What is it about?

We propose a microphysical completion for the scalar sector of dilatonic gravity by identifying the dilaton with the coarse-grained stiffness mode of a constrained complex tension field carried by a discrete network of Relational Tension Quanta (RTQ). At the microscopic level, these RTQ form a relational graph or hypergraph, with no continuum spacetime metric assumed a priori. Under a controlled ordered-regime coarse-graining, the real projection of the tension scales as Φ(Θ) = Φ₀ cos Θ, so the effective Planck mass varies with the phase angle Θ and the Einstein-frame canonical scalar becomes φ ∝ ln[Φ(Θ)/Φ₀]. This logarithmic structure emerges naturally from the Weyl map and provides the appropriate canonical variable for vacuum models inspired by the Logarithmic Schrödinger Equation (LogSE). We outline how this scalar–tensor interface can satisfy Solar-System constraints through environmental locking and discuss avenues for laboratory and astrophysical tests based on stiffness–coherence coupling. This paper does not introduce a new scalar–tensor EFT class as such; rather, it provides a controlled microphysical origin for a specific scalar stiffness law, Φ(Θ) ∝ cos Θ, and for the resulting logarithmic Einstein-frame canonical structure.

Featured Image

Why is it important?

Scalar-tensor theories and dilaton gravity have traditionally relied on the introduction of scalar fields at the continuum level, often without a clear microscopic origin. This article suggests that the dilaton need not be postulated independently, but may instead emerge as the effective stiffness mode of a constrained complex tension field defined on a discrete relational substrate. In this construction, the real projection of the tension generates the Jordan frame stiffness, while the Einstein frame canonical structure becomes naturally logarithmic once the stiffness is field dependent. This gives a controlled conceptual bridge to LogSE-inspired vacuum models and reframes the scalar sector as an emergent, testable component of a deeper relational dynamics. More broadly, the work points toward a picture in which gravitational rigidity and phase coherence are not separate ingredients, but complementary aspects of a common underlying structure, with possible consequences for screening mechanisms, cosmological anomalies, and laboratory scale probes.

Perspectives

This paper represents an important milestone in the development of a graph-based pre-geometric framework in which spacetime, matter and physical interactions are explored as emergent structures arising from a discrete network of Relational Tension Quanta (RTQ). Our broader goal is to investigate whether ingredients of physics that are usually introduced separately — geometry, matter, coherence and fundamental constants — may instead arise from a more economical relational architecture. This article deliberately tests only one controlled part of that wider program: whether a constrained complex tension field can generate a familiar scalar–tensor/dilaton sector after coarse-graining. We see this bridge as particularly important because it connects a pre-geometric construction to established continuum physics without asking the reader to accept the entire framework at once. Several complementary directions follow from this result. On the observational side, the same logarithmic stiffness framework can be confronted with structured cosmological environments, including the possibility that local variations of effective metric stiffness leave observable signatures in the low-redshift Hubble field. On the more foundational side, the discrete relational construction can be pushed upstream, asking whether a finite pre-geometric grammar can identify a physical branch before electromagnetic, electroweak, gravitational or particle readouts are evaluated, and whether those readouts then emerge as correlated consequences of the same underlying structure. Our longer-term goal is to determine how far this relational grammar can be extended without ad hoc retuning, whether it can connect consistently to additional relativistic and quantum sectors, and above all whether it can generate precise, independently testable predictions. We therefore see this paper not as an endpoint, but as a first controlled interface between established physics and the broader pre-geometric framework we call Meta-Connective Physics (MCP).

Dr Tony Cyril Scott
RWTH-Aachen University

This paper represents an important milestone in the development of a graph-based pre-geometric framework in which spacetime, matter and physical interactions are explored as emergent structures arising from a discrete network of Relational Tension Quanta (RTQ). Our broader goal is to investigate whether ingredients of physics that are usually introduced separately — geometry, matter, coherence and fundamental constants — may instead arise from a more economical relational architecture. This article deliberately tests only one controlled part of that wider program: whether a constrained complex tension field can generate a familiar scalar–tensor/dilaton sector after coarse-graining. We see this bridge as particularly important because it connects a pre-geometric construction to established continuum physics without asking the reader to accept the entire framework at once. Several complementary directions follow from this result. On the observational side, the same logarithmic stiffness framework can be confronted with structured cosmological environments, including the possibility that local variations of effective metric stiffness leave observable signatures in the low-redshift Hubble field. On the more foundational side, the discrete relational construction can be pushed upstream, asking whether a finite pre-geometric grammar can identify a physical branch before electromagnetic, electroweak, gravitational or particle readouts are evaluated, and whether those readouts then emerge as correlated consequences of the same underlying structure. Our longer-term goal is to determine how far this relational grammar can be extended without ad hoc retuning, whether it can connect consistently to additional relativistic and quantum sectors, and above all whether it can generate precise, independently testable predictions. We therefore see this paper not as an endpoint, but as a first controlled interface between established physics and the broader pre-geometric framework we call Meta-Connective Physics (MCP).

Michaël Vaillant

Read the Original

This page is a summary of: A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics, Entropy, May 2026, MDPI AG,
DOI: 10.3390/e28050544.
You can read the full text:

Read

Contributors

The following have contributed to this page