It would be easy to develop Poincaré’s argument. If all the objects in
the universe were to become, for instance, a thousand times taller, a
thousand times broader, we should be quite unable to detect it, because
we ourselves—our retina and our measuring rod—would be transformed
to the same extent at the same time. Indeed, if all the things in
the universe were to experience an absolutely irregular spatial
deformation—if some invisible and all-powerful spirit were to distort
the universe in any fashion, drawing it out as if it were rubber—we
should have no means of knowing the fact. There could be no better
proof that space is relative, and that we cannot conceive space apart
from the things which we use to measure it. When there is no measuring
rod, there is no space.
Poincaré pushed his reasoning on this subject so far that he came to
say that even the revolution of the earth round the sun is merely a
more convenient hypothesis than the contrary supposition, but not a
truer hypothesis, unless we imply the existence of absolute space.
It may be remembered that certain unwary controversialists have tried
to infer from Poincaré’s argument that the condemnation of Galileo was
justified. Nothing could be more amusing than the way in which the
distinguished mathematician-philosopher defended himself against this
interpretation, though one must admit that his defence was not wholly
convincing. He did not take sufficiently into account the agnostic
element.
Poincaré, in any case, is the leader of those who regard space as a
mere property which we ascribe to objects. In this view our idea of
it is only, so to say, the hereditary outcome of those efforts of our
senses by means of which we strive to embrace the material world at a
given moment.
It is the same with time. Here again the objections of philosophic
Relativists were raised long ago, but it was Poincaré who gave them
their definitive shape. His luminous demonstrations are, however, well
known, and we need not reproduce them here. It is enough to observe
that, in regard to time as well as space, it is possible to imagine
either a contraction or an enlargement of the scale which would be
completely imperceptible to us; and this seems to show that man
cannot conceive an absolute time. If some malicious spirit were to
amuse itself some night by making all the phenomena of the universe a
thousand times slower, we should not, when we awake, have any means of
detecting the change. The world would seem to us unchanged. Yet every
hour recorded by our watches would be a thousand times longer than
hours had previously been. Men would live a thousand times as long, yet
they would be unaware of the fact, as their sensations would be slower
in the same proportion.
Public-domain text, read in full here on John Shaqi.
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