Ontology V8.2:An Effective Model of Spacetime Granularity

Within the Lorentz-transformation framework of special relativity, and with an additional time-quantization assumption ($dt=t_P$), this paper solves back for the minimal spatial granularity$dx(v)=\dfrac{1-\sqrt{1-v^2/c^2}}{v}\sqrt{\hbar G/c}$.This formula simultaneously contains the quantum constant $\hbar$, the gravitational constant $G$, and the speed of light $c$, and gives the continuous variation of the spacetime granularity with the object's velocity $v$: at low speed $dx\to0$ (spacetime approaches continuity), and at the speed of light $dx\to l_P$ (the Planck-length upper bound). Under this additional assumption, the paper shows: (1) this granularity can serve as a physical ultraviolet cutoff $\Lambda_{\mathrm{eff}}=1/dx(v)$, rendering loop integrals finite at that cutoff; (2) after introducing a dynamic gravitational constant $G_{\mathrm{eff}}(D)$, the modified field equations reduce to general relativity at low energy; (3) in the semiclassical limit the form $G_{\mu\nu}=8\pi G_{\mathrm{eff}}\langle T_{\mu\nu}\rangle$ is formally recovered; (4) in the WKB approximation, using the D field as an internal clock formally recovers time-dependent evolution. The paper constructs a self-consistent effective model, rather than a complete quantum-gravity theory derived from first principles.