Einstein’s dream to unify all forces finally materializes: a revived de Broglie’s pilot-wave theory with novel solutions

Abstract

Starting from Louis de Broglie’s pilot wave-theory, this paper unifies gravity and quantum mechanics under a single mathematical field theory for all forces in Nature. Two families of potentials coexist as mathematical solutions for the homogeneous Klein-Gordon equation which is the same homogeneous classical wave equation: (a) Neo-Laplacian local time-independent background potentials, and (b) Novel time-distance entangled Q(q) potentials which are isomorph to distance-time-velocity transformations based on any of the competing relativistic theories (Lorentz, Poincaré or Einstein), or on the pre-relativistic Galilean invariant Doppler equations. This remarkable property makes present theory compatible with all previous empirical evidence, including experiments conventionally interpreted as supporting Einstein’s special relativity. We report explicit closed solutions for potentials solving the one-dimensional and three-dimensional classical wave equations, and describe in detail how to calculate time-independent neo-Laplacian background forces and relativistically isomorph time-dependent entangled forces. The scale of the problem appears as a required parameter, thus making our theory applicable to all scales of Nature from quarks to cosmos. A usually overlooked neo-Laplacian logarithmic potential predicts the observed high values of non-Keplerian tangential speeds at the galactic scale. At the human scale, calculations relative to hurricanes and tornadoes may be facilitated by the closed form of our unified forces. A novel torsion component of gravity automatically appears from our new solutions.