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)
On the other hand Turner has recently made a very interesting
point,9 namely, that the fourth dimension as actually treated
by the mathematicians is not time itself, but time multiplied
by a constant--the velocity of light.10 Without affecting the
astronomical proofs of relativity at all, this simplifies our
conceptions enormously. In ordinary everyday life time and space
cannot be identical, any more than a yard can be identical with a
quart. On what is known to physicists as the centimeter-gram-second
system, distance is represented by $l$, mass by $m$, and time by
$t$. Velocity is then distance divided by time, $l/t$, or as we say
in English units, so many feet per second, and the fourth dimension
may be expressed as time multiplied by velocity, $t \times l/t =
l$. That is to say, it is simply distance, just like the other three
dimensions. To say that time is the fourth dimension from this point
of view, appears to us just as ridiculous as it would be to attempt
to measure the velocity of a train in quarts. It is quite correct,
however, although unusual, to speak of a given train as moving at a
speed of 10 quarts per square inch per second, $l^3/l^2 t = l/t$. This
would be equivalent to a velocity of 33 miles per hour.
If I wish to give a complete dimensional description of myself in my
four dimensions, I must give my length, my breadth, and my thickness,
ever since I came into being, and also the course I have traversed
through space since that time. This latter distance will be expressed
in terms of a unit whose length is 186,000 miles, the distance
traversed by light in one second. The distance which I travel through
space annually is enormous, and very complex as to direction. It
involves not merely my own motions as I cross the room, or take a
train or steamer, but also those due to the rotation of the earth on
its axis, its revolution round the sun, and the motion of the latter
through the heavens. In general I travel, or in other words increase
my length in the fourth dimension, by over 4,000 units a year. The
fourth dimension accordingly, if this view is accepted, is simply a
distance like the other three, and perfectly easy to understand.
Public-domain text, read in full here on John Shaqi.
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