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

[Tuco]

Question's in the title really, why is the SI unit for mass kilogram and not gram, when for length it's metre and not kilometre?

[Colophon]

Well, the unit is based on the prototype kilogram, a lump of metal that is kept in Sèvres, France. My assumption is that a gram would be too small, as the uncertainty in mass would be a thousand times greater (relatively speaking).

Incidentally, the kilo is the last SI unit that is still based on something macroscopic and "physical", rather than being redefined at the atomic level. I believe they are trying to redefine it using the mole, but they haven't figured out the Avogadro number to a sufficient level of accuracy yet.

[Colophon]

From this site: http://www.lenntech.com/unit-convers...ass-weight.htm

The mass has a strange unit, because in the unit is a prefix. This is due to the history of the SI. The unit supposed to be equal to one liter of water. This would be called a grave. The volume unit liter is derived from the unit of length. The French thought that the unit was too big and thought that it could give problems with trading and daily use. That is why they have rejected the grave and introduced a new unit. This unit is equal to one milliliter of water. That is 1/1000 of the liter. This new unit got the name gram. This did not seem to be so practical at all and that is why they wanted go back to the grave, but with a new name. The gram was exactly one thousandth of a grave, so the new unit was kilogram, in other words: 1000 gram. That is why there is a prefix in the SI. Later the definition was rejected, because is was not so exact.

[Derleth]

I thought there were two SI entities: MKS and CGS.

MKS = Meter/Kilometer/Second
CGS = Centimeter/Gram/Second

People use MKS to measure things on the human scale and above, and CGS to measure below the human scale. Or so I've been told.

[Derleth]

D'oh! The K in MKS should be Kilogram, not Kilometer. Damn.

[mnemosyne]

I've had people (professors) tell me that although CGS is used on a regular basis, it still isn't considered to be "SI", even though it is easily converted to MGS. I don't know for sure, though.

[g8rguy]

Originally posted by r_k
Incidentally, the kilo is the last SI unit that is still based on something macroscopic and "physical", rather than being redefined at the atomic level. I believe they are trying to redefine it using the mole, but they haven't figured out the Avogadro number to a sufficient level of accuracy yet.

Actually, my understanding is that the kilogram is now defined through atomic considerations, which does involve Avogadro's number. But everything I've ever heard defines 12 grams to be the mass of Avogadro's number of ¹²C atoms. I suppose you could look at this as a definition of Avogadro's number instead of a definition of the gram, but...

CGS is not, to the best of my recollection, technically, SI. It is, however, used pretty widely.

[Dr_Paprika]

Since a square meter of water weighs a kilogram, it seems to work out pretty conveniently. But there are indeed the cgs and mks Systemes Internationales.

[Dr_Paprika]

This is why I shouldn't post after working a long shift. Obviously, a cubic decimetre (10c*10cm*10cm) of water weighs one kilogram. A cubic metre of water weighs 1000 kilograms; measuring in grams would just be silly.

[Agback]

G'day

In the CGS system (which was the version of the Metric System current before about 1960), the gramme was the unit of mass (though the centimetre was the unit of distance--go figure). When the SI was being developed to base the system as far as possible on reproducible standards the metricists took advantage of the opportunity to re-jig the units of distance and mass so that the units of force and energy would turn out not to be so tiny. It would have been a good idea if they had renamed the kilogramme, but perhaps they felt a bit awkward about the fact that it was the only fundamental unit they weren't re-defining.

By the way, according to an article the The New Scientist a few weeks ago, metricists are searching for a reproducible standard for distance. But as yet none of the suggestions is practicable. This search is on partly because the uniqueness of the International Standard Kilogramme and the fact that it is an artifact are considered embarrassing, and partly because techniques for determining mass are now two orders of magnitude more precise than the constancy of the mass of facsimilies of the ISK.

Regards,


Agback

[Agback]

Originally posted by Derleth
People use MKS to measure things on the human scale and above, and CGS to measure below the human scale. Or so I've been told.

Actually, the MKS (a.k.a System Internationale) largely replaced CGS (a.k.a System Metrique(?)) about 1960. The only discipline that still uses the CGS is Astrophysics (of all things). So the titanic masses of stars are normally listed in tiny grammes, and their staggering power output in miniscule ergs per second. Perhaps the astrophysicists figured that they would have to use gigantic numbers either way, and not to bother risking confusion.

Regards,


Agback

[Achernar]

Originally posted by Agback
The only discipline that still uses the CGS is Astrophysics (of all things). So the titanic masses of stars are normally listed in tiny grammes, and their staggering power output in miniscule ergs per second. Perhaps the astrophysicists figured that they would have to use gigantic numbers either way, and not to bother risking confusion.

I've wondered about this too. I think it may be because, like you said, MKS is not any better for expressing the masses of stars or dust grains than cgs, and also, E+M is a little easier in cgs (although you could easily rework MKS to do the same).

Incidentally, I don't know how it is in other branches of Physics, but in Astrophysics, you have to be able to work with a moderate range of units. Looking over one page of lecture notes, I see Angstroms, parsecs, kiloparsecs, keV, MeV, and years. We also use constants, like Solar Masses, as units as well.

[viking]

I remember from elementary school (mid-eighties in Sweden, to both date myself and give someone a snowball's chance of knowing what I'm talking about...), we were taught that to be technically correct, we should only use the powers of a thousand (mm, m, km/ µg, mg, g, kg/ etc.), but that other prefixes (cm, dm, etc) were acceptable for ``everyday'' use. I think the rationale was that it would be obvious if you forget the unit, which one you're talking about, because being off by a factor of a thousand would be noticable. But now I can't remember if that system of officialdom had a name or whether that was just our shop teacher's idiosyncratic view of the world.

[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. This means only that all masses are expressed in the SI as grams, or grams prefixed by some multiplier, kilo-, mega-, et cetera. They aren't expressed as grains, pounds, or tuns, in other words.

The SI standard of mass is indeed a kilogram of platinum-iridium alloy, kept in Sevres, I think. This standard is just the ultimate, no-more-argument definition of the gram. The gram is defined to be 1/1000 of the mass, whatever it is, of the standard. You use the standard like this: you (or rather a government agency like the NIST) buy a scale with an adjustable dial. You take it to Paris and put the standard on it. You twiddle the adjustment until the dial reads exactly 1000 g. Then you go weigh things.

However, there's nothing magically primal about the kg. The standard happens to weigh exactly 1 kg, but it need not. Those amusing Napoleonic Frenchmen could just have easily picked out a cylinder and said zis, mon ami, is ze standard for mass, and she weigh exactly 3.14159 kg. Then, you would take your new scale, put the standard on it, twiddle the knob until the dial read exactly 3141.59 g, and go weigh things. No compromise in accuracy is implied.

Indeed, other standards are not exact units. The standard for the second, for example, is 9,129,631,770 oscillations of a Cs-133 atom under certain circumstances. So, to use the standard, you take your clock, fetch a cesium atom, hit GO on the clock, wait for one oscillation of the cesium atom, hit STOP. Twiddle the knob until the clock reads 1/9129631770 second, then go time things.

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.

Coulomb's Law is a usual source of this nonsense, for example. If you use meters for distance and Coulombs for charge, and expect a force in Newtons, i.e. you use the "MKS" set of basic units, then you have to put in an annoying and relatively meaning-free numerical constant called "the permittivity of free space." On the other hand, if you use centimeters for distance and statcoulombs for charge, and expect your force in dynes, i.e. you use the "CGS" set of basic units, then the numerical constant is conveniently 1 (and neither named nor used). For this reason, people working with electromagnetic things tend to use CGS.

Any practising physicist uses whatever set of units are most convenient. Which are not always or often SI units. For example, atomic physicists often use "atomic units", which are the units such that Planck's constant divided by 2 pi comes out to 1. Relativists tend to use "relativistic units", such that this is true and also the speed of light comes out to 1. Particle physicists often use eV, cosmologists light-years, and so forth.

Incidentally, when folks wonder why our benighted ancestors took so long to come up with the SI, it's worth remembering that units are most useful if natural to the problem at hand. The old units were in many ways more natural, because they were based on standards readily available for anyone to use in calibration or argument. An inch was the width of a man's thumb, and a foot was, of course, the length of his foot, thus making each man his own ruler, a laudably democratic goal. The English inch was later defined, sometime before the Normans Conquest, as 3 barleycorns laid end to end, which would be an early attempt to define a less variable standard which is, nevertheless, still readily available (in the nearest barley field). Other units have similar, very practical, origins. The furlong is "one furrow long", roughly the distance an ox can pull a plow before needing to rest, about 220 yards. An English mile is 8 furlongs, and was chosen to be close to the Roman mile, which was itself reckoned as 1000 paces of a Roman legion when marching. The acre was the amount of land plowable by a team of oxen team in one morning. And so forth.

These old standards are arguably more in line with modern thinking than the SI. The meter was originally defined, for example, as 1/10,000,000 of the distance from the North Pole to the Equator, passing through Paris. So, while in the English system each man was his own ruler, in the newfangled French system you calibrate your ruler by stretching a piece of string tautly between the North Pole and the Equator -- not forgetting to pass through Paris -- and cutting it into ten million equal pieces. Voila. And blech.

Modern standards seek to return to the ideal of materials readily at hand to anyone. The standard second, for example, is available to anyone with (admittedly fancy) equipment and a cesium atom or two. The meter is defined as the distance light travels in a certain number of seconds -- so all you need is a source of light and a clock you've calibrated in Step One. Only the gram remains tied to an artifact.

[Derleth]

viking, the general abhorrence for prefixes of magnitudes less than a thousand different has spilled over into the American medical world. The amount of ingredient in pills, for example, is always measured in milligrams, even if it comes out to something like 500mg, which would be 5 decigrams or 0.5 grams. We've just settled on the milligram as being just as precise as it has to be and we're not going to muck about with any other prefix.

Fluid volumes, interestingly enough, are not measured in milliliters, as the use of the milligram would lead you to suspect. They are, stereotypically, measured in ccs, or cubic centimeters.

1cc = 1mL

It's an odd system.

[Desmostylus]

Originally posted by 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.

Coulomb's Law is a usual source of this nonsense, for example. If you use meters for distance and Coulombs for charge, and expect a force in Newtons, i.e. you use the "MKS" set of basic units, then you have to put in an annoying and relatively meaning-free numerical constant called "the permittivity of free space." On the other hand, if you use centimeters for distance and statcoulombs for charge, and expect your force in dynes, i.e. you use the "CGS" set of basic units, then the numerical constant is conveniently 1 (and neither named nor used). For this reason, people working with electromagnetic things tend to use CGS.

You sure you know what you're talking about?

I think that what you are referring to is the Gaussian system of units.

Statcoulombs are a feature of the Gaussian system, as are statvolts, statamps, maxwells, gauss, oersteds, and some things that are shared with CGS, like cm, g, dynes and ergs.

And the permittivity of free space under the Gaussian system isn't 1, it's 1/4p.

The Gaussian system has other really weird stuff in it as well. Like, capacitance has units of cm, rather than farads.

And, it's not a system in wide use. "People working with electromagnetic things", in my experience, don't tend to use Gaussian units, or CGS either. There are only pockets of it here and there.

[Crafter_Man]

Originally posted by cgrayce
However, there's nothing magically primal about the kg. The standard happens to weigh exactly 1 kg.

When you say it just “happens” to weigh 1 kg, you seem to be implying that another standard exists outside this weight that it’s trying to “match.” This is not the case.

Let’s go back in time (early 19th century?) and pretend a mass standard did not exist. The French king has ordered you to come up with one. How do you do it? Conceptually it’s extremely simple:

1. Grab a hunk of platinum-iridium.
2. Stick it on a lathe.
3. Make a cylinder.
4. Polish it.
5. Stamp “1 kg” on it.
6. Stick it a velvet-lined box.
7. Show it to the king.

And that’s it. You would not need to “tweak” the mass of it. In other words, since this is a primary standard, the actual mass would not matter. Whatever amount of mass you end up with, you simply define it to be exactly 1 kg, and leave it at that.

Of course, in actuality some “tweaking” would likely occur. This is because the makers of standards try their best to “match” the new standard to old standards. This is strictly done for convenience sake; it is not a necessity.

[Crafter_Man]

Originally posted by Dr_Paprika
This is why I shouldn't post after working a long shift. Obviously, a cubic decimetre (10c*10cm*10cm) of water weighs one kilogram. A cubic metre of water weighs 1000 kilograms; measuring in grams would just be silly.

Are you saying water should be used to define mass? I think it could be done, but there would be problems, especially when trying to come up with the density of water. I’m fairly certain water density is a function of temperature, pressure, and impurities.

[Dr_Paprika]

I'm not saying water is used to define mass -- clearly the metal block in Sevres does that. I'm saying that for a system to be of practical use, it has to be scaled for common applications, and water is a reasonable benchmark due to its engineering performance and widespread availability. Water is used on temperature scales, for example, even though I agree density is a function of all the things you state.

Said another way, a system scaled so that the numbers don't apply well to water probably would be unwieldly for many other things too.

[Achernar]

Originally posted by Desmostylus
I think that what you are referring to is the Gaussian system of units.

Statcoulombs are a feature of the Gaussian system, as are statvolts, statamps, maxwells, gauss, oersteds, and some things that are shared with CGS, like cm, g, dynes and ergs.

And the permittivity of free space under the Gaussian system isn't 1, it's 1/4p.

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 ep₀ in Coulombs² / dyne · cm², 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.

[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/second² (kg m/s²). 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 ep₀ in Coulombs² / dyne · cm², 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 q²/r is 1 in Gaussian units; ergo 4pe₀ = 1, and the permittivity is 1/4p.

Heaviside-Lorentz units are in my view vastly vastly superior, because we lose the 4p in Maxwell's equations, but this does mean that the energy is q²/4pr. I suppose this means that the permittivity is 1 in Heaviside-Lorentz, which is also a CGS type system, just with the 4p 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 4pe₀ 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 4p 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 q₁ q₂/r².


F is the force between two point charges q₁ and q₂ separated by a distance r. In Gaussian units k=1, in Heaviside-Lorentz units k=1/4p, and in SI units

k=1/4pe₀ = 10^-7c²kg m C^-2,

with e₀ = 8.854 x 10^-12 Fm^-1 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/publ...n/CP027116.PDF

CGS esu

D = E + 4pP
H = c²B - 4pM

CGS emu

D = E/c² + 4pP
H = B - 4pM

CGS Gaussian
(unrationalized)

D = E + 4pP
H = B - 4pM

CGS Heaviside–Lorentz
(rationalized)

D = E + P
H = B - M

SI system

D = e_oE + P
H = B/µ_o - M

Note. The universal constants are the speed of light in vacuum c = 2.99792458 × 10¹⁰ cm/s, the permittivity of free space e_o = 1/(36p) × 10^-9 SI units, and the permeability of free space µ_o = 4p × 10^-7 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.../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 e_o and m_o. 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 = 1/4p

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

[Achernar]

Originally posted by g8rguy
The constant by which we divide q²/r is 1 in Gaussian units; ergo 4pe₀ = 1, and the permittivity is 1/4p.

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 q², 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, e and m 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(4p) 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 4p from Maxwell's equations, it makes the equations for quantizing the vector potential a tad easier to work with.