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Related Concept Videos

The Uncertainty Principle04:08

The Uncertainty Principle

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Published on: September 5, 2019

Uncertainty relation for photons.

Iwo Bialynicki-Birula1, Zofia Bialynicka-Birula

  • 1Center for Theoretical Physics, Polish Academy of Sciences Al. Lotników 32/46, 02-668 Warsaw, Poland. birula@cft.edu.pl

Physical Review Letters
|May 1, 2012
PubMed
Summary
This summary is machine-generated.

This study derives a new uncertainty relation for photons in three dimensions using quantum electrodynamics. Photon energy density acts as probability density, establishing a spatial extension measure akin to the Heisenberg relation.

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Area of Science:

  • Quantum Electrodynamics
  • Quantum Mechanics
  • Photon Physics

Background:

  • The standard Heisenberg uncertainty principle is fundamental in quantum mechanics.
  • A photon position operator does not exist, posing challenges for applying uncertainty relations to photons.
  • Photon behavior requires specific theoretical frameworks like quantum electrodynamics.

Purpose of the Study:

  • To derive a three-dimensional uncertainty relation for photons.
  • To address the challenges posed by the nonexistence of a photon position operator.
  • To establish a quantum mechanical framework for photon spatial extension.

Main Methods:

  • Utilizing quantum electrodynamics (QED) to formulate the uncertainty relation.
  • Employing photon energy density as a probability density in configuration space.
  • Analyzing the spatial energy distribution to define a measure of spatial extension.

Main Results:

  • A novel uncertainty relation for photons in three dimensions has been derived.
  • Photon energy density effectively serves as the probability density.
  • An inequality analogous to the standard Heisenberg relation was established based on spatial energy distribution.
  • The derived relation is a natural counterpart to the standard Heisenberg relation.

Conclusions:

  • The derived uncertainty relation overcomes limitations associated with the photon position operator.
  • The photon wave function in momentum space, under conditions saturating the uncertainty relations, follows a Schrödinger-like equation in coordinate space.
  • This framework provides new insights into the spatial properties and behavior of photons within quantum electrodynamics.