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QM V

QM V: Precision Phenomenology and Falsifiable Predictions

Graham Fincham, Daniel Hilton

Reader summary

QM V is the scorecard. It collects everything PDT predicts into one place and pins each prediction to a number, an experiment and a sensitivity. The organising quantity is a single scale, Λ\Lambda_Φ\Phi, the phase-locking scale, which sits around 1.2 TeV. From that scale you get the Standard Model gauge coupling ratios, a Higgs at 125 GeV with siblings at 290, 500 and 1 to 2 TeV, Higgs coupling deviations of one to five percent, an electroweak shift around 10⁻³, gravitational-wave dispersion at 10⁻¹⁵ to 10⁻¹², and interferometric coherence noise at 10⁻²¹ to 10⁻¹⁸. The theory stands or falls on those numbers. The paper says so, in plain language.

Abstract

Phase Differential Theory (PDT) proposes that geometry, matter, and interactions emerge from a dynamical phase manifold. This paper develops the precision phenomenology of the framework, deriving testable predictions for gauge couplings, scalar spectra, Higgs coupling deviations, electroweak precision observables, gravitational-wave dispersion, and macroscopic phase-coherence effects. Gauge couplings arise from normalisation integrals over defect-localised currents, yielding representative coupling ratios at the phase-locking scale. Scalar excitations of the defect produce a discrete spectrum, with the lowest mode potentially identifiable with the observed Higgs boson and additional states in the 300 GeV–2 TeV range. Integrating out heavy modes generates a controlled dimension-six operator basis with coefficients of order unity, leading to percent-level Higgs coupling deviations and electroweak corrections near current experimental sensitivity. Long-wavelength phase fluctuations modify gravitational-wave propagation and induce interferometric coherence noise at potentially observable levels. All predictions follow from a low-energy effective-field-theory analysis. Detailed numerical scans and higher-order corrections are deferred to future work.

Falsifiable predictions

  1. 01
    Phase-locking scale Λ\Lambda_Φ≈\Phi \approx 1.2 TeV. Gauge coupling ratios at this scale: g₃ : g₂ : g₁ ≈\approx 1 : 0.65 : 0.35.
  2. 02
    Additional scalar states between 300 and 800 GeV. PDT is falsified if no such states exist below ∼1 TeV.
  3. 03
    Higgs coupling deviations 1–5 %; electroweak shift Δρ\Delta\rho ∼ 10⁻³. Matching the SM at 0.1 % level falsifies the framework.
  4. 04
    Gravitational-wave dispersion 10⁻¹⁵ to 10⁻¹² and interferometric noise Δ\DeltaL/L ∼ 10⁻²¹ to 10⁻¹⁸. Absence of macroscopic coherence effects falsifies the framework.
  5. 05
    A stochastic gravitational-wave background from early-universe defect networks with Ω\Omega_GW ≈Λ\approx \Lambda_Φ\Phi / MPM_{P}².

Full paper

1. Introduction

A viable fundamental framework must not only reproduce known physics but also generate quantitative deviations that can be tested experimentally. PDT proposes a unified microscopic origin for geometry, matter, and interactions, but its physical relevance depends on its phenomenological consequences.

Earlier papers in this series established the emergence of quantum mechanics, particle states, gauge symmetry, scalar structure, and interaction dynamics from a common phase manifold. The present work consolidates these results into a precision-phenomenology framework linking a small number of microscopic parameters to observable effects across multiple experimental domains.

The central organising quantity is the phase-locking scale Λ\Lambda_Φ\Phi, which controls the scalar spectrum, effective-operator coefficients, gauge-coupling normalisation, and macroscopic coherence phenomena. All numerical values presented here should be interpreted as order-of-magnitude EFT estimates dependent on Λ\Lambda_Φ\Phi and stabilisation structure.

Assumptions

- **A1.** EFT truncation. - **A2.** Stable topological defects with well-defined fluctuation spectra. - **A3.** Integrating out heavy modes yields a controlled dimension-six operator basis. - **A4.** Scalar mixing angles remain perturbative. - **A5.** Long-wavelength phase fluctuations persist at observable scales.

2. Gauge coupling relations

Gauge couplings arise from 1/gig_{i}² = ∫\int d³x |ψ\psi_i(x)|², where ψ\psi_i is the internal defect mode for gauge factor i. At Λ\Lambda_Φ\Phi the representative ratios are g₃ : g₂ : g₁ ≈\approx 1 : 0.65 : 0.35. RG running reproduces the observed SM hierarchy.

3. Scalar spectrum

mn≈cnΛm_{n} \approx c_{n} \Lambda_Φ\Phi with c₁ ≈\approx 0.10, c₂ ≈\approx 0.23, c₃ ≈\approx 0.40. Setting m₁ = 125 GeV gives Λ\Lambda_Φ≈\Phi \approx 1.2 TeV. Higher states: m₂ ≈\approx 290 GeV, m₃ ≈\approx 500 GeV, m₄ ∼ 1–2 TeV.

4. EFT operator basis

Below Λ\Lambda_Φ\Phi, LeffL_{eff} = LSML_{SM} + Σ\Sigma (cic_{i} / Λ\Lambda_Φ\Phi²) OiO_{i}. Dominant operators include OHO_{H} = (H†H)³, OWO_{W} = (H† W_μν\mu\nu H)², OBO_{B} = (H† B_μν\mu\nu H)². Coefficients cic_{i} are generically O(1).

5–6. Higgs coupling and electroweak precision

δ\deltag/g ≈\approx v²/Λ\Lambda_Φ\Phi² ∼ 1–5 % for Λ\Lambda_Φ≈\Phi \approx 1 TeV. Custodial symmetry breaking gives Δρ≈\Delta\rho \approx v²/Λ\Lambda_Φ\Phi² ∼ 10⁻³.

7. Collider predictions

σ\sigma(pp →\to h₂) ≈\approx (0.01–0.1) σ\sigma_SM(m₂). Decays h₂ →\to ZZ, WW, hh.

8. Gravitational-wave dispersion

ω\omega² = k² (1 + k/Λ\Lambda_Φ\Phi²) giving Δ\Deltav/v ∼ 10⁻¹⁵ to 10⁻¹².

9. Interferometric signatures

Δ\DeltaL/L ≈\approx L / Λ\Lambda_Φ\Phi² ∼ 10⁻²¹ to 10⁻¹⁸.

10. Cosmological signatures

Defect networks formed during early-universe phase locking generate a stochastic GW background with Ω\Omega_GW ≈Λ\approx \Lambda_Φ\Phi / MPM_{P}².

11. Unified prediction summary

- Higgs coupling deviations: 1–5 %. - Additional scalar states: 300–800 GeV. - Electroweak shift: Δρ\Delta\rho ∼ 10⁻³. - GW dispersion: 10⁻¹⁵ to 10⁻¹². - Interferometric noise: 10⁻²¹ to 10⁻¹⁸.

12. Falsifiability criteria

PDT is falsified if no additional scalars exist below ∼1 TeV, Higgs couplings match the SM at the 0.1 % level, no electroweak deviations at Δρ\Delta\rho ∼ 10⁻³ appear, or no macroscopic coherence effects are observed.

13–14. Limitations and conclusion

Scalar spectrum depends on stabilisation parameters. Gravitational-wave and cosmological predictions are order-of-magnitude. The framework yields a tightly constrained and testable phenomenology.

Suggested citation

@article{fincham_hilton_qm_v,
  author  = {Fincham, Graham and Hilton, Daniel},
  title   = {Phase Differential Theory: Precision Phenomenology and Falsifiable Predictions},
  journal = {Phase Differential Theory Series, QM V},
  year    = {2025}
}