Force Acting on the Photon. Elementary Theory and Astrophysical Implications

The relativistic equation of Newton’s second law of motion for massive photons is expressed in terms of frequency with the aid of the optical dispersion equation in vacuum—dependence of the speed of light on frequency of radiation in free space resulting from the Proca equation for massive vector bosons of spin 1. The force causing the acceleration of a massive photon is proportional to the first order of time derivative of its frequency. It turns out the expression of the force retains its physical meaning for a massless photon as well if the force and the light velocities are colinear vectors. But in this case, the force reveals itself not through the acceleration of the photon (which is impossible), but through the change in frequency over time. The effect of the massiveness in a wide range of astrophysical scenarios is extremely weak because the detection of the rest mass of the photon lies far below the threshold of experimental and observational possibilities. Therefore, when estimating the magnitude of the force acting on the photon, we can neglect that effect and consider only massless photon for simplicity. The magnitude of a force, acting upon the photon in the visible part of spectrum in different physical and astrophysical scenarios involving gravitational shift in frequency of radiation (such as Pound-Rebka experiment, light deflection by the Sun and clusters of galaxies) and the expanding accelerating Universe, was estimated to vary between (~10−45 - 10−31) N which is many orders of magnitude falls below the magnitude of the weakest force ever recorded (4.2 × 10−23 N). The effect of massiveness of the photon on the change in frequency of galaxies turned out to be extremely small and virtually undetectable (~10−58).