https://github.com/JuanHuaXu/OTR/blob/main/OTR.md

Foundations and Derivation of Omega Time Rotation (OTR)

Author: Juan Hua Xu Affiliation: Independent Researcher Date: June 2025

Abstract

This paper presents the chronological reasoning, theoretical motivation, and mathematical derivation of Omega Time Rotation (OTR), a framework proposing that spacetime curvature and gravity arise from fermionic exclusion-induced temporal gradients. By extending symbolic reasoning into physical geometry, we demonstrate how exclusion structures induce anisotropic time slicing, generating curvature consistent with general relativity. This manuscript formalizes the evolution of OTR from conceptual insight to mathematical formulation and establishes the groundwork for its integration into broader quantum geometric frameworks.

1. Motivation and Initial Observations

The core motivation of OTR arose from the mismatch between quantum field theory and general relativity in describing the origin of curvature and the passage of time. Traditional GR treats time as an input, while quantum systems define time relationally. The paradox deepens around black holes, where time becomes spacelike, and within fermionic systems, where the Pauli exclusion principle introduces persistent structure.

Initial insight (March 2025): Time may be emergent from fermionic exclusion.

Observational support:

Strong gravitational effects localize around high fermion density.
Temporal dilation is observable in exclusion-dense environments (e.g., neutron stars).
Anisotropies in time alignment (symbolic curvature gradients) appear to be linked with gravitational structure.

2. Symbolic Exclusion as the Root of Curvature

We posit a symbolic exclusion field, $N(x)$, representing the density of frozen fermionic states at location $x$. This exclusion field is not energetic but symbolic: a record of forbidden states that geometrically induces anisotropy in time slicing.

Postulate:

The exclusion field $N(x)$ modulates the local rate of proper time.

This leads to the omega rotation hypothesis:

As $N(x)$ increases, the local time axis rotates away from the global frame, creating effective curvature.