The Alternative Version of Heisenberg Uncertainty Relations

Abstract

This study is mainly focused on the alternative version of Heisenberg uncertainty relation. We have shown the separation of the total angular momentum of the electromagnetic field into its orbital and spin parts. It is dictated by quantum mechanics of photons reproduces. Therefore, the results are derived from the proprieties of Maxwell fields by Darwin. Then, we deal with the uncertainty relation for photons. The uncertainty relation was obtained as a sharp inequality by using the energy distribution on space. The relation we obtain here is an alternative to the one given by Heisenberg by the use of the position of the center of the energy operator. The fact that the components of the center is non commutative affected the right hand side of the Heisenberg inequality. But this is resolved by the increase of the photon energy.