# Planned upgrades to the SI

We kick off 2017 with an article for metric geeks.

But before imperial enthusiasts jump in to claim this shows how impractical metric units are, it should be pointed out that since 1963 (for mass and length) and 1985 (for volume), imperial units have been defined in terms of the metric unit for the same quantity. Electrical units have, of course, always been metric since they were defined by British scientists in the middle of the nineteenth century.

On 10 November 2016, the International Bureau of Weights and Measures published a draft of its ninth SI Brochure. It contains some notable changes to the current SI standard. We ought to remember that this is still a draft document and contains planned changes to the next version of the SI, scheduled to be implemented in 2018. These changes have not yet been finalised and the final document could be different.

One of the most important changes is the establishment of the exact values of a number of constants. These changes will affect the fundamental definitions of several base units. These base units are the ampere, kelvin, mole and kilogram. The ampere’s new definition will be based on the elementary charge, the kelvin’s new definition will be based on the Boltzmann constant, the mole’s new definition will be based on the Avogadro constant and the kilogram’s new definition will be based on the Planck constant.

The proposed new definition of the kilogram is especially significant because it would mean that its definition is no longer based on a physical object. It is now the only base unit with a definition tied to a physical object. This kilogram definition has been tied to an object called the “International Prototype Kilogram” or IPK since 1889.

The new SI will be based on seven defining constants, whose numerical values have no uncertainty. These constants enable any unit of the SI to be based on one of these defining constants or through products or ratios of defining constants. The seven defining constants are:

• The unperturbed ground state hyperfine transition frequency of the caesium 133 atom (the symbol for which is difficult to reproduce here) is 9 192 631 770 Hz.
• The speed of light in vacuum c is 299 792 458 m/s.
• The Planck constant h is 6.626 070 040 ×10-34 J s.
• The elementary charge e is 1.602 176 620 8 ×10-19 C.
• The Boltzmann constant k is 1.380 648 52 ×10-23 J/K.
• The Avogadro constant NA is 6.022 140 857 ×1023 mol-1.
• The luminous efficacy Kcd of monochromatic radiation of frequency 540 ×1012 hertz is 683 lm/W.

The metre, second and candela use the same basic definitions as the previous SI but with different wording and more precise definitions. No big changes there. These are the new definitions for these base units:

• Metre: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of the caesium frequency.
• Second: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s–1.
• Candela: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 ×1012 Hz, Kcd, to be 683 when expressed in the unit lm/W, which is equal to cd sr/W, or cd sr/kg/m2 s3, where the kilogram, metre and second are defined in terms of h, c and the caesium frequency.

The other four base units see big changes in their definition. The proposed new definitions of these base units are:

• Kilogram: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 040 ×10–34 when expressed in the unit J s, which is equal to kg m2/s, where the metre and the second are defined in terms of c and the caesium frequency.
• Ampere: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 620 8 ×10–19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of the caesium frequency.
• Kelvin: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 648 52 ×10–23 when expressed in the unit J/K, which is equal to kg m2/s2/K, where the kilogram, metre and second are defined in terms of h, c and the caesium frequency.
• Mole: The mole, symbol mol, is the SI unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles. It is defined by taking the fixed numerical value of the Avogadro constant NA to be 6.022 140 857 ×1023 when expressed in the unit mol-1.

Phew!!

You can find the draft ninth SI Brochure at http://www.bipm.org/en/measurement-units/new-si/#communication.

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### 9 Responses to Planned upgrades to the SI

1. Martin Vlietstra says:

Ronnie has given a very good rundown of what is likely to be happening this year and next year in the world of SI, but it might be worthwhile explaining why it is happening. The new definition of the kilogram might seem bizarre; the underlying reason however is quite sound – are we sure that the International Prototype Kilogram has the same mass as it had in 1889? Nobody knows. Moreover when the various national prototype kilograms have been compared to the IPK, small changes have been identified – changes that are equivalent to a grain of sugar in a 1.5 kg packet and we don't know which prototype has changed. (One suggestion for the changes has been that some of the prototypes might have absorbed mercury vapour from the environment in which they are kept).
One reason for defining the kilogram using the Planck constant is that with current technology the repeatability of measuring the Planck constant is as good, if not better than the repeatability of measuring the mass of the IPK (which, according to the 2014 CODATA definition) is about 12 parts per billion. Another advantage of using the Plank constant is that it is a fundamental constant of nature – we will not be dependent upon a single artefact which might get lost or damaged, but anybody with a decent laboratory can recreate their own kilogram standard which will be equivalent to everybody else's standard.
Similar arguments apply for the other base units that are being redefined. I do however wonder how long the current definition will be kept? The definition of the metre, for example, changed twice during the last century – up to 1960 it was the length of the International Prototype Metre, from 1960 until 1983 it was defined in terms of the wavelength of a particular line in the spectrum of krypton-86 and since 1983 has been defined by assigned a specific value to the speed of light. My own guess is that we might well see the definitions of the Avogadro constant and the kilogram being merged with the kilogram being defined in terms of one or another atom. Before that happens however, the appropriate technology must be developed to make the measurement (though the Avagadro experiment is heading that way).

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2. Mark Williams says:

Some tips for HTML markup which posters and commenters might find useful:

•The Planck constant h is 6.626 070 040 ×10-34 J s.
•The elementary charge e is 1.602 176 620 8 ×10-19 C.
•The Boltzmann constant k is 1.380 648 52 ×10-23 J/K.

When the exponents are negative, put the minus signs inside the superscript tags. It would be nice if we could have at least superscript tags `<sup>` and `</sup>` in the comments section of all posts, too (they are currently stripped out of comments).

•The Avogadro constant NA is 6.022 140 857 ×1023 mol-1.

Suggest thin spaces for digit group separator of long numbers and [normal-width] spaces both sides of `&times;`.

•The luminous efficacy Kcd of monochromatic radiation of frequency 540 ×1012 hertz is 683 lm/W.

Splitting values over line breaks, as it was in my browser, can be avoided with `&nbsp;` and `&zwj;&thinsp;&zwj;` or a non-breaking span in CSS (which could also enforce roman/ upright type). The BIPM web site uses the [now deprecated] `<nobr />` element, but we probably shouldn't.

...or cd sr/kg/m2 s3

Use brackets rather than multiple slashes when dividing by more than one unit.

... expressed in the unit J s

Suggest use of `&middot;` to signify multiplication of units (and hopefully prevent line breaks).

... equal to kg m2/s

Leave the slashes outside the superscript tags for division of units.

p.s. I have no idea how easy WordPress (and its `WYSIWYG' article editor, if used) make any of the above!

p.p.s. Could we also have back the posts which have become unavailable in the past year, such as http://metricviews.org.uk/2009/11/signs-review-disregards-welsh-road-users/ and http://metricviews.org.uk/2015/05/50-years-on/?

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3. BrianAC says:

Yes, I also would like to see those lost posts returned. Broken links cause problems, this started 'a few months back'.

(Editor. The re-posting of missing articles is in hand and should be completed this week.)

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4. Jackthesmilingblack says:

As the symbol for's Planck constant is "h", doesn't render both mph and km/h gibberish?
Symbol for hour, hr.

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5. John Steele says:

@Jack,

The SI Brochure says the symbol for hour is "h." Planck's constant should be an italic "h" but I don't know how to render italics in the comments of this blog. (See tables 6, 7 of SI Brochure)

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6. Mark Williams says:

@Jackthesmilingblack:

You'll be wanting `mins' (with the extraneous `s') next for minutes---and `mph' is always gibberish. Do you work for UK DFT, by any chance? 😉

@John Steele:

Italics in HTML/ WordPress comments marked up by `<i>` tag before and `</i>` after, as opposed to `<em>` and `</em>` for emphasised text. Problem with that is nesting---e.g. italics inside italics, emphasis or blockquotes, ATM---might toggle the inner one back to non-italic. It would be nice if we had CSS like `<span style="white-space: nowrap; font-style: normal">…</span>` for closer approximation to SI brochure layout. You can still put italics inside one of these for Planck's constant, etc. Preferably abstract this out to a `<span class="SI">…</span>` style available to the whole 'blog [theme?] and maybe even augment the `WYSIWYG' post editor to apply it on a new button.

•The Planck constant h is 6.626 070 040 × 10-34 J·s.

Would the Metric Views webmaster(s) consider installing plugins for ex post facto changing and `WYSIWYG' editing comments (latter is not marked as compatible with current version, possibly merely not tested), which might be useful? I sometimes mess up the markup and then notice shortly after submission.

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7. Martin Vlietstra says:

@Jack

Many physical quantities have symbols that correspond to SI units. Wikipedia has a list of physical quantities at https://en.wikipedia.org/wiki/List_of_physical_quantities. In that table, physical quantities are written in italic script, units of measure in upright Roman script and dimensions in bold upper-case Roman script. Likewise, in the Wikipedia article Phiscal Constant at https://en.wikipedia.org/wiki/Physical_constant, physical constants (and equations) are written in italic script using the same format as physical quantities. This is consistent with the SI Brochure and, I believe, with ISO-80000. (For the record, vector quantities are written in bold italics).

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8. Ezra Steinberg says:

Just wondering if anyone has any information on the preferred or required unit of measurement for pressure in the EU (not the SI in general) when printing warning labels, stickers, metal plates attached to equipment, etc.

I ask because my company is printing a warning label that mentions XX psi along with the equivalent pressure in "bars". I questioned the engineer about this and he referred me to an EU directive of some years ago that specifically mentions using "bars" for pressure, which struck me as odd.

I would like the company to (at least) add kilopascals to the label (if not drop "bar" and use "kilopascals" instead) but I need some justification beyond what the BIPM publications say in general about SI units since the label has to conform to what the EU specifically requires.

Any guidance would be much appreciated!

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9. Daniel Jackson says:

Ezra,

In all countries that are signatories to the SI and where SI is the legal system, the pascal is not only the legal unit but the preferred unit. However, if the bar is also accepted for use along with the pascal individual industries and companies may choose to use the bar over the pascal.

Countries that have been metric prior to SI are as bad as countries like the US when it comes to ridding themselves of older, deprecated units and going strictly to SI. In the EU, however, the bar is not deprecated. The same can be said for the "kgf/cm^2" for example which is still found in Asia.

The calorie is another unit that refuses to die out. Australia is the only country I know of that has adopted the joule.

I can only hope that with the renewed interest in SI with the redefinition of some of the units making SI fully based on natural constants, that there will also be an awaking in all countries to complete the conversion to SI and rid themselves of not only non-metric units but pre-SI units once and for all.

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