On the Origin of Inertia: Implications for Dark Matter and Dark Energy

Abstract: In this paper, we present a new theory explaining the origin of inertia based on two key ideas: gravity as a spin-1 gauge field theory and the relativity of all kinds of motion. This theory proposes that inertial mass is influenced by the distribution of matter across the Universe, offering potential insights into dark matter and dark energy. For gravity to be described by a spin-1 gauge field theory, we propose that gravitational mass, distinct from inertial mass, is a Lorentz invariant and should be replaced by an imaginary mass for like masses to attract. According to this theory, while gravitational mass is imaginary, inertial mass remains a real quantity. These two key ideas, lead to the principle of Equivalence and the conclusion that gravity shapes the geometry of spacetime, which is Finsler-Randers spacetime. However, for bodies with gravitational mass, this curved spacetime is equivalent to a flat Minkowski spacetime with an additional gravitomagnetic field. Using this, the theory shows that external inertial forces are inductive effects from the entire Universe, while internal forces depend on the structure of the body. In free fall, all bodies experience only external forces, explaining why they fall at the same rate regardless of internal structure.