Re: Stop using calories?

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Jim Green wrote:
> Thank you for your kind thought.  There *is* an SI standard -- it is the K.
> It seems to me that unless there is a *clear* and *compelling* advantage to
> the use of a non-SI unit and only in a class intended for non-physical
> science people), that the SI be used exclusively -- no matter what the
> instructor is more *comfortable* with -- let the instructor get off his/her
> mental rear end and be professional about it.

Comfort or convenience *is* a clear and compelling reason.  One of the
classes I teach is an intro level astronomy course.  In that course it is
more convenient to us A.U. and years for motions involving objects which
orbit the Sun for the same reason it is more convenient to use calories when
doing calorimetry involving water.  (In both cases a dimensioned nuisance
factor takes on the numerical value of 1.)  When discussing the parallax
method of measuring the distances to nearby stars it is more convenient to
use the parsec.  The definition of the parsec automatically builds in an
order of magnitude scale factor for the relationship between typical sizes of
interplanetary orbits in our solar system and the typical distances to nearby
stars.  The SI system gives no such insights.  The built-in fact that there
are 60*60*360/(2*[pi]) A.U. in 1 parsec helps students get a feel for how
much farther away the second nearest star from the earth is than the nearest
star is.  In other contexts the lightyear or redshift may be more convenient
and useful units.  It is certainly easier to do relativity using the fact
that c = 1 ly/yr.

For more advanced courses it would be better to push for theoretically
sensible, simple and consistent units (such as some version of Planck units)
rather than the SI system if real understanding is the objective.  What the
SI system does to electromagnetism is a travesty.  It would almost be hard
to come up with a system (maybe an electrical version of the English Imperial
system would do it) which did a more efficient job of obscuring the
theoretical structure of electromagnetism and its relationship to relativity
than SI units do.  Even our recent discussion about capacitors raised the
issue of the capacitance of the Earth and an understandable mistake of
multiple orders of magnitude was made in reporting it in the SI unit of the
Farad.  Things would have been far clearer if capacitance was just reported
in the natural unit of capacitance (which has the same dimension as the unit
of length) which measures fundamentally what is, after all, a geometric
property.

Much conceptual confusion about thermodynamics (esp. the meanings of its
fundamental quantities) would be cleared up if the kelvin was never invented
as a unit of temperature.  If (thermodynamic) temperature was measured in
energy units, and entropy in (proper) dimensionless information units things
would be much clearer for students (and many teachers as well).

In relativity, the proper geometric structure of spacetime shows up most
clearly when all 4 directions in Minkowski space have the same unit.  Imagine
trying to teach plane analytic geometry to high school students if we always
insisted on measuring displacements along the x-axis in microns and
displacements along the y-axis in miles.  That would sure make understanding
the Pythagorean theorem difficult, and the procedure for rotating a vector
would be a nightmare.  The fundamental constant of nature of
1.609344 x 10^9 microns/mile would keep popping up in our calculations.  Four
dimensional spacetime is difficult enough, why add unnecessary complications
because the SI system is so perverse?

Quantum mechanics clues us in as to real meaning of the classical notion of 
action that occurs in Lagrangian/Hamiltonian/Hamilton-Jacobi mechanics.  Of
course the SI unit of action, the J*s, is no help.  Who would have guessed
that action is really the phase angle for a complex amplitude (properly
measured in radians or cycles, etc.)?  (Well, maybe Sommerfeld would have.)
Now we know that Planck's constant tells us that there are
6.62608 x 10^(-34) J*s of action in one cycle of action and there are
1.05457 x 10^(-34) J*s of action in one radian of action.  With a sensible
system of units the equations E = h*[nu] = h_bar*[omega] and p = h/[lambda]
would not be so mysterious since energy would already come in frequency units
and momentum would already come in wave number units.

Understanding the conceptual meaning of Einstein's equations of General
relativity might be a little easier if the dimensions of the
stress-energy-momentum tensor of matter and radiation happened to come in the
same units as those of curvature (i.e. 1/length^2).

It should be recognized that a system of units which is convenient and
natural for understanding the deep concepts of physics is neither convenient
nor natural for the needs of everyday life.  I would hate to force carpenters
and plumbers to begin using a theoretically satisfying unit system (such as
Planck units) which has precious little to do directly with their needs.  For
those needs it seems that either the SI system (in the world at large) or the
US customary system (inside the US domestic construction industry) seem to
work out about equally well when it comes to building structures that are
safe and won't accidentally fall down.

When it comes to convenience in international trade it certainly is best to
have all trading partners denominating their goods and services in the same
units.  Although, for some reason, they seem to be able to get along OK even
in this realm with scores of separate domestic currency units.

The upshot of my polemic here is that the most compelling reason for any
choice of units is convenience, and just what constitutes convenience depends 
on the situation at hand.  Since there are multiple different conflicting
measures of convenience across different situations, it seems that having
multiple sets of units, each most convenient for the situation at hand, is
best.

> This philosophy pervades many of the threads on this list.  We often hear
> things like "Well you are correct (strictly), but why can't I do it my old
> fashioned (read 'incorrect') way none-the-less."  This is often the same as
> saying "I am too lazy to improve my teaching.

I'm not sure what this statement is supposed to mean in the context of
whether or not calories (or Calories, for that matter) should be allowed to
share space with joules in the classroom.  Do you think that somehow the
calorie unit is 'incorrect', and if it is, just how less correct is it than
the joule, and why?

David Bowman
dbowman@gtc.georgetown.ky.us