Talk:PlanetPhysics/Heuristic Value of the Theory of Relativity
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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: The Heuristic Value of the Theory of Relativity %%% Primary Category Code: 03.30.+p %%% Filename: HeuristicValueOfTheTheoryOfRelativity.tex %%% Version: 2 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}
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\subsection{The Heuristic Value of the Theory of Relativity}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html} Our train of thought in the foregoing pages can be epitomised in the following manner. Experience has led to the conviction that, on the one hand, the principle of relativity holds true and that on the other hand the \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} of \htmladdnormallink{transmission}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html} of light in vacuo has to be considered equal to a constant $c$. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates $x, y, z$ and the time $t$ of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from \htmladdnormallink{classical mechanics}{http://planetphysics.us/encyclopedia/NewtonianMechanics.html}, the \emph{\htmladdnormallink{Lorentz transformation}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}}.
The law of transmission of light, the acceptance of which is justified by our actual knowledge, played an important part in this process of thought. Once in possession of \htmladdnormallink{The Lorentz transformation}{http://planetphysics.us/encyclopedia/LorentzTransformation.html}, 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 \htmladdnormallink{space-time}{http://planetphysics.us/encyclopedia/SR.html} variables $x, y, z, t$ of the original coordinate \htmladdnormallink{system}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html} $K$, we introduce new space-time variables $x', y', z', t'$ of a co-ordinate system $K'$. In this connection the \htmladdnormallink{relation}{http://planetphysics.us/encyclopedia/Bijective.html} between the ordinary and the accented \htmladdnormallink{magnitudes}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} is given by the Lorentz transformation. Or in brief: General laws of nature are co-variant with respect to Lorentz transformations.
This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.
\subsection{References} This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.
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