B So what is the new definition of the kilogram?

[lpetrich]

BIPM - About the BIPM -- the Bureau International des Poids et Mesures (International Bureau of Weights and Measures) is the custodian of the world's primary measurement standards, the Système Internationale (International System) or SI. It maintains seven primary units: the meter, kilogram, second, ampere, kelvin, mole, and candela.

The candela is a unit of luminous intensity. Standards were originally the luminosities of lamps with various specifications of construction. In 1948, the candela was defined in terms of the blackbody luminosity of melting-point platinum, and in 1979, it was redefined as a certain amount of energy per unit time.

The mole is gram molecular weight, and it's the number of grams that is equal to its component parts' numbers of atomic mass units or daltons. The proportionality constant is Avogadro's number, the number of amu's in a gram. The amu has this history:

• 1803: hydrogen atom -- John Dalton's atomic-weight table
• 1912: 1/16 of an oxygen atom -- led to a split between chemists' natural oxygen and physicists' oxygen-16
• 1961: 1/12 of a carbon-12 atom
• A few days ago: Avogadro's number officially fixed, making the amu a fixed number of grams

The kelvin is temperature, and it has this history:

• 1742: Andreas Celsius makes 100 = freezing point of water, 0 = boiling point of water
• 1743: Independently invented by Jean-Pierre Christin, with 0 = freezing, 100 = boiling
• 1744: Celsius's scale flipped to present form by Carl Linnaeus
• 1802: William Thompson, Lord Kelvin, proposes a scale based on absolute zero with Celsius degrees as its increment. He calculated 0 C = 273 K
• 1948: Triple point of water = 0.01 C
• 1954: Triple point of water = 273.16 K (0 C = 273.15 K)
• A few days ago: Boltzmann's constant officially fixed, defining temperature in terms of energy

 

[lpetrich]

Electromagnetic units are a nightmare, with at least four sets of units that have been used: electrostatic, electromagnetic (or more precisely, magnetoelectric), Gaussian, and MKSA (SI). The ampere is electric current, electric charge per unit time. Until a few days ago, its official definition was in terms of the electromagnetic force that two electric currents make on each other. The new definition involves fixing the elementary charge.

The reason for this odd move is because of two effects that permit very high precision of voltage and current measurements: the Josephson effect and the quantum Hall effect. The Josephson effect permits very high-precision measurements of voltage, and the quantum Hall effect very high-precision measurements of resistance. The Josephson constant is h/(2e), and the QHE or von Klitzing constant is h/e², both in terms of Planck's constant h and the elementary charge e. Both h and e were recently fixed, thus fixing these two constants.

This has the consequence that the magnetic permeability of the vacuum becomes a measured quantity, though the electric permittivity of the vacuum continues to have a fixed relationship with it.

So:

• (Voltage) ~ (h/e) * (frequency)
• (Current) ~ (voltage) / (resistance) ~ (h/e) / (h/e²) * (frequency) ~ e * (frequency)
• (Power) ~ (voltage) * (current) ~ (h/e) * e * (frequency)² ~ h * (frequency)²

 

[lpetrich]

Now for the meter. It has gone through these definitions:

• 1798: 10^-7 of the equator-pole distance.
• 1799: Platinum bar
• 1889: Platinum-iridium bar at 0 C
• 1927: Clarified: pressure = 1 atm, the bar is to be on rollers
• 1960: A multiple of the wavelength of an electronic transition of krypton-86
• 1983: The speed of light in a vacuum officially fixed, defining length in terms of time

The speed of light in a vacuum is related to the geometry of space-time.

The second has gone through these definitions:

• Prehistoric: day, month, year from astronomical observations
• Antiquity: division of daytime and nighttime into 12 hours each
• Antiquity: recognition of approximate constancy of total day (daytime+nighttime)
• Antiquity: recognition of variations of total day, leading to definition of mean solar day
• Late medieval Europe: division of total day into 24 equal-length hours
• Late medieval and early modern Europe: division of hour into 60 of pars minuta prima (first small part: the minute), division of minute into 60 of pars minuta secunda (second small part: the second). No continuing to a pars minuta tertia (third small part).
• 1956: a fraction of some year used as a reference
• 1967: from the cesium-133 ground-state hyperfine-transition frequency

Astronomical measurements were more precise than clocks for all of humanity's history until the 1960's.

 

[lpetrich]

The (kilo)gram has gone through these conventions:

• 1795: gram = mass of one cubic centimeter of water at 0 C
• 1799: changed to 4 C, where water has maximum density
• 1799: platinum cylinder
• 1889: platinum-iridium cylinder
• A few days ago: Planck's constant is officially fixed, defining mass in terms of length and time

Thus using quantum mechanics.

The current realization of relating mass to electromagnetic and quantum phenomena is the Kibble balance, formerly called the Watt balance. It measures the gravitational force on an object by making an electromagnetic force with an electric current going through a coil in a magnet's magnetic field. That field, in turn, is measured by making the coil oscillate and then finding the coil's induced voltage. Gravitational force is related to mass by measuring the local acceleration of gravity very precisely. Thus,

• (Mass) ~ (force) ~ (current) * (magnetic field)
• (Magnetic field) ~ (voltage)
• (Mass) ~ (voltage) * (current) ~ (power) ~ h

(omitting length and time factors)

An alternate approach involved making very precisely machined spheres of single-crystal silicon-28, the most common isotope. The atoms in them would then be counted by measuring the sizes of the spheres and then measuring the crystal-lattice unit sizes. One may then measure the masses of the individual silicon atoms by making them orbit magnetic field lines and then pushing them up and down in their orbits with radio waves (cyclotron resonance).

 

[diogenesNY]

New York Times coverage of the redefinition of the Kilogram - Interesting and contains a good bit of history and background color.

The Kilogram Is Dead. Long Live the Kilogram!
After a vote (and a century of research), the standard measure for mass is redefined, and the long reign of Le Grand K is ended.

By XiaoZhi Lim
Nov. 16, 2018

Since 1889, Le Grand K, a sleek cylinder of platinum-iridium metal, has ruled from its underground vault in Paris. An absolute monarch, it was the very definition of one kilogram of mass. Scientists from around the world made pilgrimages to it, bringing along their national kilogram standards to weigh in comparison.
[Article Continues]: https://www.nytimes.com/2018/11/16/...k&module=Well&pgtype=Homepage&section=Science

-----------------------------------

diogenesNY

 

[gmax137]

On the contrary, this is eminently practical. Instead of an unreliable and privately held nearly inaccessible standard we now have a reliable standard that can be accessed by everyone anywhere. This is the most practical improvement since the abrogation of the prototype meter.

The (kilo)gram has gone through these conventions:

• 1795: gram = mass of one cubic centimeter of water at 0 C
• 1799: changed to 4 C, where water has maximum density
• 1799: platinum cylinder

Interesting, is seems "we" went from an measurement (mass of one cc) to a physical blob of metal, and now back to a specified measurement?

 

[Dale]

Yes. The problem was that the water standard was very un-reproducible. The SI system is very practical and sacrificed their aesthetic goal for the highest possible reproducibility.

 

[brainpushups]

 

[A.T.]

1742: Andreas Celsius makes 100 = freezing point of water, 0 = boiling point of water

I guess seeing "coldness" as something "positive" makes sense, if you live in Scandinavia.

 

[Sooty]

So the old platinum 'Standard Kg' is now obsolete... can I have it please?

 

[diogenesNY]

I don't think the formal redefinition takes effect until sometime next year. Pretty sure the NY Times article details the date.

I am curious as to whether the physical reference kilograms will still be used as some sort of practical reference calibration standard... or whether they will be completely retired. Any insight?

diogenesNY

 

[Dale]

Currently there is some traceability in the system in that you can compare your "bag of sugar" to a reference that has itself been compared with the international reference. Will some official body continue to provide the final step in the traceability tree?

In the US the NIST will continue to do that, but now the traceable standards will be measured against the watt balance rather than the IPK.

 

[synch]

There is a point I have deliberately not thought about much.. the old kilo was often referenced in terms of weight which depends on g of course. However the earth-moon system alters effective g on a daily cycle, very roughly a part in ten thousand IIRC...so the kilo (as a weight) varied every couple of hours. Often labs have excellent electronic scales measuring weight to the nth place, calibrated, referenced back to the standard...but the daily variation must be significant (?).
(Obviously using a mass balance bypasses this but actual balances are not used much these days.)

 

[f95toli]

I don't think the formal redefinition takes effect until sometime next year. Pretty sure the NY Times article details the date.

I am curious as to whether the physical reference kilograms will still be used as some sort of practical reference calibration standard... or whether they will be completely retired. Any insight?

diogenesNY

Calibrations for end-users are always almost done using "artifacts". Even a big NMI will only have one or two setups for a primary standard and in some cases this is only operated part of the time (this is e.g. true for the Quantum Hall resistance standard, and yes I know that the ohm is not a base unit). Moreover, the primary standard will usually only come in one value (or in a certain range of values) meaning this will then have to be transferred before it can be calibrated (if someone want to calibrate a 1000 kg reference mass if it s bit awkward to compare it to a 1 kg reference)

Hence, most actual calibration work is done with secondary or tertiary standards.

Btw, the Watt balance has changed its name. It is now officially called the Kibble balance after the inventor (Bryan Kibble, who passed away a couple of years ago).

 

[Dale]

the old kilo was often referenced in terms of weight which depends on g of course.

You are correct, the watt balance also requires an accurate gravimeter to measure mass.

http://iopscience.iop.org/article/10.1088/0026-1394/51/2/S32/meta

 

[lpetrich]

There is a point I have deliberately not thought about much.. the old kilo was often referenced in terms of weight which depends on g of course.

Where?

 

[jbriggs444]

Where?

In the lab where you are employing a very precise scale based on force measurements. The scale was presumably calibrated in the place of its use against standard mass artifacts. The readings it presents reflect that calibration and are in mass units. The accuracy of those readings depends on an assumption that g in the lab is unchanging over time. But (we are told) g does vary measurably over time.

 

[lpetrich]

In the lab where you are employing a very precise scale based on force measurements. The scale was presumably calibrated in the place of its use against standard mass artifacts. The readings it presents reflect that calibration and are in mass units. The accuracy of those readings depends on an assumption that g in the lab is unchanging over time. But (we are told) g does vary measurably over time.

I don't know what kind of a lab that is, but if one wants to do super precise measurements, that strikes me as a rather naive practice. If one tries to do super precise force measurements with a balance, then one will have to correct the acceleration of gravity by including the effects of the Sun and the Moon. Their tidal effects are about 5.6*10^-8 and 2.6*10^-8 each, and one also has to take into account elevation changes from Earth body tides, and likely also the gravitational effects of that tidal distortion. That's rather close to the relative accumulated discrepancies in the standard-kilogram cylinders.

 

[lpetrich]

I don't think the formal redefinition takes effect until sometime next year. Pretty sure the NY Times article details the date.

https://www.bipm.org/en/measurement-units/rev-si/

I am curious as to whether the physical reference kilograms will still be used as some sort of practical reference calibration standard... or whether they will be completely retired. Any insight?

They are likely to use used as secondary standards. In fact, the IPK cylinder, the Big K, will likely get a lot more use now, since risking damage to it is now much more tolerable.

 

[lpetrich]

Interesting, is seems "we" went from an measurement (mass of one cc) to a physical blob of metal, and now back to a specified measurement?

That is indeed what happened. It also happened to the meter.

Even for physical references, the trend has been to reduce their number and to replace them with references to other standards using well-established theories. Something like what happened with energy long ago.

• Meter: the Earth's size, Kr-86 wavelength, now from time with relativity
• Kilogram: the mass of some specified volume of water, now from length and time with quantum mechanics
• Atomic mass unit: Oxygen mass, carbon-12 mass, now a fixed mass
• Kelvin: melting and boiling points of water, triple point of water, now from energy with thermodynamics

So there is now one physical reference that underlies all our standards of measurement: the Cs-133 ground-state hyperfine splitting.

 

[GTrax]

So there is now one physical reference that underlies all our standards of measurement: the Cs-133 ground-state hyperfine splitting.

Indeed! You have it all. It seems the clock-makers have finally won!
However much we (rightly) desire to to lock our measurements to quantities we perceive to be constant, we always need some physical phenomenon with such unvarying properties that we can use it as a standard. Le Grand K and it's copies were pretty good for most practical needs, and may even remain so into the future, but with the advantage that we now have a way to calibrate them against something better.

Getting to a metre via the agreed (constant) speed of light, and a time standard, requires the second be set to an extraordinary degree of precision, and the NIST folk have managed just that! Cs-133 appears to vary so little we may consider it to be a constant good enough to use to define the second.

As I understand it, Planck's constant is now held to a fixed value, and we use a Kibble balance, or any other future apparatus, to determine an offered mass to be calibrated. The other route to a kilogram is via Avogadro's number, and our ability to create a sphere of purest silicon-28 with something close to the correct number of Si atoms in it. The two routes can be used each to check the other into the future, perhaps with ever better apparatus.

Measuring the Si-28 sphere is determining distance, so leads back to Cs-133 as the constant-setter.

 

[GuyBarry]

I rather like this handy little diagram:

https://en.wikipedia.org/wiki/2019_...#/media/File:Unit_relations_in_the_new_SI.svg

As I understand it, Planck's constant is now held to a fixed value, and we use a Kibble balance, or any other future apparatus, to determine an offered mass to be calibrated. The other route to a kilogram is via Avogadro's number

I don't think Avogadro's number will have any relation to the definition of the kilogram. Avogadro's number will be used to define the mole, and the connection between the mole and the kilogram will be broken.

Under the new definition the mole isn't really a "unit" as far as I can see - it's just a scale factor, 6.022 140 76×10²³. That number has been chosen because it makes the definition of the mole as close as possible to the old one based on 0.012kg of carbon-12, but really any scale factor could have been chosen and the definition would still have been consistent. Avogadro's number isn't really a genuine physical constant like the other ones whose value is being fixed.

 

[lpetrich]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram, and the amu or dalton has gone through various definitions that I'd posted on earlier.

 

[GuyBarry]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram,

Well it was, but it won't be any more. It will be a number chosen to be as close as possible to the number of atomic mass units in the gram, but it won't actually be the number of atomic mass units in the gram. It will simply be a number laid down in the definitions of the SI, with no actual connection to the atomic mass unit or to the gram.

Here's the new definition:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

And that's all it says. The new definition of the mole is completely independent of all the other definitions of the SI.

 

[lpetrich]

That scale factor, Avogadro's number, is the number of atomic mass units in the gram,

Well it was, but it won't be any more. It will be a number chosen to be as close as possible to the number of atomic mass units in the gram, but it won't actually be the number of atomic mass units in the gram. It will simply be a number laid down in the definitions of the SI, with no actual connection to the atomic mass unit or to the gram.

Why do you think that that is the case? The atomic mass unit was recently defined as 1/12 of the mass of one carbon-12 atom, unbound and in its ground state. Avogadro's number is the number of amu's in a gram. Since that number is now fixed, the amu will no longer be 1/12 the mass of a carbon-12 atom, but 1/(A's N) grams.

 

[GuyBarry]

Why do you think that that is the case? The atomic mass unit was recently defined as 1/12 of the mass of one carbon-12 atom, unbound and in its ground state. Avogadro's number is the number of amu's in a gram. Since that number is now fixed, the amu will no longer be 1/12 the mass of a carbon-12 atom, but 1/(A's N) grams.

Is the definition of the amu going to change as the result of the SI redefinitions then? I understood that the amu was a non-SI unit accepted for use with the SI, and that its value was obtained experimentally. That's certainly what it says in the BIPM's https://www.bipm.org/utils/en/pdf/si-revised-brochure/Draft-SI-Brochure-2018.pdf:

The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state

I'm not aware that the definition of the amu is due to be changed when the new SI definitions are adopted.

 

[GTrax]

As I understand it, the Plank constant was chosen as a current definition, but other natural constants can be used to provide a check, and there is definitely effort at NIST to define NA with greater precision. Avoadro's number depends on the mass of a substance, so it is easy to see why a very well-defined Avogadro number can provide a new kilogram definition to compete with, and to augment the Planck definition.
The present effort is based on spheres of a known number of atoms of Silicon-28

Instead of fixing Planck's constant, we could have fixed NA, and defined the kilogram as 1000*NA/12 atoms of carbon-12. Now that we have decided on Planck's constant definition, we still have to now accurately find a new NA in agreement.

Regarding the spheres, it seems they now have it to less than 10 parts per billion if the work in several countries is combined!

I don't know if making spheres of pure enough Si-28 is any more convenient and less costly than a Kibble balance, but clearly it is not like keeping a (changing) platinum-iridium cylinder in Paris, and similarly divergent copies at various other places. Anyone could polish up such a sphere to the required dimension, though admittedly first having to find/make some pure enough silicon. Though made using standard optical polishing techniques, the radius accuracy would likely be something less than about 50 atoms, but I am still looking around for some verification of just how well these have to be made.

I was distracted by the beauty of thing, but I came across the information about the efforts by Bureau International Des Poids et Mesures and NIST at these links..
https://www.bipm.org/en/bipm/mass/avogadro/
https://www.nist.gov/si-redefinition/kilogram-silicon-spheres-and-international-avogadro-project.

One part of the rationale mentions that NA can also be used to obtain Planck’s constant using the well-known values of other constants. I do not yet know which constants these are, nor how the relationships work.

We start with something we hold to be "constant", and find the factor agreed to get close enough, as best we can, to the le Grand K as was widely used, and then stop messing with it, and let the new Planck definition be the definer.

Other quantities may need some consequential revision to be "in agreement". Either way, the generation of stable accurate standards, completely in sync with the Planck definition, and possibly less costly, would seem to be a possible positive benefit.

 

[f95toli]

I don't know if making spheres of pure enough Si-28 is any more convenient and less costly than a Kibble balance,

.

Don't underestimate how difficult it is to make Si-28 with the required purity. The "Avogadro Silicon" has uses outside of the redefinition of the SI and small pieces are used in other research project (in some cases literally off-cuts from the sphere) but it is still extremely rare and expensive; it is certainly not something you can buy commercially,.
The project to create this was -if I understand correctly- originally a cost-is-no-object effort to keep a number of very talented scientists from the former Soviet Union busy. That is, the point of the project was to make sure that people/facilities who were very good a purifying isotopes had something meaningful to do, and to make sure they did not take up an offer to go off and purify isotopes somewhere else...say plutonium in the ME.

The point is that the Kibble balance is not THAT complicated. Moreover, simpler versions are under development which will be good enough for most commercial calibration labs to use. That is, these labs will not need to send their standards to NMI once a year to be calibrated.

Note that one of the main point of the new SI is that it will allow for end-users to have their own primary standards that will never need to be calibrated. The accuracy of these will of course be lower than what will be used at NMIs, but most users do not need that accuracy anyway.
Moreover, the fact that you don't need a calibration chain almost automatically gives you a gain of 10-1000 in accuracy depending on the unit (you loose about one order of magnitude per step in the chain).

 

[Dale]

there is definitely effort at NIST to define NA with greater precision.

Not any more. Avogadro’s number is now exact.

Instead of fixing Planck's constant, we could have fixed NA, and defined the kilogram as 1000*NA/12 atoms of carbon-12. Now that we have decided on Planck's constant definition, we still have to now accurately find a new NA in agreement.

This is not correct. Both numbers are now fixed.

 

[GuyBarry]

Indeed they are. And the reason why it's been possible to fix both numbers is that the Avogadro constant is unconnected with the definition of the kilogram. It is the number of elementary entities in one mole. Fixing both numbers required the breaking of the connection between the kilogram and the mole.

The molar mass constant, which until now has been defined at exactly 1 g/mol, will now be determined experimentally.