The Boltzmann transport equation is the rigorous continuity equation for the angular flux f(r, t, v) of photons at positions r, time t, moving in direction v, and interacting with a surrounding medium by localized collisions. This equation is not necessarily Lorentz-covariant, but can be specialized to a Lorentz-covariant equation describing the propagation of a photon distribution through space. However, this requirement of Lorentz-covariance of the Boltzmann transport equation then leads to a wave-particle duality, in which an ensemble of photons behave as waves, but in which each individual photon interferes only with itself. Applied on cosmological scales, this requirement of Lorentz-covariance of the Boltzmann transport equation also leads to an apparent quantum multiplication, which could explain the existence of the huge amounts of the mysterious “dark energy” that appears to permeate the universe. In addition, it also requires the universe to appear subjected to an exponential expansion as observed, similar to a perspective distortion in time, and then also as a consequence to appear surrounded by a cosmic microwave background radiation (CMB) with an exact Planck spectrum, as observed.

boltzmann’s transport equation, cosmological expansion, dark energy/dark matter, wave/particle duality