De-artifacting the kilogram

[lpetrich]

That is, redefining the kilogram so that it is no longer dependent on some artifact. It is the last of the SI or metric units that depends on an artifact, a cylinder of platinum-iridium kept under some bell jars in a suburb of Paris, France. But by the end of the year, that will be no more. All metric units will be defined in terms of the spin-flip frequency of ground-state cesium-133, and that cylinder will become a secondary standard.

SI = Système Internationale, International System, managed by the BIPM: Bureau International de Poids et Mesures, the International Bureau of Weights and Measures.

On the future revision of the SI describes what will be done. The second is already fixed as a multiple of that spin flip's period, and the meter fixed by fixing the speed of light in a vacuum. The kilogram is to be fixed by fixing the value of Planck's constant.

Some other parameter fixings are to be done.

Avogadro's number is to be fixed, making the atomic mass unit or dalton a fixed multiple of the kilogram, though a very tiny one.

The elementary charge is to be fixed, making the electric permittivity of the vacuum a measured quantity, along with its relative the magnetic permeability. That is done so that one can continue to use the Josephson effect for precision voltage measurements and the quantum Hall effect for precision electrical-resistance measurements, both very high-precision sorts of measurements. The constants in these effects will be fixed by the fixing of the elementary charge and Planck's constant.

Boltzmann's constant is to be fixed, expressing temperature in energy units.

A reason that it has taken so long to do so is to have continuity with existing standards. One must get results close to them, and one must get results with suitable measuring equipment.

 

[lpetrich]

That platinum-iridium cylinder is officially named the International Prototype Kilogram, but it has a nickname: Le Grand K, The Big K.

Here is a history of definitions of the meter (or metre):

• 1798 -- 1/40,000,000 part of the Earth's circumference at some longitude
• 1799 -- Platinum bar
• 1889 -- Platinum-iridium bar at 0 C
• 1927 -- Platinum-iridium bar at 0 C, 1 atm pressure, and supported by two rollers
• 1960 -- 1,650,763.73 wavelengths of a certain electronic transition in krypton-86
• 1983 -- Defined in terms of time by fixing the speed of light in a vacuum at 299,792,458 m/s

Of the (kilo)gram:

• 1795 -- 1 Gram = mass of 1 cubic centimeter of water at 0 C (freezing point at 1 atm pressure)
• 1799 -- 1 Gram = above, but at 4 C (maximum-density point)
• 1799 -- Platinum cylinder (Kilogramme des Archives, Kilogram of the Archives)
• 1889 -- Platinum-iridium cylinder (International Prototype Kilogram)
• 2018? -- Defined in terms of time by fixing Planck's constant and the speed of light

I won't get into electromagnetic units, because they are a huge mess. But I will get into temperature.

The original version of the Celsius temperature scale, from Anders Celsius himself in 1742, had water's freezing point at 100 C and water's boiling point at 0 C. That was quickly flipped to freezing = 0 C and boiling = 100 C.

In the early nineteenth century, it became evident that there was a minimum possible temperature, an "absolute zero".

• 1848 -- William Thomson, Lord Kelvin proposed absolute zero as a good choice for a zero value of temperature. Its temperature increment would be a degree Celsius, giving absolute zero (0 K) as - 273 C. Thus, (Kelvin) = (Celsius) + 273
• 1954 -- The temperature of the triple point of water was set to be 273.16 K. (Kelvin) = (Celsius) + 273.15
• 2005 -- The water for this measurement is to have the isotopic composition of Vienna Standard Mean Ocean Water
• 2018? -- Defined in energy units by fixing Boltzmann's constant

Usage note: kelvin(s) is often preferred to degree(s) Kelvin.

 

[lpetrich]

Astronomers have long used some rather weird units.

They have long measured distances in Astronomical Units (AU's), roughly the average distance between the Earth and the Sun. That is because all known astronomers and astronomy hardware have resided on the Earth until very recently, and also because one could measure some distances relative to the Earth-Sun distance with much more accuracy than the Earth-Sun distance itself until very recently.

The astronomical unit gets fixed : Nature News & Comment (2012) -- it is now defined as 149,597,870,700 m.


For measuring interstellar and intergalactic distances, they use a unit called the parsec, a parallax second. That is the distance where 1 AU makes 1 second of arc. It is about 3.2616 light years, meaning that light travels across a parsec in 3.2616 years.

They often report times in days and years, the days being mean solar days of 86400 seconds each. I can't find any canonical year for reporting in years, but I'm guessing that it's Julian years of 365.25 mean solar days.


They also like to use Earth, Jupiter, and Sun units for various quantities. Here are some nominal values, values useful as references: [1510.07674] IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties That's the International Astronomical Union.

The Sun:
Radius = 6.957*10^8 m
Light flux at 1 AU = 1361 W/m -- combined across the electromagnetic spectrum
Luminosity = 3.828*10^26 W
Surface temperature = 5772 K -- calculated from the Stefan-Boltzmann law
G*Mass = 1.3271244*10^20 m^3/s^2 -- combined with gravitational constant G because of how it is measured

A recent nominal value of G is 6.67408(31)*10^(-11) m^3/kg/s^2

The Earth:
Radius(equator) = 6.3781*10^6 m
Radius(poles) = 6.3568*10^6 m
G*Mass = 3.986004*10^14 m^3/s^2

Jupiter:
Radius(equator) = 7.1492*10^7 m
Radius(poles) = 6.6854*10^7 m
G*Mass = 1.2668653*10^17 m^3/s^2

 Standard gravitational parameter, Planetary Satellite Physical Parameters at JPL list more masses reported in this fashion, multiplied by G.

 

[bilby]

Usage note: kelvin(s) is often preferred to degree(s) Kelvin.

IMO it is absolutely required - Unless we are to allow people to discuss distances in "degree(s) metre", and times in "degree(s) second".

 

[lpetrich]

Now for time. The first time units were the day, the month, and the year. Daytime was divided into 12 hours for centuries, though hour lengths were eventually fixed as making the entire day 24 hours long. That made daytime sometimes more than 12 hours, sometimes less.

Hours, like angle degrees, were divided into smaller parts in the late Middle Ages:

1 hour = 60 of
Pars minuta prima (Latin) = First small part = minute

1 minute = 60 of
Pars minuta secunda (Latin) = Second small part = second

That makes a day 24 hours = 1440 minutes = 86400 seconds

But there is a problem. The Earth's spin axis is tilted to its orbit axis by about 23.45 degrees, and its orbit eccentricity is about 0.0167. That makes the noon-to-noon or midnight-to-midnight solar day sometimes fast and sometimes slow. So one defines an average, the "mean solar day", with the position of an averaged-out "mean Sun".

By the early 20th cy., it was evident that the Earth's rotation rate was not constant, and in 1960, the second was officially defined as a certain fraction of a certain year. But in the 1960's, human artifacts finally caught up to the celestial bodies, and in 1967, the second was redefined as a certain multiple of the period of emissions of a certain spectral line of a certain nuclide of a certain element. That is,

the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

In 1997, it was improved with

This definition refers to a caesium atom at rest at a temperature of 0 K.

The appropriate sort of clock here is a microwave atomic clock. Next up may be an optical atomic clock, but that's still up in the air.

 

[lpetrich]

Earth-rotation time is  Universal time (UT) or Greenwich Mean time, and it is adjusted for the Earth's rotation with leap seconds. The first time standard independent of the Earth's rotation is  Ephemeris time (ET), introduced in 1952, and using Newtonian mechanics.

Relativity produces an additional problem. When a photon departs from something, that object's gravity makes the photon redshifted as it escapes. That is a teeny teeny tiny effect in the Solar System, but atomic clocks are good enough to measure the effect for GPS satellites. The satellites' clocks are thus run very very slightly slow, or else their broadcasts would be too fast from their getting blueshifted at the Earth's surface. The gravitational potential makes their broadcasts run fast by 45 microseconds per day, though the satellites' velocities give them a time-dilation effect of 7 microseconds per day, leaving 38 microseconds per day (GPS and Relativity).

On the Earth's surface, the time on its "geoid" is used as a reference, the geoid being the surface with sea-level gravitational potential.  Terrestrial Time (TT) is the time on the geoid. It is implemented with  International Atomic Time, TAI from its French initials, a combined time standard from 400 atomic clocks in 50 national laboratories all over the world.

One can extrapolate to infinity from the Earth's surface, ignoring other celestial bodies, and one gets  Geocentric Coordinate Time (TCG). It flows faster than TT does, at about 7.0*10^(-10), or 60 microseconds per day or 22 milliseconds per year.

For the Solar System, one can work out  Barycentric Dynamical Time (TDB), for the Solar System's barycenter, though that has been superseded by  Barycentric Coordinate Time (TCB), the time at infinity for the Solar System. That time flows faster than Earth-surface time by about 1.6*10^(-8), or 1.4 milliseconds per day or half a second per year.

For our Galaxy, that flow-rate difference is about 10^(-6) or 100 milliseconds per day or 30 seconds per year.

 

[steve_bank]

Back in the 90s I read about an effort to develop a new mass standard. It is the last non reproducible standard. There was also someting about minute changes to the standard kg.