Freundlich Red-Shift Formula

Abstract

Freundlich has attempted to explain various anomalous observations by suggesting that the red shift be reinterpreted as an effect proportional to radiation density and length along the path of a photon. For a star of radius $R$ the contribution of the outside radiation field exceeds that within the atmosphere (thickness ${l}_{0}$) by a factor of the order of $\frac{R}{{l}_{0}}=1000$ for average stars; this makes Freundlich's original formula untenable. The question is here examined whether the objections to Freundlich's conception can be removed if one reduces his constant of proportionality by ${10}^{\ensuremath{-}3}$. To give the conception a full trial the calculations are made realistically, taking into account the extension of the star, and the deviations from Lambert's law of emission which result from the radiative transfer conditions in the photosphere. The resultant formula for the radiation shift gives an approximate fit with solar observations out to near the limb without retaining, as Freundlich does, an additional relativity shift equal to one fifth of the expected value. However, the rise of the observed shift at the limb to the gravitational value (and even higher) is unaccounted for. The serious objections to Freundlich's interpretation from other astronomical evidence still stand, though the order of magnitude of the discrepancies is in some instances considerably reduced.