Informational Time Index (ITI): A Dimensionally Consistent Framework for Time as Informational Phase Rate

Kevin L. Brown, Independent Researcher
October 2025
DOI: 10.5281/zenodo.17410783

Informational Physics Ontology Paper

Abstract

This paper introduces the Scalar Time Index (ITI) — a falsifiable, dimensionally consistent framework that defines time as the rate of informational phase change within the Triune Harmonic Dynamics (THD) formalism.

Conventional clocks measure time through periodic motion—pendulums, resonators, or atomic transitions. The ITI replaces oscillatory recurrence with a direct informational metric derived from the rate of scalar-phase evolution, converting bits and joules to seconds through universal physical constants.

By anchoring temporal flow in the Landauer energy limit and Planck’s constant, the ITI establishes an unambiguous link between information processing, entropy, and time measurement. This formulation enables the creation of scalar-referenced clocks whose stability potentially surpasses atomic and optical standards by two orders of magnitude.

Core Definition

Time is defined as a phase-integrated informational rate:

dΦSdt=κℏdIdtR(t),STI(t)=I˙(t)I˙refR(t),\frac{d\Phi_S}{dt}=\frac{\kappa}{\hbar}\frac{dI}{dt}R(t), \qquad \mathrm{STI}(t)=\frac{\dot I(t)}{\dot I_{\mathrm{ref}}}R(t),dtdΦS=ℏκdtdIR(t),STI(t)=I˙refI˙(t)R(t),

where:

• ΦS\Phi_SΦS — dimensionless scalar phase

• κ=kBTrefln⁡2\kappa = k_B T_{\mathrm{ref}}\ln 2κ=kBTrefln2 — Landauer constant (J/bit)

• τκ=ℏ/κ\tau_\kappa = \hbar / \kappaτκ=ℏ/κ — information–time constant (s·bit)

• R(t)R(t)R(t) — bounded tri-harmonic modulation function derived from THD

• I˙=dI/dt\dot I = dI/dtI˙=dI/dt — information flux (bits·s−1^{-1}−1)

Time in this model is the accumulated informational phase, integrated through a dimensionless rate multiplier:

TS(t)=∫t0tSTI(u) du.T_S(t) = \int_{t_0}^t \mathrm{STI}(u)\,du.TS(t)=∫t0tSTI(u)du.

This construction ensures full dimensional consistency: [STI]=1[\mathrm{STI}] = 1[STI]=1, [TS]=s[T_S] = \mathrm{s}[TS]=s.

Key Contributions

1. Dimensional Consistency Across Information–Energy–Time
Eliminates the prior ambiguity between energy per bit (J/bit) and time (s) by introducing the invariant conversion constant
τκ=ℏ/(kBTrefln⁡2)\tau_\kappa = \hbar / (k_B T_{\mathrm{ref}}\ln 2)τκ=ℏ/(kBTrefln2).

2. Informational Timekeeping Model
Defines time as the rate of informational evolution rather than physical oscillation. This enables measurement in systems where no mechanical or atomic oscillator exists.

3. Triune Harmonic Modulation Law
Implements the THD 3–6–9 harmonic structure as a dimensionless modulation term:

R(t)=1+η[λsin⁡3ωt+λ2sin⁡6ωt+λ3sin⁡9ωt],R(t)=1+\eta[\lambda\sin3\omega t+\lambda^2\sin6\omega t+\lambda^3\sin9\omega t],R(t)=1+η[λsin3ωt+λ2sin6ωt+λ3sin9ωt],

linking temporal drift to recursive information flow.

4. Self-Sustain Threshold
Establishes the scalar stability limit λ⋆≈0.543689\lambda_\star \approx 0.543689λ⋆≈0.543689,
analogous to the Barkhausen boundary in feedback theory, identifying the threshold for steady informational timing.

5. Phase-Rate Interferometry Protocol
Proposes a falsifiable experimental design: twin entangled-photon ensembles measure scalar phase drift arising from differential information flux. Predicted time variance: σt≈10−18 s \sigma_t \approx 10^{-18}\,\mathrm{s}σt≈10−18s over 105^55 s integration—100× finer than optical lattice clocks.

6. Scalar Second Definition
Operationalizes a scalar-referenced second:

1 sS= ⁣∫tt+1 sUTC ⁣ ⁣ ⁣STI(u) du,1~\mathrm{s_S}=\!\int_{t}^{t+1~\mathrm{s_{UTC}}}\!\!\!\mathrm{STI}(u)\,du,1 sS=∫tt+1 sUTCSTI(u)du,

maintaining UTC alignment while allowing scalar deviations under informational modulation.

Falsification and Experimental Design

Falsification Criteria

1. Under reference conditions (η ⁣→ ⁣0,I˙=I˙ref\eta\!\to\!0, \dot I=\dot I_{\mathrm{ref}}η→0,I˙=I˙ref), measured STI≠1\mathrm{STI}\neq1STI=1 beyond the combined uncertainty budget.

2. No detectable 3–6–9 harmonic structure in phase spectra under controlled η>0\eta>0η>0.

3. Variation in TrefT_{\mathrm{ref}}Tref fails to scale τκ\tau_\kappaτκ linearly, violating τκ=ℏ/κ\tau_\kappa=\hbar/\kappaτκ=ℏ/κ.

Uncertainty Model

uSTI=uϕ2+(uI˙/I˙)2+(uT/T)2+uenv2,u_{\mathrm{STI}} = \sqrt{u_\phi^2+(u_{\dot I}/\dot I)^2+(u_T/T)^2+u_{\mathrm{env}}^2},uSTI=uϕ2+(uI˙/I˙)2+(uT/T)2+uenv2,

where terms represent phase readout noise, flux stability, temperature control, and environmental bias.

Replication Pathways

• Scalar interferometry using synchronized logic streams at I˙=1010\dot I=10^{10}I˙=1010 bits/s.

• Thermal scaling validation by varying TrefT_{\mathrm{ref}}Tref 290–310 K.

• Frequency-domain analysis for 3–6–9 harmonics.

Scientific Significance

The Informational Time Index provides the first falsifiable, physics-consistent model of time emerging directly from information flow. It unifies thermodynamics, quantum measurement, and information theory under a single scalar law:

Time=Information Change×(Energy–Planck Ratio).\text{Time} = \text{Information Change} \times \text{(Energy–Planck Ratio)}.Time=Information Change×(Energy–Planck Ratio).

By grounding temporal measurement in information rather than motion, STI bridges the gap between thermodynamic irreversibility, entropy flow, and relativistic time dilation. It opens experimental pathways to a post-oscillatory metrology, where clocks become informational phase monitors rather than resonant oscillators.

Validation Pathways

• Laboratory Replication:
  Implementation via entangled-photon interferometers and information-rate-locked control channels.

• Cross-Laboratory Comparison:
  Verify reproducibility of scalar drift at 3, 6, 9 × ω frequencies.

• Temperature Scaling Test:
  Confirm linear relationship between τκ\tau_\kappaτκ and Tref−1T_{\mathrm{ref}}^{-1}Tref−1.

• Public Data Challenge:
  Open dataset release through CreationUnified.com enabling independent falsification.

Supplemental Reviewer Guidance

Evaluation Criteria

• Dimensional homogeneity across all equations

• Clarity of the τκ\tau_\kappaτκ constant as a universal conversion factor

• Replicability of interferometric falsification

• Soundness of thermodynamic and information-theoretic derivations

• Alignment with established THD framework (3–6–9 harmonic law)

Reviewer Deliverables
Provide quantitative assessments (0–100 %) for:

• Mathematical rigor and internal consistency

• Dimensional correctness and physical plausibility

• Falsifiability and reproducibility

• Experimental clarity and potential for validation

and confirm whether the Informational Time Index constitutes a falsifiable, physics-consistent extension of THD unification.

Keywords: Time Index, informational phase rate, Triune Harmonic Dynamics, informational timekeeping, Landauer limit, Planck constant, entropy flow, phase-rate interferometry, falsifiability, post-oscillatory metrology, quantum–thermodynamic unification.