Scale-Invariant Information Thermodynamics Proof

In the paper's words

We derive precise, falsifiable formalisms showing how gravity emerges from scale-invariant information dynamics and how all fundamental forces unify under a single information-theoretic principle. The framework is explicitly falsifiable via observational signatures. Axiom 1 (Local Scale Invariance).

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Each fundamental force corresponds to a symmetry of the information measure $\kappa$: Force Symmetry Group Information Current Field Equation Electromagnetism $U(1)$ $J^\mu_{\text{EM}} = q \bar{\psi} \gamma^\mu \psi$ $\partial_\nu F^{\mu\nu} = \mu_0 J^\mu_{\text{EM}}$ Strong $SU(3)$ $J^{\mu a}_{\text{strong}} = g_s \bar{q} \gamma^\mu T^a q$ $D_\nu G^{\mu\nu a} = J^{\mu a}_{\text{strong}}$ Weak $SU(2)$ $J^{\mu I}_{\text{weak}} = g_w \bar{\psi} \gamma^\mu \tau^I \psi$ $D_\nu W^{\mu\nu I} = J^{\mu I}_{\text{weak}}$ Gravity Diffeomorphism $J^\mu_{\text{grav}} = T^{\mu\nu} u_\nu$ $G_{\mu\nu} = 8\pi G T_{\mu\nu}$ Theorem 1 (Unification via RG Fixed Point).

   from II.

2. Dilaton–Higgs Mixing : - Prediction : Higgs couplings suppressed by $\cos\theta$, with $\sin\theta = \sqrt{\xi_H / (\xi_H + \xi_\sigma)}$. - Test : HL-LHC will measure $\mu_{h\gamma\gamma} = \sigma / \sigma_{\text{SM}}$ to 2% precision. - Falsification : $\mu_{h\gamma\gamma} = 1 \pm 0.02$ rules out significant mixing.

   from III.

3. The total action is: $$ S = \int d^4x \sqrt{-g} \left[ -\alpha C_{\mu\nu\rho\sigma} C^{\mu\nu\rho\sigma} + \mathcal{L}_{\text{GUT}}(H, \psi, A_\mu) + \mathcal{L}_{\text{dilaton}} \right], $$ where $\mathcal{L}_{\text{GUT}}$ is scale-invariant (no $\mu^2$ terms), and $\mathcal{L}_{\text{dilaton}} = \frac{1}{2} (\partial \sigma)^2 - V(\sigma)$ with $V(\sigma) = \lambda \sigma^4$.

   from IV. Mathematical

4. Following Jacobson (1995), but generalized for variable $\kappa$: Energy Flux : For a local Rindler horizon with tangent vector $\xi^\mu$, the energy flux is: $$ \delta Q = \int T_{\mu\nu}^{\text{(matter)}} \xi^\mu d\Sigma^\nu. \tag{3} $$ Temperature : Unruh temperature for acceleration $a = \sqrt{\xi^\mu \xi_\mu} / \delta$ is: $$ T = \frac{\hbar a}{2\pi c k_B}. \tag{4} $$ Entropy Change : From (1), the area change $\delta A$ induces: $$ dS = k_B \kappa \frac{\delta A}{4\ell_P^2} = \frac{k_B c^3 \kappa}{4G\hbar} \delta A. \tag{5} $$ Raychaudhuri Equation : For null geodesics, $\delta A = -\int R_{\mu\nu} \xi^\mu d\Sigma^\nu$ to first order.

   from I.

5. Primordial Gravitational Waves : - Prediction : Scale-invariant initial conditions suppress tensor-to-scalar ratio: $r \lt 0.01$. - Test : CMB-S4 will measure $r$ to $\sigma(r) = 0.001$. - Falsification : $r \gt 0.01$ rules out scale-invariant inflation.

   from III.

How it is done

1. As Scale-Invariant Information Thermodynamics and Unification of Forces Author: Rowan Brad Quni-Gudzinas Affiliation: QNFO Contact: rowan.quni@qnfo.org ORCID: 0009-0002-4317-5604 ISNI: 0000 0005 2645 6062 DOI: https://papers.qnfo.org/papers/scale-invariant-information-thermodynamics-proof/ Publication Date: 2025-09-28 Version: 1.0 We derive precise, falsifiable formalisms showing how gravity emerges from scale-invariant information dynamics and how all fundamental forces unify under a single information-theoretic principle.

   from Gravity

2. Each fundamental force corresponds to a symmetry of the information measure $\kappa$: Force Symmetry Group Information Current Field Equation Electromagnetism $U(1)$ $J^\mu_{\text{EM}} = q \bar{\psi} \gamma^\mu \psi$ $\partial_\nu F^{\mu\nu} = \mu_0 J^\mu_{\text{EM}}$ Strong $SU(3)$ $J^{\mu a}_{\text{strong}} = g_s \bar{q} \gamma^\mu T^a q$ $D_\nu G^{\mu\nu a} = J^{\mu a}_{\text{strong}}$ Weak $SU(2)$ $J^{\mu I}_{\text{weak}} = g_w \bar{\psi} \gamma^\mu \tau^I \psi$ $D_\nu W^{\mu\nu I} = J^{\mu I}_{\text{weak}}$ Gravity Diffeomorphism $J^\mu_{\text{grav}} = T^{\mu\nu} u_\nu$ $G_{\mu\nu} = 8\pi G T_{\mu\nu}$ Theorem 1 (Unification via RG Fixed Point).

   from II.

What would falsify it

1. As Scale-Invariant Information Thermodynamics and Unification of Forces Author: Rowan Brad Quni-Gudzinas Affiliation: QNFO Contact: rowan.quni@qnfo.org ORCID: 0009-0002-4317-5604 ISNI: 0000 0005 2645 6062 DOI: https://papers.qnfo.org/papers/scale-invariant-information-thermodynamics-proof/ Publication Date: 2025-09-28 Version: 1.0 We derive precise, falsifiable formalisms showing how gravity emerges from scale-invariant information dynamics and how all fundamental forces unify under a single information-theoretic principle.

   from Gravity

2. The framework is explicitly falsifiable via observational signatures.

   from Gravity

3. Falsifiability: Concrete Observational Signatures The framework makes quantitative, falsifiable predictions : A.

   from III.

Where the claim stops

1. Assume the Clausius relation $\delta Q = T dS$ holds for all local causal horizons.

   from I.

Where to read

1. I.463 words · 2 min
2. II.312 words · 1 min
3. III.295 words · 1 min
4. IV. Mathematical102 words · 1 min