Eight Lectures on Yoga

25. I feel almost ashamed of the world that I have to tell you that in the year 1900, four years before the appearance of Einstein's world- shaking paper, I described space as 'finite yet boundless,' which is exactly the description in general terms that he gave in more mathematical detail.[4] You will see at once that these three words do describe a curved geometry; a sphere, for instance, is a finite object, yet you can go over the surface in any direction without ever coming to an end. I said above that Riemann's Geometry was not quite sufficient to explain the phenomena of nature. We have to postulate different kinds of curvature in different parts of the continuum. And even then we are not happy! 26. Now for a spot of Sullivan! 'The geometry is so general that it admits of different degrees of curvature in different parts of space-time. It is to this curvature that gravitational effects are due. The curvature of space-time is most prominent, therefore, around large masses, for here the gravitational effects are most marked. If we take matter as fundamental, we may say that it is the presence of matter that causes the curvature of space-time. But there is a different school of thought that regards matter as due to the curvature of space-time. That is, we assume as fundamental a space-time continuum manifest to our senses as what we call matter. Both points of view have strong arguments to recommend them. But, whether or not matter may be derived from the geometrical peculiarities of the space-time continuum, we may take it as an established scientific fact that gravitation has been so derived. This is obviously a very great achievement, but it leaves quite untouched another great class of phenomena, namely, electro-magnetic phenomena. In this space-time continuum of Einstein's the electro-magnetic forces appear as entirely alien. Gravitation has been absorbed, as it were, into Riemannian geometry, and the notion of force, so far as gravitational phenomena are concerned, has been abolished. But the electro-magnetic forces still flourish undisturbed. There is no hint that they are manifestations of the geometrical peculiarities of the space-time continuum. And it can be shown to be impossible to relate them to anything in Riemann's Geometry. Gravitation can be shown to correspond to certain geometrical peculiarities of a Riemannian space-time. But the electro-magnetic forces lie completely outside this scheme.' 27. Here is the great quag into which mathematical physics has led its addicts. Here we have two classes of phenomena, all part of a unity of physics. Yet the equations which describe and explain the one class are incompatible with those of the other class! This is not a question of philosophy at all, but a question of fact. It does not do to consider that the universe is composed of particles. Such a hypothesis underlies one class of phenomena, but it is nonsense when applied to the electro- magnetic equations, which insist upon our abandoning the idea of particles for that of waves. Here is another Welsh rabbit for supper!