Why is the SI unir for mass kg and not g?

[robby]

*Originally posted by cgrayce *
**It might be useful to distinguish between what we might call the “SI base unit of mass” and the “SI standard of mass.”

The SI base unit of mass is, indeed, the gram. **

I disagree with this. Every reference on the SI system that I have ever seen defines the SI base unit for mass as the kilogram.

Cite:
http://physics.nist.gov/cuu/Units/units.html

For a supporting argument, note that SI derived units are all defined as some combination of SI base units. For example the newton (N) is defined as a kilogram-meter/second[sup]2[/sup] (kg m/s[sup]2[/sup]). It is not defined in terms of grams.

[Chronos]

Quoth cgrayce:

The difference between MKS and CGS has to do with the appearance of physical constants in various equations. You can use whatever units you like in any equation, but for each set of units you will have different physical constants that appear in the equation.

I would disagree with this. The fundamental constants are the same, no matter what system of units you’re in. How you write each constant may change, and some systems may be more convenient than others for working with particular constants, but the constants do not change value. To say that they do is equivalent to saying that a person is taller in centimeters than they are in inches.

As for standards, I’ve been trying to push for CGS and MKS to both be replaced by the MTS system: Meter, ton, second. The ton, like the gram, is a “primitive” unit, in the sense that it’s named without any prefices or suffices, and like the CGS system, the MTS system has the advantage that one cubic length unit of water is one mass unit (not as a standard, but close enough). Of course, then we should re-name the kilogram and the gram as the milliton and the microton, but that’s a small price to pay for logic and consistency.

[g8rguy]

*Originally posted by Achernar *
**Hello. Effectively, Gaussian and cgs are the same thing. Whenever someone is using the cgs units of mechanics, they will also be using the Gaussian units of E+M. If you can find me a source that quotes the value of ep[sub]0[/sub] in Coulombs[sup]2[/sup] / dyne · cm[sup]2[/sup], though, I shall stand corrected.

In Gaussian (cgs), the permitivity of free space is equal to 1. I believe. I can’t find a cite either way. **

The constant by which we divide q[sup]2[/sup]/r is 1 in Gaussian units; ergo 4[symbol]pe[/symbol][sub]0[/sub] = 1, and the permittivity is 1/4[symbol]p[/symbol].

Heaviside-Lorentz units are in my view vastly vastly superior, because we lose the 4[symbol]p[/symbol] in Maxwell’s equations, but this does mean that the energy is q[sup]2[/sup]/4[symbol]p[/symbol]r. I suppose this means that the permittivity is 1 in Heaviside-Lorentz, which is also a CGS type system, just with the 4[symbol]p[/symbol] in a different place.

I have to dispute the claim that people who use E&M tend to do SI. In my experience, SI is a common system for electrical engineers and the like because the units are conveniently sized. For theorists, having to include 4[symbol]pe[/symbol][sub]0[/sub] needlessly clutters the equations, and almost every theorist I’ve ever met prefers to use Gaussian or Heaviside-Lorentz, in which all one needs are the 4[symbol]p[/symbol] and c.

[Desmostylus]

Achernar:

http://rkb.home.cern.ch/rkb/PH14pp/node200.html

In spite of the attempted standardization to SI, several other unit systems are in use in electromagnetism: the Gaussian, CGS electrostatic and electromagnetic, and Heaviside-Lorentz system (for details on conversion of the units [Jackson75] and the physical quantities , appendix). Electrostatic and electromagnetic units differ only by factors of c.

The parallel use of different unit systems can produce confusion, as physical quantities are defined up to multiplicative constants, which depend on the unit system. For instance, in all unit systems the force F on a charge q in an electric field E is F = qE , hence (unit of force) = (unit of charge) (unit of field).

However, this does not fix the units of charge and field separately, only their product. One way to fix the unit of charge is to fix by convention the proportionality constant k in Coulomb’s law

F = k q[sub]1[/sub] q[sub]2[/sub]/r[sup]2[/sup].
F is the force between two point charges q[sub]1[/sub] and q[sub]2[/sub] separated by a distance r. In Gaussian units k=1, in Heaviside-Lorentz units k=1/4[symbol]p[/symbol], and in SI units

k=1/4[symbol]pe[sub]0[/sub][/symbol] = 10[sup]-7[/sup]c[sup]2[/sup]kg m C[sup]-2[/sup],

with [symbol]e[sub]0[/sub][/symbol] = 8.854 x 10[sup]-12[/sup] Fm[sup]-1[/sup] the permittivity of free space. Strictly speaking, the SI unit C = coulomb is defined not from Coulomb’s law, but from Ampère’s law for the force between parallel currents, plus the relation between the units for charge, current and time.

This differs from the source I got my info from, (Physics, Halliday & Resnick) which apparently used the term “Gaussian” when it should have been “Heaviside-Lorentz”.

Interestingly, the quote above and the text I looked at use the same cite: Classical Electromagnetism, J. D. Jackson, 1975.

So if anyone happens to have a copy of that lying around, I’d be interested to hear what it says.

And on preview, gr8guy says something different.

[Desmostylus]

To further add to the confusion:

http://www.aero.ufl.edu/~zhaiyh/publication/CP027116.PDF

CGS esu

D = E + 4[symbol]p[/symbol]P
H = c[sup]2[/sup]B - 4[symbol]p[/symbol]M

CGS emu

D = E/c[sup]2[/sup] + 4[symbol]p[/symbol]P
H = B - 4[symbol]p[/symbol]M

CGS Gaussian
(unrationalized)

D = E + 4[symbol]p[/symbol]P
H = B - 4[symbol]p[/symbol]M

CGS Heaviside–Lorentz
(rationalized)

D = E + P
H = B - M

SI system

D = [symbol]e[/symbol][sub]o[/sub]E + P
H = B/µ[sub]o[/sub] - M

Note. The universal constants are the speed of light in vacuum c = 2.99792458 × 10[sup]10[/sup] cm/s, the permittivity of free space [symbol]e[/symbol][sub]o[/sub] = 1/(36[symbol]p[/symbol]) × 10[sup]-9[/sup] SI units, and the permeability of free space µ[sub]o[/sub] = 4[symbol]p[/symbol] × 10[sup]-7[/sup] SI units.

[Desmostylus]

Now I know why I prefer SI. I don’t have to worry about which flavour of CGS is being used.

A bit of history I dug up (the language is a bit mangled coz it’s been translated from French):

http://perso.wanadoo.fr/j.p.serodino/Anglais/answer/gauss_sys.htm

In 1880, the International Electrotechnical Commission temporarily ended the controversy about a useful unit system, by the adoption of the volt, ampere and ohm, that is to say by the adoption of the units which was advocated by the Germans. In 1889, meter and kilogram will replace centimetre and gram. The suggestions made by Giorgy in 1901, and next, the suggestions for the rationalization of the system have led to the present system, the International Unit System SI or MKSA. The International Electrotechnical Commission adopted it in 1946.

In France, until the beginning of the 1950’s, engineers continued to use the systems EMCGS and ESCGS for calculation of magnetic and electric fields. But physicists, which tried to use only the electrostatic system, were subdivided into two groups. Mr. Pauli, Einstein and some others German physicists used the system just described. This system was called the Gaussian system. Others, mainly English physicists, rationalised the system that became the Heaviside-Lorenz’s system. But this constant, which was equal to the value of the speed of light, was very strange for many physicists. Einstein tried to cancel it by a change of the time unit. He tried to use as unit of time the time that the light takes to cover one centimetre, but that led to no useful thing.

Now, the International System is widely used. It hides the problem of the speed of light in the constants [symbol]e[/symbol][sub]o[/sub] and [symbol]m[/symbol][sub]o[/sub]. However, we must notice that this system is mainly the result of the controversy between Werner Siemens, a manufacturer only interested by the use of units which make easier the construction of telegraphic lines, and a scientific, James Clark Maxwell, for whom the theoretical coherence was the essential objective. The untimely end of Maxwell made easier the adoption of these “practical” units. To paraphrase Ernst Mach, it is only an historical accident that led us to the present unit system. However, one can wonder what would be the consequences if, in this alternative, the other proposition had been chosen.

Okay, now.

It’s clear to me now that gr8guy is correct. I guess it was cgrayce’s equation of the constant k in Coulomb’s law with the term “permittivity of free space” that threw me off.

I think I have it now:

CGS Gaussian (unrationalized),
k = 1
permittivity = 1/4[symbol]p[/symbol]

CGS Heaviside–Lorentz (rationalized),
k = 1/4[symbol]p[/symbol]
permittivity = 1

[Achernar]

*Originally posted by g8rguy *
The constant by which we divide q[sup]2[/sup]/r is 1 in Gaussian units; ergo 4[symbol]pe[/symbol][sub]0[/sub] = 1, and the permittivity is 1/4[symbol]p[/symbol].

This is not necessarily true, because the q in SI is not the same as the q in Gaussian. There is a sqrt(4pi) worked into the conversion, so when you have q[sup]2[/sup], it’s gone. At least, that’s how I understood it, but I’m still looking for a good cite. Radiative Processes in Astrophysics by Rybicki & Lightman is the book I learned cgs E+M from, and on p. 52 it says “In the absence of dielectric or permeable media, epsilon = mu = 1.” I don’t consider this the best source, because they’re not very picky with their units. But it’s at least where I got the idea from.

I also am unclear whether I was correct when I said that Gaussian and cgs are “effectively the same”. That is, I know that for astrophysicists, we use whatever it is that R+L use. I think it’s cgs Gaussian. But I don’t know if anyone uses Heaviside-Lorenz.

[g8rguy]

Good point, Achernar. And now that I think on it, you’re right. From Jackson, [symbol]e[/symbol] and [symbol]m[/symbol] are both 1 in both Gaussian and Heaviside-Lorentz. Should have known that; I’ll be forgetting me own name next. But you’re quite correct in that factor of sqrt(4[symbol]p[/symbol]) in that conversion factor for Gaussian; it’s in Heaviside-Lorentz that the conversion factor is apparently not included.

Interestingly, Jackson has a table in the same appendix which gives us what I’ve posted above… And he lists Gaussian as using cgs for non-E&M units, if there’s still any doubt on that.

Heaviside-Lorentz is used in field theory; because it removes all the factors of 4[symbol]p[/symbol] from Maxwell’s equations, it makes the equations for quantizing the vector potential a tad easier to work with.