Antimatter as Reverse-Cascade: A Geometric Resolution of the Dirac Time-Reversal Paradox in Fractal Mechanics

Abstract

The Dirac equation predicts antimatter as negative-energy solutions equivalent to particles propagating backward in time — an interpretation that has remained physically unsatisfying for 95 years. We propose a geometric resolution within Fractal Mechanics (FM): antimatter is not a time-reversed particle but a particle whose cascade evolves in the reverse direction ξ₋ = (D₃→Dₙ), opposite to the matter cascade ξ₊ = (Dₙ→D₃). The observed arrow of time is a *projection* of this dual cascade structure, not a fundamental dimension. This reinterpretation (i) dissolves the Dirac paradox without modifying the mathematics, (ii) predicts a gravitational M-AM repulsion from the opposite cascade gradients without invoking negative inertial mass (resolving the Bondi runaway problem), (iii) explains the M-AM asymmetry of the universe as a statistical fluctuation of cascade direction with no CP violation required, and (iv) identifies cosmic voids as antimatter-dominated regions whose collective gravitational repulsion drives the observed dark energy. We define a CPG symmetry (C=charge, P=parity, G=cascade inversion) that replaces the CPT symmetry, and derive explicit predictions for AEGIS (gravitational asymmetry), Euclid/DESI (equation of state), and the Euclid void survey.