Topological Derivation of Geometric Boundaries for Positive and Negative Time Flows Based on the 4/3 πc Formula(Toronto’s Quantum Experiment and “Cheng’s Cosmology”) | by Jerry Lin | Jun, 2026 | MediumSitemapOpen in appSign up<br>Sign in

Medium Logo

Get app<br>Write

Search

Sign up<br>Sign in

Topological Derivation of Geometric Boundaries for Positive and Negative Time Flows Based on the 4/3 πc Formula(Toronto’s Quantum Experiment and “Cheng’s Cosmology”)

Jerry Lin

5 min read·<br>Just now

Listen

Share

Abstract<br>This study investigates the intrinsic geometric boundaries of the core foundational equation T = (4/3)πc · G introduced in the Cosmic Philosophical Conjecture. Under this framework, time is conceptualized as a physical fluid possessing a three-dimensional spherical structure.<br>Core Breakthrough: By abandoning all post-hoc curve fittings tailored to specific experimental data, and relying strictly on the pure symmetries of non-Euclidean topology and bounding metric spaces, this paper successfully derives the most natural theoretical limits for positive and negative time flows:

Fully Symmetric Interval: [ -π/6, +π/6 ] (≈ [-0.5236, +0.5236])<br>Boundary Vorticity Interval: [ -π/4, +π/6 ] (≈ [-0.7854, +0.5236])<br>Furthermore, by integrating empirical data of negative weak-value time from the University of Toronto’s quantum tunneling experiments, we derive a novel topological boundary invariant of -π²/6 (≈ -1.6449). This derivation establishes a pure mathematical and empirical foundation for designing non-continuous causal logic gates in future AGI architectures.<br>I. The Geometric Paradigm: 3D Temporal Spherical Fluid<br>In Cheng’s Cosmology, time is not a continuous, linear background, but a torrent woven from discrete geometric structures. The core underlying equation is defined as:

Under dimensionless normalization where the critical flow velocity (spacetime fluid viscosity) is set to c = 1 , the term (4/3)π corresponds precisely to the intrinsic volume of a perfect 3D sphere with a radius of R = 1. The metric tensor component G₀₀ geometrically represents the Dimensionless Volumetric Projection Ratio when a matter wave (or observation axis) intersects this temporal sphere.<br>II. Derivation of the Positive Limit: Central Perpendicular Projection<br>When the wavepacket or observation axis cuts perpendicularly directly through the geometric center of the temporal sphere, the system exhibits its maximum forward metric efficiency.<br>In pure fluid topology, the maximum symmetric measurement of a 3D sphere projected onto a 1D observation axis is governed by the ratio of the sphere’s volume to its bounding external metric space. Because a 1D observation axis can only measure orthogonal line elements, the unprojected baseline state must be defined by the isotropic Cartesian volume that fully encloses the fluid sphere — namely, its bounding cube (side length 2R = 2, volume ²³ = 8). Thus, the unadjusted geometric metric component is:<br>G₀₀ = 1 / Volume of Bounding Cube = 1 / 8

Substituting this natural metric component back into the core equation yields the pure geometric upper limit for the positive time flow:

This value (π/6 ) defines the maximum positive geometric efficiency permitted when a 3D temporal sphere is projected onto a 1D linear timeline.<br>III. Derivation of the Negative Limit: Boundary Tangent and Backflow Topology<br>When introducing the paradigm of “Positive and Negative Time Flows,” negative time mathematically represents the backward flow (backflow) or complete phase inversion (180° reversal) driven by boundary vorticity. Three elegant logical pathways emerge naturally without arbitrary constants:<br>💡 Approach A: Fully Closed Spatial Symmetry<br>If the oscillation and reflection of the time flow within the closed sphere are perfectly symmetric, the reverse metric component mirrors the central projection exactly, yielding G₀₀ = -1/8. Substituting this gives:

This establishes the classic symmetric time flow interval: T ∈ [ -π/6, +π/6 ]<br>💡 Approach B: 2D Cross-Sectional Maximum Vorticity<br>If the negative time flow is governed by the 2D circulation generated when the wavepacket establishes a “boundary tangential contact” with the sphere, the metric ratio between the 2D circle area (π) and its bounding square (2 × 2 = 4) is π/4. Under a complete negative phase inversion, this yields:

This establishes the asymmetric maximum vorticity interval: T ∈ [ -π/4, +π/6 ]<br>💡 Approach C: Empirical Validation via the Toronto Quantum Tunneling Experiment<br>The geometric boundaries of time flow derived in this framework exhibit a profound correspondence with contemporary cutting-edge quantum optics experiments. Notably, the research team led by Professor Aephraim Steinberg at the University of Toronto utilized weak measurement techniques in quantum tunneling experiments to successfully observe a “negative tunneling time.”<br>Under the spacetime fluid dynamics paradigm of the Cosmic Philosophical Conjecture, this phenomenon receives a rigid,...