## Natural units (brief)

It occurred to me the other day why it makes a lot of sense to work in natural units where h, c, k, and G all equal to one. Or at least in part. We measure energy in a lot of different ways:

$E=h\nu\\ E=\frac{f}{2}NkT\\ E=\sqrt{m^2c^4+p^2c^2}\\$

We can use frequency (or wavelength) to measure the energy in a quantum mechanical sense. We look at the energy of a particle relativistically. We can look at the ‘temperature’ of a bunch of such particles (a system) and we’re talking about the same thing each time. The constants h,c,and k are all just proportionality constants to convert between units we didn’t initially think were measures of energy (mass, frequency and temperature).

To think about G I need to also think about $4\pi\epsilon_0$. I don’t know at the moment if we can make them both unit as well. If so that would be cool as it would then be consistent with the above idea that all of these constants are just to relate some property of a particle (or collection of particles) to the energy of the particle (or particles). The particle is wavy, it has mass (perhaps) or momentum, it may have charge, the system will have a temperature, etc. Different ‘flavors’ of energy connected by constants who’s existence is somewhat historical. Just a thought.