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

What is it about?

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.

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