# SI: Why relying to such a definition of a kilogram?

1. Sep 19, 2011

### fluidistic

The definitions of other units that doesn't depend on the kilogram are somehow constants, like the speed of light, the second, the meter (defined with respect to the previous 2) and so on. However when it comes to the kilogram, we're still using a definition of 1889. It's definied as the mass of an alloy prototype kept near Paris. Of course its mass changes over time and so does our definition of kilogram, which is (or should be) unacceptable IMO, nowadays. Why are scientists waiting for so long to change the definition to something like "1 kilogram is the mass of 250/3 moles of carbon 12"?
If you say that the mass of the prototype doesn't change noticeably, then why did we even bother to "fix" the speed of light and also get such an accurate definition for the second?
The definition of the kilogram influences the definition of the coulomb, the ampere, the joule and thus, I'm guessing, the electron volt.

P.S.:I had posted a similar post over 1 year ago and the thread got deleted after 1 day. I don't think it was an admin work (they would have locked the thread if it had went bad, which I don't think it had), more likely like a database error, hence I "repost it".

2. Sep 19, 2011

### xts

1. Definition of mole depends on definition of kg, so such def as you propose would be a circular one. So you'd have to define mole a 6.02214078 1023. But... till now we are not still able to count up to 1023 with precision better than comparing the mass with good old weight kept in Sèvres.

2. We have no proposition of better definition (better = repeatable with better precision) than 19th century scale weight.

Wiki (http://en.wikipedia.org/wiki/Kg) discusses the issue of stability of kg and alternative definitions in details.

3. Sep 19, 2011

### f95toli

There are a couple of reasons. One is practical, it has turned out to be very difficult to find a "natural" replacement for the artefact that can be realized with sufficient accuracy.
This is a key point that many (most) people don't understand about the SI: all the definitions are written in such a way that it is possible to perform practical calibrations of secondary standards, or in other words perform the experiment (=realization).
Hence, "1 kilogram is the mass of 250/3 moles of carbon 12" does not work, simply because there is no way of actually measuring 250/3 moles with sufficient accuracy.

The other reason is simply that there is very little interest from industry (who are after all the people who actually use calibration services) or even the mass people, they are actually quite happy with the way things are; simply because using an artefact is not really a problem in their day-to-day calibration work. Most of the push for change (which will come, eventually) has been coming from people in electrical metrology and other areas, where "natural" realizations are already used.

4. Sep 19, 2011

### I like Serena

Hi fluidistic!

First off, the platina-iridium bar in Paris may change mass, but the actual kilogram is carefully corrected for these changes, so the kilogram does not change (within the margin of error).

As said, it has turned out as yet to be too difficult to define the kilogram any other way within acceptable precision and with acceptable reproducibility.

Afaik there are 3 directions which are actively being researched.
1. A globe of pure silicon with an exact number of atoms. The number of atoms would become fixed.
2. Fixing the gravitational constant, which is still inescapably inaccurate for unknown reasons (actual measurements are accurate enough, but measurements from different teams are confusingly different).
3. Fixing Planck's constant.

Every now and then there is news how the research goes, but the search is still going on.

5. Sep 19, 2011

### nonequilibrium

Fluidistic, I think you might be interested in some paper I read last year. There it was stated that the definition of the unit of mass in the usual sense was superfluous and that theoretically it would be much more pleasing if we simply defined a unit for mass using that $ma = \frac{G m M}{r^2}$ such that $M = a r^2/G$ and if we take G=1 for a moment, then one kg can simply be defined by "that amount of mass that causes an acceleration of 1 m/s² at a distance of 1m".

The reason we don't use this theoretically pleasing definition, is due to practical issues: imagine measuring the mass of objects using this definition.

I realize this isn't your original question, but I think it's interesting to realize that a definition of mass using any reference object is superfluous and is merely practical, and it seems to give G the same kind of status as Boltzmann's constant.

Well I found it to be interesting at least ;) if you want a more specific reference, I'm sure I can dig up the article if you want.

Last edited: Sep 19, 2011
6. Sep 19, 2011

### Jocko Homo

I've been following this (very interesting) thread so far but I don't understand this. How can the change of mass of said bar be "carefully corrected?"
Thank you...

7. Sep 19, 2011

### btbam91

Funny, this was briefly mentioned today in my Materials Science class. I never knew of this until this morning. If its mass changes (like you say) and our definition of what 1 Kg changes with it, then change is a must!

8. Sep 19, 2011

### I like Serena

From wikipedia (http://en.wikipedia.org/wiki/Kilogram):

"Since the IPK and its replicas are stored in air (albeit under two or more nested bell jars), they gain mass through adsorption of atmospheric contamination onto their surfaces."

"The BIPM even developed a model of this gain and concluded that it averaged 1.11 µg per month for the first 3 months after cleaning and then decreased to an average of about 1 µg per year thereafter. Since check standards like K4 are not cleaned for routine calibrations of other mass standards—a precaution to minimize the potential for wear and handling damage—the BIPM’s model of time-dependent mass gain has been used as an “after cleaning” correction factor."

"What is known specifically about the IPK is that it exhibits a short-term instability of about 30 µg over a period of about a month in its after-cleaned mass. The precise reason for this short-term instability is not understood"

9. Sep 19, 2011

### fluidistic

Thanks guys for all the replies.
IMO we could still define the mole as a certain exact number of a substance; like 6.02214179×10^23. If we consider this number as exact, then we can use the definition for the kilogram as being a multiple (yet to be determined) of this number multiplied by the mass of carbon 12 atoms for example. It wouldn't make the kilogram a well defined unit in the sense that it will have an uncertainty that should be reduced with time/experiments, but at least if there's a fire in Sevre we won't have a different mass and thus weight.

Or we could even define perfectly the mole and the kilogram. Take 6.02214179×10^23 as exact and the number to be determined to be 250/3. Would this be wrong?

10. Sep 19, 2011

### epenguin

21st CGPM, 1999
■ The definition of the kilogram (CR, 331 and Metrologia, 2000, 37, 94)
Resolution 7
The 21st Conférence Générale des Poids et Mesures,
considering
the need to assure the long-term stability of the International System of Units (SI),
the intrinsic uncertainty in the long-term stability of the artifact defining the unit of
mass, one of the base units of the SI,
the consequent uncertainty in the long-term stability of the other three base units of
the SI that depend on the kilogram, namely, the ampere, the mole and the candela,
unit of mass to fundamental or atomic constants,
the desirability of having more than one method of making such a link,
recommends that national laboratories continue their efforts to refine experiments that
link the unit of mass to fundamental or atomic constants with a view to a future redefinition
of the kilogram.

http://physics.nist.gov/Pubs/SP330/sp330.pdf

I do not remember the principles of any method (I think it did depend on counting mmbers of atoms) but at least the problem is realised where it needs to be.

Last edited: Sep 20, 2011
11. Sep 19, 2011

### Staff: Mentor

It is not yet possible to count that number of atoms exactly, in practice, as far as I know. People are working on it, but they haven't reached that level of precision yet.

To take a similar situation, when the meter was re-defined as an exact number of wavelengths of the light emitted by a certain atomic transition, it was possible at that time to implement that definition exactly, using technology that was available at that time. The re-definition would not have taken place otherwise.

12. Sep 20, 2011

### f95toli

*The "rule-of-thumb" is that we need to be able to realize any new definition with an accuracy better than 1 part in 10^8. This might be doable to for the kilogram in a few years time. Ideally we would also like the Si sphere experiments and several Watt balance measurements to agree , although at the moment there is only one "serious" Watt balance in operation (at NIST), but the balance that is now in Canada one will be up and running relatively soon.

*No one actually knows if the kg is changing, the idea that it is changing comes from measurements on some of the copies. However, the primary standard hasn't actually been used in very long time (they are talking about taking it out within the next few years to compare it with the copies). Also, if one plots all measurements in the same graphs, it is is quite striking that there is some disagreement with between the NMIs*. The measurements from some of the more experienced NMIs tend to agree quite well, and do NOT indicate any serious change. The is -as you might imagine- quite a sensitive political issue.

*NMI=National Measurement Institute. The institutes that maintain national standards, the big ones are NIST (USA), NPL (UK) and PTB (Germany).

13. Sep 20, 2011

### Jobrag

Slightly off topic; but since the standard kilogram is being measured with such precision does the weight change by a measurable amount if it is measured at a time of day when the speed of the Earth's spin adds to the Earth's orbital speed and when it subtracts.

14. Sep 20, 2011

### f95toli

No, because we can't measure absolute weight very accurately. All measurements are done by comparing two masses using a balance.