed by the one exploring
device we possess--measurement.
Public-domain text, read in full here on John Shaqi.
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