QM V: Precision Phenomenology and Falsifiable Predictions

Daniel Hilton

Earlier research paper

This paper remains available as part of the development of Phase Differential Theory. The R00–R13 foundational suite provides the current formulation of the theory. Read this paper in its original model and publication context.

Current foundations Research history

Current foundational treatment

Specific claim correctedPrincipal topic: Interactions, matter and refinement.

Proposed phenomenology relates to matter models (R09) and cosmological stress (R11). A testable prediction requires a specified model, calculation and protocol.

Specific qualification: Prediction equations on pages 3 to 4 contain dimensional inconsistencies; the estimates are not established predictions..

A topic connection does not mean that every claim in this paper is retained or that a current paper reproduces its proof.

Author review required

Prediction equations require correction

The prediction equations on pages 3 to 4 contain dimensional inconsistencies. The affected estimates are not established predictions. A corrected, versioned paper is required before those equations can support scientific or experimental claims. The existing PDF remains available as the identified version and has not been silently rewritten.

Earlier PDT papers proposed a coherence floor, a Yukawa-type force signature and photon parity or helicity effects. These proposals are retained in the historical research record, but are not current predictions of the foundational suite. A testable prediction requires a specified physical model, a quantitative calculation and an experimental protocol.

Current context

A present-day website summary. It is not part of the original manuscript.

QM V, in its original form, collected a set of proposed signatures organised around a phase-locking scale, together with numerical estimates for additional scalar states, coupling deviations, gravitational-wave effects and the earlier experimental trio. The prediction equations contain dimensional inconsistencies, so these estimates are not established predictions. They are retained here as part of the historical research record.

Original abstract

Preserved from the original manuscript.

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.

Claims requiring correction

01
Phase-locking scale $\Lambda$ _ $\Phi \approx$ 1.2 TeV. Gauge coupling ratios at this scale: g₃ : g₂ : g₁ $\approx$ 1 : 0.65 : 0.35.
02
Additional scalar states between 300 and 800 GeV. Absence of such states below ∼1 TeV would bear on this model only.
03
Higgs coupling deviations 1–5 %; electroweak shift $\Delta\rho$ ∼ 10⁻³. Agreement with the SM at the 0.1 % level would bear on this model only.
04
Gravitational-wave dispersion 10⁻¹⁵ to 10⁻¹² and interferometric noise $\Delta$ L/L ∼ 10⁻²¹ to 10⁻¹⁸. These estimates require correction before any test.
05
A stochastic gravitational-wave background from early-universe defect networks with $\Omega$ _GW $\approx \Lambda$ _ $\Phi$ / $M_{P}$ 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

\Lambda

_

\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

\Lambda

_

\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/

g_{i}

² =

\int

d³x |

\psi

_i(x)|², where

\psi

_i is the internal defect mode for gauge factor i. At

\Lambda

_

\Phi

the representative ratios are g₃ : g₂ : g₁

\approx

1 : 0.65 : 0.35. RG running reproduces the observed SM hierarchy.

3. Scalar spectrum

m_{n} \approx c_{n} \Lambda

_

\Phi

with c₁

\approx

0.10, c₂

\approx

0.23, c₃

\approx

0.40. Setting m₁ = 125 GeV gives

\Lambda

_

\Phi \approx

1.2 TeV. Higher states: m₂

\approx

290 GeV, m₃

\approx

500 GeV, m₄ ∼ 1–2 TeV.

4. EFT operator basis

Below

\Lambda

_

\Phi

,

L_{eff}

=

L_{SM}

+

\Sigma

(

c_{i}

/

\Lambda

_

\Phi

²)

O_{i}

. Dominant operators include

O_{H}

= (H†H)³,

O_{W}

= (H† W_

\mu\nu

H)²,

O_{B}

= (H† B_

\mu\nu

H)². Coefficients

c_{i}

are generically O(1).

5–6. Higgs coupling and electroweak precision

\delta

g/g

\approx

v²/

\Lambda

_

\Phi

² ∼ 1–5 % for

\Lambda

_

\Phi \approx

1 TeV. Custodial symmetry breaking gives

\Delta\rho \approx

v²/

\Lambda

_

\Phi

² ∼ 10⁻³.

7. Collider predictions

\sigma

(pp

\to

h₂)

\approx

(0.01–0.1)

\sigma

_SM(m₂). Decays h₂

\to

ZZ, WW, hh.

8. Gravitational-wave dispersion

\omega

² = k² (1 + k/

\Lambda

_

\Phi

²) giving

\Delta

v/v ∼ 10⁻¹⁵ to 10⁻¹².

9. Interferometric signatures

\Delta

L/L

\approx

L /

\Lambda

_

\Phi

² ∼ 10⁻²¹ to 10⁻¹⁸.

10. Cosmological signatures

Defect networks formed during early-universe phase locking generate a stochastic GW background with

\Omega

_GW

\approx \Lambda

_

\Phi

/

M_{P}

².

11. Unified prediction summary

- Higgs coupling deviations: 1–5 %. - Additional scalar states: 300–800 GeV. - Electroweak shift:

\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

\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

Graham Fincham, Daniel Hilton. “QM V: Precision Phenomenology and Falsifiable Predictions.” Phase Differential Theory research programme. https://www.phasedifferentialtheory.com/papers/qm-v

@misc{pdt_qm_v,
  title = {QM V: Precision Phenomenology and Falsifiable Predictions},
  author = {Graham Fincham and Daniel Hilton},
  url = {https://www.phasedifferentialtheory.com/papers/qm-v}
}

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