The Quantum Information Feedback Loop (QIFL): A Mathematical Framework for Dimensional Energy–Information Reciprocity.

Abstract

We formalize the Quantum Information Feedback Loop (QIFL) as a dynamic system describing the reciprocal conversion of energy and information within a single-universe cosmological substrate. Extending prior conceptual work on chaos as a potential first cause, this version introduces coupled differential equations that model oscillatory feedback between energy and informational density. The framework integrates Landauer’s thermodynamic principle, Penrose’s conformal cyclic cosmology (CCC), and black-hole entropy conservation to propose a testable mechanism for dimensional recycling without recourse to multiverse hypotheses. The resulting system predicts oscillatory patterns observable through galactic spin correlations, entropy symmetry in Hawking radiation, and potential spin-state anomalies at high-energy particle scales.

1. Introduction

Arkani-Hamed (2018) proposed that energy observed in particle collisions may arise from “out there,” suggesting an origin beyond the visible spacetime manifold. Rather than invoking multiple universes, we interpret this “out there” as a higher-dimensional informational substrate—a hidden layer from which energy and matter manifest through feedback processes. Building on prior qualitative proposals (Eales, 2025), we formalize the Quantum Information Feedback Loop (QIFL) as a dynamic system coupling thermodynamics, information theory, and cosmological geometry.

2. Mathematical Model

2.1 Energy–Information Coupling

We define two coupled differential equations describing the time evolution of energy density E(t) and information density I(t):dE/dt = -γI + ηE(1 - E/E_c)dI/dt = +δE - λI(1 - I/I_c)where γ and δ represent coupling coefficients (loss and gain), η and λ regulate self-limiting feedback, and E_c and I_c denote critical saturation thresholds. This system is structurally analogous to a Lotka–Volterra oscillator with logistic damping, allowing energy–information equilibrium and cyclical behavior under specific parameter ratios (γδ < ηλ).

2.2 Landauer Bridge

Thermodynamic equivalence between information and energy (Landauer, 1961) provides:ΔE = k_B T ln2 · ΔIlinking changes in information entropy ΔI to corresponding energetic cost ΔE at temperature T. This defines the conversion constant anchoring the QIFL model.

2.3 Black-Hole Feedback Node

The conservation of information across conformal aeons (Penrose, 2018) suggests:dI_substrate/dt = ξ · dS_BH/dtwhere ξ (0 ≤ ξ ≤ 1) denotes recycling efficiency between black-hole entropy (S_BH) and the informational substrate (I_sub). This expresses black holes as feedback engines converting matter–energy into encoded information for re-emergence in successive cosmological cycles.

2.4 Dimensional Projection Operator

Spacetime x^μ is treated as a projection of a higher-dimensional informational manifold Φ^i:x^μ = P^μ_i Φ^iwhere P^μ_i is a conformal projection operator approximated by:P^μ_i = Ω^(-1)δ^μ_iwith Ω representing the conformal scaling factor linking the substrate and observable spacetime (Penrose, 2010). This supports the interpretation of spacetime as an emergent Schlegel projection of an informational geometry.

3. Predictions and Observables

1. Galactic Spin Correlations: Large-scale structure should exhibit coherent spin-alignment beyond ΛCDM predictions, with correlation coefficient deviations proportional to f(γ,δ,λ,η).2. Entropy Symmetry in Hawking Radiation: Radiation spectra from black holes should show partial entropy conservation consistent with ξ ≈ 0.5 ± 0.2.3. High-Energy Spin-State Anomalies: Particle collisions approaching critical energy E_c may display non-random spin misalignments or apparent “energy leaks,” reflecting dimensional coupling thresholds.

4. Discussion

The QIFL framework unifies thermodynamic, quantum, and cosmological processes within a feedback model rather than invoking untestable multiverse scenarios. Chaos—the zero-state of maximal entropy—functions as the initial condition of this loop, embedding mathematical potential that iteratively manifests as order. By framing black holes as information recyclers and spin as the fundamental carrier of information, QIFL bridges quantum and cosmological scales through measurable relationships.

5. Conclusion

QIFL provides a testable model describing energy–information reciprocity as the structural basis of reality. Its mathematical formalization converts the philosophical notion of “chaos as first cause” into a quantifiable feedback system, aligning with empirical frameworks from Landauer thermodynamics to Penrose CCC. Future work should focus on constraining parameters (γ, δ, η, λ, ξ) through cosmological data and developing numerical simulations to test phase stability and oscillation periodicity.

References (APA Style)

·         Arkani-Hamed, N. (2018). Lectures on the future of fundamental physics. Institute for Advanced Study.

·         Eales, S. (2025). Chaos as the First Cause: Rethinking Causality Through the Quantum Information Feedback Loop. OSF Preprint.

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