Si and nothing else

[LUDWIK KOWALSKI <KOWALSKIL@alpha.montclair.edu>]

On Tue, 14 Oct 1997 22:54:47  Hugh Haskell <hhaskell@mindspring.com> wrote
about pound (force) and pound (mass) units "diabolically designed to confuse 
the uninitiated". This reminded me of another "diabolic system of units" 
and of the earlier thread on SI. 
..........................................................................
On Tue, 23 Sep 1997 09:32:57  Leigh Palmer <palmer@sfu.ca> wrote:

> > Then there's the h = c = pi = 1 crew. (That last is called the "small 
> > circle approximation"). My thesis advisor used to refer to the "GOU" 
> > system, standing for "God's Own Units". He meant cgs, of course. 
> >                                      Leigh (The Devil made me do it!)
 
By contrast the acronym for the h=c=pi=1 approach shoul be DOU, where 
D stands for devil. Let me tell you what I once wrote about this approach.
The elementary particles people use the DOU in certain considerations. What
I did was to explore a possibility of using it in all areas of physics;
just for the fun of it. 

The system has only one arbitrary unit (rather than four as in electro-
mechanical part of SI). The c and the h_bar are dimentionless quantities 
equal to one, BY DEFINITION. In SI GeV (giga-eV) is a derived unit; we know
how to express it in terms of four basic units (kg, m, s and A). In DOU, on 
the other hand, GeV is the basic unit; it could be defined as the mass-energy 
of one proton. Why not, proton is as good natural standard as C-12 will be. 
Actually the mass-energy of a proton is a little less than 1 GeV (as defined 
in SI). To match the old and new GeV we must define the new GeV as a 0.93879 
fraction of the protons rest energy; this is not significant in my story.

It turns out (see below) that units can be assigned to all physical 
quantities in terms of only one basic unit, in this case GeV. There is a 
price to pay for this unusual arrangment; a physical quantity can no longer 
be recognized by its unit. Silly? Yes. Anti-pedagogical? Certainly! Highly 
impractical? No doubt about this. But see my comment at the end.
  
                Here how it goes (my own informal playing):
              **********************************************
      Start with E=h_bar*ni. If E is in GeV then the unit of frequency, 
      ni, is GeV because h_bar=1 is dimentionless. Same for c=1. 

time (1/ni)        ---> GeV^(-1)
dist=c*t           ---> GeV^(-1) (same as the unit of time.)
mass               ---> GeV (same unit as energy. m=E/c^2)
momentum           ---> GeV (same as mass, v is dimensionless)
acceleration       ---> GeV [dist/(time*time)]
force              ---> GeV^2 (m*a)
pressure           ---> GeV^4 (F/dist^2)
work               ---> GeV (F*d)
speed              ---> dimensionless by definition (c=1)
angular momentum   ---> dimensionless by definition (h_bar=1)
kinetic energy     ---> GeV (0.5*m*v^2 where v is dimentionless)
potential energy   ---> GeV (m*g*h  GeV*GeV/GeV)
charge=sqrt(F*R^2) ---> dimensionless
current            ---> GeV (as 1/t)
dop ("voltage")    ---> GeV, (Energy/Q, charge is dimensionless)
resistance         ---> dimensionless (using Ohm's law)
capacitance        ---> GeV^(-1) (C=Q/dop, Q is dimensionless)

You can continue by yourself. Observe that each line above could be 
clarified by a sentence or a paragraph. For example, for TIME one could 
say: "one GeV^(-1) is a time interval between two maxima of E(t) for
an e.m. wave at a fixed vacuum location. And for DISTANCE one could say: 
"one GeV^(-1) distance is covered, in time of one GeV^(-1), by a photon, 
or by any ultra-relativistic (v=c) particle.

But what could one say about the dimentionless unit of CHARGE? It is a 
charge which interacts with another charge of that magnitude, with the 
force of one GeV^2 when the distance between them is one GeV^(-1). Similar 
descripions can be composed for all lines. Then we can use them to convert 
new unit quantities into corresponding SI quantities. For example, how 
many meters in the displacement of one GeV^(-1), or how many coulombs in 
one dimentionless unit of charge, or how many kilograms in one GeV of mass, 
or how many pascals in one GeV^4 of pressure, or how many seconds in the 
time interval of one GeV^(-1), or how many amperes in the current of one 
GeV, etc. etc.? 

Silly, you would say. Yes, it is, if you try to apply DOU to all parts 
of physics. But high energy physicists do not do this. They use DOU in a
subfield of physics for which it was conceived. In that area it offers 
several advantages, such as computational convenience, conceptual simplicity 
and mental shortcuts. Try to convince a high energy physicist to give up 
the GeV based system in favor of SI. S/he would say "I prefer to use both
systems, and not only two of them." And s/he would try to make fun of those 
who are slaves of the "one for all" system called SI. As David Bowman, s/he 
could say: units are invented to keep things as simple as possible, not to 
obscure problems or to create complications. Many physicists still use old 
CGSE and CGSM units, even in publications.

I played with DOU while on sabbatical at Brookheaven National Laboratory, 
ten years ago. Now I have a chance of sharing what I did. Let me know if 
this little essay makes sense to you. I never tried it on anybody else. 
Thanks for reading it.
                                                   Ludwik Kowalski
P.S.
You can replace GeV by another energy unit, such as calorie, joule or kWh.
Even the mass-energy of an electron, or of the sun, can be used to define
one basic diabolic unit. Once this is done your chosen unit should be
used instead of GeV, in the above considerations.  

      A new diabolic system of unit for anybody? Two for a quoter.