TITLE:
Interference-First Reality Theory: The Variational Principle and Emergent Gravitation—The IFR Action, Field Equations, and Informational Curvature [IFR Theory Series, Part II of VI]
AUTHORS:
Michele Bianchi
KEYWORDS:
Interference-First Reality, Information Geometry, Jensen-Shannon Distance, IFR Action, Fubini-Study Metric, Informational Curvature, Informational Stress Tensor, Emergent Gravitation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
20,
2026
ABSTRACT: This is Part II of the six-part series presenting the Interference-First Reality (IFR) Theory. Part I established the kinematic foundations and the definition of objectivity as stable multi-observer contraction; the present part supplies the dynamical principle. We formulate the IFR action, whose kinetic term is shown to be fixed uniquely by unitary invariance on the projective interference-state space (Fubini-Study form), and whose curvature coupling is fixed in sign and dimensional normalisation by semiclassical matching. The action is defined from the outset as a double integral over the ordering parameter and over a comparison domain
Ω⊂ℳ
equipped with its Riemannian volume measure, whose smoothness, dimension, signature, boundary conditions and topology are stated before any variation is performed. Variation with respect to the interference state, the information geometry and the observer maps yields the interference equation, the informational field equation
G
ij
Γ
=
κ
IFR
T
ij
IFR
, and the observer condition. This part further establishes the conditions under which effective spacetime curvature, and hence Einstein-type gravitational dynamics, emerge from informational curvature.