How close to ideal is the photon gas Corrections to Planck's laws at kT. much lt. m sub e

Journal Article · Tue Jan 01 00:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90237-3· OSTI ID:7235468

Barton, G ^[1]

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1. Univ. of Sussex (United Kingdom)

At temperatures well below the electron rest mass, the electron-positron concentrations in black-body radiation (BBR) are negligible, and deviations from Planck's laws are due to the photon-photon coupling described (in natural units) by the classic Euler-Heisenberg local interaction Lagrangean density ({alpha}{sup 2}/360{pi}{sup 2}m{sub e}{sup 4})((E{sup 2}{minus}B{sup 2}){sup 2}+7(E{center dot}B){sup 2}). Though unobservably small, these corrections answer the question in the title. They are best expressed in terms of the (frequency-independent) shift in the refractive index {kappa} = (1+{Delta}{kappa}) of BBR, where {Delta}{kappa} = {alpha}{sup 2}(kT/m{sub e}){sup 4}44{pi}{sup 2}/2025 {approx} 7.5 {times} 10{sup {minus}35}(T/300){sup 4}. There are fractional changes of 3 {Delta}{kappa}/2 in the free-energy density and the pressure; 7 {Delta}{kappa}/2 in the energy density; and 2 {Delta}{kappa} in the mean-square electric field in any frequency range, whence only the intensity of the Planck spectrum is shifted but not its shape. The dielectric constant {var epsilon} = (1 + {Delta}{var epsilon}) and magnetic susceptibility {mu} = (1 + {Delta}{mu}) of BBR are equal, with {Delta}{var epsilon} = {Delta}{mu} = {Delta}{kappa}, whence the author compares the BBR shifts with those in an ordinary linear nondispersive medium having {var epsilon} = {mu} = {kappa} {triple bond} {radical}{epsilon}{mu}.

• OSTI ID: 7235468
• Journal Information: Annals of Physics (New York); (United States), Vol. 205:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PLANCK LAW
CORRECTIONS
BLACKBODY RADIATION
ELECTRONS
HEISENBERG PICTURE
PHOTONS
PLANCK RADIATION FORMULA
POSITRONS
QUANTUM ELECTRODYNAMICS
REFRACTIVITY
THERMODYNAMICS
ANTILEPTONS
ANTIMATTER
ANTIPARTICLES
BOSONS
ELECTRODYNAMICS
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
LEPTONS
MASSLESS PARTICLES
MATTER
OPTICAL PROPERTIES
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
RADIATIONS
661300* - Other Aspects of Physical Science- (1992-)