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2026-10-05
The doors open into the cold, hazy atmosphere of Proxima Centauri b. Plans are afoot for a new workshop, fully equipped with sets of super-high-precision callipers, but alas! the cabin boy forgot to pack the International prototype metre he picked up on his trip to Paris.
Thankfully, as of 2019, we can work out all of our SI units from physical constants that we've arbitrarily fixed!
At various points in time, we've had lumps of metal in Paris that were the official kilogram, metre etc. These kinds of definitions have some issues - notably that they can change (the kilo has got a bit lighter) and they're not universal (as in we'd have to drag one all the way to Proxima Centauri b).
For the new definitions, we just fix the constants (eg. the speed of light in a vacuum) and derive the units from them.
A reminder of our units:
s)m)A)kg)K)cd)(We're going to ignore Moles - "a Mole" is like "a dozen").
The "experiments" below aren't exactly what might be done in a metrology lab, but the principles should be the same. Email me any corrections.
Vibrate some caesium. Like a tuning fork, it has a natural frequency. Count 9,192,631,770 back and forths, and that's a second.
Measure the distance some light travels, in a vacuum, in 1 / 299,792,458 seconds, that's a metre.
The speed of light is fixed at 299,792,458 m ⋅ s⁻¹
Measure the current produced by 1 / (1.602176634 × 10⁻¹⁹) electrons per second, that's one ampere.
The charge of an electron (in coulombs) is fixed at e = 1.602176634 × 10⁻¹⁹ A ⋅ s
This section isn't particularly satisfying, email me if you have a nicer explanation.
To work out the remaining units, it would be really useful to be able to produce a known amount of electrical power.
Power (kg ⋅ m² ⋅ s⁻³) is equal to current (A) times voltage (kg ⋅ m² ⋅ s⁻³ ⋅ A⁻¹), so we need to work out voltage.
A Josephson junction is another tuning-fork-like component. Sending microwaves into it at a known frequency produces voltage in discrete steps proportional to h / e.
Note, a photon with frequency f has its energy (kg ⋅ m² ⋅ s⁻²) fixed at f ⋅ h where h is 6.62607015 × 10⁻³⁴
Firstly let's drop something in a vacuum and see how fast it accelerates, this is the local gravitational field g (m ⋅ s⁻²).
Using an electromagnet of known power (kg ⋅ m² ⋅ s⁻³), we can lift a mass x upwards at velocity v, this will require a power of x ⋅ g ⋅ v. If we divide the known power by g ⋅ v, we get kilograms.
Note that we're assuming a perfect conversion of electrical to mechanical power. A Kibble balance does the same kind of thing as above, but with some clever tricks to avoid this assumption.
Heat N molecules of Helium (nearly an ideal gas) with 3/2 ⋅ 1.380649 × 10⁻²³ joules (kg ⋅ m² ⋅ s⁻²) of energy (we've already worked out how to build an electric heater with a known power output), that will yield a temperature difference of 1 / N kelvin (assuming no other thermodynamic losses).
The Boltzmann constant is fixed at 1.380649 × 10⁻²³ J ⋅ K⁻¹ == kg ⋅ m² ⋅ s⁻² ⋅ K⁻¹. The 3/2 is something to do with the degrees of freedom that the molecules can move in when they're heated.
Shine a 1 watt (kg ⋅ m² ⋅ s⁻³) beam of 540 × 10¹² Hz light, it delivers a luminous flux of 683 lumens.
One candela is one lumen per steradian (a 3D angle unit).