Maximum Determinacy V: Gravity

In Maximum Determinacy gravity is the difference of depth between neighbouring cells,carried across the join between them (the author’s ruling); its effects are objects hoppingacross cells whose dimensions differ. The lattice is set by sources, and where there is nonethe vacuum is one undivided cell. A join between cells of different depth acts as a springwhose network relaxation is harmonic, so a held difference spreads as 1/r: the Newtoniansector, with G a relationship rather than a constant of the join. The difference moves asa depth walk with light’s dispersion, sourced by energy; matter in it has the dispersion ofa static metric and falls universally in the continuum limit, and light is bent by twice thelapse-only value. Carried between neighbouring cells the squeeze is a symmetric tensor: onderivatives defined on histories it has two polarisations at every momentum except light’sdoubler points and an exact relabelling constraint; relabelling invariance with closure underconserved sources forces the linearised Einstein operator, whose static field has γ = 1 andwhose source is Tolman’s ρ + 3p. Compared with distant cells a source moves the time andspace pairs in lockstep, which is the content of γ = 1. With refoliation (P5), kept as aconditional premise, the full action follows. Two-pair locks give horizon thermodynamics: thefirst law, the area quantum 8πℓ2 P, Hawking’s, Gibbons–Hawking’s and Unruh’s temperaturesand S = A/4. The paper carries a quantum model of the Newtonian sector, gravitons as MDpairs, the constraint algebra on finite cells, a bounce and its continuations, the arena anddark energy, and the confrontation with observation. Matter couples to the tensor throughthe author’s conserved lattice stress (Paper IV), and relabelling invariance forces any localcoupling to have that form, up to the choice of local energy and improvement terms; hoppingon resized cells and the fixed-cell turn are its long-wavelength descriptions. The depth is thetensor’s h00, the lapse, a constraint: MD’s exchange is pure massless spin 2 and a binary losesenergy at general relativity’s quadrupole rate, while a depth propagating in its own rightis excluded at full strength by the Hulse–Taylor pulsar. Owed: the non-linear completion(β = 1), the joint lattice’s dynamics in 3+1, and the strong field. Every result carries itsgrade.