Page:The Meaning of Relativity - Albert Einstein (1922).djvu/15

Rh this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition.

We now come to our concepts and judgments of space. It is essential here also to pay strict attention to the relation of experience to our concepts. It seems to me that Poincaré clearly recognized the truth in the account he gave in his book, "La Science et l'Hypothese." Among all the changes which we can perceive in a rigid body those are marked by their simplicity which can be made reversibly by an arbitrary motion of the body; Poincaré calls these, changes in position. By means of simple changes in position we can bring two bodies into contact. The theorems of congruence, fundamental in geometry, have to do with the laws that govern such changes in position. For the concept of space the following seems essential. We can form new bodies by bringing bodies $$B, C,...$$ up to body $$A$$; we say that we continue body $$A$$. We can continue body $$A$$ in such a way that it comes into contact with any other body, $$X$$, The ensemble of all continuations of body $$A$$ we can designate as the "space of the body $$A$$." Then it is true that all bodies are in the "space of the (arbitrarily chosen) body $$A$$." In this sense we cannot speak of space in the abstract, but only of the "space belonging to a body $$A$$." The earth's crust plays such a dominant rôle in our daily