Article

# Heisenberg uncertainty relation for photons

05/2012;
Source: arXiv

ABSTRACT The idea to base the uncertainty relation for photons on the electromagnetic
energy distribution in space enabled us to derive a sharp inequality that
expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)].
An alternative version of the uncertainty relation derived in this paper is
closer in spirit to the original Heisenberg relation because it employs the
analog of the position operator for the photon---the center of energy operator.
The noncommutativity of the components of the center of energy operator results
in the increase of the bound $3/2\,\hbar$ in the standard Heisenberg
uncertainty relation in three dimensions. This difference diminishes with the
increase of the photon energy. In the limiting case of infinite momentum frame,
the lower bound in the Heisenberg uncertainty relations for photons is the same
as in nonrelativistic quantum mechanics.

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### Keywords

alternative version

analog

center

energy operator

energy operator results

Heisenberg uncertainty relations

infinite momentum frame

limiting case

nonrelativistic quantum mechanics

original Heisenberg relation

photon energy

photons

position operator

sharp inequality

uncertainty relation

uncertainty relation [Phys