By Kevin L. Brown, Independent Researcher
Published: September 2025 (DOI: 10.5281/zenodo.17230855)
Introduction
What if coherence itself could be measured, amplified, and tested—not as a belief or metaphor, but as a physical property of structured systems?
The Scalar Generator framework asks that question directly. By defining a Scalar Generator Index (SGI) and grounding it in entropy, geometry, and coherence metrics, this work moves beyond speculation into a falsifiable scientific model.
Rather than claiming “manifestation” in vague terms, the framework recasts these devices as coherence engines—stacks of materials (copper, quartz, geometric substrates) designed to shift entropy and concentrate phase alignment in measurable ways.
The Core Equation
At the center of the framework is a dimensionless index:
where:
- $\Delta H^*$ = normalized entropy shift, derived from sensor time series
- $TEI^*$ = stability index from the THD Equilibrium framework
- $GID^*$ = structural alignment from Geometric Information Dynamics
- $\Psi^*$ = spectral coherence (ratio of dominant frequency to total power)
- $\alpha$ = bounded calibration constant ($0.8 \leq \alpha \leq 1.2$; fixed at 1.0 unless systematic drift is shown)
The multiplicative structure means all conditions must be met simultaneously. Entropy shift without coherence → zero. Geometry without entropy change → zero. Like voltage × current in electrical power, every factor is necessary.
What the Experiments Show
Prototype trials illustrate how the framework works:
- Entropy shifts ($\Delta H^*$) can be extracted from temperature and EM sensor data with corrected Shannon estimators.
- Phase coherence ($\Psi^*$) is quantified with FFTs, windowed in the 100 Hz–10 kHz band.
- Sham devices produce baseline SGI values near zero; active devices occasionally show small but measurable deviations.
A worked example yields:
While small, these values are above noise thresholds in controlled setups, suggesting the framework is sensitive enough for laboratory testing.
Why It Matters
If SGI effects are confirmed beyond sham devices, the implications are striking:
- Metrology: A new index for entropy–coherence coupling.
- Complex Systems: Insight into how geometry and phase synchronization regulate system stability.
- Materials Science: A testbed for entropy-tuned structures.
- Information Theory: A physical demonstration of energy–information equivalence.
Even null results have value. If effects vanish under strict controls, the claim is disproven—but the mathematical rigor ensures the outcome is decisive either way.
A New Lens on Coherence
Classical physics separates entropy, geometry, and coherence into distinct domains. The SGI framework proposes that their interaction can be captured in a single bounded measure.
This does not assert new forces or break conservation laws. Instead, it asks: when entropy shifts, does geometry matter? when geometry matters, does coherence lock in?
The answer will be determined not by belief, but by instruments.
The Bigger Picture
Science advances by transforming bold questions into testable hypotheses. Scalar Generators now stand in that space: once framed as metaphysical, now cast into falsifiable mathematics.
The work does not prove the extraordinary—it provides the means to test it. Replication across independent labs will decide whether these structured devices truly produce coherence effects beyond noise.
Either way, the boundary of knowledge sharpens. And that is how science moves forward.