RMB Theory III: A Quantum Field Theory of Inertia with α_RMB = α and Natural Galactic Screening

The RMB Theory III presents a compact quantum field theoretic (QFT) formulation of the Space–Matter–Motion (RMB) framework. In this model, inertia emerges from the dynamics of a spatial field Φμ, and the associated RMB tensor

M^{μν} = ρ v^{μ} v^{ν} + α_RMB F^{μν}

extends the classical inertial term by a field contribution. Using the frequency-charge formalism introduced in earlier RMB work, the coupling α_RMB is identified directly with the fine-structure constant α, without introducing free parameters.

The QFT action includes a nonlinear density-dependent suppression term Z(I), where the field invariant

I = −1/2 F_{μν} F^{μν}

generates strong density-dependent screening of the RMB field. In astrophysical and terrestrial environments the screening reaches:

Z_lab ~ 10⁻⁵²
Z_halo ~ 1

This implies an effective RMB source suppression of more than 50 orders of magnitude between galactic and laboratory environments. This resolves the apparent conflict between strong galactic-scale RMB effects and the absence of laboratory anomalies.

The theory naturally reproduces flat galactic rotation curves without invoking dark matter and contributes only a small, subdominant correction (≈ 2 kHz) to isotope-shift King-plot nonlinearities, consistent with experimental data (O(10⁴) kHz).

Key elements of the work include:

• a parameter-free coupling (α_RMB = α)
• a nonlinear screening mechanism based on Z(I)
• a full RMB tensor structure
• an effective field equation ∇_ν [α_RMB Z(I) F^{νμ}] = J_RMB^μ
• a realistic density contrast (halo vs. laboratory) of ~10²⁴
• an extended scientific outlook: 3+1D formulation, renormalisation flow, cosmological implications

Related Works

This preprint builds directly on earlier RMB foundations:

• RMB Core Theory 2.1: Fundamental Tensor Structure and Frequency Charge
Dellomonaco (2025). Zenodo DOI: 10.5281/zenodo.17805182

• RMB Theory II: Dynamic Field Equations and the Frequency-Charge Formalism
Dellomonaco (2025). Zenodo DOI: 10.5281/zenodo.16568735

These works introduce the tensor definitions, field structure, and frequency-charge coupling that form the basis for the QFT formulation presented here.

Supplementary Material

This Zenodo record includes additional files that complement the main manuscript:

• GIF animation illustrating the density-dependent RMB suppression for halo-to-laboratory density contrasts.
• Python source code (rmb_qft_screening_realistic_gif.py) used to generate the numerical screening plots and the animation.
• PNG version of the screening figure used in the manuscript.

These supplementary materials enhance reproducibility and provide a transparent numerical demonstration of the screening mechanism shown qualitatively in Fig. 1 of the PDF.

Limitations

• Supplementary Material Context:
The GIF animation, Python code, and PNG file are supplementary and not part of the main PDF, which contains only the qualitative version of Fig. 1. This is Zenodo-compliant but readers should note that numerical details appear only in the supplementary files.

• Model Dimensionality:
The current manuscript presents a one-dimensional screening model. Full 3+1D formulations, renormalisation analysis, Bullet Cluster tests, and cosmological-scale simulations are identified as future work and are not included here.

• No speculative elements introduced:
The description strictly follows the scope of the PDF manuscript. No additional claims or interpretations beyond the provided mathematical and numerical content are introduced.

The model expands the RMB framework beyond previous versions and establishes the theoretical foundation for forthcoming 3+1D simulations, renormalisation analyses, and cosmological validation of the RMB field.