Uncertainty Relation for Photons

Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
Phys. Rev. Lett. 108, 140401 – Published 3 April 2012

Abstract

The uncertainty relation for the photons in three dimensions that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in configuration space. It is shown that the measure of the spatial extension based on the energy distribution in space leads to an inequality that is a natural counterpart of the standard Heisenberg relation. The equation satisfied by the photon wave function in momentum space which saturates the uncertainty relations has the form of the Schrödinger equation in coordinate space in the presence of electric and magnetic charges.

  • Received 10 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.140401

© 2012 American Physical Society

Authors & Affiliations

Iwo Bialynicki-Birula*

  • Center for Theoretical Physics, Polish Academy of Sciences Al. Lotników 32/46, 02-668 Warsaw, Poland

Zofia Bialynicka-Birula

  • Institute of Physics, Polish Academy of Sciences Al. Lotników 32/46, 02-668 Warsaw, Poland

  • *birula@cft.edu.pl

Comments & Replies

Comment on “Uncertainty Relation for Photons”

Zhi-Yong Wang, Cai-Dong Xiong, and Qi Qiu
Phys. Rev. Lett. 109, 188901 (2012)

Bialynicki-Birula and Bialynicka-Birula Reply:

Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
Phys. Rev. Lett. 109, 188902 (2012)

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Vol. 108, Iss. 14 — 6 April 2012

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