Units Rant

May 10, 2010

Way Back in the 1960s (spot that quote) our physics teacher told us that in the funny old days the absorption of sound was measured in cubic yards of Standard British Cushion, but now that we lived in enlightened times we measured it in square metres of open window. That helped to teach us the necessity of converting carefully between units, but also gave us a healthy disrespect for any particular units, and reminded us that units are operationally defined. They are not philosophical magic.

Wind forward a few years and I was in the thick of my astronomy PhD, in the wonderful world of parsecs and solar masses. In X-ray astronomy we also had Uhuru Flux Units (UFU) and my good friend the milli-crab. Such weird units are of course awfully important to protect the mystique of a specialism. We don’t want any old fool thinking they can be an X-ray astronomer, now do we we ? I believe Antarctic ozone hole pundits use Dobson Units. But they are also truly natural units, in two ways. First, they give sensible human sized numbers you can think with. Would you like the distance to your star to be 3.2 parsec or 9.9 times 10^16 m ? Second, you can get on with stuff even before you have solved all your problems – quasar A is seven times as bright as quasar B whether you know the absolute flux of the Crab or not. You can sort that later.

Wind forward another few years and I was about to teach my first lectures at QMW. Time to shed those quirky units and do everything in SI. This held one or two surprises. The Eddington limit, the largest luminosity a body can have without blowing away its atmosphere, is very big for black holes. Every X-ray astronomer knows the number – 1.3 times 10^38 erg per second per solar mass. Yes, we love BIG numbers. What I do is extreme astrophysics. Black holes are the solution to quasars because they are the most efficient known power source !

Now lets have that in SI.  What I got was L=6.39M. Feeble. I checked it six times, but it was right. A one kg black hole gives you a pathetic 6 watts. My little electric fire does three hundred times better than a black hole of similar mass ! Ahh… but its not the electric fire that makes the power … its the enormous power station its connected to. In a similar way, accretion is not particularly impressive or efficient per unit mass of accretee – its efficient per unit mass of accretor. Once you have that huge black hole, you only need to drip a tiny amount of stuff onto it to generate lots of power. So whats my point here ? That its all about building physical instincts. There is no perfect global unit system. Switching between systems is like switching between physical domains, and that act in itself can teach you lessons.

You can only be “natural” within a domain.This is why the “natural units” touted by theorists, where h=c=1, are a bit irritating, just because they often come bundled with a kind of arrogant mysticism, as if this idea was revealing something deep about the structure of the universe. Au contraire, they are a convenience, just like parsecs.  They are jolly sensible if you are doing some kinds of calculations, because you don’t have to carry round awkward numbers and the equations are easier to follow. But if you are calculating real world quantities, those awkward numbers have to pop back out somewhere.

I have lots of other units rants (I bet you do too) but I had better stop there.

Oh hang on, just one more. This Galactic Guide web page is quite fun. My favourite bit is right at the end, where they recommend students answer a question by saying “The answer is 12.7 Meulens, where the Meulen is defined via this problem”.