The kilogram and Planck’s constant

[sophiecentaur]

[Note: this thread was spun off from another metrology discussion]

Actually, they redefined the kilogram in 2019. Now it is defined in terms of Planck's constant, just like the meter is defined in terms of the speed of light.

OMG! How does that work, starting with h? I'm trying to think of formulae with h in - as you do. I read about the 2019 definition but, unlike the definitions of length and time, starting from scratch with the mass definition and aiming at calibrating a set of bathroom scales (on the planet Zog) seems very hard.

What sort of method gives good accuracy and repeatability?
I read that the Planck based definition came in for a fair bit of criticism. Is it really practical and is it any more than an intellectual exercise?

 

[Motore]

I know it's pop sci, but I still think it's good enough of a explanation:

 

[vanhees71]

The best I've read on this is an article in Physics Today by Wolfgang Ketterle:

https://doi.org/10.1063/PT.3.4472

 

[vanhees71]

What? I think that any physicist who cares about metrology at all is simply excited about the redefinition of the SI. Finally it's almost everything defined through defining the fundamental constants. The only exception is time which is still defined based on a specific atom (Cs). The reason is that one cannot measure the Gravitational constant at sufficient precision.

How together with the definition of the second (by setting $\nu_{\text{Cs}}$ to a certain value) and the meter (by setting the speed of light $c$ to a certain value) the setting of Planck's $h$ determines the kg is very nicely described by W. Ketterle in a Physics Today article:

https://doi.org/10.1063/PT.3.4472

 

[Dale]

OMG! How does that work, starting with h? I'm trying to think of formulae with h in - as you do.

What sort of method gives good accuracy and repeatability?
I just looked as some info about it. The 2019 definition was not too well received at the time. it seems.

I believe that the current best measurement is still using a Kibble balance. Basically it is a device that measures the electrical power required to produce a force that exactly balances a certain mass. If you have a known mass then you can use it to measure Planck’s constant. If you know Planck’s constant you can use it to measure an unknown mass.

The reproducibility is not great compared to measurements of time, but it is better than the reproducibility of measuring the mass of the prototype kg.

 

[sophiecentaur]

The best I've read on this is an article in Physics Today by Wolfgang Ketterle:

https://doi.org/10.1063/PT.3.4472

Good article. Hard to get the head round, though.

 

[Dale]

unlike the definitions of length and time, starting from scratch with the mass definition and aiming at calibrating a set of bathroom scales (on the planet Zog) seems very hard

So, previously, if we wanted to set Zogian bathroom scales to measure kg then we would need to make a few chunks of metal, compare them to the IPK to get their mass in kg.
Leave some on Earth and send some to Zog, preferably on different rockets. Remeasure the masses on Zog and periodically rotate masses back to Earth to re compare with the IPK. As their Zogian standard. Note that the Zogian standard is a secondary standard.

Then the bathroom scale manufacturer can get a tertiary standard calibrated against the Zogian standard which is calibrated against the IPK.

Now, we can simply transmit Planck’s constant, and schematics for a Kibble balance to Zog. So the Zogian bathroom scale manufacturer can build a primary standard themselves and use it to calibrate their scales.

 

[Vanadium 50]

. The only exception is time which is still defined based on a specific atom (Cs).

Yeah, but every atom of cesium is the same (and unchanging), whereas every prototype kilogram is different (and changing at the rate of 10^-10 per year or so.).

 

[Nugatory]

Now, we can simply transmit ... schematics for a Kibble balance to Zog.

And perhaps receive in exchange schematics for a Zogian device that performs the necessary measurement more accurately or less expensively?

 

[jtbell]

The best I've read on this is an article in Physics Today by Wolfgang Ketterle:

https://doi.org/10.1063/PT.3.4472

The new kilogram definition fixes the relativistic mass of a photon at the Cs hyperfine frequency as m_ph = 6.777 265 × 10⁻⁴¹ kg.

OMG! Relativistic mass lives on!

 

[Nugatory]

OMG! Relativistic mass lives on!

Applied to a photon, that’s just an unusual-units way of specifying the energy.

 

[sophiecentaur]

Now, we can simply transmit Planck’s constant, and schematics for a Kibble balance to Zog.

That's fine and you couldn't contemplate sending actual stuff to Zog but what's wrong with using the mass of a proton, neutron or, more conveniently, a bucket of N atoms of one isotope or even a known mixture of isotopes of an element, that's stable and separable? I guess you will bring in the inevitable half life problem. Perhaps that's it?

 

[Vanadium 50]

but what's wrong with using the mass of a proton, neutron or, more conveniently, a bucket of N atoms of one isotope or even a known mixture of isotopes of an element, that's stable and separable?

You can. You could say a kilogram is the weight of a block of monocrystalline silicon 7.54xxxxx cm on a side at absolute zero. Or you could say it is the weight of 2.15xxx 10²⁵ atoms of silicon. But actually realizing such a standard is harder than using a Kibble Balance.

 

[sophiecentaur]

You can. You could say a kilogram is the weight of a block of monocrystalline silicon 7.54xxxxx cm on a side at absolute zero. Or you could say it is the weight of 2.15xxx 10²⁵ atoms of silicon. But actually realizing such a standard is harder than using a Kibble Balance.

I suspected as much.

 

[Dale]

what's wrong with using the mass of a proton, neutron or, more conveniently, a bucket of N atoms of one isotope or even a known mixture of isotopes of an element, that's stable and separable?

Nothing is wrong with that. In fact, that is one of the complementary methods considered. As of today we can measure mass with a Kibble balance more accurately than we can count atoms.

The nice thing about the new definition is that it need not change as technology advances. The kilogram can remain defined using Planck’s constant. As new, more accurate and precise, methods are developed they can simply be immediately used to improve the mass measurements without requiring the BIPM to meet and make changes.

Edit: @Vanadium 50 for the win!

 

[Vanadium 50]

https://www.bipm.org/en/measurement-units/faqs.html has some interesting information, especially on why they made the choices they did, as well as continuity conditions so that the old and new kilograms are consistent.

 

[vanhees71]

OMG! Relativistic mass lives on!

Well, Ketterle is an experimentalist not working in the HEP community...

 

[f95toli]

You can. You could say a kilogram is the weight of a block of monocrystalline silicon 7.54xxxxx cm on a side at absolute zero. Or you could say it is the weight of 2.15xxx 10²⁵ atoms of silicon. But actually realizing such a standard is harder than using a Kibble Balance.

Indeed. As is always the case with the SI one of the main issues is that you need to be able to realize the unit. Work on Kibble balances (then called Watt balance) started in 70s, but it took decades of work to get to the point where "metrology grade" systems could be built (and there are only a few of those in the world).

One nice thing about this realisation is that it is possible to build relatively simple desktop Kibble balances. These will be nowhere near as accurate as a metrology grade system; but good enough for many applications and would mean you don't need to send off your scales to be calibrated every year.

 

[sophiecentaur]

Brilliant array of information there chaps. So, as a standard, it's actually fairly recent (in Sophiecentaur years, that is).
Thanks for all the input. I'll have to get into the details of the Kibble Balance better. We had better hurry up with that message for the Zoggian Metrologists - or perhaps they have already launched a message to us!