Re: gauge concepts

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:24 AM 3/2/01 -0600, Gary Karshner wrote:
>  "To gauge" something in technology means to compare it with a standard. For
> example the gauge or spacing of railroad tracks is typically set not using
> a measuring tape but a tool that is designed to easily check the spacing.
> This tool need not be setup by an absolute measure of its spacing but by
> comparing it to another tool. Back before there were good absolute
> calibrations of  measuring  devices, this was away to establish uniformity.
>  For example in medieval cities in the cathedral wall were bored a couple
> of holes. These set the spacing for the tool that was used to rap skeins of
> yarn. This was a way of standardizing the amount of yarn sold in each skein.
>  Gauging is a way of standardizing measures when you don't have or want to
> use an absolute measure.

That is a really nice way of looking at it.  Thanks, Gary!  That gives a
unified view of several meanings of the word "gauge".

So I would say a gauge is
  1) A system of measurement based on an artifact or an arbitrary reference
  2) An artifact used to define such a system, or to propagate it
  3) By extension, any measuring device.

Certainly choosing a gauge for measuring electrostatic potential falls
squarely within definition 1.  Saying that Swedish railroads use Standard
gauge while Finnish railroads use Russian gauge also falls within
definition 1.  Johansson blocks fall squarely within definition 2.

===========

Using this viewpoint, we can see certain types of dimensional analysis as a
form of gauge invariance.

Note that the meter has been redefined several times.  Initially, it was
defined in terms of the size of the earth.  From 1889 to 1960, it was
defined in terms of an artifact kept in a vault in Paris.  Now it is
defined in terms of atomic wavelength.  Meanwhile, the inch has (since 1893
or so) been defined in terms of the meter, so all these redefinitions
affect it, too.

Now these redefinitions haven't changed the size of the meter very much ---
but suppose that they had.  Every time the definition changed, you would
need to obtain a new set of Joe blocks (or re-label the old ones in messy
ways).  Suppose you were manufacturing some super-precise components, such
as ball bearings and the races into which they fit.

Suppose your contract requires you to produce balls that measure exactly 1"
in diameter.  Any balls you made before getting the new Joe blocks would
now be the wrong size, even if they were the right size when they were
made!  So diameter measurements are not gauge-invariant.  A change in the
gauge, i.e. a change in the gauge-block, changes the measured size.

Meanwhile, there are important things that ARE gauge-invariant.  In
particular, the question of whether the ball fits into its race is gauge
invariant, provided both items were produced using the same gauge.

To reiterate:  If you want to have interchangeable parts, you have a
problem with gauge dependence.  If you don't, i.e. if the balls are
consistently mated to their races, then you have gauge invariance and life
is simple.

=========

A change in gauge block results in a *multiplicative* change in the results
of size-measurement.  In contrast, a change in the gauge for electrostatics
results in an *additive* change in the results of
voltage-measurement.  Other than that trivial distinction, it seems the two
concepts are very closely related.