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Results of Relativity without the Theory of Tensors*

Published online by Cambridge University Press:  03 November 2016

R. A. M. Kearney
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Extract

The Special Theory of Relativity leads to the following conclusions :

  1. (i) The three dimensions of space and one of time constitute an isotropic fourfold, in which there is no unique time-direction, just as there is no unique space direction.

  2. (ii) Specifying the velocity of a body is equivalent to specifying its “ time-direction”, that is, the direction of its path through space-time (its “ world-line ”).

  3. (iii) If the units of distance and time are taken to correspond with each other, so that the velocity of light is unity, then the lines in our diagram (L'OL, M'OM, and lines parallel to these) which represent the paths of light pulses (Robb's “ optical lines ”) are at right angles for light going in opposite directions, and in this case the time direction (T'OT) of a particle and its corresponding space-direction (X'OX) are equally inclined to the optical line (L'OL) between them, so that setting a particle in motion involves “ rotating ” its time-direction and its space-direction through equal angles (T1OT2, X1OX2 towards the optical line which goes in the direction of motion of the particle.

Type
Research Article
Information
The Mathematical Gazette , Volume 18 , Issue 229 , July 1934 , pp. 145 - 164
Copyright
Copyright © Mathematical Association 1934

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Footnotes

*

In the original form of the paper, as prepared for the Annual Meeting of the Mathematical Association on 4th January, 1934, the argument was based on the consideration of matter as a process, without assuming the Principle of Relativity or Laplace's Equation. This being too lengthy for inclusion in the Gazette, the more fundamental parts of the paper have been omitted, and the argument modified so as to make use of the results of the Special Theory of Relativity and to obtain the new law of gravitation as a natural extension of Laplace's Equation.

References

* In the original form of the paper, as prepared for the Annual Meeting of the Mathematical Association on 4th January, 1934, the argument was based on the consideration of matter as a process, without assuming the Principle of Relativity or Laplace's Equation. This being too lengthy for inclusion in the Gazette, the more fundamental parts of the paper have been omitted, and the argument modified so as to make use of the results of the Special Theory of Relativity and to obtain the new law of gravitation as a natural extension of Laplace's Equation.