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
 

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