Wednesday, July 12, 2017

SI units: \(h,k_B,e,N_A\) will be set to known constants

Between 13th and 16th of November, 2018, the 26th meeting of The General Conference on Weights and Measures will convene in Versailles, France. The Symmetry Magazine tells us that it is expected to cause a revolution in the definition of SI units.

In 2012, I became somewhat loud while screaming "let us fix the value of Planck's constant" although I was recommending it more silently for decades. Last year, my goal finally got closer while plans to redefine one ampere were already around, too.

According to Daniel Garisto, the seven basic SI units will be defined in ways that are generally closer to fundamental physics:
  1. second: 9,192,631,770 periods of the radiation for a Cesium-133 atom, kept
  2. meter: 1/299,792,458 of a light second, kept
  3. kilogram: by setting \(h=6.626070040\times 10^{34}\) joule-seconds precisely, retiring the platinum-iridium cylinder
  4. kelvin: by setting \(k_B=1.38064852\times 10^{-23}\) joules per kelvin precisely, retiring triple point of water and \(273.16\)
  5. candela: as \(1/683\) watts per steradian if the frequency is \(5.4\times 10^{14}\) hertz, kept
  6. mole: by setting \(N_A=6.022140857\times 10^{23}\) per mole, retiring 12 grams of carbon-12
  7. ampere: by setting \(e=1.6021766208\times 10^{-19}\) coulombs, replacing a fixed value of \(\mu_0\)
OK, what do I think about these changes?

I think that the retirement of the platinum-iridium kilogram – and the corresponding fixation of Planck's constant to a known value – is clear progress towards natural units. \(\hbar\) is one of the truly most fundamental dimensionful constants in Nature, the constant that defines the strength of all quantum mechanical effects, the constant quantifying how much wrong every classical ("realist") theory of Nature has to be. And the platinum-iridium kilogram is pretty but volatile, hard to clone accurately, and generally obsolete.

The meter and second have been linked by setting the vacuum speed of light \(c\) to \(299,792,458\) meters per second since the early 1980s. It's nice, \(c\) is fundamental, too.

Now, the redefinition of one mole by fixing Avogadro's constant \(N_A\) to a known constant is surely progress, too. Carbon-12 may look natural but it is just some element. Moreover, saying "carbon-12" doesn't quite determine the mass of one atom. The mass depends on energy, including the energy obtained from compression etc. Moles were always just counting "the number of molecules or atoms" in some rescaled way, and because we know how many atoms or molecules were in a mole rather accurately, they should effectively be replaced by counting of the atoms and molecules.

I also fully endorse the redefinition of one kelvin. The Boltzmann constant is the primary and most profound constant that links kelvins to the "major" kilogram, second, meter units and is surely more fundamental than the triple point of some water. Why water and not ethanol, for example, readers such as Tony could ask? ;-) The Boltzmann constant is independent of these details.

One candela (which is approximately the luminosity of a candle) isn't changing. At some frequency of light, it's equivalent to some watts per squared radian. What different frequencies do depends on the human eye. Because one candela is designed to be useful for the human eye, anyway, and the human eye isn't a rigorously defined object, there will be some uncertainty about "what we need by one candela". We could define the precise "optimized sensitivity of the human eye to different frequencies" in order to make one candela more precise or rigorous. But no one seems to demand it. I have never used candelas in my life. After all, it's a bit incomplete to define just one luminosity – the human eye may detect three independent colors on top of that, so there should be R,G,B luminosities as well, and so on.

The definition of one second isn't changing – and is linked to the periodicities of the cesium atomic clocks.

The most controversial change is the newly fixed value of the elementary electric charge \(e\). It means that \(\mu_0\) will no longer be a known constant – it has been \(4\pi\times 10^{-7}\) of the appropriate SI units so far. Well, I personally find a fixed value of \(\mu_0\) to be somewhat more natural than a fixed value of \(e\) because it seems natural to say that the fine-structure constant may be evolving, and this could be parameterized as the evolution of \(e\). But of course, we may keep \(e\) fixed and reinterpret a hypothetical evolution of \(\alpha\) as an evolution of \(\mu_0\).

But what could be a good idea would be to fix both \(e\) and \(\mu_0\) to known constants. In that way, we could get rid of the cesium definition of one second. Cesium may be more important than water or platinum-iridium for practical purposes – but otherwise it's a similarly "random material". If \(e,\mu_0\) were set to constants, however, we couldn't easily interpret what the atomic clocks measure because we wouldn't exactly know how many periodicities of the radiation are equal to one second. So maybe it's not yet the right time to abandon cesium in the definition of one second...

Otherwise, it's good progress. My next plan up to 2023 is to set the constants \(c,\hbar,N_A,k_B, \mu_0\) equal to one and to convince the mankind to use some relativistic quantum units of adult fundamental physicists.

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