Wednesday, April 16, 2014

Wien displacements in many dimensions

can you show that the Wien displacement law for frequencies for a Planck-spectrum in $n$ dimensions is identical to the displacement law for wave lengths in $n+2$ dimensions?

Wednesday, April 9, 2014

braking by scattering

can you estimate the time-scale on which a cluster of galaxies slows down due to the kinetic Sunyaev-Zel'dovich effect? (PS: there's something remarkable about the solution if one assumes small velocities and if CQW didn't make a mistake)

Wednesday, April 2, 2014

Planck, Bose and Boltzmann

the Planck-spectrum is determined by the Bose-distribution for indistinguishable integer-spin particles and not by the Boltzmann-distribution for classical distinguishable particles. can you show that the difference between the Stefan-Boltzmann-laws derived with both distributions vanishes in the limit of many dimensions? can you show this mathematically and give an intuitive argument?

Wednesday, March 26, 2014

fundamentals of cosmology

can you give an intuitive explanation why one needs general relativity for describing the dynamics of the Universe?

Wednesday, March 19, 2014

fat Hubble sphere

the Hubble sphere is a spherical surface around an observer in a FLRW-universe at which the recession velocity becomes larger than the speed of light. at what scale factor are the recession velocities stationary?