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\begin{document}

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\section*{gauge}

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{related_entries}{Related entries}\dotfill \pageref*{related_entries} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

According to (\href{Science+of+Logic#714}{Hegel, Science of Logic, \S{}714}):

\begin{quote}%
Ein Maa\ss{}, als Maa\ss{}stab im gew\"o{}hnlichen Sinne, ist ein Quantum, das als die an sich bestimmte Einheit gegen \"a{}u\ss{}erliche Anzahl willk\"u{}rlich angenommen wird. Eine solche Einheit kann zwar auch in der That an sich bestimmte Einheit seyn, wie Fu\ss{} und dergleichen urspr\"u{}ngliche Maa\ss{}e; insofern sie aber als Maa\ss{}stab zugleich f\"u{}r andere Dinge gebraucht wird, ist sie f\"u{}r diese nur \"a{}u\ss{}erliches, nicht ihr urspr\"u{}ngliches Maa\ss{}.---So mag der Erddurchmesser, oder die Pendell\"a{}nge, als specifisches Quantum f\"u{}r sich genommen werden. Aber es ist willk\"u{}rlich, den wievielsten Theil des Erddurchmessers oder der Pendell\"a{}nge und unter welchem Breitengrade man diese nehmen wolle, um sie als Maa\ss{}stab zu gebrauchen. Noch mehr aber ist f\"u{}r andere Dinge ein solcher Maa\ss{}stab etwas \"A{}u\ss{}erliches. Diese haben das allgemeine specifische Quantum wieder auf besondere Art specificirt, und sind dadurch zu besondern Dingen gemacht. Es ist daher th\"o{}richt, von einem nat\"u{}rlichen Maa\ss{}stab der Dinge zu sprechen. Ohnehin soll ein allgemeiner Maa\ss{}stab nur f\"u{}r die \"a{}u\ss{}erliche Vergleichung dienen; in diesem oberfl\"a{}chlichsten Sinne, in welchem er als allgemeines Maa\ss{} genommen wird, ist es v\"o{}llig gleichg\"u{}ltig, was daf\"u{}r gebraucht wird. Es soll nicht ein Grundmaa\ss{} in dem Sinne seyn, da\ss{} die Naturmaa\ss{}e der besondern Dinge daran dargestellt und daraus nach einer Regel, als Specifikationen Eines allgemeinen Maa\ss{}es, des Maa\ss{}es ihres allgemeinen K\"o{}rpers, erkannt w\"u{}rden. Ohne diesen Sinn aber hat ein absoluter Maa\ss{}stab nur das Interesse und die Bedeutung eines Gemeinschaftlichen, und ein solches ist nicht an sich, sondern durch \"U{}bereinkommen ein Allgemeines.

A measure taken as a gauge in the usual meaning of the word is a quantum which is arbitrarily assumed as the intrinsically determinate unit relatively to an external amount. Such a unit can, it is true, also be in fact an intrinsically determinate unit, like a foot and suchlike original measures; but in so far as it is also used as a standard for other things it is in regard to them only an external measure, not their original measure. Thus the diameter of the earth or the length of a pendulum may be taken, each on its own account, as a specific quantum; but the selection of a particular fraction of the earth's diameter or of the length of the pendulum, as well as the degree of latitude under which the latter is to be taken for use as a standard, is a matter of choice. But for other things such a standard is still more something external. These have further specified the general specific quantum in a particular way and have thereby become particular things. It is therefore foolish to speak of a natural standard of things. Moreover, a universal standard ought only to serve for external comparison; in this most superficial sense in which it is taken as a universal measure it is a matter of complete indifference what is used for this purpose. It ought not to be a fundamental measure in the sense that it forms a scale on which the natural measures of particular things could be represented and from which, by means of a rule, they could be grasped as specifications of a universal measure, i.e. of the measure of their universal body. Without this meaning, however, an absolute measure is interesting and significant only as a common element, and as such is a universal not in itself but only by agreement.


\end{quote}
\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

\begin{itemize}%
\item [[physical unit]]


\item [[gauge symmetry]]


\item [[gauge theory]], [[gauge field]]


\item [[gauge transformation]]


\item [[gauge group]]


\item [[gauge fixing]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

A discussion of ``gauge'' and [[gauge transformation]] in [[metaphysics]] is in

\begin{itemize}%
\item [[Georg Hegel]], \href{Science+of+Logic#714}{\S{}714} of \emph{[[Science of Logic]]}

\end{itemize}
[[Hermann Weyl]]`s historical argument motivating [[gauge theory]] in [[physics]] from rescaling of units of length was given in 1918 in

\begin{itemize}%
\item [[Hermann Weyl]], \emph{Raum, Zeit, Materie: Voerlesungen \"u{}ber die Allgemeine Relativit\"a{}tstheorie}, Springer Berlin Heidelberg 1923

\end{itemize}
Quick reviews include

\begin{itemize}%
\item Quigley, \emph{On the origins of gauge theory} (\href{http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf}{pdf})


\item Afriat, \emph{Weyl's gauge argument} (\href{http://hal.inria.fr/docs/00/76/96/90/PDF/WGA.pdf}{pdf})



\end{itemize}
[[!redirects gauges]]



\end{document}