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Space and Time. Space and Time.

Address delivered at Cologne on Sept. 21st, 1908, by the Late of Göttingen.

[Translated by Ganesh Prasad.]

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The views on space and time which I propose to expound to you have grown in the field of Experimental Physics. It is in this that their strength lies. Their tendency is a radical one. From this moment, space by itself and time by itself shall sink in the background, and only a certain union of these two shall retain substantiality.

I should like ﬁrst to explain how, starting from the generally accepted Mechanics, one may, with the help of purely mathematical considerations, arrive at altered ideas about space and time. The equations of Newtonian Mechanics show a two-fold invariance. Their form remains unchanged first, if one subjects the underlying system of space co-ordinates to an arbitrary change of position; secondly, if one imposes any uniform translation on this system. Also the zero-point of time does not play any part. People are accustomed to look upon the axioms of Geometry as settled before they feel themselves ripe for the study of the axioms of Mechanics; for this reason, these two invariances are rarely mentioned in one breath. Each of them signifies a certain group of transformations in itself for the differential equations of Mechanics. The existence of the first group is looked upon as a fundamental attribute of space. On the other hand, people delight in punishing the second group with scorn, in order to thoughtlessly pass by it to the conclusion, that it is impossible to decide from the physical phenomena whether the space, which is supposed to be at rest, is not really in a state of uniform motion. Thus the two groups follow a separate career side by side. Their thoroughly dissimilar character may have frightened people from any attempt at combining them; but it is exactly the combination of these groups which gives us a good deal to meditate upon.