Download Differential Geometry and Relativity Theory: An Introduction by Richard L. Faber PDF

By Richard L. Faber

ISBN-10: 082471749X

ISBN-13: 9780824717490

There are a few pencil writing marks within the booklet as a rule within the first 28 pages. many of the 255 pages are fresh. Binding is tight.

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Extra resources for Differential Geometry and Relativity Theory: An Introduction

Example text

Once in possession of the Lorentz transformation, however, we can combine this with the principle of relativity, and sum up the theory thus: Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original coordinate system K, we introduce new space-time variables x1, y1, z1, t1 of a co-ordinate system K1. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation.

I do not believe we ought to if we wish to remain consistent ; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the "Galileian space" first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.

But the experiment gave a negative result — a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the æther produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the differeace in time mentioned above. Comparison with the discussion in Section 11 shows Albert Einstein 49 Part I: The Special Theory of Relativity that also from the standpoint of the theory of relativity this solution of the difficulty was the right one.

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