Page:Eddington A. Space Time and Gravitation. 1920.djvu/72

56 diamonds would have been very elongated, and the unit-divisions $$OF$$, $$OH$$ very large. This kind of partition would be made by an observer whose course through the world is $$OT_1$$, and who is accordingly travelling with a velocity approaching that of light relative to $$S$$. In the limit, when the velocity reaches that of light, both space-unit and time-unit become infinite, so that in the natural units for an observer travelling with the speed of light, all the events in the finite experience of $$S$$ take place "in no time" and the size of every object is zero. This applies, however, only to the two dimensions $$x$$ and $$t$$; the space-partitions parallel to the plane of the paper are not affected by this motion along $$x$$. Consequently for an observer travelling with the speed of light all ordinary objects become two-dimensional, preserving their lateral dimensions, but infinitely thin longitudinally. The fact that events take place "in no time" is usually explained by saying that the inertia of any particle moving with the velocity of light becomes infinite so that all molecular processes in the observer must stop; many things may happen in $$S$$'s world in a twinkling of an eye—of $$S_1$$'s eye.

However successful the theory of a four-dimensional world may be, it is difficult to ignore a voice inside us which whispers "At the back of your mind, you know that a fourth dimension is all nonsense." I fancy that that voice must often have had a busy time in the past history of physics. What nonsense to say that this solid table on which I am writing is a collection of electrons moving with prodigious speeds in empty spaces, which relatively to electronic dimensions are as wide as the spaces between the planets in the solar system! What nonsense to say that the thin air is trying to crush my body with a load of 14 Ibs. to the square inch! What nonsense that the star-cluster, which I see through the telescope obviously there now, is a glimpse into a past age 50,000 years ago! Let us not be beguiled by this voice. It is discredited.

But the statement that time is a fourth dimension may suggest unnecessary difficulties which a more precise definition avoids. It is in the external world that the four dimensions are united—not in the relations of the external world to the individual which constitute his direct acquaintance with space