# Notation notation notation

By Marcus Wilson 14/01/2014

Physicists and engineers have a particular fondness for using symbols for things. Thus, the speed of light becomes 'c'. Planck's constant is 'h'. And so forth. Not content with the latin alphabet, they have commandeered the greek one too: The Stefan-Bolztmann constant is  'sigma', the permittivity of free space is epsilon0 (the greek letter epsilon with a subscript zero) and so forth.

It comes as no surprise that even those two alphabets aren't sufficient. While mathematicians resort to using the Hebrew alphabet to allow for more possibilities, physicists take the approach of using the same symbol to mean different things. So, for example, 'k' is used for spring constant, Boltzmann's constant, wavenumber and so on. Usually this causes no ambiguity – spring constants are used for describing the stiffness of springs, Boltzmann's constant in used in thermodynamics to relate temperature to energy, and the wavenumber is used to describe wave phenomena. Occasionally we might need to use Boltzmann's constant and wavenumber at the same time, though when we do which is which is generally fairly obvious. It's just like language – one word might have multiple meanings, and mostly we don't get confused.

Just occasionally, however, we run into trouble. I've been preparing some notes for our third-year Electromagnetic Waves paper. It's a paper that is taken by a combination of engineering students and physics students. I'm a physicist, but most of the students are engineering students, and the textbook that the paper draws heavily from is an electronic engineering textbook. While there is a great deal of overlap between the two disciplines, there are also clashes. I ran into trouble over terminology a couple of years ago in a mechanical engineering paper – you can read about that here. Now, in the Electromagnetic Waves paper, we have the greek symbol 'delta' being used for two very much related things.

Electromagnetic waves don't go through good conductors at all well. The energy is taken from the wave very quickly. A parameter used to describe how quickly is known as the 'skin-depth' (and here) (it's roughly the distance that the wave will penetrate to), and is conventionally given the greek letter 'delta'. That's the physics part. What do we mean by a 'good' conductor? We can characterize how conductive a material is, relative to the frequency of the wave (which is what matters for determining the depth of penetration) by something known to electronic engineers as the 'loss tangent'.  That's given the notation 'tan delta' – the tangent of delta. Unfortunately delta and delta are not the same thing, but are very much related to each other. Confused? Poor students.