Approach to Gravity and Cosmology Beyond Einstein’s Relativity

We present a novel formulation of general relativity derived from operator algebra over sedenionic spacetime, replacing the conventional differential-geometric framework with a non-associative, hypercomplex algebra. In this model, displacement operators on a micro-causal lattice define curvature through their commutators, and Einstein’s field equations emerge as projections of nested operator relations. A key achievement of this framework is the elimination of two long-standing problems in modern physics: the missing-mass problem and the cosmological constant puzzle. Galaxy rotation curves and cluster dynamics are explained without invoking dark matter or MOND, as the algebra naturally produces an additional force term at large scales. Likewise, the cosmological constant (Λ) is not an ad hoc insertion but arises as a derived property of the sedenionic commutator algebra, resolving the long-standing vacuum catastrophe. Beyond these breakthroughs, the model avoids black hole singularities through algebraic saturation, predicts fermionic gravitinos, and provides new insights into gravitational entropy and the arrow of time. Distinct from string and M-theory—which require extra dimensions and remain decoupled from the Standard Model—our approach offers a self-contained algebraic geometry that unifies gravity with quantum phenomena and lays the foundation for a grand unified description of all fundamental forces and particles.