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The Mathematical Gazette
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Results of Relativity without the Theory of Tensors

Results of relativity without the theory of tensors
Authors: Kearney, R. A. M.;

Results of Relativity without the Theory of Tensors

Abstract

The Special Theory of Relativity leads to the following conclusions : (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. (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 ”). (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 (T 1 OT 2 , X 1 OX 2 towards the optical line which goes in the direction of motion of the particle.

Keywords

relativity theory

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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