Talk:PlanetPhysics/Theorem of the Addition of Velocities Employed In

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%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: The Theorem of the Addition of Velocities Employed in %%% Primary Category Code: 03.30.+p %%% Filename: TheoremOfTheAdditionOfVelocitiesEmployedIn.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 Theorem of the Addition of Velocities Employed in Classical Mechanics} From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}

Let us suppose our old friend the railway carriage to be travelling along the rails with a constant \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} $v$, and that a man traverses the length of the carriage in the direction of travel with a velocity $w$. How quickly or, in other words, with what velocity $W$ does the man advance relative to the embankment during the process? The only possible answer seems to result from the following consideration: If the man were to stand still for a second, he would advance relative to the embankment through a distance $v$ equal numerically to the velocity of the carriage. As a consequence of his walking, however, he traverses an additional distance $w$ relative to the carriage, and hence also relative to the embankment, in this second, the distance w being numerically equal to the velocity with which he is walking. Thus in total be covers the distance $W=v+w$ relative to the embankment in the second considered. We shall see later that this result, which expresses the theorem of the addition of velocities employed in \htmladdnormallink{classical mechanics}{http://planetphysics.us/encyclopedia/NewtonianMechanics.html}, cannot be maintained; in other words, the law that we have just written down does not hold in reality. For the time being, however, we shall assume its correctness.

\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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