Re: Zero with units?

[John Denker <jsd@AV8N.COM>]

leinoffs@SUNYACC.EDU wrote:

> I think that it is pretty important to include the units in stating
> the value of a temperature, even if the value is zero (e.g. 0 degrees
>  Celsius)  I don't think any of us would have it any other way.
>
> Obviously this is a problem with temperature (and any other
> quantities?) since the value of zero on the Celsius and Fahrenheit
> scales are based on an arbitrary temperature.  Those zero values of
> temperature do not coincide and do not represent an "absolute"
> temperature value.

There are lots of other quantities that exhibit similar issues.

1) If you're in Colorado and you're supposed to fly down to an
altitude of 2000 feet AGL and instead you try to proceed down to
2000 feet MSL you're probably going to have a bad day.
  (AGL = above ground level;  MSL = above mean sea level)

2 There are tricky rules about whether wind direction should
be reported using magnetic or true directions -- I won't foist
the details on you.

3) Similarly zero power is not to be confused with 0dBm or 0dBu.
I've worked with devices where applying 0dBm to the input
would let the magic smoke out.

4) Also 0PSIa is not to be confused with 0PSIg.

5) A whole class of examples concerns anything with gauge
invariances, such as position or electric potential.
Position relative to what?  Potential relative to what?

The list goes on and on.....

======================

Note that in many of these cases, technically the issue
is not connected to the *unit* of measurement.  The
*unit* of the Kelvin scale is the same size as the *unit*
of the centigrade scale, strictly speaking.  Items 1, 2,
4, and 5 above provide additional examples of this kind.

So we need to think not just about units, but also about
the reference level ... or in fancy physics lingo, the
gauge.

Even when you have a gauge invariance (e.g. redefining
the zero of potential doesn't change anything) you can
still get into trouble if you use one gauge for part of
the problem and a different gauge for another part.  And
of course in many cases a gauge-change is not an invariance;
nobody thinks that shifting the zero of temperature is
an invariance.

Changing from Fahrenheit to centigrade involves a change
in units *and* a shift in reference level.

Reference levels are a source of confusion.  Our habits
and our language focus attention on the units, while the
reference level gets short shrift.  I don't have any
specific constructive suggestions ... so for now I guess
the bottom line is "be careful about the reference level".