Ciro Santilli
OurBigBook.comThe key thing in a good system of units is to define units in a way that depends only on physical properties of nature.
Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.
- number of times some light oscillates per second
- number of steps in a quantum Hall effect or Josephson junction
What we don't want is to have macroscopic measurement artifacts, (or even worse, the size of body parts! Inset dick joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the Avogadro project still attempted otherwise well into the 2010s!
Standards of measure that don't depend on artifacts are known as intrinsic standards.
A dimension in a system of units is something like length, weight or time, without considering how to assign numerical values ot them, which requires units of measurement such as the meter, kilogram or second.
Talking about dimensions can be useful when explaining new derived units without worrying about the exact units involved. See e.g. this table: en.wikipedia.org/w/index.php?title=Lumen_(unit)&oldid=1233810964#SI_photometric_units
The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.
Learning the modern SI is also a great way to learn some interesting Physics.
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Great overview of the earlier history of unit standardization.
Gives particular emphasis to the invention of gauge blocks.
web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:The breakdown is:
- the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
- the speed of light in vacuum c is 299 792 458 m/s
- the Planck constant h is 6.626 070 15 × J s
- the elementary charge e is 1.602 176 634 × C
- the Boltzmann constant k is 1.380 649 × J/K
- the Avogadro constant NA is 6.022 140 76 × mol
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
- actually use some physical constant:
the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
Defines the second in terms of caesium-133 experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.the speed of light in vacuum c is 299 792 458 m/s
Defines the meter in terms of speed of light experiments. We already had the second from the previous definition.the Planck constant h is 6.626 070 15 × J s
Defines the kilogram in terms of the Planck constant.the elementary charge e is 1.602 176 634 × C
Defines the Coulomb in terms of the electron charge.
- arbitrary definitions based on the above just to match historical values as well as possible:
the Boltzmann constant k is 1.380 649 × J/K
Arbitrarily defines temperature from previously defined energy (J) to match historical values.the Avogadro constant NA is 6.022 140 76 × mol
the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W
Arbitrarily defines the Candela in terms of previous values to match historical records. The most useless unit comes last as you'd expect.
Made possible by the Kibble balance.
Unit of electric current.
Affected by the ampere in the 2019 redefinition of the SI base units.
Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.
This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!
Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:
- quantum Hall effect, which has discrete resistances of type:for integer values of .
- Josephson effect, used in the Josephson voltage standard. With the Inverse AC Josephson effect we are able to produce:per Josephson junction. This is about 2 microvolt / GHz, where GHz is a practical input frequency. Video "The evolution of voltage metrology to the latest generation of JVSs by Alain Rüfenacht" mentions that a typical operating frequency is 20 GHz.Therefore to attain a good 10 V, we need something in the order of a million Josephson junctions.But this is possible to implement in a single chip with existing micro fabrication techniques, and is exactly what the Josephson voltage standard does!
Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.
Unit of mass.
Defined in the 2019 redefinition of the SI base units via the Planck constant. This was possible due to the development of the Kibble balance.
Whichever problem you present a German, they will look for a mechanical solution to it!
The Kibble balance is so precise and reproducible that it was responsible for the 2019 redefinition of the Kilogram.
It relies rely on not one, but three macroscopic quantum mechanical effects:How cool is that! As usual, the advantage of those effects is that they are discrete, and have very fixed values that don't depend either:One downside of using some quantum mechanical effects is that you have to cool everything down to 5K. But that's OK, we've got liquid helium!
- atomic spectra: basis for the caesium standard which produces precise time and frequency
- Josephson effect: basis for the Josephson voltage standard, which produces precise voltage
- quantum Hall effect: basis for the quantum Hall effect, which produces precise electrical resistance
- on the physical dimensions of any apparatus (otherwise fabrication precision would be an issue)
- small variations of temperature, magnetic field and so on
The operating principle is something along:Then, based on all this, you can determine how much the object weights.
- generate a precise frequency with a signal generator, ultimately calibrated by the Caesium standard
- use that precise frequency to generate a precise voltage with a Josephson voltage standard
- convert that precise voltage into a precise electric current by using the quantum Hall effect, which produces a very precise electrical resistance
- use that precise current to generate a precise force on the object your weighing, pushing it against gravity
- then you precisely measure both:
- local gravity with a gravimeter
- the displacement acceleration of the object with a laser setup
The Kibble Balance, realizing the Kilogram from fundamental constants of nature by Richard Green
. Source. Presented in 2022 for a CENAM seminar, the Mexican metrology institute. The speaker is from the Canadian metrology institute- youtu.be/ZfNygYuuVAE?t=854: they don't actually use the Quantum Hall effect device during operation, they only use it to calibrate other non-quantum resistors
The Watt balance and redefining the kilogram by National Physical Laboratory
. Source. Nothing much, but fun to hear Kibble talking about his balance in beautiful English before he passed.Bibliography:
Candela is Lumen density per solid angle. A sphere emitting 1 Candela uniformly in all directions produces 4π Lumen total power.
Bibliography:
1 Watt equals 683 Lumens of light power at wavelength 555 nm. At other wavelengths 1 Watt is less Lumens as it takes into account the sensitivity of the average human eye.
Candela is lumen density per solid angle.
Bibliography:
Named after radio pioneer Heinrich Hertz.
How a quartz watch works by Steve Mould (2017)
Source. Mentions feedback loop loop with the quartz tuning fork for the piezoelectricity and an amplifier. Also mentions the choice of 32768 Hertz () as the first power of 2 that is outside of the human hearing range, and then how a frequency divider is used to reduce the frequency to get the second counter.How an atomic clock works, and its use in the global positioning system (GPS) by EngineerGuy (2012)
Source. Shows how conceptually an atomic clock is based on a feedback loop of two hyperfine structure states of caesium atoms (non-radioactive caesium-133 as clarified by the Wikipedia page). Like a quartz clock, it also relies on the piezoelectricity of quartz, but unlike the quartz clock, the quartz is not shaped like a tuning fork, and has a much larger resonating frequency of about 7 MHz. The feedback is completed by producing photons that resonate at the right frequency to excite the caesium.Inside the HP 5061A Cesium Clock by CuriousMarc (2020)
Source. A similar model was used in the Hafele-Keating experiment to test special relativity on two planes flying in opposite directions. Miniaturization was key.
Contains a disposable tube with 6g of Caesium. You boil it, so when it runs out, you change the tube, 40k USD. Their tube is made by Agilent Technologies, so a replacement since that opened in 1999, and the original machine is from the 60s.
Detection is done with an electron multiplier.
youtu.be/eOti3kKWX-c?t=1166 They compare it with their 100 dollar GPS disciplined oscillator, since GPS satellites have atomic clocks in them.
Quick presentation of the atomic clock at the National Physical Laboratory (2010)
Source. Their super accurate setup first does laser cooling on the caesium atoms.Uses the frequency of the hyperfine structure of caesium-133 ground state, i.e spin up vs spin down of its valence electron , to define the second.
International System of Units definition of the second since 1967, because this is what atomic clocks use.
TODO why does this have more energy than the hyperfine split of the hydrogen line given that it is further from the nucleus?
Why caesium hyperfine structure is used:
Highlighted at the Origins of Precision by Machine Thinking (2017).
A series of systems usually derived from the International System of Units that are more convenient for certain applications.