There Is No Matter: The Energy-Momentum Tensor as Coherence Gradient Density, and the Completion of the Jacobson Program

Jacobson (1995) derived the left-hand side of Einstein’s field equations — geometry — from thermodynamics and the holographic entropy-area relation. The right-hand side — the energy-momentum tensor T_μν, representing matter — was left as input. This paper completes the Jacobson program: T_μν is the local density of the coherence free energy gradient ∇V(K). Matter is not a fundamental substance that sources geometry. Matter and geometry are both descriptions of the same underlying field: the coherence field K(t,x) and its free energy landscape V(K). The left-hand side is curvature, the right-hand side is gradient density — both from one field. The cosmological constant is V(K*), not the sum of quantum zero-point energies, potentially dissolving the 10^120 discrepancy as a category error. Particles conjectured as topological defects of the coherence field. G_μν = 8πG T_μν is 1=1 written in differential geometry. Part of the Spektre research corpus.