Structural Emergence Model of Space-Time from $\rho(x)$

This work introduces the fundamental formulation of a new theory of spacetime, based on a structural scalar field $\rho(x)$ whose dynamics determine the very existence of geometry, causality, and physical propagation.

 

In contrast to the traditional paradigm, in which spacetime is treated as a preexisting geometric entity—whether classical or subject to quantization—this work proposes a more radical framework: that the spacetime structure is not fundamental, but emergent from a structural scalar field $\rho(x)$, whose dynamics govern the very possibility of the existence of geometry, causality, and propagation.

 

From this hypothesis, a Lagrangian formalism without an a priori metric is developed, in which gravity appears as an effect derived from the gradients of $\rho(x)$, and matter does not curve spacetime, but rather destructures it. This framework allows us to reinterpret fundamental phenomena—such as quantum collapse, cosmic acceleration, or gravitational singularities—as structural transitions in $\rho$, and proposes a new conception of the absolute vacuum as a real physical limit: a state without space, without time, but structurally definable and quantizable.

 

The model presented here constitutes a coherent, falsifiable, and radically innovative alternative to conventional geometric theories, and lays the groundwork for a complete reconstruction of fundamental physics from first structural principles.