Since p 2 = E 2 − p → 2 = m 2 and E = h ν = h c λ and | p → | = h λ we have that p 2 = h 2 c 2 λ 2 − h 2 λ 2 If I go to Planck-units ( c = 1 , h = 1), this becomes zero. Is this a correct thing to do?

Question

Since       p    2    =      E    2    −                    p        →              2    =      m    2   and  E  =  h  ν  =            h      c        λ   and      |              p      →            |    =      h    λ  we have that      p    2    =                    h        2                    c        2                    λ      2        −            h      2              λ      2      If I go to Planck-units (  c  =  1  ,  h  =  1), this becomes zero. Is this a correct thing to do?

wintern90 · Accepted Answer

You&#039;re right that, if the result of a calculation depends on the units you use, there&#039;s something wrong with it. In fact, even more than that, you can&#039;t even get any result out of       p    2    =                    h        2                    c        2                    λ      2        −            h      2              λ      2       in SI units, because you&#039;d be taking a difference between two quantities with different units.In this case, if you&#039;re using SI units, the energy-momentum relation is       p    2    =            E      2              c      2        −      |              p      →                  |        2  ; that extra factor of       c    2   is necessary to keep the units