Pagina-afbeeldingen
PDF
ePub

and duration, though both essential attributes of body, are not relations, it follows that space and time are not relations. Finally, the truth about space and time is that in themselves they are essentially extension and duration, and are also conditions of extended and enduring finite bodies being related to one another as coexistent and successive.

Having dispensed with 'motion in space', as he does, Professor Einstein can hardly be expected to define motion, which, however, through the whole history of mechanics, from Aristotle to Galileo and Newton, and from them to the text-books on the kinematics of the present day, has been defined as a change of a finite body through space during time, and reduced to the equations for velocity (v), space (s), and time (t); namely, v = s/t..s=vt..t=s/v. Professor Einstein is of course well aware of these primary equations, and applies them in Chapter VIII to the velocity of the propagation of light as being c = 300,000 kilometres a second, where c is a special symbol for the velocity of light. On the other hand, he does not surrender his former preference for motion relative to a practically rigid body of reference'. But the truth is that velocity is essentially a change through the extension of space during the duration of time, though involving, but only as a consequence, a change in the relative position of bodies. As a method the use of these relative positions is a useful measure of velocity; but it is not the only method, and it does not afford a definition of the velocity of motion at all.

с

When we say with confidence that the earth moves in its orbit round the sun with the velocity of about 30 kilometres a second, that a ray of light moves from the sun to the earth with a velocity of 300,000 kilometres a second in about 8 minutes, that the illustration on page 127 of Professor Einstein's book represents a ray of light first issuing far away from

a fixed star, then being deflected into a curve by the sun, and finally reaching the earth, and when we reflect that the whole starry heaven displays one vast illumination, what space, and of what body do we mean? It cannot be the space of the finite body moving, nor of any body perceptible. It may seem to be the space of ether, well defended by Professor Fleming on March 31, in The Times, but even that is not sufficient for all motion through space, because there is no proof that ether, when it comes into contact with dark bodies such as the earth, is the only vehicle of the motions of all bodies through the earth, and a fortiori through the multitudes of bodies, which have never been proved to consist entirely of ether. What then? Sursum corda. Space and time are both continuous, and as such not a mere continual series, even when so measured, but absolutely continuous extension and duration from infinity to infinity, as the ancient geometers saw and Newton saw after them. The bodies again which are near us consist of corpuscles and are again themselves corpuscles in larger and larger bodies, until at last they are all united in one body of the universe containing all bodies as its parts, and containing their extensions and durations and motions, as well as all their other attributes. I believe then that space is the infinite extension, and time the infinite duration, of the infinite and absolute body of the universe. Professor Einstein is right in recognizing bodies, but he has omitted the all-containing body. April 3, 1921.

III. IS SPACE PHYSICAL?

FROM The Times, DECEMBER 3, 1921.

In a letter which you published on November 25, Sir Oliver Lodge quoted with approval a statement of Professor Einstein that according to the general

K k

theory of relativity space is endowed with physical qualities'. How far is this statement true?

Space is one of the many attributes of body, and to that extent Professor Einstein's statement is true. But it does not follow that space is a physical attribute of body; on the contrary, it is without the most essential physical attributes of body. It is not impenetrable, since all finite bodies, resting or moving, penetrate space during time. It offers no resistance. It is neither passive as matter nor active as force. Therefore, though one attribute of body, space is not 'endowed with physical qualities'.

Space is a quantitative not a qualitative attribute, but that of being extended long, broad, and deep; and only one quantitative attribute, while another quantitative attribute closely connected with, but different from, space is time, which is the attribute of being enduring, past, present, and future. A third quantitative attribute is number, different from both; but it is not true that any of these three quantitative attributes of body is endowed with physical qualities', though the body itself as a whole is so endowed.

Professor Einstein's theory of space is the Achilles' heel of his system. If he had said that the same body is quantitative, qualitative, and relative, all might have been well, except that relativity would have sunk into a subordinate and proper position in the analysis of body. But his ignorance of the fact that space is body only so far as triply extended has concealed from him the consequence that space so limited is the object of the pure geometry of the Greeks. In the very first section of his popular book on Relativity, translated by Dr. Lawson, Professor Einstein begins by declaring that pure Euclidean geometry deals with ideas, and therefore is not true about things. He then flies off to the contrary extreme that, in order to become true about things,

the Euclidean propositions resolve themselves into propositions on the possible relative positions of practically rigid bodies, and adds that geometry supplemented in this way is to be treated as a branch of physics. But the truth lies in the middle: pure Euclidean geometry deals neither with mere ideas nor with rigid bodies, but with space, which is body so far as triply extended long, broad, and deep, and therefore a real thing but not a physical thing.

Pure geometry and physics are closely connected, but not the same. The former is a mathematical science, the latter a natural science. Pure geometry has to define and divide space into its segments, and to discover and demonstrate their universal laws: physics has to discover particular facts and causes and to account for them by geometrical as applied to physical laws. Thus the Greek mathematician, Apollonius, in the third century B. C., laid down the purely geometrical major premiss that a curve in which the ordinate squared varies with the abscissa is a parabola. After a gap of some eighteen centuries the Italian physicist, Galileo, added the mechanical minor premiss that the motion of a projectile tends to be such a curve; and by combining these two different premisses, one geometrical and the other physical, he deduced the mechanical conclusion that the motion of a projectile tends to be a parabola. This combination of pure geometry and physics, the one supplying the principles of space and the other applying these principles to the facts of nature, is necessary to the progress of physics. But Professor Einstein would spoil this order of two different sciences by confounding them together.

The cause of his error is his oblivion of the fact that one and the same body is on the one hand mathematical as continuous extended space and enduring time, and on the other hand physical and discrete as consisting of finite bodies, from the

smallest corpuscles to ourselves, thence to the earth and other planets, thence to the sun and other stars, up to the permeating and illuminating ether, which is apparently the greatest finite body; while every one of these finite bodies, small and great, is on the one hand spatially extended and temporarily enduring, and on the other hand physically impenetrable, resistant, passive matter and active force. Professor Einstein, however, obliterates the distinction contained in this analysis of body into its mathematical and its physical being; and that too, not only in the passage quoted by Sir Oliver Lodge, but also in the very last section of his book on Relativity, translated by Dr. Lawson. He begins the section as follows:

According to the general theory of relativity the geometrical properties of space are not independent but determined by · matter.'

He ends the section as follows:

'Since in reality the detailed distribution of matter is not ' uniform, the real universe will deviate in individual parts 'from the spherical-id est, the universe will be quasi'spherical.'

But is the universe spherical, or does it only appear to be spherical to any man at any place looking round him? The truth is that the geometry of Einstein is a false relapse to primitive mensuration by hands and feet, rods and plumb-lines, and, what is still worse, to the illusion of the blue sky and the spherical firmament of antiquity.

Corpus Christi College, Oxford, Dec. 3, 1921.

IV. THE INFINITE BODY OF THE UNIVERSE

SPACE DURING TIME

FROM The Times, DECEMBER 24, 1921.

I concluded in my letter of December 3, with an analysis which I hope you will allow me to develop.

« VorigeDoorgaan »