Instead of revealing reality to us, space and time are, according to
Einstein, only moving veils, woven by ourselves, which hide it from us.
Yet—strange and melancholy reflection—we can no more conceive the
world without space and time than we can observe certain microbes under
the microscope without first injecting colouring matter into them.
Are time and space, then, merely hallucinations? And, if so, what
_is_ real?
No. Once the Relativist has thrown down the tottering ruins, he begins
to reconstruct. Behind the veils, now torn down and trodden under foot,
a new and more subtle reality is about to appear.
If we describe the universe in the usual way, in separate categories
of space and time, we see that its aspect depends upon the observer.
Happily, it is not the same when we describe it in the unique category
of the four-dimensional continuum in which Einstein locates phenomena,
and in which space and time are inseparably united.
If I may venture to use this illustration, time and space are like
two mirrors, one convex, the other concave, the curvature of which
is accentuated in proportion to the velocity of the observer. Each
of these mirrors gives us, separately, a distorted picture of the
succession of things. But this is fortunately compensated for by the
fact that, when we combine the two mirrors so that one reflects the
rays received by the other, the picture of the succession of things is
restored in its unaltered reality.
The distance in time and the distance in space of two given events
which are close to each other both increase or decrease when the
velocity of the observer decreases or increases. We have shown
that. But an easy calculation—easy on account of the formula given
previously to express the Lorentz-Fitzgerald contraction—shows that
there is a constant relation between these concomitant variations of
time and space. To be precise, the distance in time and the distance in
space between two contiguous events are numerically to each other as
the hypotenuse and another side of a rectangular triangle are to the
third side, which remains invariable.[6]
[6] In the geometrical calculus or representation that may be
substituted for this the hypotenuse of the triangle is the distance in
time, each second being represented by 300,000 kilometres.
Taking this third side for base, the other two will describe, above
it, a triangle more or less elevated according as the velocity of the
observer is more or less reduced. This fixed base of the triangle, of
which the other two sides—the spatial distance and the chronological
distance—vary simultaneously with the velocity of the observer, is,
therefore, a quantity independent of the velocity.
Public-domain text, read in full here on John Shaqi.
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