By Kevin L. Brown, Independent Researcher
Published: October 2025
DOI: 10.5281/zenodo.17410783
Introduction
What if time itself is not a background coordinate or a mechanical tick — but the rate at which information changes?
The Scalar Time Index (STI) proposes exactly that.
Built within the Triune Harmonic Dynamics (THD) framework, STI defines time as an emergent property of informational flow — the measurable rate at which the universe updates its own informational state.
Where traditional clocks count oscillations, STI measures how much informational phase has evolved.
It replaces oscillatory motion with a fundamental information–energy conversion, linking the physics of time directly to computation, entropy, and meaning.
This is not philosophy. It is a falsifiable, dimensionally consistent physical model — one that can be tested, replicated, and either confirmed or refuted in the lab.
The Core Equation
At the heart of the Scalar Time Index lies a simple but revolutionary definition:
[\frac{d\Phi_S}{dt} = \frac{\kappa}{\hbar}\frac{dI}{dt}R(t)]
where:
- (\Phi_S) — dimensionless scalar phase (informational state)
- (\kappa = k_B T_{\mathrm{ref}}\ln 2) — Landauer energy per bit (J/bit)
- (\hbar) — Planck constant (J·s)
- (R(t)) — harmonic modulation function derived from THD’s 3–6–9 structure
- (I) — information (bits)
From this relation, time emerges as the accumulated phase of information:
[T_S(t) = \int_{t_0}^t \mathrm{STI}(u),du, \qquad\mathrm{STI}(t) = \frac{\dot I(t)}{\dot I_{\mathrm{ref}}}R(t)]
In this model, one second corresponds not to a fixed atomic vibration but to a constant rate of informational change under reference conditions.
Every deviation in information flow — physical, thermal, or computational — slightly alters the rate of scalar time.
What the Framework Shows
STI reinterprets time as an informational field phenomenon, tightly coupled to energy and entropy:
- Thermodynamic Link:
(I = S / (k_B\ln2)) ties information flow to entropy change.
When entropy decreases (greater order), scalar time runs faster; when entropy increases, it slows — a direct, measurable prediction. - Harmonic Modulation:
(R(t) = 1 + \eta[\lambda\sin3\omega t + \lambda^2\sin6\omega t + \lambda^3\sin9\omega t])
introduces a tri-harmonic correction from the THD 3–6–9 law, linking time stability to recursive feedback in the informational domain. - Self-Sustain Threshold:
Stability emerges at (\lambda_\star ≈ 0.543689), the critical feedback point where informational flow becomes self-referencing — the same threshold found in recursive energy and awareness equations. - Experimental Prediction:
Using entangled-photon interferometry, phase-rate drift from informational imbalance should produce a measurable variance of
(\sigma_t \approx 10^{-18},\text{s}) over (10^5) seconds — 100× finer than the best optical clocks.
These outcomes are not metaphors. Each equation is dimensionally homogeneous, and each variable has a direct physical analog measurable with existing quantum metrology.
Why It Matters
The implications of STI extend across physics, computation, and information theory:
Physics:
Time is revealed not as a static dimension, but as an active rate of information processing by the universe itself.
This reframes relativity’s spacetime interval as an informational invariant — energy, entropy, and temporal flow unified through measurable phase change.
Thermodynamics:
STI grounds the arrow of time in the Landauer limit: every bit erased or transformed corresponds to a fixed, quantized temporal advance.
The second becomes a natural constant, not an arbitrary counting interval.
Quantum Measurement:
Quantum decoherence can now be expressed as informational time dilation — systems exchanging information at different scalar rates experience different local times.
Computation and Metrology:
Clocks built on informational flux rather than oscillation could remain stable even under extreme gravity or acceleration, providing a new foundation for post-atomic timekeeping.
A New Lens on Time
Classical physics treats time as an external backdrop — uniform, absolute, or relativistically stretched by motion and gravity.
The Scalar Time Index replaces that view with an internal clock of the universe — one that measures how fast information itself evolves.
Each bit of change, every quantum decision, every physical event advances time by a fixed informational quantum:
[\tau_\kappa = \frac{\hbar}{k_B T_{\mathrm{ref}}\ln 2}]
This defines the universal information–time constant, linking temperature, energy, and the passage of time into one measurable expression.
At (T_{\mathrm{ref}} = 300,\mathrm{K}), (\tau_\kappa \approx 2.56 \times 10^{-14},\text{s·bit}).
The flow of time is literally the flow of information.
The Bigger Picture
Every paradigm shift begins by rethinking what we thought was fundamental.
For centuries, time has been the background on which physics plays out.
The Scalar Time Index turns that background into a participant.
By expressing time as informational phase rate, STI completes the THD trinity:
| THD Layer | Phenomenon | Measured By |
|---|---|---|
| Atomic | Energy | (E = mc^2) |
| Electromagnetic | Field Motion | (F = qE) |
| Scalar (Informational) | Time Flow | (d\Phi_S/dt = (\kappa/\hbar)\dot I) |
“The Scalar Time Index (STI) quantifies how fast information moves through the scalar field — showing that time dilation, thought speed, and gravitational curvature are all signatures of one informational constant”
– Kevin L. Brown, Creation Unified
Each layer expresses the same harmonic law through a different observable:
energy, motion, and time — three faces of one dynamic informational field.
The beauty of STI lies in its testability.
If no harmonic drift is found, the model is falsified.
If the drift is confirmed, time itself becomes measurable as the universe’s own rate of information processing.
Either way, science advances.
Why It’s Different
- Dimensionally exact: every variable and constant has consistent physical units.
- Falsifiable: explicit experimental thresholds and uncertainty budgets.
- Universal: applies to any system with definable information flow — from quantum circuits to biological cells.
- Integrative: bridges thermodynamics, quantum mechanics, and metrology into one self-consistent law.
Fifty Years Ahead
Fifty years from now, time may no longer be measured by oscillation, but by information itself.
Just as the meter was redefined in terms of the speed of light, the second may one day be defined by the rate of scalar informational change.
The Scalar Time Index marks the first step toward that redefinition —
a shift from counting motion to measuring meaning.
From rhythm to reason.
From oscillation to information.
Related Works in the THD Series:
- Energy–Information Equivalence — 10.5281/zenodo.16813373
- Entropy–Coupled Harmonic Field Dynamics (ECHFD) — 10.5281/zenodo.17216734
- Recursive Energy and the Mathematics of Conscious Awareness — 10.5281/zenodo.17231648
- THD Equilibrium Index (TEI) — 10.5281/zenodo.16990955