tion of the connection between the notional construction and the sense

Tion of the connection between the notional

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tion of the connection between the notional construction and the sense experience upon which connection, alone, the sig- nificance of geometry for physics rests. The fatal error that the necessity of thinking, preceding all experience, was at the basis of Euclidian geometry and the concept of space
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March, 1936.] PHYSICS AND REALITY. 357 belonging to it, this fatal error arose from the fact that the empirical basis, on which the axiomatic construction of Euclidian geometry rests, had fallen into oblivion. In so far as one Can speak of the existence of rigid bodies in nature, Euclidian geometry is a physical science, the useful- ness of which must be shown by application to sense experi- ences. It relates to the totality of laws which must hold for the relative positions of rigid bodies independently of time. As one may see, the physical notion of space also, as originally used in physics, is tied to the existence of rigid bodies. From the physicist's point of view, the central importance of Euclidian geometry rests in the fact that its laws are inde- pendent of the specific nature of the bodies whose relative positions it discusses. Its formal simplicity is characterized by the properties of homogeneity and isotropy (and the existence of similar entities). The concept of space is, it is true, useful, but not indis- pensable for geometry proper, i.e. for the formulation of rules about the relative positions of rigid bodies. In opposition to this, the concept of objective time, without which the formu- lation of the fundamentals of classical mechanics is impossible, is linked with the concept of the spacial continuum. The introduction of objective time involves two state- ments which are independent of each other. (I) The introduction of the objective local time by con- necting the temporal sequence of experiences with the indica- tions of a " clock," i.e. of a closed system with periodical occurrence. (2) The introduction of the notion of objective time for the happenings in the whole space, by which notion alone the idea of local time is enlarged to the idea of time in physics. Note concerning (I). As I see it, it does not mean a " petitio principii " if one puts the concept of periodical occurrence ahead of the concept of time, while one is con- cerned with the clarification of the origin and of the empirical content of the concept of time. Such a conception corre- sponds exactly to the precedence of the concept of the rigid (or quasi rigid) body in the interpretation of the concept of space. Further discussion of (2). The illusion which prevailed VOL. 22I, NO. I323--26
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358 ALBERT EINSTEIN. [J. F. I. prior to the enunciation of the theory of relativity--that, from the point of view of experience the meaning of simul- taneity in relation to happenings distant in space and con- sequently that the meaning of time in physics is a priori clear, --this illusion had its origin in the fact that in our everyday experience, we can neglect the time of propagation of light.
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