These concepts that space and time are not as immutable as they
appear: that our universe may suffer distortion, that time may lag
or hasten without our being in the least aware, may be made
interestingly clear by an illustration first suggested by Helmholtz,
of which the following is in the nature of a paraphrase.
If you look at your own image in the shining surface of a teapot, or
the back of a silver spoon, all things therein appear grotesquely
distorted, and all distances strangely altered. But if you choose to
make the bizarre supposition that this spoon-world is real, and your
image--the spoon-man--a thinking and speaking being, certain
interesting facts could be developed by a discussion between
yourself and him.
You say, "Your world is a distorted transcript of the one in which I
live."
"Prove it to me," says the spoon-man.
With a foot-rule you proceed to make measurements to show the
rectangularity of the room in which you are standing. Simultaneously
he makes measurements giving the same numerical results; for his
foot-rule shrinks and curves in the exact proportion to give the
true number of feet when he measures his shrunken and distorted rear
wall. No measurement you can apply will prove you in the right, nor
him in the wrong. Indeed he is likely to retort upon you that it is
your room which is distorted, for he can show that in spite of all
its nightmare aspects his world is governed by the same orderly
geometry that governs yours.
The above illustration deals purely with space relations, for such
relations are easily grasped; but certain distortions in time
relations are no less absolutely imperceptible and unprovable. So
far from having any advantage over the spoon-man, our plight is his.
The Principle of Relativity discovers us in the predicament of the
Mikado's "prisoner pent," condemned to play with crooked cues and
elliptical billiard balls, and of the opium victim, for whom
"space swells" and time moves sometimes swift and sometimes slow.