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January 14, 20260 citationsOpen Access

Emergence of Spacetime and Gravitation from Consistency Dynamics of a Pre-Geometric Field

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LSLana SabirovaNSNaelle S`Air

Key Points

  • To develop a pre-geometric framework in which spacetime and causal structures emerge from underlying field dynamics.
  • Proposed a pre-geometric framework based on an underlying field F(x,τ).
  • Established a Consistency Criterion balancing fluctuations and binding response.
  • Analyzed the propagation of perturbations and their effective speed c_eff.
  • Spacetime emerges as a coherent regime of the underlying field.
  • Dynamics match those of Minkowski spacetime under specific conditions.
  • Causal structure is induced by the evolution coordinate τ, aligning with Minkowski metrics.

Abstract

We develop a pre-geometric framework in which relativistic spacetime emerges as the coherent, coarse-grained regime of a single underlying field F (x, τ). In this approach, locality, metric structure, and inertial motion are not assumed a priori but arise from the internal dynamics of F. A central role is played by a Consistency Criterion that balances environmental fluctuations against the intrinsic binding response of the field. When this criterion is satisfied, small perturbations propagate with a uniform effective speed cₑff, and the resulting dynamics become indistinguishable from those of Minkowski spacetime. Lorentz symmetry thus appears as an emergent symmetry of the high-coherence phase of the field. In this setting, the parameter τ functions as an intrinsic evolution coordinate rather than a primitive notion of time. In coherent domains, the monotonic flow of τ induces an emergent causal structure that reduces to the Minkowski metric as a stable phenomenological limit. Spatial variations in the coherence of Fₑnv naturally deform this structure, generating controlled departures from Lorentz invariance without requiring ad hoc modifications of fundamental principles. This framework recovers all experimentally tested predictions of special relativity while embedding them in a more general dynamical theory. It offers a unified perspective in which spacetime geometry, causal structure, and relativistic propagation arise not as fundamental primitives but as phase-dependent features of the underlying field dynamics.

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Cite This Study

Sabirova et al. (2026) studied this question.

synapsesocial.com/papers/6966e72c13bf7a6f02bffaaahttps://doi.org/10.5281/zenodo.18215496
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  1. 1Emergent Relativistic Geometry from Time–Scalar Field Theory2026
  2. 2Causal Foundations of Relativistic Spacetime: Ontological and Dynamical Constraints on Spacetime Emergence2026
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  4. 4Special Relativity as an Emergent Structure in a Timeless Euclidean Model2025
  5. 5Relational Coherence Dynamics and Emergent Geometric Structure: An Exploratory Pre-Geometric Model Toward Spacetime Emergence2026