"Precisely the same is true if you substitute light rays for sound
waves. If with the naked eye or with a telescope you watch a clock
moving away from you, you will find that its minute hand takes a longer
time to cover its five-minute intervals than does the chronometer in
your hand, and if the clock travelled with the velocity of light you
would forever see the minute hand at precisely the same point. That
which is true of the clock is, of course, also true of all time
intervals which it measures, so that if you moved away from the earth
with the velocity of light everything on it would appear as still as
on a painted canvas."
Your time has apparently come to a standstill in one position and
is moving in another! All this seems absurd enough, but it does show
that time alone has little meaning.
Minkowski's Conclusion. The relativity theory requires that we
thoroughly reorganise our method of measuring time. But this is
intimately associated with our method of measuring space, the distance
between two points. As we proceed we find that space without time has
little meaning, and vice versa. This leads Minkowski to the conclusion
that "time by itself and space by itself are mere shadows; they are
only two aspects of a single and indivisible manner of coordinating
the facts of the physical world." Einstein incorporated this time-space
idea in his theory of relativity.
How We Measure a Point in Space. Suppose I say to you that the chemical
laboratory of Columbia University faces Broadway; would that locate
the laboratory? Hardly, for any building along Broadway would face
Broadway. But suppose I add that it is situated at Broadway and 117th
Street, south-east? there could be little doubt then. But if, further,
this laboratory would occupy but part of the building, say the third
floor; then the situation would be specified by naming Broadway,
117th Street S. E., third floor. If Broadway represents length, 117th
Street width, and third floor height, we can see what is meant when we
say that three dimensions are required to locate a position in space.
The Fourth Dimension. A point on a line may be located by one
dimension; a point on a wall requires two dimensions; a point in the
room, like the chemical laboratory above ground, needs three. The
layman cannot grasp the meaning of a fourth dimension; yet the
mathematician does imagine it, and plays with it in mathematical
terms. Minkowski and Einstein picture time as the fourth dimension. To
them time occupies no more important position than length, breadth,
or thickness, and is as intimately related to these three as the three
are to one another. H. G. Wells, the novelist, has beautifully caught
this spirit when in his novel, "The Time Machine," he makes his hero
travel backwards and forwards along time just as a man might go north
or south. When the man with his time machine goes forward he is in
the future; when he goes backwards he is in the past.
Public-domain text, read in full here on John Shaqi.
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