Institution(s): 1. International Centre for Physics
From philosophical considerations, Boscovich proposed around 1760 a unified force of nature. Boscovich’s force turns out to be a particular case of the novel solutions for the homogeneous wave equation in spherical coordinates found by the present author in the 1990s [Found. Phys. Lett. 10, 31-41 (1997)]. As noted by J. J. Thomson before Bohr’s quantum theory, Boscovich’s force exhibits quantization in energy and distance.
For each quantum number, our non-harmonic functions of the first kind (NHF-1k) predict the existence of a discrete number of spherical surfaces in dynamical equilibrium (SSDE), leading to both Titius-Bode and ring structures. Predictions agree with observed Titius-Bode patterns in our planetary system, and in the moons of Mars, Jupiter, Uranus, Saturn, and Neptune. At distances beyond the quantum structure associated with SSDEs, for even NHF-1ks the force becomes Newton’s inverse-square law; however, odd NHF-1ks exhibit a non-zero limit as distance tends to infinity, which immediately explains the flat rotation rate of spiral galaxies without additional asumptions as dark matter or MOND models. The SSDEs provide the physical counterpart to the mathematical spheres that appear in the recent solution of the three-body problem and the orbits of Trojan moons [Suvakov & Dmitrasinovic, Phys. Rev. Lett. 110, 114301 (2013)]. The inner-most SSDE is a photon-sphere, but inside it there is a monotonously increasing repulsion, thus acting as a “white” hole; this could be relevant in the context of the contradictory appearance of a black and a white hole in the creation of black holes in the laboratory [Leonhard & Philbin ArXiv:0803.0669 5 March 2008].
Deflection of light does not occur at the SSDEs but at intermediate locations where gravitational attraction reaches a maximum. Calculation of deflection involves three non-Newtonian aspects: the force is not exactly Newton’s, the distance is larger than the radius of the physical surface, and there are several loci for deflection.