# Why is the candela a SI base unit?

Well, why* is* the candela a base unit in SI?

It’s basically a measure of how bright something looks to ‘average’ humans, and is calculated from EM radiation flux (in already-existing SI units of Watts and meters) and an empirically derived luminosity function describing the sensitivity of typical human eyes at each wavelength. Not only is the function empirically derived, SI doesn’t even provide it. From wikipedia: “An appendix to the SI Brochure makes it clear that the luminosity function is not uniquely specified, but must be selected to fully define the candela.”

That… doesn’t seem like a base unit to me, for at least three or more reasons. Can someone (paging CalMeacham) explain why it is one of the fundamental units of SI? Sure, it’s useful for interior lighting designers and what-not, but why isn’t it a SI derived unit (like the calorie) or really more appropriately an ISO standard rather than an SI unit at all?

I looked into the history of the candle and the candela a while back, and just now I’ve been writing about th Munsell quality of Value, which is related. It’s all interesting.

I didn’t realize that the candela was an SI “Base Unit”. You’re quite right that it’s not directly related to anything physical, but depends upon human sensation. You can physically measure radiant intensity using detectors, but you need human eyes to give a reading of luminous intensity. And humans are notoriously variable. So the only reason I can see for the candela being there is because you need some measurement that connects the measurable physical world out there to the world of human sensation brightness, and they decided that they could use the candela for this, instead of one of the other constants.

There’s some historic basis for it – the candela is the more rigorous cousin of the candle, which was based on the output of a candle made from spermaceti and beeswax – I kid you not. The problem was that, even as people were installing the Candle as a unit, plenty of other people knew it wasn’t a reliable measure, and said so. It persisted, I suspect, because it was easy to make that standard candle and use it in measurements. Certainly it would be easier to obtain than the current definition:

As for the human sensation, although it’s nominally based on this candela, as a practical matter it probably lies with a series of measurements made in the first half of the twentieth century. People had been trying to quantify human response to a given input since the 18th century and the work of Pierre Bouguet. He was looking for the smallest detectable difference between two light sources. Many others in the next centuray and a half approached the how-much-human-sensation -for-given-illumination from the standpoint of what the minimum detectable difference was. They came up with two different and incompatible equations. When Albert Henry Munsell started work on his standard color description, he was faced with these two competing laws, and started measuring people’s responses himself. He died in 1918, not having finishe4d the work. His laboratory and his son, Alexander Ector Orr Munsell, carried it on. They eventually produced a curve relating human sensation to illumination, and validated it by getting input from multiple test subjects and averaging the results. People DO vary, and the minimum detectable difference varies from person to person, and with the brightness of the light.
With the curve in hand, they could parcel out equal levels of brightness, and did so. The gray levels in a Color Checker Chart don’t differ by equal reflectivities or equal optical densities – they differ by equal-sized steps on a Munsell chart.

If you want to know what the curve looks like, it’s roughly a fractional power law. Early formulations tried to fit it to a square root or a cube root, but a good fit requires a polynomial or a two-stage formula. There are eleven different formulas for it on this Wikipedia page: https://en.wikipedia.org/wiki/Lightness

The situation seems to me to be analogous to the rem or sievert, as radiation units. Physically, radiation can be measured in units like rads, curies, or becquerels, each of which is some number of radiation particles per second (the becquerel, to make things simple, is just 1 particle per second, meaning that prefixes or scientific notation are always needed for making useful measurements). But different kinds of radiation affect humans differently, so the rem or sievert were introduced to normalize for that: If one source of radiation will do twice as much damage to a human than another, then it’s producing twice as many sieverts.

But the thing is, nobody ever tries to pretend that the sievert is an SI base unit. The SI base unit is just the inverse second, and then you’ve got an empirically-determined lookup table for converting that to sieverts for different kinds of radiation. If we ever meet aliens, they might well have some convenient unit that they use for radiation safety, or for how bright light appears to them, but it won’t be convertable to our units, because their sensitivities will be different from ours.

In other words, I’ve never understood why the candela was considered a base unit, either.

Partly because at the time it was defined, people didn’t realize there was a relationship between the “luminosity” they were trying to measure and other things. They were trying to invent dimensional analysis without yet having a very clear idea of which and how many dimensions would be necessary. As the OP states, it is a derivation of electromagnetic flux - keyword IS, present tense. At the time the candela was defined, people hadn’t discovered electromagnetic flux, nor did they realize how closely electricity and magnetism are linked, nor knew that visible light was part of a much-larger spectrum.

Nowadays it is considered a “base unit” only in that it gets its own name; it doesn’t correspond to a dimension. And it gets its own name because we happen to find it more practical than expressing “apparent electromagnetic flux within the spectrum visible by the average human” in terms of its dimensionality.

So it’s pretty much like measuring area in football fields or weight in double-decker buses.

So there’s a group of scientists whose idea of a meaningful struggle is getting the accuracy of unit definitions and actual measurements from one part in 10^8 to one part in 10^9, and spending decades arguing about how to define the kilogram, and they keep candela around as a ‘base’ unit because, basically, “Sure, it’s not really a base unit but but it’s close enough” and “it would take work to change a few words in the definition and definitions aren’t really important, anyway” ?!? :dubious:

The original Metric centimetre/gram/second system (CGS) system was largely replaced with the MKS system to deal with inconsistencies directly related to electromagnetism.

CGS works fine for non electromagnetic needs, but the dyne has problems that the newton does not and erg/s has problems that the watt fixes. Noting that both the watt and the erg/s power units have a time function, how would you create the derived units that do not have a time component now?

Lumin is: cd⋅sr
Lux is: lm/m2

Fields that care about Lumin and Lux care about visible light, not radiant flux which would contain all energies.

Remember that the SI system is more about trade, taxation and product standards then about QFT or other sciences.

The system is far more targeted at selling and regulating car headlights than measuring quantum energies. There were lots of units for visible light around the world so it makes sense to create one. The units they were replacing didn’t have a time dimension so the unit they developed didn’t either. As the eye response to visible light was in the standards tables and blackbody radiation was understood it worked for the need.

The dyne has no problem that the newton does not, nor is the erg/s any more problematic than the watt. Meaningful differences between the systems occur only in electromagnetism, and then only because they describe two subtly different quantities that both get called “charge”, even though they’re not the same thing (but are proportional). And to the extent that CGS and MKS do handle electromagnetism differently, physicists working in the field generally prefer CGS.

And why would you care whether a derived unit includes time? That’s not a problem. We can measure time.

I must have communicated that wrong, erg/s and dynes problem in EM was why they were swapped out.

The OP suggested using watts for Candela

In Base units Watt = kg*m[sup]2[/sup]s[sup]−3[/sup]

In CSG units Watt = 1 * 10[sup]7[/sup] erg s[sup]-1[/sup]

Watt just isn’t a good direct replacement for candela even ignoring the visible light goal, because candela and it’s derived units like lux do not have time right now.

But yes some in fields like astrophysics, theoretic physics still use CGS out of historical convention and laziness. Many groups like the IAU technically require MKS and SI as a policy but yes many people ignore it.

I’m going to bookmark this post of yours though for the next time we have a discussion about USCS units, which people also do not move off of due to historical convention and laziness.

What do you mean, there’s no time in the definition of the candela? It’s right there:

“The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10[sup]12[/sup] hertz and that has a radiant intensity in that direction of 1 / 683 watt per steradian.”

See that “watt” in the definition?

I was talking about the 1946 “new candle” version.

The move away from defined base units and to defined constants ∆ν[sub]Cs[/sub], c, h, e, k[sub]B[/sub], N[sub]A[/sub], K[sub]cd[/sub]
The 1946 version was:

Note that the “international watt” wasn’t adopted for a couple more years after this. It also took decades before they tried and failed to define Candela on a photon-number-based quantities and moved to the modern version.

It’s worth pointing out that the definition of Candela has “watt” in the definition as a way of standardizing the conditions of observation. But that observation of Luminous Intensity still has to be made, ideally by an Average Human Eye (or, failing that, averaged over a bunch of human eyes). But a human observer is an essential input in defining the candela, because it’s all about how bright that source looks to a human being.

Or at least, a mathematical model of an ideal human observer.