Saturday, February 4, 2023

The Seven Pillars of SI Wisdom

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Early metrology is sometimes exemplified by the King’s foot, a convention established in the 12th Century by Henry I of England. The most obvious problem with the King’s foot was the need to recalibrate when the regime changed.  The underlying problem was more subtle. Any anthropocentric metric—by which I mean a metric based on human attributes or performance--- is both statistically and conceptually more fragile than one based on universal constants of nature.


Nowadays (  we start with seven precisely related constants of nature and derive from them seven reference units which are said to be all we’ll ever need.   The constants are cesium hyperfine frequency ΔνCs , Planck’s constant h, the speed of light in vacuum c, the elementary charge e, Boltzmann’s constant k, Avogadro’s number NA , and the luminous efficacy of a defined visible radiation K.  The basic units are mass (kilogram), distance (meter), time (second), amount of matter (mole), electric current (Ampere), temperature (kelvin degree), and luminous intensity (candela). The whole system, called SI, comprises what we might call the seven pillars of SI wisdom.  The system seems to have no anthropocentrism.   


But wait! The seventh constant and the seventh unit are not like the others. This seventh pillar depends not only on humanity in general, but on particular observers whose flicker sensitivity and brightness data the CIE aggregated to define the 1924 luminous efficiency function V) in visible wavelength λ .


The history of the candela in Wyszecki and Stiles (Color Science, 2nd ed, Wiley 1982; pp. 254-255) is quite educational.  Rather than use the whole 1924 V(λ) curve (which was to be obsoleted and conditionalized a lot in the next century), standards bodies defined the candela with only two human-related numbers: the peak wavelength (555 nm) of V(λ) and the watt-to-lumen ratio (1/683).  Interestingly, the SI does not define the candela for any light other than monochromatic at 555 nm, so, for example, I cannot ask SI what the candela count is for a given wattage of light at 460 nm.  This illustrates that any reduction of the candela’s dependence on human vision decreases the universality of SI.


The candela didn’t enter the SI system uncontested.  A sign of the struggle was that for many years the US National Bureau of Standards (NBS) divorced itself from all human factors including metrology of vision and other senses.  When NBS deflected responsibility for calibration of color-measurement instruments, the need for such calibration was satisfied by private companies such as Hemmendinger Color Lab.  Fortunately, NBS (now NIST) takes on metrology of a more human sort, so they’re helping to manage the seventh pillar.


We’ve come a long way in the standardization of fundamental constants and their units.  But one of the seven basic units of SI, the candela, is tied to a human-based standard.  Even in the newest refinement of SI, a vestige of the King’s foot remains!


That the SI metrologists felt forced to include a human-vision metric in one of its seven pillars reminds us of the importance of vision in our understanding of the universe. A question to ponder: Of all the five senses, why was vision salient? 


Michael H. Brill

Retired Color Scientist




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