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%%% Primary Title: Space and Time in Classical Mechanics
%%% Primary Category Code: 03.30.+p
%%% Filename: SpaceAndTimeInClassicalMechanics.tex
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%%% Author(s): bloftin
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\begin{document}
\subsection{Space and Time 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}
The purpose of \htmladdnormallink{mechanics}{http://planetphysics.us/encyclopedia/Mechanics.html} is to describe how bodies change their
\htmladdnormallink{position}{http://planetphysics.us/encyclopedia/Position.html} in space with ``time." I should load my conscience with grave
sins against the sacred spirit of lucidity were I to formulate the
aims of mechanics in this way, without serious reflection and detailed
explanations. Let us proceed to disclose these sins.
It is not clear what is to be understood here by ``position" and
"space." I stand at the window of a railway carriage which is
travelling uniformly, and drop a stone on the embankment, without
throwing it. Then, disregarding the influence of the air resistance, I
see the stone descend in a straight line. A pedestrian who observes
the misdeed from the footpath notices that the stone falls to earth in
a parabolic curve. I now ask: Do the ``positions" traversed by the
stone lie ``in reality" on a straight line or on a parabola? Moreover,
what is meant here by motion ``in space"? From the considerations of
the previous section the answer is self-evident. In the first place we
entirely shun the vague word ``space," of which, we must honestly
acknowledge, we cannot form the slightest conception, and we replace
it by ``motion relative to a practically rigid body of reference." The
positions relative to the body of reference (railway carriage or
embankment) have already been defined in detail in the preceding
section. If instead of ``body of reference'' we insert ``\htmladdnormallink{system}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html} of
co-ordinates," which is a useful idea for mathematical description, we
are in a position to say: The stone traverses a straight line
relative to a system of co-ordinates rigidly attached to the carriage,
but relative to a system of co-ordinates rigidly attached to the
ground (embankment) it describes a parabola. With the aid of this
example it is clearly seen that there is no such thing as an
independently existing trajectory (lit. ``path-curve"\footnotemark), but only
a trajectory relative to a particular body of reference.
In order to have a complete description of the \htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}, we must specify
how the body alters its position with time; {\it i.e.} for every point on
the trajectory it must be stated at what time the body is situated
there. These data must be supplemented by such a definition of time
that, in virtue of this definition, these time-values can be regarded
essentially as \htmladdnormallink{magnitudes}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} (results of measurements) capable of
observation. If we take our stand on the ground of \htmladdnormallink{classical mechanics}{http://planetphysics.us/encyclopedia/NewtonianMechanics.html}, we can satisfy this requirement for our illustration in the
following manner. We imagine two clocks of identical construction;
the man at the railway-carriage window is holding one of them, and the
man on the footpath the other. Each of the observers determines the
position on his own reference-body occupied by the stone at each tick
of the clock he is holding in his hand. In this connection we have not
taken account of the inaccuracy involved by the finiteness of the
\htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} of propagation of light. With this and with a second
difficulty prevailing here we shall have to deal in detail later.
\footnotetext[1]{That is, a curve along which the body moves.}
\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.
\end{document}
