Weyl's gauge theory and railroad tracks

Question

There is a claim I occasionally read that the origin of the word "gauge" refers to a track gauge used in railroad tracks (the distance between two rails). It's a claim I have seen here, here, on this wikipedia article, as well as on various answers regarding the etymology of the word[1][2]. Some papers also note specifically that this is not the original meaning of the word.

As far as I can tell, none of the original Weyl papers[3][4][5] mention that idea, using Eichung (or earlier on, Maßstab) in the original German, which does not have the specific meaning of a track gauge. His 1929 paper on gravitation and the electron in English translates it as gauge, but again no specific mention of this analogy. As far as I can tell, while track gauge is a possible meaning of the word, it is by no mean the only one.

Despite that, I still see the occasional claim that this is the origin of the word. Is there an origin to that idea?

Answer 1

In German the word "Eichung" (translated as "gauge") is not used for the width of railroad tracks but rather refers to a general standard for measurements similar to the broader meaning of English "gauge".

Looking at Weyl's 1919 paper cited in the OP, the first occurence of the word "eich..." is in the sentence (p. 102):

An jeder einzelnen Weltstelle muß die Streckeneichung vorgenommen werden, diese Aufgabe kann nicht einem zentralen Eichamt übertragen werden.

This translates as:

At each space-time position this gauging of distance needs to be performed, a task that cannot be given to a central gauging office.

The word "Eichamt" (literally "gauging office") means a bureau of standards which has the legal task of ensuring proper measurements. Its remit is thus metrology including the choice and administration of units everyone has to adopt and employ. From the first two pages of his paper one can infer that this is the original context Weyl had in mind - even if his use of the term "Eichamt" is metaphorical: Weyl's "gauging" deals with mathematics of local scale invariance, hence the choice of local distance scales.

The comparison with track gauges (not made by Weyl) makes sense as the latter correspond to a gauging of distance (in a metrological or technological sense).