13 papers · a modular site of reconstruction regimes
Quantum gravity is not primarily the quantization of material objects in spacetime. It is the reconstruction of spacetime, matter, causality, and measurement from invariant representation structures. Twelve companion regimes — from classical Lorentzian geometry to indefinite causal order — each execute one reconstruction, composed honestly by a weakest-link epistemic calculus.
Each part is a self-contained reconstruction, tagged throughout with its own standard / heuristic / speculative status. The synthesis states how they compose — and, just as importantly, where they must be kept apart.
This paper collects twelve companion studies into one structure without collapsing them into one theory. The organizing thesis is that quantum gravity, in the sense used across this program, is not the quantization of matter fields on a fixed background. It is the reconstruction of spacetime, matter, causality, and…
We treat the classical regime of general relativity as one layer of a broader program in which spacetime, matter, and causality are reconstructed from invariant representation structures rather than obtained by quantizing material fields on a fixed background. In this regime the invariant is diffeomorphism…
We treat the gauge and constraint layer of quantum gravity not as a nuisance to be removed before quantization but as invariant representation structure whose cohomology reconstructs the physical observable algebra. The technical vehicle is the Batalin–Vilkovisky (BV) and Becchi–Rouet–Stora–Tyutin (BRST) formalism…
We develop quantum spatial geometry as representation-theoretic data attached to a graph, following the reconstruction thesis that quantum gravity is not the quantization of matter placed in a fixed spacetime but the reconstruction of spacetime, matter, causality, and measurement from invariant representation…
A spin foam is a two-complex whose faces and edges carry representation labels and whose state sum defines a transition amplitude between spin-network boundary states. We treat this construction as the covariant, sum-over-histories layer of a reconstruction program in which spacetime, causality, and measurement are…
We treat holographic emergence as one regime of a modular program in which spacetime, matter, causality, and measurement are reconstructed from invariant representation structures rather than obtained by quantizing fields on a fixed background. In this regime the invariant is compact: many boundary representatives…
We treat perturbative scattering amplitudes not as objects derived from a spacetime Lagrangian, a Feynman expansion, or a path integral, but as canonical forms of positive geometries: top-degree rational differential forms determined uniquely by the requirement that their singularities are simple logarithmic poles…
We treat perturbative gravity amplitudes not as output of the Einstein–Hilbert action expanded into an infinite tower of vertices, but as reconstructions of gauge-theory data. The mechanism is the double copy of Bern, Carrasco and Johansson: once one exhibits a representation of a gauge-theory amplitude in which the…
We give a self-contained account of celestial conformal field theory as a representation of the flat-space S-matrix, organized around a single epistemic thesis: quantum gravity in this regime is not the quantization of matter in a fixed spacetime but the reconstruction of the scattering process from invariant boundary…
We treat asymptotic safety as one regime of a modular program in which spacetime, matter, causality, and measurement are reconstructed from invariant representation structures rather than obtained by quantizing fields on a fixed background. In this regime the invariant is not a geometric or algebraic object attached…
We give a self-contained account of the local-to-global structure of quantum observables, organized around a single invariant: the way the observable algebra of a large region is assembled from the observable algebras of small regions by a gluing (colimit) law rather than by restriction. The technical vehicles are the…
We treat one regime of a modular reconstruction program in which spacetime, matter, and causality are recovered as invariants of representation data rather than obtained by quantizing fields on a fixed background. The regime here is metric spin geometry, and the carrier of its content is Connes's spectral triple…
We treat causal order not as a fixed backdrop for physics but as a piece of representation data to be reconstructed from operational or combinatorial invariants, in the same spirit in which a metric is reconstructed from a spectrum or a bulk from a boundary. Two formalisms carry the load. The process-matrix formalism…