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
'He who finds a thought that lets us even a little deeper into the eternal mystery of nature has been granted great grace.'