This is how Poincaré, whose ideas still dominate the minds of
thoughtful men, though his mortal frame perished years ago, expressed
himself, the triumphant sweep of his wings reaching further every day:
“One cannot form any idea of empty space.... From that follows the
undeniable relativity of space. Any man who talks of absolute space
uses words which have no meaning. I am at a particular spot in
Paris—the Place du Panthéon, let us suppose—and I say: ‘I will come
back _here_ to-morrow.’ If anyone asks me whether I mean that I
will return to the same point in space, I am tempted to reply, ‘Yes.’ I
should, however, be wrong, because between this and to-morrow the earth
will have travelled, taking the Place du Panthéon with it, so that
to-morrow the square will be more than 2,000,000 kilometres away from
where it is now. And it would be no use my attempting to use precise
language, because these 2,000,000 kilometres are part of our earth’s
journey round the sun, but the sun itself has moved in relation to the
Milky Way, and the Milky Way in turn is doubtless moving at a speed
which we cannot learn. Thus we are entirely ignorant, and always will
be ignorant, how far the Place du Panthéon shifts its position in space
in a single day. What I really meant to say was: ‘To-morrow I shall
again see the dome and façade of the Panthéon.’ If there were no
Panthéon, there would be no meaning in my words, and space would
disappear.”
Poincaré works out his idea in this way:
“Suppose all the dimensions of the universe were
increased a thousandfold in a night. The world would
remain the same, giving the word ‘same’ the meaning
it has in the third book of geometry. Nevertheless,
an object that had measured a metre in length will
henceforward be a kilometre in length; a thing that
had measured a millimetre will now measure a metre.
The bed on which I lie and the body which lies on it
will increase in size to exactly the same extent. What
sort of feelings will I have when I awake in the morning,
in face of such an amazing transformation? Well,
I shall know nothing about it. The most precise
measurements would tell me nothing about the revolution,
because the tape I use for measuring will have
changed to the same extent as the objects I wish to
measure. As a matter of fact, there would be no
revolution except in the mind of those who reason as
if space were absolute. If I have argued for a moment
as they do, it was only in order to show more clearly
that their position is contradictory.”
Public-domain text, read in full here on John Shaqi.
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