The universe pays for its own existence.
The receipt is dark energy.

Information Relativity derives the critical density of the universe from three established results — Bekenstein-Hawking entropy, Gibbons-Hawking temperature, and Landauer's principle — with zero free parameters.

$\displaystyle \frac{S \cdot T}{V} = \frac{3H^2 c^2}{8\pi G} = \rho_{\text{crit}}$
The Landauer energy cost of the Hubble horizon's information content, divided by enclosed volume, equals the Friedmann critical density exactly. Only $c$, $G$, and $H$ remain — $\hbar$ and $k_B$ cancel entirely.

The Argument

Every causal horizon carries entropy proportional to its area and radiates at a temperature set by the expansion rate. The energy required to maintain that information — the Landauer cost — is real, gravitating energy. Divide it by the volume the horizon encloses, and you get the critical density that governs cosmic expansion.

This is not a coincidence, an approximation, or a fit. It is an algebraic identity that holds for any value of $H$. Dark energy is the thermodynamic cost of the universe's causal boundary.

What This Completes

Ted Jacobson showed in 1995 that Einstein's field equations emerge from local thermodynamics at causal horizons — heat crossing a horizon is equivalent to spacetime curvature. His derivation leaves the cosmological constant undetermined. Information Relativity supplies the global integral form: $\Lambda = 3H^2/c^2$, fixed exactly. Together, the local differential and global integral forms recover all of general relativity from thermodynamics alone.

Analogous to Maxwell's equations: Jacobson gives the differential form, IR gives the integral form. Neither is complete without the other.


Current Status

The paper "On the Origin of Dark Energy" is in preparation for submission to Foundations of Physics. Interactive walkthroughs, annotated literature, and the derivation chain are available in the Tools and Papers sections.

Papers & Documents

Research documents, annotated literature, and reference materials. Core paper documents listed first, followed by annotated source papers and supporting references.

Core Paper

In Preparation J. Vermeire, 2026 · Target: Foundations of Physics
Derives the Friedmann critical density as the Landauer energy cost of the Hubble horizon's Bekenstein-Hawking entropy at the Gibbons-Hawking temperature. Zero free parameters. Completes Jacobson's 1995 thermodynamic derivation of GR by fixing the cosmological constant.
Working Draft March 30, 2026
Current structural outline — 13 sections, ~8,500 words. Includes the Jacobson connection as climax, DESI equilibrium attractor prediction, and surface energy interpretation.

Two-Column Annotated Papers

Original source text on the left, clear rewrite with IR annotations on the right.

Annotated March 7, 2026
Establishes $S = A / 4\ell_P^2$. The first ingredient in the IR derivation.
Annotated March 7, 2026
Establishes $T = \hbar H / 2\pi k_B$. The second ingredient. Extends Hawking radiation to cosmological horizons.
Annotated March 7, 2026
Derives Einstein's field equations from $\delta Q = T \, dS$ at local causal horizons. IR supplies the global complement: $Q = TS \Rightarrow \Lambda$.
Annotated March 16, 2026
Updates and refines the 1995 thermodynamic gravity program using entanglement entropy.
Annotated March 24, 2026
Established the right scaling $\rho \sim H^2 M_P^2$ but not the exact coefficient, equation of state, or mechanism. IR supplies all three.
Annotated March 16, 2026
Had all three ingredients but embedded them in holographic dark energy with a free parameter $d$. Never computed $ST/V$ directly.
Annotated March 24, 2026
Same three ingredients, per-bit approach using Misner-Sharp energy. Factor-of-2 discrepancy. IR's boundary-only approach ($S \times T$, no bulk energy) gives exact match.
Annotated March 14, 2026
Independent confirmation via Helmholtz free energy and equipartition. Maps the dynamic approach to IR's de Sitter attractor.
Annotated March 14, 2026
Cosmic expansion as the drive toward holographic equipartition of surface and bulk degrees of freedom.
Annotated March 30, 2026
Surface tension of cosmological horizons in de Sitter space.
Annotated 2026
The original paper on the zeta function, annotated for connections to information geometry.

Reference Documents

February 25, 2026
Step-by-step derivation of the Friedmann equations with physical interpretation at every step.
Master reference document
Complete framework reference — rules, mechanisms, translations, appendices. 14,437 lines.

Interactive Tools

Self-contained walkthroughs with MathJax equations, step-by-step derivations, and physical interpretations. Each opens as a standalone page.

Core Derivation Chain

Walkthrough March 19, 2026
The complete derivation path: from a single-bit Szilard engine through Bekenstein-Hawking entropy and Gibbons-Hawking temperature to $\rho_{\text{crit}}$. Every algebraic step shown.
Walkthrough March 12, 2026
The narrative arc of the derivation — how horizon entropy, horizon temperature, and erasure cost combine to produce dark energy.
Walkthrough March 22, 2026
Statistical mechanics foundations — how the partition function connects to the thermodynamic quantities used in the IR derivation.

Surface Energy & Horizon Thermodynamics

Walkthrough March 29, 2026
The dual conjugate pair structure: thermal pair ($T \times S$) and surface pair ($\gamma \times A$) give identical energies. Dark energy is surface energy projected into the bulk volume.
Interactive March 30, 2026
Mapping the constraint relationships between horizon surface tension, Landauer costs, and the Friedmann equations.
Interactive March 30, 2026
The raindrop analogy: single surface, different phases on each side, forms spontaneously. The correct analog for the Hubble horizon — not a soap bubble.
Walkthrough March 30, 2026
How the UV/IR connection manifests as Laplace pressure across the Hubble horizon.
Reference March 14, 2026
The minimum cell of spacetime — Planck area as the fundamental unit of horizon information.

Pedagogy & Visualization

Explainer March 12, 2026
A dialogue-style walkthrough of Jacobson's insight — how heat flux across a causal horizon is equivalent to spacetime curvature.
Walkthrough March 22, 2026
Information erasure as a source of effective viscosity in cosmological dynamics.
Reference March 1, 2026
The holographic principle applied to the IR framework — how boundary information encodes bulk physics.

About

The Researcher

Jeff Vermeire is an independent theoretical physics researcher developing Information Relativity — a framework that derives quantum behavior, gravity, and cosmological phenomena from information-processing principles.

The work began in June 2025, originating from questions about helium-3 spin coherence in polarized target experiments. The central insight — that the Landauer energy cost of maintaining information at a causal horizon exactly produces the observed dark energy density — emerged through six months of systematic development.

The Framework

Information Relativity builds on established physics: Bekenstein-Hawking entropy (1973), Gibbons-Hawking temperature (1977), Landauer's principle (1961), and Jacobson's thermodynamic derivation of gravity (1995). The contribution is recognizing that these four results, combined without additional assumptions or free parameters, produce the Friedmann critical density exactly.

The framework treats the Hubble horizon as a causal thermal one-way membrane. Energy crossing a causal horizon is heat by definition (Jacobson's insight). The total heat content is the Landauer cost of the horizon's information. Dividing by the enclosed volume yields a density — and that density is the critical density that governs cosmic expansion.

Acknowledgments

Brian Mederos (Jefferson Lab) for ongoing discussions on polarized helium-3 experiments and the physical intuitions that seeded the framework.