The Fartela

Following on from the great interest in my discussion of the mole, I thought I'd move on to the Candela, a unit of light intensity. This is one of the seven base units of the SI system, and most people would assume that it is important.

Why, in this case, despite studying physics for longer than is healthy, have I never used the unit Candela? Or seen anyone who used the unit? Or derived anything from this unit? Or ever bought a 10 Candela lightbulb?



The Candela describes how bright a light source is. Whichever way you look at light, the important thing is that it transmits energy, and the energy in a certain time is a power, measured in Watts: Hence the 60 Watt lightbulb. A Watt is already defined in terms of metres, kilograms and seconds, so it would appear that light intensity doesn't need its own base unit. A pre EU-directive shopper may wish to disagree, though.

Imagine that you bought a 60 Watt light bulb, and found out that it didn't light up despite drawing the full 60 Watt. It might give you a warm feeling, or a sunburn, but if the wavelength isn't between 400 and 700 nanometres you won't see anything. This is why the Candela is needed: it combines the power emitted with the sensitivity of the human eye to find the perceived brightness of something.

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This seems fair enough, and most useful to know when buying a lightbulb, or looking for a new star to orbit your planet around. But why make it a base unit? The Candela is strictly only of any meaning to a human with working eyes. In the kingdom of the blind, how many Candelas does a lightbulb emit?

Seeing as the Candela describes the human perception (brightness) of an physical property (flow of energy), why not do the same for the other senses, and give them each an SI base unit. Sound is a wave, which transmits power, but humans only hear certain wavelengths (most people would say frequencies, but I'm trying to be consistent). Multiply the sound wave power by a human ear function, and you have a new unit: the Bella. Sounds for which the ear is sensitive would earn more Bellas than those at the limit of human hearing.

Smells are concentrations of certain molecules in the air, best measured physically as moles/cubic metre (although it may depend on the speed of those molecules, too, for all I know. Physicists don't worry much about smells, or personal hygiene). Multiply this concentration by a wuffiness factor which describes the sensitivity of the human nose and you have a new unit: the Fartela.

So why is the Candela a base unit? I think it is something to do with unification. This website lists lots of old units of perceived brightness: The Hefner Candle, the Violle, the Apostilb, the Blondel, the Footlambert, the Nit, the Skot and the Stilb. The world's photometric experts were probably so besides themselves with happiness when the Candela came into standard use that they made it a base unit.

Writing this, I've grown to like the Candela. It's useful, practical, and although it probably shouldn't be a base unit it surely deserves recognition in the google calculator.

She's the 1.66053886(28) × 10-24 moles

Here's a useful google calculator calculation: How many moles is a baker's dozen?. The google calculator will return any dimensionless unit in moles if you ask nicely, such as lightyear/foot (both distances), or kilogram/electron mass (both masses). The former means that a mole of footsteps will transport you millions of lightyears, the latter that a mole of electrons will weigh much less than a bag of sugar.

Google calculator thinks that a mole is just a large number. This is how I would think of it, too. The official definition of a mole is, however, as follows.

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

An amount of substance is "defined to be proportional to the number of specified elementary entities in a sample".

This is of course a load of bollocks (number yet unspecified, but hopefully less than a mole). The phrase "atoms, molecules, ions, electrons, other particles" is ridiculous. Do other particles include cows, donuts, shoes, ships and tins of sealing wax? If not, why not? If so, why not add a couple to the list:

...the elementary entities must be specified and may be atoms, molecules, cows, ions, dildos or other particles.

And don't go all "complex objects" and "elementary particles": an atom isn't elementary in the slightest, and despite the name can be cut open at will.

Why do the SI want to make this distinction between "elementary entities" and everyday objects? Why not use moles to count things? The problem is that the mole is defined in terms of kilograms, and the definition of a kilogram is "equal to the mass of the international prototype of the kilogram." The fact that all known masses are dependent on a lump of metal in Paris staying intact has annoyed scientists for a while. One cow is presently 1.66053886 x 10-24 moles of cows, but if the prototype kilogram loses mass—and in the last century it did—it could in the future be less.

Another problem is that nobody knows quite how many units are in a mole. This is why there is a (28) in the brackets of the title. This means that you could add (or subtract) 28 to (or from) the last two digits (86) and still be within the margin of error. So a cow could as much as 1.66053904 x 10-24 moles of cows, or as little as 1.6605358 x 10-24 moles of cows.

So presuming google calculator and I are correct in treating the mole as a counting unit (and who would wish to doubt this), all scientists don't know how many things they have, and are continously losing/gaining them too, depending on a lump of metal in Paris.

One way out of this crisis would be to count in units (the one), and define the kilogram in terms of electron masses. Thus scientists could again count with with the rest of the population. I don't think the chemists would like it, though.

As a reward for sticking with this post, here is The Answer in moles.

[Disclaimer: The Answer in moles contains error bars and may increase or decrease with time. The author accepts no responsibility for future changes to The answer in moles.]

Feierabend

I went to work today, and am now enjoying that relieved feeling at the end of a working day. Germans like to call this Feierabend (literally celebration evening).

My first work project is to help prepare an exam about electromagnetism. I've forgotten almost everything I knew about this subject, so I had to get a textbook from the library. I was most pleased to see my old friend "Electromagnetic Waves and Radiating Systems" by Edward Jordan and Keith Balmain. It is a delightful book, although a little dated. Luckily electromagnetic theory hasn't changed over the last 50 years, although labour relations, feminism and household appliances have come on a bit since the 50's, as demonstrated by the following quote from the book.

A man can do work for a 12-hour day at the rate of about 40 Watts, which is less than the power required to run his wife's electric washing machine.