Re: SI and nothing else

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

Ludwik writes:
>  ...                                                   . Do you remember 
> when epsilon-zero was a dimensionless quantity equal to one? We did not 
> learn about permittivity in elementary electrostatics, it was introduced to 
> us when we learned about capacitors. From the point of view of science the 
> 1/(4*PI*epsilon-zero) in Coulomb's law is OK, from the point of view of 
> padagogy it is not.

The factor [epsilon_0] is not good for much of anything except further 
complicating an already complicated subject.  The idea of having *two*
different factors (i.e. [epsilon_0] and [mu_0]) to represent what is really
just one factor of c is ludicrous.

> But I would not support the idea of returning to the old CGSE/CGSM system; 
> that Gaussian hybrid was also anti-pedagogical in many ways.

As bad as those systems were they were not any worse than the current SI
system (and they were in some ways better).  At least the Gaussian system
keeps the physical dimensions of the physical quantities straight and
sensible.  The factors of c in the Gaussian system always occur in places
(such as Maxwell's equations) where they can be absorbed into the time
parameter t if need be to see the relativistic structure of the theory.  The
Gaussian system keeps the E and B fields with the same dimensions as they
really ought to have--being just different components of the antisymmetric
2nd rank EM field strength 4-tensor.  Similarly the A and [phi] potential
fields form a 4-vector with consistent dimensions and units.  The worst part
about the Gaussian system is that it is not a 'rationalized' system--meaning
that factors of 4*[pi] occur at inopportune places.  If a rationalized
version of Gaussian units called the Lorentz-Heaviside units is used (what
Leigh's E&M professor called, I believe, God's Own Units, GOU) then that
system has all the theoretical structural advantages of the Gaussian system
and the asthetic advantages of a rationalized system.

The SI system OTOH is a muddled mess.  It proports to be a rationalized
system in that the 4*[pi] factors do not explicitly occur in the wrong
places.  But this is actually a clever ruse.  Those 4*[pi] factors are still
present but hidden in the gratuitious factor of [mu_0] which has a numerical
value of 4*[pi]*10^(-7).  Thus, not only are the 4*[pi] factors still
present, but there is an additional 10^(-7) factor present as well.  No
wonder they needed to invent the symbol [mu_0] to hide these skeletons.  This
factor can be traced to an idiotic definition of the ampere that requires
that the magnetic force per unit length of two long parallel wires separated
by 1 meter and each carrying a current of 1 A be 2*10^(-7) N/m.  There may a
somewhat decent theoretical reason for the factor of 2 (actually a 1/(2*[pi])
would be better for a rationalized system though), but there is no valid
reason for the 10^(-7) other than to complicate the system.  This factor is
put in only because the speed limit of causation (aka speed of light in a
vacuum) c is so large compared to typical terrestrial speeds.  Because
electromagnetism is intrinsically relativistic some quantities tend to be
smaller than others by a factor of 1/c^2.  The Gaussian and Lorentz-Heaviside
systems deal with this sensibly by splitting the c^2 factors into two so some
quantities tend to be c times larger than others at terrestrially slow speeds.
This keeps only single factors of 1/c in Maxwell's equations and their
presence helps rather than hurts the understanding of the relativistic nature
of E&M.  The SI system OTOH splits off a factor of 10^7 from the c^2 factor
and places it elsewhere in the theory and then hides it in the [mu_0] factor.
This is why the numerical value of the electrostatic constant
1/(4*[pi]*[epsilon_0]) is (c^2)*10^(-7) = (299792458^2)*10^(-7) =
8.98755178737 x 10^9 (kg)*(m^3)*(A^(-2))*(s^(-4)).
BTW the crazy dimensions in the quantity above can also be expressed more 
compactly as m/F, m*J/C^2, m*V/(A*s) etc.

>                                                             The SI Ampere 
> is the most basic electric unit. Doesn't this suggest that learning about 
> electricity in motion should preceed learning about electricity at reast?
> Light bulbs, electroplating and electromagnets instead of pith balls and 
> electrostatic generators? In my opinion a decision of switching to SI 
> should have been matched with a decision to modify the teaching sequence
> in electricity. And who said it is now too late for this?

I wouldn't want to let the unfortunate choices made by the SI system to
dictate the order of pedogogical presentation of the topics of physics.  I
would prefer that that order be determined by a natural flow of fundamental
concepts from the simple to the more complex.  I believe that an electric
current is conceptually more complicated than an electric charge.  The very
fact that the SI system chooses the ampere as a fundamental base unit is
evidence of the perversity of the SI system for pedogogical purposes.  As
far as I know the reason that the SI system is based on the ampere rather
than on a charge is that steady-state currents are easier to maintain for
the purposes of calibration of standards than are static charge
distributions.  All this is moot now since both electrical potential
differences and electrical resistances can be measured now much more
precisely using the Josephson effect and the quantized Hall effect than can
steady state currents anyway.  The only reason for basing the system on the
ampere has evaporated.

David Bowman
dbowman@gtc.georgetown.ky.us