Pregeometric Relational Dynamics and Universal Causal Structure. Spectral Constraints and Conditions for a Common Low-Energy Cone
Year: 2026
Type: preprint
Abstract: This work develops a unified framework for pregeometric relational dynamics, asking how locality, geometry and a universal causal structure can arise as effective properties of an underlying system that is not assumed to possess a manifold, metric or causal order from the outset. The analysis separates several questions that are often conflated: the emergence of quasilocal sectors, the formation of massless collective modes, the coincidence of their propagation cones, and the appearance of strict microcausality. A central spectral result shows that a common network operator alone cannot equalise distinct microscopic propagation speeds. Instead, for several retained massless branches, a universal leading causal cone exists precisely when the kinetic-normalised spatial form becomes scalar on the massless subspace: D₀₀ = v²Iᵣ. This converts the universality of propagation into a basis-independent spectral condition rather than an assumed numerical value of the speed of light. Controlled response limits further show that finite microscopic systems may possess analytic nonzero tails while nevertheless converging to a local continuum theory in which those tails disappear outside the causal cone and exact microcausality is recovered. The resulting concept of Universal Null Calibration shifts the emphasis from the dimensionful number 299,792,458 to the invariant physical statement that independently identified sectors share one Lorentzian characteristic structure. The convention c = 1 is then a common calibration of an already established cone, not an explanation of why that cone is universal. The manuscript formulates explicit conditions for reconstruction invariance, spectral length–time correspondence and quantum continuum convergence, showing in particular that microscopic unitary systems with nonvanishing finite-scale response tails can converge to a unitary local free field with exact causal commutator support. The relevant invariant is therefore not a preferred numerical value of c, but the existence and preservation of one common null structure across admissible descriptions, scales and physical sectors. This also sharply identifies what remains open: the dynamical origin and stability of the required local geometry, massless sector and intersector matching from genuinely neutral relational data. The final layer tests the functional consequences of this common causal structure in a controlled Maxwell sector. Propagation, phase, energy, momentum, energy flux, momentum flux and radiation pressure are shown not to be arbitrary independent primitives once a single effective Maxwell functional and the required observer, gauge, boundary and quantum data are specified. For a null electromagnetic sector, the same stress-energy structure yields S = cu n, gₘₒₘ = S/c² = (u/c)n, and Πₙₙ = u = I/c, linking energy transport directly to momentum transport and longitudinal stress. An independent radiation-pressure loop gives the closure relation cF/(bIA) = c|k|/ω = 1, providing an operational comparison between optical propagation and mechanical momentum transfer rather than another definition of c. The result is a layered consistency programme in which common-cone universality, reconstruction invariance, quantum microcausality and Maxwell functional closure become mutually testable structural statements, while their required assumptions remain explicit rather than being hidden inside a numerical calibration.
Authors: Preece, Andrei, Batenin, Boris
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208821133
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