A Hypothetical Model Based on Complex Energy Probability Distribution: Topological Integration of Five Cosmic Mysteries via Euler's Identity
Year: 2026
Type: article
Abstract: 0. Motivation Modern physics often responds to new anomalies by introducing ad-hoc energies, unknowns, or hypothetical particles, which sometimes increases the overall mystery. This hypothesis proposes a shift: redefining universal energy not as a "geometry of space" or a "simple scalar," but as a single probability density function existing in a complex space. This allows for the integration of multiple cosmological puzzles into a single structural framework. 1. The Core Axiom: The Euler Universe It is hypothesized that all energy in the universe is distributed according to the base of the natural logarithm (𝑒), with its physical state determined by the phase angle (θ). E(θ) = ρ₀ · 𝑒^(𝑖πθ) Component Definitions: · ρ₀: Total energy scale (Real scale). · 𝑒: The natural base of probability distribution, determining the most natural decay/growth ratio of imaginary energy in space. · 𝑖: Imaginary unit, designating energy components orthogonal to real space. · π: The half-period of phase inversion. Per Euler's identity 𝑒^(𝑖π) = -1, it generates the negative state of antimatter. · θ: The phase angle, determining the specific physical state of energy. Phase-based Categorization: · θ = 0 (Result: 1, Real): Observable Matter — Energy anchored to the Real axis (ℝ) via Higgs decay. · θ = 1/2 (Result: 𝑖, Imaginary): Dark Matter / Dark Energy — Energy pushed into the orthogonal imaginary axis; acts as repulsive pressure. · θ = 1 (Result: -1, Negative): Antimatter — Defined as a negative probability state. · θ = 2 (Result: 1, Restoration): Information Conservation — 𝑒^(𝑖2π) = 1; Full recovery of information back to real space. 1-1. Supplemental Explanation on Antimatter (θ = 1) · Observed Antimatter: Antiparticles generated in labs are interpreted as momentary projections of the θ = 1 state into real space at the boundary of the event horizon (θ = 1/2). · Missing Antimatter: The majority of antimatter remains in the θ = 1 imaginary phase space, acting as a "negative probability" (-1) that serves as a destructive interference term in the path integral of real matter. · Connection to Feynman Path Integrals: Negative probability is a concept used in Feynman's path integrals, where negative contributions cancel out certain paths. 2. Mathematical Applications A. Geometric Explanation of Hubble Tension Expansion is the evolution of a complex vector. The discrepancy between early (CMB) and current (SN) measurements arises because observers are anchored to the real axis and only project the real component. ΔH₀ = | 𝑖 · H₀_imaginary | · cosφ · cosφ: The observer's phase projection angle. · Phase 2 Task: Determining the specific functional forms to quantitatively reproduce the ~5.6 km/s/Mpc discrepancy. B. Cosmic Web (Filaments and Voids) The large-scale structure is defined by the interference between real and imaginary parts of the complex energy function E(θ). · ρ_galaxy(x) = |Ψ₀|² · cos²θ(x) · ρ_dark(x) = |Ψ₀|² · sin²θ(x) · ρ_galaxy² + ρ_dark² = |Ψ₀|⁴ = constant C. Hawking Radiation and Information Paradox The Event Horizon is a phase boundary where energy transitions from real space (θ ≈ 0) to imaginary space (θ = 1/2). · Hawking Radiation: Defined as a phase fault phenomenon where extreme phase differences across the boundary create energy density discontinuities (Δρ = 2ρ₀) that eject back into real space. · Information Paradox: Information undergoes a 2π phase rotation. Upon completion, 𝑒^(𝑖2π) = 1, and all information is restored to real space. · New Prediction: Hawking radiation should exhibit a subtle non-blackbody micro-structure based on the θ distribution. 3. Relation to Prior Work · Hawking-Hartle No-Boundary Proposal (1983): Uses imaginary time to remove the singularity. This hypothesis extends this by establishing imaginary energy as an ontological reality. · Antonov’s Hidden Multiverse (2015-): Uses complex numbers to explain dark matter. This hypothesis differs by proposing a single unified complex function E(θ). 4. Conclusion & Future Work By consolidating Matter, Dark Matter, and Dark Energy into a single complex probability distribution, we perceive cosmic phenomena as geometric shadows of the phase angle θ. Current Status: · Phase 1 (Complete): Qualitative re-description and consistency check of physical phenomena. · Phase 2 (In Progress): Formalization of ε(t) and quantitative derivation of cosφ. Phase 3 (Target): Quantitative prediction of non-blackbody micro-structures in Hawking radiation.
Author: Yu, Sujeong
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7135245374
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