A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics

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 defined on a discrete relational network. Under a controlled ordered-regime coarse-graining, the real projection of the tension scales as Phi⁡(theta)=Phi_0*⁡cos⁡(theta), so the Planck mass varies with the phase angle theta and the Einstein-frame canonical scalar becomes varphi=ln⁡[Phi⁡(theta)/Phi_0]. This logarithmic structure emerges naturally from the Weyl map and provides the correct 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, Phi⁡(theta) propto cos⁡(theta), and for the resulting logarithmic Einstein-frame canonical structure.

Featured Image

Photo by Julien L on Unsplash

Photo by Julien L on Unsplash

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