SI base units

I've just been catching up on the redefinitions of the base units of the international system of units (SI units), which were agreed to in 2018.

At the time, the redefinition of the kilogram got most of the press, but in fact several of the definitions have changed. This has some interesting implications.

Almost all of the base units are now defined by fixing the values of some fundamental physical constants.

second
Defined as exactly 9 192 631 770 oscillations in the frequency of the ground state hyperfine transition of caesium-133, which is set to exactly 9 192 631 770 Hz.

This definition hasn't changed. It makes the second one of the few units that still relies on an experimental measurement.

metre
Defined to be exactly 1/299 792 458 of the distance travelled by light in vacuum in 1 second.

This one hasn't changed either. The definition fixes the speed-of-light constant as c=299 792 458 m/s.

kilogram
Defined with reference to a fixed value of Planck's constant:
\(h=6.626 070 15 \times 10^{−34} \text{kg.m}^2\text{s}^{-1}\)

This is a big change, since previously the kilogram was defined as the mass of a physical object - the "prototype kilogram" kept in Paris. Previously, the value of Planck's constant had to be determined by experiment. Now it is defined.

ampere
Defined as 1 electron charge per second, where the electron charge is defined to be exactly
\(e=1.602 176 634\times 10^{-19} As\).

This is another big change, since previously the ampere was defined with reference to the force exerted between two parallel electric currents.

Interestingly, the previous definition of the ampere effectively defined the permeability of free space to be exactly \(\mu_0 = 4\pi \times 10^{-7} \text{N.A}^{-2}\), but now that quantity has to be determined experimentally.

One further implication of this is that, with the old definition, the permittivity of free space was also an exact value, since \(c^2 = 1/\epsilon_0 \mu_0\), but now it, too, is variable. On the other hand, having a fixed elementary charge seems like a good idea.

Kelvin
Defined with reference to a fixed value of the Boltzmann constant:
\(k=1.380 649 \times 10^{-23} \text{J.K}^{-1}\)

where the Joule is, of course, a derived unit based on the kilogram, metre and second.

This is yet another big change. Previously, the Kelvin was defined experimentally with reference to the triple point of water: that is, the triple point of water was defined to be exactly 273.16 K. From now on, the temperature of the triple point of water has to be determined experimentally, and we have a fixed Boltzmann constant instead, which once again seems more useful.

mole
Defined as exactly $6.022 140 76 \times 10^{23}$ elementary entities (of whatever).

This is yet another major change. Previously, the mole was defined to be the number of atoms of carbon 12 in exactly 12 grams of carbon 12, which is equivalent to setting the molar mass of carbon 12 to be exactly 12 grams per mole. From now on, the mass of carbon 12 has to be determined experimentally. Since the masses of all other atoms are usually tabulated as "relative atomic masses" - i.e. effectively as multiples of the carbon 12 mass, it means that all atomic masses are "up for grabs" now.

candela
Defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency \(540\times 10^{12}\) Hz, $K_{cd}$, to be 683 when expressed in the unit $\text{lm.W}^{-1}$, which is equal to $\text{cd.sr.W}^{−1}$, where the watt (W) is a unit derived from kilograms, metres and seconds.

I don't think this has changed, but then I've never really been too clear about what luminous intensity actually is.

 

The SI people refer to the experimental "realisation" of the units.

There's no experimental way that you can prove that the metre, for example, is "wrong".

Thanks. I've edited the post to correct the error (hopefully).

Right. I didn't think people would be too worried about it.

Thanks again. That was a typo which is now fixed.