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January 20, 20260 citationsOpen Access

Causal Foundations of Relativistic Spacetime: Ontological and Dynamical Constraints on Spacetime Emergence

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RSR. Steinmann

Key Points

  • The study aims to explore how relativistic spacetime can be derived from pre-geometric conditions and constraints.
  • Combined weak ontological requirements with general physical viability constraints.
  • Imposed causal continuity and background independence as pre-geometric conditions.
  • Examined various alternative causal organizations for their viability against imposed requirements.
  • Demonstrated that relativistic spacetime emerges as the simplest causal organization satisfying required conditions.
  • Found that unbounded causality and non-Lorentzian geometries are not viable under the given constraints.
  • Established that the Lorentzian signature and constant c arise as structural conditions rather than assumptions.

Abstract

Relativistic spacetime is usually introduced as a foundational postulate, justified by empirical success rather than derived from more primitive considerations. This status becomes conceptually problematic in cosmological and quantum-gravity contexts where spacetime itself is expected to emerge from non-geometric processes. In such settings, the observed universality of relativistic causality calls for explanation rather than assumption. In this work, we investigate the emergence of relativistic spacetime from a unified framework combining weak ontological requirements with general constraints on physical viability. We show that when causal continuity and background independence are imposed as minimal pre-geometric conditions, and when dynamical stability, mass generation, and interaction consistency are required at the effective level, relativistic spacetime emerges as the simplest causal organization that can simultaneously support dynamical stability and consistent interactions. Our approach is structural rather than model-dependent. We do not derive General Relativity from a specific microscopic theory, nor do we claim formal uniqueness. Instead, we demonstrate that broad classes of alternative causal organizations—such as unbounded causality, sector-dependent propagation bounds, or non-Lorentzian effective geometries— fail to remain viable when the requirements imposed by matter fields and consistent interactions are explicitly accounted for. While our framework shares the foundational emphasis on causal order characteristic of causal-order–based approaches, it adopts a complementary perspective. Rather than taking a discrete causal structure as a primary kinematic postulate, we pursue a structural–dynamical approach, asking which causal architectures can persist once dynamical stability, mass generation, and interaction consistency are required. From this viewpoint, the Lorentzian signature and the universality of the conversion constant c do not enter as assumptions but emerge as structural conditions for a physically viable spacetime manifold, as argued in Sec. IV.E. In this light, relativistic spacetime appears not as a contingent postulate, but as a foundational structure selected by converging requirements of ontological admissibility, dynamical robustness, and interaction coherence.

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Cite This Study

R. Steinmann (2026) studied this question.

synapsesocial.com/papers/696f1a9f9e64f732b51eee6fhttps://doi.org/10.5281/zenodo.18288392
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