New SI gets measurable significance

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In 1983, the metre was redefined in terms of an exact speed of light in vacuum, c = 299792458 m/s. Not only was this a theoretically nice move, but in this case it improves fine length measurements by an almost an order of magnitude, because atomic clocks had much better relative uncertainty.

Since 2007, the International Committee for Weights and Measures (CIPM) started considering various proposals to redefine more units in terms of physical constants, similarly to the speed of light. For example, the current definition of kelvin, the unit of temperature, is based on the triple point of pure water—and there not only difficulties in getting water pure enough to the accuracy modern metrologists want, but this turns out to be inconvenient for accurate measurements below about 20 K or above 1300 K. To redefine temperature, the Boltzmann constant k could be measured in multiple independent ways, to similar uncertainty, a requirement which was met a few months ago.

Deadline for publication of results was 1 July 2017, with new values to be considered in Sep 2017, most likely to be later adopted as exact in Nov 2018, at the 26th General Conference for Weights and Measures

But by far the worst SI unit is the kilogram, defined as the mass of a particular platinum-iridium cylinder since 1889, nicknamed 'le grand K'. This represents a logistical nightmare of copying the artefact accurately, disseminating it to many nations, all the while worrying about whether or not they drift from one another.
Article:
Several years ago, NIST had to reissue certificates for its kilograms because they were 45 micrograms off the French prototype — about the weight of an eyelash. This meant that companies that produce weights based on the NIST standards had to reissue their own weights, and they were not happy about it. Lawmakers were called. NIST was accused of being incompetent. In the end, it turned out that the problem stemmed from le grand K, not NIST.
Source: [url=https://www.washingtonpost.com/news/speaking-of-science/wp/2017/07/05/scientists-are-about-to-change-what-a-kilogram-is-thats-massive/]Washington Post[/url]

Well, it also turned out that pretty much all official copies drift from le grand K, typically on the order of some tens of micrograms, and hence also from each other.

Fortunately, there is an important physical constant, Planck's constant h, that has essentially no reason to exist in physics but for the historical insistence that mass be a base unit, taken as axiomatic by Newton, which is convenient but not strictly necessary. With only one day to the deadline, NIST got it done:
Article:
The new NIST measurement of Planck's constant is 6.626069934×10⁻³⁴ kg·m²/s, with an uncertainty of only 13 parts per billion. NIST's previous measurement, published in 2016, had an uncertainty of 34 parts per billion.
Source: [url=https://www.nist.gov/news-events/news/2017/06/new-measurement-will-help-redefine-international-unit-mass]NIST[/url]

There's a pretty nice youtube video explaining how their method works:

It relies on some very accurate quantum electric effects, so the electron charge is also expected to be fixed as exact.

The other independent way of measuring the kilogram, based on counting atoms, will be used to define the mole as exact instead. So the list of expected substantive changes for New SI are as follows (the values here are from 2014 CODATA; one should expect the adopted to be slightly different based on the newer published measurements):
  • kilogram: by an exact value of Planck's constant, h ≈ 6.626070040×10⁻³⁴ J/Hz,
  • mole: by an exact Avogadro's number, NA​ ≈ 6.022140857×10²³/mol,
  • kelvin: by an exact Boltzmann's constant, k ≈ 1.38064852×10⁻²³ J/K,
  • ampere: abrogated as a base unit; redefined through the coulomb with an exact fundamental charge instead, e ≈ 1.6021766208×10⁻¹⁹ C.
(Erratum: for historical continuity, the ampere will most likely be kept as a base unit, but its definition will be based on the fundamental charge charge in coulombs = ampere-seconds. Though by defining things in terms of physical constants, which is considered the 'base unit' loses significance.)

In the current SI definition, the impedance of free space is exact and the electron charge is uncertain. This will flip things around, so that the electron charge is exact, but the impedance of free space has to be measured. It's a bit inconvenient for people who got used to quantum electrodynamics, since in the current system the (dimensionless) fine structure constant basically corresponds to the strength of an electron's charge, which is intuitive in that system. Well, ultimately both are just a unit choice that doesn't affect anything fundamental.

If one fixes both the speed of light and the impedance of free space (equivalently, magnetic permeability) to an exact value, that would be theoretically very nice, but not very practical, since it would be force one to abandon atomic frequencies as an exact standard for time. That would be unfortunate, because atomic clocks are extremely consistent, reliable, and stable. It's possible that in the future, the time standard will move from caesium-133, though.
 
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Fortunately, as an EE, I don't have to care about these redefinings at all. We just round to the nearest tenths/one hundredths place anyway unless working in say a semiconductor fab
 
It's just a shame that due to legacy effects meaning it would disrupt current standards, they can't use convenient numbers.
For instance if meters were defined as 1/300,000,000 of the distance light travels in a second.
Or even throwing out that legacy definition entirely and going for really nice numbers like 1/500,000,000.

I wonder what a system of units would look like if you tried to maximize the number of physical constants that were powers of 10
 
I don't approve of SIs. I think that they're a bad trend of fanfiction.

Oh, wait, a different sort of SI? I'm not sure then.
It was obviously a different kind of SI. The idea of an SI fanfic ever being measurably significant is, after all, absurd.

Note that I'm still not quite sure what this new, different kind of SI actually is. But it's very clearly different.
 
Not really no one measures in natural units, they are just there to make math easy as a lot of things work out to be equal to 1 with them. Makes multiplication and division a lot easier.
Planck units themselves don't get much use outside fundamental theory, but units of c = ħ = k = 1 get used commonly in particle physics and cosmology, often also with Coulomb's constant 1/(4πε₀) = 1 as well. From there, Planck units only set Newton's constant G = 1 as well. So we can consider these 'almost' Planck units. The problem with that in practice is that G is not very accurately measured in terms of things we can do in the lab, so G = 1 would flip this around and cause the lab measurements to have those large uncertainties instead. That would be a nightmare for a metrologist.

(Historical sidenote: 19th century astronomers and possibly earlier ones sometimes used an alternative system of units in which Mass = Length³/Time² as well, which is essentially taking G = 1 only. That's partly because in astronomy, the product GM is very often measured much more accurately than either G or M separately, so in that context G = 1 is not a loss of accuracy.)

Curiously, Boltzmann's constant k was actually invented by Planck after Boltzmann's death. Boltzmann himself considered entropy to be dimensionless, which is much more natural in light of modern information theory. Planck modified it to have units energy/temperature, and thus wound up inventing two constants, h and k, which are completely avoidable in physics.

Conceptually, h is essentially forced by Newton's original assumption that mass is an independent unit. But Newtonian mechanics can be formulated in terms of the principle of extremal action (minimum or maximum), which has units of energy×time. Since its magnitude doesn't matter, merely whether it is extremal or not, we can rescale it arbitrarily—or even take it to be dimensionless. Doing so gives Mass = Time/Length², rather an independent unit, and nothing about Newtonian mechanics breaks when mass is treated in this way, in any formulation.

Similarly, the speed of light being dimensionful is a result of human convention that length and time should have different units. Which is fundamentally just like insisting that distances in one direction be measured in different units than another. Which might be exactly the case, say on the sea measuring depth in fathoms but distances along the sea level in nautical miles.

To be fair, the vast and unnecessary redundancy is part of why having different units is useful in the first place: they enable easy book-keeping and sanity checks on what one is even talking about.

It's just a shame that due to legacy effects meaning it would disrupt current standards, they can't use convenient numbers.
For instance if meters were defined as 1/300,000,000 of the distance light travels in a second.
Or even throwing out that legacy definition entirely and going for really nice numbers like 1/500,000,000.
A bit different than this, but if we're going for completely alt-history scenarios, or ones ignoring legacy measurements, I've wondered about metricating based on the fathom (6 ft) rather than the metre. Early in the 20th century, there used to be an international standard ångström, and hence a conventional interferometric standard for the metre, based on a certain red cadmium line, which was found to be particularly convenient to work with. What's cute about it is that although there were historically over a dozen different inches used throughout Europe, sometimes several even within the same country, they tended to cluster around 40 000 wavelengths of this red cadmium line. Since in interferometry, one can literally count out the wavelengths, take 72 of those for the fathom:
1 F = 2 880 000 λCd​
This fathom would about 73/72 of a British imperial one, or 131/144 of French royal one, etc. It gives a pretty round speed of light, not perfectly so, but rounder than in m/s:
c = 161 676 000 F/s (to <2×10⁻⁸ rel err),​
which could be used as a standard instead (the difference is about 1/20th of an extra cadmium wavelength).

Moreover, it arguably fits the original conception of the metre just as well. You see, the metre was conceived as part of a failed decimalisation campaign of defining a gradian ('metric degree') so that a right angle is 100 grad, as opposed to 90° as is traditional. The prototype metre was based on a geodetic survey instantiating the following relationship:
1000 m = 1/100 grad on the Paris meridian of the Earth.​
Thus, a metre was conceived such that the kilometre would be nothing more or less than the decimalised version of the nautical mile, the latter being 1/60 of a degree on a meridian, an arc-minute. However,
1000 F = 1/60 degree of arc,​
to very good accuracy for practical purposes; it's actually closest to the average of meridional and equatorial nautical miles. Plus, the etymology of 'mile' is basically Latin for a thousand, anyway...

Don't judge me. ;)
 
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It was obviously a different kind of SI. The idea of an SI fanfic ever being measurably significant is, after all, absurd.

Note that I'm still not quite sure what this new, different kind of SI actually is. But it's very clearly different.

The Kg used to be defined by a lump of metal. Replicated across the globe for reference. These lumps actually changed mass slightly over time.

For the average joe, no big deal. For precision manufacturing, it could be a factor.

The Kg is soon, instead, going to be defined by Planck's Constant and Avogadro's Number. Similar to how the Meter is now defined by the speed of light, a Kg will be a Kg will be a Kg, even if the physical weights change. If someone needs their own Kg mass, they can reverse engineer the calculation and generate it (still nontrivial, but when you get into THIS level of precision, the lengths needed are significant).

The sort of manufacturing needs that care about this sort of thing are things line in .

Note that the foot is defined by the meter, the pound is defined by the kilogram, etc, so American units are also soon to be fully defined by fundamental constants rather than lumps of metal.
 
Damnit, I liked having a measurement being literally defined by "weighs as much as this thing". It was nicely fantastic and pretension-puncturing. :(
 
And now, with a defined basis for the kilo, the world is one step closer to everyone using metric.
 
From personal experience, it's a damn hassle trying to read the small numbers on a speedometer. :(
Nearsighted FTW. Never thought I'd say that. And, you can order after market speedometers with different font sizes for speed. Installing them is a pain though.

BTW, what does this mean for older weights, based on the original kg?
 
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Nearsighted FTW. Never thought I'd say that. And, you can order after market speedometers with different font sizes for speed. Installing them is a pain though.

BTW, what does this mean for older weights, based on the original kg?

Any older weights that needed that precision were already being modified/adjusted as needed, given the mass drift difference between the Kg weights around the world.
 
A bit different than this, but if we're going for completely alt-history scenarios, or ones ignoring legacy measurements, I've wondered about metricating based on the fathom (6 ft) rather than the metre...
Wow, what a missed opportunity.

Have you ever proposed it on AH.com? It's probably too late to include in LTTW, but it definitely sounds like a nice AH possibility.
(I'm assuming that chronologically it first gets defined as 1/1000 of a nautical mile - around 1.852 OTL meters [exactly 50/27 if we take the nautical definition of the meter] - then redefined by the wavelength in the early 20th century.)

That said, one big OTL circumstance in favor of the meter was that a common early proposal (notably by John Wilkins and Titus Livius Burattini, the latter actually using the word "meter" for it) was to take the length of a 1-second pendulum as the main length unit, and by sheer coincidence this happens to be within one part in 100 from the nautical meter (more precisely, about 0.994 of it, but the last digit depends on latitude).
Fun fact: if the meter was defined by the second pendulum, Earth's surface gravity would have been exactly pi^2 m/s^2 (about 9.87, as compared to about 9.81 with the OTL meter).
 
Wow, what a missed opportunity.

Have you ever proposed it on AH.com? It's probably too late to include in LTTW, but it definitely sounds like a nice AH possibility.
I briefly mentioned it on an AH.com thread in the context of one of its SI stories (lol@tag) into a pre-metric British monarch, since it's highly implausible without a fiat like an interferometry-knowledgeable insert to do so early, and it would be very radical for 20th century, since by that time the need for precise length standards would be very entrenched.

I still have some notes from when I fiddled with this...

As a bit of trivia, the modern definition of an international inch as 2.54 cm was a compromise of the British and American inches: the Americans defined their foot that made 1 in = 100/3937 m exactly, which is a tiny bit larger than 2.54 cm, and British measured their prototype yard to give 1 in = 0.025399956 m using the cadmium standard in 1922. (The US still uses those older feet in survey measurements, thus still having two different units both called feet.)

So I was curious: what happens if one makes a wider interferometric compromise with other inches, before they were replaced with metric? And what you get is things like:
(73/72)(British inch) = 39998.2 λCd​,
(137/144)(French royal inch) = 40000.3 λCd​,​
etc. Other inches are less certain as I could only find very precise measurements for those, but they were all not too dissimilar from one another, some shorter, some longer. Taking 40k exactly gives a nautical mile (kilofathom) of about 1854.3 m, pretty good compared to one based on the volumetric mean radius of the Earth, 1853.3 m: a compromise between meridional and equatorial measurements.

The resulting units of mass based on a metric-analogue relationship of, say, 1 G ∼ 1 cF³ of pure water at highest density gives 1 G = 6.375505 g, which makes the European apothecaries' system pretty close:
1 gran ≈ 10 mG, 1 scruple ≈ 200 mG, 1 dram ≈ 600 mG, etc.​
to only about 1.6% difference or so relative to the late British ones (internationally, they also varied a bit, but I was too lazy to look up by how much). So alternative-metrication would proceed by standardising the apothecaries' system, which was used internationally for scholarly work.

Burattini, the latter actually using the word "meter" for it) was to take the length of a 1-second pendulum as the main length unit, and by sheer coincidence this happens to be within one part in 100 from the nautical meter (more precisely, about 0.994 of it, but the last digit depends on latitude).
Fun fact: if the meter was defined by the second pendulum, Earth's surface gravity would have been exactly pi^2 m/s^2 (about 9.87, as compared to about 9.81 with the OTL meter).
I was momentarily confused because I would tend to interpret '1-second pendulum' as meaning per period rather then per beat. But yes.

Another fun fact: speaking of units of G = 1 as earlier, the Sun's mass is 4π² AU³/yr². Before 2006, the astronomical unit was effectively defined in terms of the Sun and a conventional length of the sidereal year (in mean solar days) originally assumed by Gauss in very early 1800s. Now, it's some exact number of metres.
 
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