Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Aug 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980amjph..48..599w&link_type=abstract
American Journal of Physics, Volume 48, Issue 8, pp. 599-603 (1980).
Physics
Condensed Matter
Statistical Mechanics
3
Thermodynamics, Classical Statistical Mechanics
Scientific paper
From the analogous properties of neutrinos and photons as quantized energy waves, the generalized ''blackbody'' radiation law for the total power radiated Rν per unit area per unit frequency ν is derived as Rν?k3/c2h2) × T3{(hν/kT)3/ [exp(hν/kT)-1] +3(hν/kT)3/ [exp(hν/kT)+1]}, where c is the speed of light, h is Planck's constant, k is Boltzmann's constant, and T is the absolute temperature. The first term in the brackets is the usual Planck radiation law for photon emission. The second term is the corresponding expression describing blackbody neutrino and antineutrino emission, which contains a factor of 3 because three different types of neutrinos are presently suspected. Otherwise the photon and neutrino terms only differ in the sign of the unity term due to the different spin statistics of photons compared with neutrinos. For photons, the spin =ℏ and Bose-Einstein statistics apply, while for neutrinos the spin =ℏ/2 and Fermi-Dirac statistics are appropriate. The wavelength (λm) at which the maximum energy is radiated is λmT=2.898 μ kK for photons and λmT=2.859 μ kK for neutrinos, while the total power radiated per unit area is R=T4 (σp+σn), where σp=5.67 W/cm2(kK)4 for photons and σn = 14.88 W/cm2(kK)4 for three types of neutrinos. Note that kK represents kilo degrees Kelvin. As is well known, the form of the blackbody law for photons demands the possibility of stimulated emission by light flux, thus allowing light to be amplified. On the other hand, the neutrino blackbody law demands that neutrino radiating transitions are suppressed in the presence of a neutrino flux. There are applications of these neutrino concepts in particle physics and astrophysics. It appears that neutrino blackbodies or graybodies may exist in nature associated with black holes, the formation of neutron stars, and the formation of the universe itself.
Gallo C. F.
Walsh Peter J.
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