Chapter 26: Experimental Protocols and Validation Pathways

Falsifiable predictions across gravitational waves, resonance, colliders, and cosmology
By John Foster | December 12, 2025 | Independent Researcher, Dimensional Relativity Project

Abstract

This chapter outlines rigorous, falsifiable experimental protocols designed to test core predictions of Dimensional Relativity. Unlike purely theoretical frameworks, DR makes specific, measurable deviations from standard general relativity and quantum field theory in higher-curvature regimes, resonance-mediated effects, and compact-dimensional signatures. Four independent observational channels are developed, each with a stated null result that would falsify the framework.

Keywords: falsifiability · gravitational wave sidebands · Kaluza-Klein excitations · dijet resonance · Hubble evolution · resonance protocols

Chapter Contents

26.1 Introduction

A framework that cannot fail is not a theory. The purpose of this chapter is to state, in advance and in measurable terms, what Dimensional Relativity requires of the world—and what observation would rule it out. DR makes specific deviations from general relativity and quantum field theory in three regimes: higher curvature, resonance-mediated coupling, and compact-dimensional structure. Each of the four protocols below isolates one of those regimes in an experiment that is either already running or buildable with current instrumentation.

The common thread is the compactification radius Rc ≈ 10-18 m. That single parameter fixes the Kaluza-Klein tower fn = n / Rc, which in turn sets the gravitational wave sideband spacing, the collider resonance mass, and the extra-dimensional energy density that modifies early expansion history. The protocols are therefore not independent fits—they are four measurements of the same number, and disagreement between them is itself a falsification.

26.2 Gravitational Wave Signature Modifications

DR predicts subtle oscillatory modulations in gravitational wave waveforms, arising from Kaluza-Klein-like excitations in the compact dimensions. The observable is not a change in the overall chirp but a set of sidebands riding on it.

Equation 26.1 — Modulated Waveform

h(t) = hGR(t) × [ 1 + Σn εn cos(2πfnt + φn) ]
fn = n / Rc,   Rc ≈ 10-18 m

yields sidebands in the kHz range | εn modulation depth per mode | φn mode phase

The protocol is a targeted reanalysis of existing binary merger events rather than a new instrument. Because the sidebands are coherent with the carrier, matched filtering against a modulated template bank recovers them at signal-to-noise well below the level at which they would appear in an unmodelled search. The kHz placement puts them in the band where detector sensitivity is already well characterized, so a null result sets a real upper bound on εn rather than an ambiguous one.

Figure 26.1 — Predicted GW template comparison: GR waveform against the DR-modulated waveform, with a sideband residual growing toward merger.
Figure 26.1 — Predicted GW template comparison. Standard GR waveform for a binary merger against the DR-predicted modulated waveform; the residual panel isolates the sideband structure that matched filtering targets, with amplitude growing toward merger as curvature rises.

26.3 Resonance Protocol

Precision acoustic and electromagnetic fields tuned to golden-ratio harmonics of the 11D metric frequencies are predicted to enhance coherence in structured matter. The frequency cascade is fully determined—there is no free parameter to tune after the fact.

Equation 26.2 — Golden-Ratio Frequency Cascade

fres = (φn / √5) × f0,   n = 1, 2, 3 …

φ = (1 + √5)/2 | cascade spans 100 Hz to 10 kHz | f0 fixed by the 11D metric, not fitted

The falsifiable content is the spacing, not the effect. A response that peaks at arbitrary frequencies, or scales with applied power rather than with proximity to a cascade line, is indistinguishable from ordinary driven resonance in the apparatus and counts against DR. The protocol therefore requires the full cascade to be scanned, with off-line control frequencies interleaved and the operator blind to which is which.

Figure 26.2 — Frequency cascade spectrum: golden-ratio scaled resonance lines from 100 Hz to 10 kHz with geometric spacing.
Figure 26.2 — Frequency cascade spectrum. Golden-ratio scaled resonance lines from 100 Hz to 10 kHz; spacing is geometric in φ, so the cascade is identifiable from any three consecutive lines regardless of where f0 sits.

Scope and Safety Constraint

The cascade prediction is a physical claim about coupling, not a validated therapeutic protocol. Any work involving biological systems belongs in bench and cell-culture assays first, under institutional review, with pre-registered endpoints and sham-exposure controls. No clinical claim is made or supported here, and none should be drawn from a positive coherence measurement alone.

26.4 Compact Dimension Leakage in Particle Colliders

Excess dijet events are predicted at invariant masses corresponding to the 1/Rc scale. This is the cleanest of the four tests: the signal is a localized bump on a smooth, well-measured background, and its position is fixed by the same Rc that sets the gravitational wave sideband spacing.

The Standard Model dijet spectrum falls monotonically over orders of magnitude, so a resonance is detectable well below the level of any inclusive cross-section anomaly. Existing LHC datasets already cover the relevant mass range; the protocol is a dedicated search with the peak position fixed in advance by the GW analysis rather than floated as a fit parameter. A bump at a mass inconsistent with the GW-derived Rc would falsify the framework as decisively as no bump at all.

Figure 26.3 — Predicted dijet excess: a DR resonance peak above the falling Standard Model background, with the ratio panel showing a localized departure from unity.
Figure 26.3 — Predicted dijet excess. Simulated invariant mass distribution showing the DR resonance peak above the falling Standard Model background; the lower panel gives the ratio to background, where the excess is a localized departure from unity at 1/Rc.

26.5 Cosmological Implications and Observables

DR predicts a modified expansion history in the early universe, driven by extra-dimensional energy density. The deviation from ΛCDM grows with redshift, which is what makes it testable: at low z the two models are degenerate within current uncertainties, and the discriminating power sits at z ≳ 2 where the extra-dimensional contribution to H(z) becomes an appreciable fraction of the total.

The relevant observables are therefore high-redshift standard candles and rulers, quasar and Lyman-α measurements of the expansion rate, and the CMB-calibrated sound horizon. A DR signature appears as a coherent tilt in H(z) rather than a shift in a single parameter—which distinguishes it from the ordinary tensions in the low-redshift value of the Hubble constant, and means it cannot be absorbed by rescaling H0.

Figure 26.4 — Hubble parameter evolution: H(z) in DR against LambdaCDM, agreeing at low redshift and diverging beyond z = 2.
Figure 26.4 — Hubble parameter evolution. H(z) in DR against standard ΛCDM; the models agree in the low-redshift regime covered by current supernova samples and diverge measurably beyond z ≈ 2, where the extra-dimensional energy density contributes.

26.6 Conclusion and Next Steps

  • One parameter, four channels: Rc ≈ 10-18 m fixes sideband spacing, resonance mass, and early expansion history simultaneously
  • No new instruments required: three of the four tests are reanalyses of existing LIGO, LHC, and cosmological datasets
  • Stated null results: absent sidebands, an off-mass bump, or a ΛCDM-consistent H(z) at high z each falsify the framework
  • Cross-consistency as a test: the four channels measure the same Rc, so mutual disagreement falsifies DR even where individual signals appear

These protocols provide clear pathways for empirical validation or falsification of Dimensional Relativity. The immediate next step is not new theory but collaboration: targeted template-bank reanalysis with gravitational wave groups, a fixed-mass dijet search with collider collaborations, and bench-level resonance work under institutional review. Each can begin with data that already exists.

Collaboration Invited

LIGO
Modulated template bank applied to catalogued binary merger events; deliverable is a bound on εn.
LHC
Dijet resonance search with mass fixed a priori by the GW-derived Rc.
Cosmology
Joint high-redshift H(z) fit testing for coherent tilt rather than a shifted H0.
Resonance
Blinded cascade scans with interleaved off-line controls, bench and cell-culture only.