What question did this study set out to answer?

To investigate the implications of information conservation in cosmic evolution through a geometric dynamics lens.

June 23, 2026Open Access

Z-Geometric Dynamics II: Information Conservation and Cosmic Evolution

Key Points

To investigate the implications of information conservation in cosmic evolution through a geometric dynamics lens.
Introduces the axiom of information conservation alongside previous axioms.
Establishes the geometric entropy constant and its implications for the observer's information reception.
Derives self-consistency principles for spatial compression and its effects in a gravitational framework.
Establishes a universal upper bound on observer's information reception as Iobs ≤ Sinfo.
Derives the relationship between geometric entropy constant and fine-structure constant as αEM/α ≈ 32/31.
Confirms that observers measure the same particle horizon radius consistently across their time scales.

Abstract

In the geometric dynamics framework established by Z-Geometric Dynamics (Paper I), the observed particle horizon radius Rp (0) is taken as the fundamental input, from which the background acceleration a0 = c²/Rp (0) is derived, thereby establishing a unified geometric framework for dark matter and dark energy. This paper further explores the origin of this horizon. Starting from quantum mechanical unitarity, we introduce the axiom of information conservation, and together with the initial condition axiom and the maximum entropy hypothesis, define the geometric entropy constant α = 1/π (Ri/lP) ² = 1/ln (Rp/lP), establishing the concept of the information universe as a non-evolving abstract entity. Through a rigorous proof of dimensional reduction equivalence, we establish the universal upper bound Iobs ≤ Sinfo on the observer's information reception, and through dimensional reduction equivalence establish the equivalence relation between the observer's information entropy Iobs = ln (Rp/lP) and the total information entropy of the universe Sinfo. Building on this, the paper further derives the ratio conjecture αEM/α ≈ 32/31 between the geometric entropy constant and the fine-structure constant, laying a numerical anchor for the microscopic unification of Paper III. More importantly, starting from the core conclusions of Paper I—the horizon surface gravity a0 = c²/Rp and the 1/r decay of the gravitational field—and combining them with the standard theory of gravitational compression of spacetime in general relativity, we rigorously derive the self-consistency of spatial compression: any observer in the universe, using their own gravitationally compressed ruler, measures the same particle horizon radius, and this value remains constant in their respective time scales. This mechanism naturally explains the physical origin of the failure of the simultaneous equations at the early singularity, while providing a solid geometric foundation for the information saturation paradigm.

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