Regarding natural units, how can h=c=1, and why is this simplification used?

Asked by: Robyn Soares

Answer

First, a technicality, but what is set to be 1 is h-bar, which is simply h divided by 2 pi. For the rest of the answer, all 'h' references should be understood to be h-bar.

The answer to why this is done is simple. For pure convenience of notation. c goes into almost every equation there is in relativity, and h goes into almost every equation in quantum mechanics. So, especially when one is working with relativistic quantum mechanics and field theory (like QED, quantum electrodynamics) which there are many more symbols to keep track of, all the c's and h's become a big bother. So, one sets them to one and just omits writing them. However, once the calculation is done, and the result is found, to calculate numerical values one puts the c's and h's back in. It is easier than it sounds, since one knows what units the answer must have, and there is only one way to add in h's and c's to make it 'right'.

Let me answer HOW one can set h=c=1. Now, c has the units of speed, or in 'base' units, length/time, or L/T. h has the units of angular momentum, or in base units it is mass*length*length/time, or ML^2/T.

First, we can start by setting c=1. This would be possible, if we changed the unit of length to be the distance traveled by light in one second, c would be exactly 1. To put it more simply, if we take one 'length unit' to be 186,000 miles, and seconds stay as they were, c = 1.

Now, h = M*L*L/T, we can set the units for mass so that the above product is exactly 1, we will have both c and h = 1. (The values here are a little more involved, and I am too lazy to look up or calculate the exact values needed).
Answered by: Yasar Safkan, Ph.D. M.I.T., Software Engineer, Istanbul, Turkey