Time Bubble Nucleation on a Riemannian 3-Manifold: A Speculative Origin Scenario within the Emergent Causal Time Theory

Autor: A. Jaster | Datum: 2026/05/26 | DOI: 10.5281/zenodo.20393270

Abstract

The causal-Machian emergent time theory \citep{Jaster2026a} defines physical proper time through matter and energy in the causal past of each event. For $\Theta=0$ the physical clock metric degenerates exactly to signature $(0,+,+,+)$ -- a purely spatial, timeless structure. This paper explores a speculative consequence: if the universe originated in such a timeless three-dimensional Riemannian manifold without a time direction, the $\Theta$ mechanism itself can account for the emergence of temporal structure. Regions where the smoothed spatial matter connection exceeds the reference level, $r(\vec r)\gtrsim1$, nucleate macroscopic \emph{time bubbles} -- local regions in which the metric signature changes from $(0,+,+,+)$ to $(-,+,+,+)$ and, once a regular Lorentzian sector is established, standard cosmology begins. The substrate is spatially unbounded, causally unordered, and without a time direction. As immediate consequences, the horizon, flatness, and homogeneity problems of standard cosmology are reformulated as properties of the timeless substrate configuration rather than dynamically solved within the Lorentzian phase. Inflation as a dynamical mechanism is not required. The scenario is explicitly speculative and requires a complete quantum gravity treatment for its development.

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