By David Bohm
ISBN-10: 0415404258
ISBN-13: 9780415404259
In those inspiring lectures David Bohm explores Albert Einstein’s celebrated Theory of Relativity that reworked perpetually the best way we expect approximately time and area. but for Bohm the results of the speculation have been way more innovative either in scope and effect even than this. Stepping again from dense theoretical and clinical aspect during this eye-opening paintings, Bohm describes how the thought of relativity moves on the middle of our very belief of the universe, whether we're physicists or philosophers.
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- Relativity, Groups and Topology; Lectures delivered at Les Houches during the 1963 Session of the Summer School of Theoretical Physics, University of Grenoble
- The Principles of Electromagnetic Theory and of Relativity
- The Large Scale Structure of Space-Time (Cambridge Monographs on Mathematical Physics)
- Geometric Theory of Generalized Functions with Applications to General Relativity
Extra resources for The Special Theory of Relativity (Routledge Classics)
Example text
Suppose a vector field A is defined over this space. Let P At P the vector A is resolved in be a general point (r, 0), as shown in Fig. 4. the radial and transverse directions, with the respective contravariant components A' and A•. Let the components of A parallel to rectangular Cartesian axes Ox and Oy be Ax and AY. 2) Suppose first that A is a constant vector field. That is, at every point its magnitude and direction are the same. This fact is expressed quantitatively by the relations: Ax= constant, AY =constant.
P and Q are two points respectively on p and q 45 SPACE-TIME CURVATURE such that OP=OQ=u. Let arc PQ=v measure the separation between p and qat a distance u from 0. Then we have the simple relation Fig. 6. (a) The deviation between the two straight lines in the Euclidean plane increases at a uniform rate with respect to the length parameter along either of them. ~-~.. v= 'I' . 16) . In Fig. 6b is shown the corresponding situation on the surface of a 2-sphere of unit radius. , great circles) through O, diverging from 0 at a small angle 4> between them.
6 The Levi-Civita Tensor We now define an important antisymmetric tensor. 41) [ijk/]. To show that E;Jkt is a tensor consider a change of coordinates x 1 -J>. x' 1• We then have, using Eq. ' t;xz = ( -g)l/2 [ijkl] . ' ()xz ()x'm ()x'n ()x'P ()x'q ()x'm ()x'n ()x'P ()x'q ( -g)1/ 2 (mnpq) J { X-J>. 42) I E mnpq· There is, however, one word of caution! In Eq. 42) we have used the square root of Eq. 26) and there could be an ambiguity of sign. This ambiguity is related to the orientation of the coordinate system.