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Selecting Microscopic Degrees of Freedom for Emergent Spacetime: Coupled Quantum Oscillators as the Substrate

Tong H

2026

Abstract

A lattice of locally coupled quantum oscillators is proposed as a hypothesis for the microscopic substrate from which continuum spacetime and its effective physical contents may ultimately emerge. The elementary coupled oscillator is defined as an elementary substrate unit (ESU): a minimal dynamical and information-bearing quantum degree of freedom, ontologically prior to spacetime, fields, and particles defined within spacetime. Collections of ESUs may form composite substrate structures—including, in principle, chains, loops, sheets, defects, and networks—of which the strings of string theory would represent one possible class rather than the fundamental starting point. The oscillator substrate is evaluated against practical criteria for a viable microscopic architecture, including collective-mode formation, ultraviolet regularization, locality, quantum compatibility, phase structure, tractability, parameter economy, and the capacity to encode and propagate physical information. What the simplest fixed cubic lattice actually demonstrates is more modest than the full hypothesis: its collective-mode dispersion relation yields continuum-like relativistic propagation, with a limiting speed set by microscopic parameters and a calculable Lorentz-violating correction, rather than the emergence of spacetime itself. Taking the lattice spacing at the Planck length, this correction is compared explicitly against current observational bounds on quadratic-order Lorentz violation and…

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