UNIFICATION I — Phase Structure and the Lightlike Boundary
Description
This work is the first technical extension of the UNIFICATION framework and develops a phase-based structural interpretation of the shared lightlike boundary between relativistic and quantum descriptions.
In UNIFICATION 0, the framework introduced the idea that relativistic and quantum expressions converge at a common invariant lightlike boundary, characterized by the relations E = pc and ω = kc. The present paper expands that foundation by introducing a phase structure intended to organize familiar relativistic and quantum behavior in a unified way.
A central contribution of this work is the introduction of the phase ratio χϕ = ωext / ωint, which compares externally expressed phase propagation to internally associated phase evolution. Under a natural relativistic identification, this phase ratio is shown to correspond to the Lorentz factor:
χϕ = γ
This provides an interpretive connection between relativistic time dilation, phase amplification, and the approach to the lightlike boundary.
The paper further explores the structural role of the dimensionless boundary parameter:
χ = v/c = pc/E = kc/ω
and the corresponding deviation parameter:
δ = 1 − χ²
showing how they organize several familiar relativistic quantities, including the Lorentz factor, proper time, and limiting boundary behavior.
The results are structural and interpretive rather than dynamical. No new equations of motion are introduced, and no modification of established relativistic or quantum theory is claimed. The contribution of this paper is to suggest that relativistic time dilation and related effects may be understood through a shared phase structure governed by proximity to a common invariant boundary.
This paper is the second work in the UNIFICATION series. Subsequent papers explore coupled limiting behavior, geometric interpretation, and candidate governing equations.
Currently Available:
UNIFICATION 0 - A Shared Lightlike Boundary for Relativity and Quantum Theory - v1.00
https://doi.org/10.5281/zenodo.19860494
UNIFICATION I - Phase Structure and the Lightlike Boundary - v1.00
https://doi.org/10.5281/zenodo.19862660
UNIFICATION II - Implications of the Lightlike Boundary and Phase Structure - v1.00
https://doi.org/10.5281/zenodo.19863301
UNIFICATION III - Toward a Dynamical Formulation of the Lightlike Boundary Framework - v1.00
https://doi.org/10.5281/zenodo.19895578
UNIFICATION IV - Consequences and Implications of the Chi Framework - v1.00
https://doi.org/10.5281/zenodo.19896296
UNIFICATION V - Concerning the Current Absence of a Governing Equation for the Chi Framework - v1.00
https://doi.org/10.5281/zenodo.19921182
UNIFICATION VI: The Chi Boundary Method and Structural Invariants - v1.00
https://doi.org/10.5281/zenodo.19925550
UNIFICATION VII - A BOUNDED UNIVERSE 0 - Reciprocal Boundary Structure and the Reinterpretation of Zero and Infinity
https://doi.org/10.5281/zenodo.20090590
UNIFICATION VIII - A BOUNDED UNIVERSE I - Math of Counting vs a New Zed/Irony Math - v1.01
https://doi.org/10.5281/zenodo.20128424
UNIFICATION IX - A BOUNDED UNIVERSE II - Toward a Bounded Interpretation of Relativistic Extremes - v1.00
https://doi.org/10.5281/zenodo.20160715
UNIFICATION X - A BOUNDED UNIVERSE III - Reciprocal Discernment and the Quantum Boundary - v1.00
https://doi.org/10.5281/zenodo.20171582
UNIFICATION - The Chi Framework - Eight Lessons on the Boundary Between Relativity and Quantum Mechanics - v1.00
https://doi.org/10.5281/zenodo.19863601
A public project archive containing all PDFs in the UNIFICATION series is also available through the Open Science Framework (OSF):
UNIFICATION SERIES: https://osf.io/mpvgj/files/osfstorage/
Files
UNIFICATION_I_Phase_Structure_v1.00.pdf
Additional details
Dates
- Copyrighted
-
2026-04-28Version 1.00 of UNIFICATION I