Least-time paths of light

Abstract

The variational principle in its original form á la Maupertuis is used to delineate paths of light through varying energy densities and to associate shifts in frequency and changes in momentum. The gravitational bending and Doppler shift are in this way found as mere manifestations of least-time energy dispersal. In particular, the general principle of least action due to Maupertuis accounts for the brightness of Type 1a supernovae versus redshift without introducing extraneous parameters or invoking conjectures such as dark energy. Likewise, the least-time principle explains the gravitational lensing without the involvement of additional ingredients such as dark matter. Moreover, time delays along curved geodesics relative to straight paths are obtained from the ratio of the local to global energy density. According to the principle of least action the Universe is expanding uniformly due to the irrevocable least-time consumption of diverse forms of bound energy to the lowest form of energy, i.e. the free electromagnetic radiation.