Derivation of Hubble’s Law: Unified Field-Theoretic Explanations for Dark Energy, Dark Matter and Huge Magnetic Toroids of the Galaxy

This paper initiates a dual-route derivations of Hubble's Law within standard relativistic and Newtonian frameworks, grounded in the intrinsic perfect symmetry of the local inertial frame. This reveals that the fundamental aim of a local inertial frame's motion is to restore Poincaré symmetry, from which it follows that the flow velocity of a strong gravitational field equals its gravitational acceleration multiplied by one second. Thus the standard theories inherently contain the seed of dynamic field theory. Mass Complex Space Theory (MCST) is the guidance to push the standard theories toward full dynamization and higher-dimensionalization. MCST introduces the “Quadruple State of the Planck Quantum ☯(h, Φ_ih, Φ_h, ih )” as the elementary complex-space generating element, whose hyper-cycle dynamically unifies matter and spacetime. A key finding is that gravitational field space is constituted by diverging negative-energy “positron state ( )”. Consequently, dark matter and dark energy are unified as field effects of hyper-cycling mass complex space. Emergent from this framework is a gravitational circulation field ( ). This field makes the apparent Keplerian mass exhibits a counter-intuitive monotonic decrease (mass inversion) in the outer halo of the Milky Way (22.5–26.5 kpc). Moreover, owing to its intrinsic “negative-energy positron state” property, naturally generates huge magnetic field toriods, the structure of which aligns remarkably with the observed galactic magnetic field, thereby achieving a preliminary structural unification of gravitation and electromagnetism on galactic scales without additional assumptions, and further providing theoretical foundation for the quantization research on the unification at the subatomic scale.