Dimensional Collapse Theory and the Law of Transdimensional Thermodynamics

Title: Version 1.0: Foundations and Predictions of Dimensional Collapse TheoryRelease Tag: v1.0 Elevator summary Dimensional Collapse Theory (DCT) proposes that when a covariant entropy density reaches a critical threshold, spacetime locally loses two dimensions and records the lost information on a 2D ledger. This mechanism—formalized via a covariant action and encapsulated in the Law of Transdimensional Thermodynamics—makes concrete, falsifiable predictions for black-hole interiors and observable signatures such as gravitational-wave echoes and modified Hawking flux. Introduction —The "Big Picture" This is the inaugural public release of the manuscript and supporting materials for Dimensional Collapse Theory (DCT). Version 1.0 lays out the foundational framework: the core postulates, the covariant action formulation that dynamically triggers collapse when entropy saturates, and the resulting phenomenology. It develops DCT from first principles, frames its information-theoretic bookkeeping, and explores implications for major puzzles in fundamental physics—black-hole singularities, the information paradox, the emergence of an arrow of time, and dark-sector phenomenology. The local dimensional reduction is supplemented by a proposed microscopic bookkeeping layer (to be pursued in follow-up work) termed Null–Pair Removal (NPR), which provides the mechanism for reversible collapse and recovery of information. What’s included in this release Complete Manuscript (PDF and LaTeX Source): The primary document (manuscript/dct.pdf) presents the theory in self-contained form. It includes the refined definition of the entropy-compression constant , the Law of Transdimensional Thermodynamics governing ledger capacity evolution, and the derivation of the core geometric and information-theoretic structures. Numerical Verification Notebook (scripts/micro_collapse_sim.ipynb): A Jupyter notebook that: Defines and computes all fundamental parameters of DCT in Planck units. Evaluates key black-hole quantities (ledger/core radius, echo delay, luminosity modification, remnant mass). Demonstrates the entropy-triggered collapse via toy simulations, offering intuitive and quantitative checks. Supporting Figures and Generation Scripts: Source material for the figures appearing in the manuscript, enabling replication or adaptation for presentations. Licensing: The manuscript is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). All code and scripts are under the MIT License, encouraging open inspection, reuse, and extension. Key features and predictions of DCT v1.0 Covariant Action Principle: Introduces a dynamical framework in which the reduction activates when a local surface reaches its information capacity, enforcing dimensional collapse in a controlled, covariant fashion. Law of Transdimensional Thermodynamics (TDT): A proposed fundamental law that governs how ledger information capacity increases as dimensions collapse—providing an intrinsic, geometric arrow of time tied to entropy bookkeeping. The αH Constant: A conjectured universal, dimensionless parameter , motivated by holographic tiling and entropy partitioning, which quantifies the split between “pure payload” and collapse metadata. It sets the core-to-horizon ratio and leakage vs. logging fraction in the snap process. Black Hole Interior Structure:Predicts a finite, physical 2D ledger core at , replacing the classical singularity with a finite-information structure, and encoding the collapsed degrees of freedom. Testable, Falsifiable Signatures: Gravitational-wave echoes: A delayed internal reflection signature with a characteristic time Modified Hawking luminosity: A predicted reduction of outgoing flux by relative to the naive Hawking rate due to the entropy bookkeeping split. Planck-mass remnants: Emergence of stable or metastable endpoint objects with mass as dark-matter candidates under the current evaporation and snap assumptions. Current status and roadmap This version rigorously addresses the “what” and “where”: that dimensional collapse occurs, how the ledger encodes the resulting information, and where the collapse surface sits inside black holes. The microscopic “how”—the detailed dynamics of Null–Pair Removal, the correlated probabilities of the four Infinity Bits in realistic backgrounds (spin, tidal bias, branch preparation), and embedding in a full quantum field theory—remains an active direction for future work. Planned next steps include: Developing the NPR microphysics and computing joint Infinity-Bit distributions in Kerr/tidally biased geometries. Detailed modeling of gravitational-wave echo spectra for comparison with LIGO/Virgo/KAGRA data. Exploring ramifications for dark matter phenomenology via remnant abundance and stability. Investigating possible cosmological consequences of rare high-D cascade leaks in early-universe settings. Limitations and assumptions Semi-classical background: current predictions assume a classical spacetime geometry with quantum fields, neglecting backreaction beyond leading order. is presently a motivated conjecture; its fundamental status depends on empirical validation. Remnant stability is model-dependent and assumes no exotic decay channels beyond those currently considered. Feedback and collaboration I welcome critical feedback, suggested improvements, and collaborative engagement. Issues, comments, and proposed extensions can be submitted via the repository; if you’d like deeper engagement or data collaboration, feel free to reach out directly.