1. Abstract:
Based on the Single Monad Model and Duality-of-Time hypothesis, a dynamic and self-contained space-time is introduced and investigated. It is shown that the resulting “time-time” geometry is genuinely complex, fractal and granular, and that the non-Euclidean space-time continuum is the first global approximation of this complex-time space in which the (complex) momentum and energy become invariant between different inertial and non-inertial frames alike. Therefore, in addition to Lorentz transformation, the equivalence principle is derived directly from the new discrete symmetry. It is argued that according to this postulate, all the principles of relativity and quantum theories can be derived and become complementary. The Single Monad Model provides a profound understanding of time as a complex-scalar quantum field that is necessary and sufficient to obtain exact mathematical derivation of the mass-energy equivalence relation, in addition to solving many persisting problems in physics and cosmology, including the arrow-of-time, super-symmetry, matter-antimatter asymmetry, mass generation, homogeneity, and non-locality problems. It will be also shown that the resulting physical vacuum is a perfect super-fluid that can account for dark matter and dark energy, and diminish the cosmological constant discrepancy by at least 117 orders of magnitude.