The Rudiments of Relativity; Lectures Delivered Under the Auspices of the University College, Johannesburg, Scientific Society (Paperback)

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: Section 6.?The General Relativity Principle. Our space-time manifold is given by the passage of our three-dimensional spatial world through time. The ideas and terminology remain the same, but I can draw no picture of it; for to obtain a picture of it would require space of four dimensions. What we can usefully do is to consider various sections of the manifold. If we keep time constant we obtain a section which is our instantaneous space; that would be a section perpendicular to our world-line. But we have seen that each observer will consider his own world-line to be straight, hence what are perpendicular sections for some observers will not be perpendicular sections for others. My instantaneous space will therefore be different from that of an observer who is moving relatively to me; space accordingly becomes a sectional aspect of a perspective in the manifold, and is robbed of all vestige of independent existence. In the manifold as a whole there must exist all sorts and conditions of world-lines, giving the history of the universe at all times. If an observer, d, drew a picture of these world-lines as he imagines them, that picture would differ from the picture drawn by another observer, O2, who is moving relatively to 0, for they view things from different perspectives. If their relative velocity were constant the distortion of one picture with respect to the other would not be a very serious matter, for straight world-lines in the one picture would still be straight world-lines in the other although with different inclinations. If, however, their relative velocity is not constant the distortion becomes serious, for what are straight lines in the one picture become curved lines in the other; and the more the relative velocity of the two observers changes the more seri...