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Re: SI and nothing else



Ludwik K. wrote
... . 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.?

Since you asked, the conversions are as follows:
1 GeV^(-1) displacement = 1.97327 x 10^(-16) m
1 DOU-charge (rationalized system) = 5.97550 x 10^(-8) C
1 DOU-charge (unrationalized system) = 1.68566 x 10^(-8) C
1 GeV mass = 1.78266 x 10^(-27) kg
1 GeV^4 pressure = 2.08521 x 10^37 Pa
1 GeV^(-1) time = 6.58212 x 10^(-25) s
1 GeV current (rationalized system) = 9.07838 x 10^16 A
1 GeV current (unrationalized system) = 2.56096 x 10^16 A
etc. etc.

Notice that the electrical unit conversions depend on whether or not a
rationalized system is used. Most high energy physicists now prefer to use
a rationalized system. In a rationalized system the differential form of
Coulomb's law takes on the form: div(E) = [rho] and the corresponding force
law has the form: F = (1/(4*[pi]))*Q*Q'/r^2. OTOH, in an unrationalized
system the differential form of Coulomb's law takes on the form:
div(E) = 4*[pi]*[rho] and the corresponding force law has the form:
F = Q*Q'/r^2. When a rationalized system is used there are no factors of
4*[pi] in any of Maxwell's equations and the electric and magnetic field
energy densities only have a simple 1/2 factor in them. A 1/(4*[pi]) factor
does appear in the Coulomb force law/potential, but this factor disappears
when this potential is written in the Fourier dual wave number/momentum
space. OTOH, when an unrationalized system is used the Coulomb potential
in position space has no 1/(4*[pi]) factor but it then has a 4*[pi] factor
appear in its wave number/momentum space representation. Also, an
unrationalized system has extra factors of 4*[pi] appear in source terms of
the differential form of both Coulomb's law and Ampere's law, and the
electric and magnetic field energy densities contain the factors of
1/(8*[pi]) in them.

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.

Remember that all of physics depends reductionistically on this 'subfield' of
physics.

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

I don't know about anybody else, but I enjoyed it.

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

Actually, I invented a system of units that I like that does not go as far
as the DOU unit system that Ludwik described. This system is what I call SU
rather than SI. (SU stands for sensible units.) The purpose of the SU system
is to fix the obvious deficiencies of the SI system regarding electromagnetic
quantities. As such, the SU system is just the normal mks/SI system
regarding all mechanical units. The SU system does not go to the
radical extreme of setting any of the constants of nature (i.e. c, h_bar, G,
or k_B) equal to 1 and it is based on the usual SI base units for things
other than electromagnetic units. The only differences occur in the area of
electromagnetism. Like the cgs Gaussian and the Lorentz-Heaviside systems of
units the SU system does not invent a separate electrical base unit (i.e. the
ampere) to confuse things. In the SU system The Coulomb force law reads:
F = (c/(4*[pi]))*Q*Q'/r^2; the Lorentz force on a charge is:
F = q*(E + v x B/c); the magnetic force per unit length of two long thin
parallel wires carrying constant currents is; F/L = (1/(2*[pi]*c))*I*I'/r;
the magnetic induction around a single long current-carrying wire (in a
steady state) is B(r) = I/(2*[pi]*r); etc. In the SU system Maxwell's
equations read: div(B) = 0, div(E) = c*[rho], curl(E) = -(1/c)*dB/dt, and
curl(B) = j + (1/c)*dE/dt. In the SU system (like other 3-base unit systems)
the electrical quantities tend to have half-integer dimensions in terms of
length L, time T, and mass M. The main virtue of the SU system over a system
like the rationalized cgs Lorentz-Heaviside is that the SU system treats
electrostatics and magnetostatics on a more symmetric footing. The SU system
yields the following set of dimensions for the various electrical units:

dim(charge) = sqrt(M*L^2/T) = sqrt(action)
dim(current) = sqrt(M*L^2/T^3) = sqrt(power)
dim(electric potential) = sqrt(M*L^2/T^3) = sqrt(power)
dim(electric field) = sqrt(M/T^3)
dim(electric flux) = sqrt( M*L^4/T^3)
dim(electric resistance) = 1
dim(resistivity) = L
dim(capacitance) = T
dim(inductance) = T
dim(magnetic potential) = sqrt(M*L^2/T^3) = sqrt(power)
dim(magnetic induction, B) = sqrt(M/T^3)
dim(magnetic flux) = sqrt(M*L^4/T^3)
dim(magnetic charge) = sqrt(M*L^2/T) = sqrt(action) <-- not known to exist.

I use a hyphenated prepended S- in front of the names of the electrical
units (like 'ab' for the cgs emu system and 'stat' for the cgs electrostatic
systems). For instance the proton charge is:

e = 3.109753 x 10^(-18) S-C = 1.6021773 x 10^(-19) C

When converting between SU units and the corresponding SI units various
factors of 19.41, 0.05152 = 1/19.41 and 376.7 = 19.41^2 repeatedly appear.
these factors are precisely equal to:

19.41 <-- sqrt(4*[pi]*10^(-7)*299792458)
0.05152 <-- 1/sqrt(4*[pi]*10^(-7)*299792458)
376.7 <-- 4*[pi]*10^(-7)*299792458
0.002654 <-- 1/(4*[pi]*10^(-7)*299792458)

1 S-C = 0.05152 C 1 C = 19.41 S-C
1 S-A = 0.05152 A 1 A = 19.41 S-A
1 S-V = 19.41 V 1 V = 0.05152 S-V
1 S-ohm = 376.7 ohm 1 ohm = 0.002654 S-ohm
^^^^^^^^^ (impedence of free space)
1 S-H = 376.7 H 1 H = 0.002654 S-H
1 S-F = 0.002654 F 1 F = 376.6 S-F
etc.

The main advantage of the SU system over the previous cgs systems is that it
treats electricity and magnetism on the same symmetric footing. For example,
both capacitance and inductance are fundamentally geometric properties with
a natural dimension of length L. In cgs electrostatic systems the unit of
capacitance comes out nicely as a length, but the unit of inductance comes
out with the dimension of square time/length = T^2/L (due to an unfortunate
factor of 1/c^2). In the cgs electromagnetic system, OTOH, the unit of
inductance comes out nicely with the dimension L but then the unit of
capacitance then has the dimension of T^2/L (again due to an unfortunate
factor of 1/c^2). In the SU system both inductance and capacitance are
treated equally and come out with dimension T (due to a common factor of 1/c
in both quantities). The SU system retains the advantages of the
rationalized Lorentz-Heaviside (L-H) system which makes the relativistic
structure of electromagnetism apparent. E and B have the same dimensions;
[phi] and A also have the same dimensions. In Maxwell's equations a factor of
c always accompanies the time parameter in the partial derivatives. This
makes the absorption of c into the t parameter convenient when converting to
4-vector notation. In the SU system a factor of c appears in Coulomb's law
(div(E) = c*[rho]) but it disappears from Ampere's law (curl(B) = j) making
for an even trade of c factors relative to the L-H system. As with the
cgs systems there is no need for a 4th base unit in the SU system (as in the
SI system), and there are no crazy factors of [epsilon]_0 or [mu]_0 appearing
anywhere.

David Bowman
dbowman@gtc.georgetown.ky.us