3 ms·
Checking your units is a basic sanity check that we teach students. But as we advance, physicists throw away that wisdom. Theorists especially have an annoyin
by adrianratnapala 9y ago
Checking your units is a basic sanity check that we teach students. But as we advance, physicists throw away that wisdom. Theorists especially have an annoying habit of doing this, because all the repetitions of "c", "hbar" etc "k_B" etc clutter up their equations.
But I preffer to keep that stuff in, even when doing pretty abstract stuff. Essentially because I wanted the type annotations. For example my favorite convention for the Minkowski metric is:
[c^2 0 0 0]
[ 0 -1 0 0]
[ 0 0 -1 0]
[ 0 0 0 -1]
That way your vectors are just $(t, x, y, z)$, where $t$ has units of time and the rest of space. Your covectors do come out oddly as $(c^2t, -x, -y, -z)$, but that's what makes them covectors.
- catnaroek 9y agoAlternatively, you can work with x^0 = ct instead of x^0 = t.
- adrianratnapala 9y agoYes, and and that a much more common convention than the one I favour. They do it partly because it keeps the factors of c out of the visible equations -- but I like my those cs. Another reason is that people instinctively feel that the elements of the coordinate tuple all have to have the same units. But that's not necessary when you have a metric around. Indeed keeping irregular units is helpful because it prevents you from accidentally forgetting to multiply through by the metric.
- catnaroek 9y agoThe c factor doesn't really go away. It just gets shifted into 4-vectors.