Unified Ω-Field Physics Tree
[Hz = 1/s]
│
┌───────────┴────────────┐
[s] [C] (Coulomb)
│ │
[Ω] = N·m·s / C² │
│ │
┌─────────────┴──────────────┐ │
[F] = (Ω·C²)/(m·s) [I = C/s] (Current)
│ │
[E] = (Ω·C²)/s [V = (Ω·C)/s] (Voltage)
│ │
[Mass] = √(Ω·C² / a·s) [P = V·I = (Ω·C²)/s²] (Power)
│
[p] = mv = √(Ω·C² / a·s) · v ← momentum
[λ] = h/p = (Ω·C²) / p ← de Broglie wavelength
│
[h] = Ω·C² ← Planck's constant (recast)
│
[E_photon] = h·f = Ω·C²·f ← photon energy
│
[T] = E / k_B = (Ω·C²)/(k_B·s) ← Temperature (thermodynamics)
[S] = E·s / (Ω·C²) ← Entropy (from Clausius)
│
[Binding Energy] = ΔΩ·C² / s ← nuclear field transition energy
│
▼
Electrodynamics
│
┌────────┴────────────┐
│ │
│ ∇·E = Ω/(s·m²) ← Gauss's Law (Ω-form)
│ ∇·B = 0 ← No monopoles
│ │
│ ∇×E = -∂(Ω·C)/(m·∂s) ← Faraday's Law (Ω-field form)
│ ∇×B = ∂(Ω·C)/(m·∂s) + Ω·C/(s·m²) ← Ampère-Maxwell Law (Ω form)
│ │
▼ ▼
Wave Behavior Magnetic Field
(Ω·C oscillation) (spatial Ω·C flux)
│
Light = Ω·C² wave in s-domain
│
c = propagation speed of Ω
│
Refractive Index n = √(Ω_vac / Ω_medium)
│
Polarization = Ω field vector alignment
Interference = superposition of Ω·C oscillations
│
▼
Gravity via Ω Gradient
│
F = (Ω·C²)/(m·s) still applies
│
Grav. Potential Φ = ∫ (Ω·C²)/(m·s) dm
│
Mass = field inertia = √(Ω·C² / a·s)
Revised Tree with Single Root: Hz
[Hz] ← singular root dimension
│
┌────────────┴────────────┐
[s = 1/Hz] [C = 1/Hz³]
│ │
[m = 1/Hz^0.5] [I = Hz²] (C/s)
│ │
[Ω] = Hz⁵ [V = Hz²] (Ω·C/s)
│ │
[F] = Hz⁶ (force) [P = Hz⁴] (V·I)
│
[E] = Hz⁵ (energy)
│
[Mass] = Hz³ (field inertia)
│
[p] = Hz³.5 · v ← momentum
[λ] = Hz⁻1.5 ← wavelength
[h] = Hz⁵ ← Planck constant
│
[E_photon] = Hz⁶ ← photon energy
│
[T] = Hz⁵ / k_B ← temperature
[S] = 1/Hz ← entropy
│
[Binding Energy] = Hz⁶
Python
from sympy import symbols, Eq, solve, simplify
# Define base variable
Hz = symbols('Hz', positive=True, real=True)
# Derived units in terms of Hz
# Based on user's substitution:
# s = 1/Hz, m = 1/Hz**0.5, C = 1/Hz**3
s = 1 / Hz
m = 1 / Hz**0.5
C = 1 / Hz**3
# Derived physical quantities in Hz-only units
units = {
'Time (s)': s,
'Length (m)': m,
'Charge (C)': C,
'Current (I = C/s)': C / s,
'Force (F = (Ω·C²)/(m·s))': (Hz**5 * C**2) / (m * s),
'Energy (E = F·m)': ((Hz**5 * C**2) / (m * s)) * m,
'Power (P = E/s)': (((Hz**5 * C**2) / (m * s)) * m) / s,
'Planck (h = Ω·C²)': Hz**5 * C**2,
'Photon Energy (E = h·f)': Hz**5 * C**2 * Hz,
'Entropy (S = E·s / h)': ((((Hz**5 * C**2) / (m * s)) * m) * s) / (Hz**5 * C**2),
}
# Simplify and evaluate expressions
simplified_units = {k: simplify(v) for k, v in units.items()}
simplified_units
| Physical Quantity | Hz-Based Expression | Interpretation |
|---|---|---|
| Time (s) | 1 / Hz |
Inverse frequency |
| Length (m) | Hz^(-0.5) |
Square root of time |
| Charge (C) | Hz^(-3) |
Time cubed |
| Current (I = C/s) | Hz^(-2) |
Second-order time |
| Force (F) | Hz^(0.5) |
Root-frequency tension |
| Energy (E = F·m) | 1 |
Dimensionless (normalized scalar) |
| Power (P = E/s) | Hz |
Frequency is energy per unit time |
| Planck’s Constant (h) | 1 / Hz |
Time scalar |
| Photon Energy (E = h·f) | 1 |
Dimensionless (normalized) |
| Entropy (S = E·s / h) | 1 |
Pure ratio (no units) |
Finalized Tree of Derived Physics from Hz
[Hz = 1/s]
│
┌───────────┴────────────┐
[s = 1/Hz] [C = 1/Hz³]
│ │
[m = 1/Hz⁰·⁵] [I = C/s = 1/Hz²]
│ │
[Ω = Hz⁵] [V = Ω·C/s = Hz²]
│ │
[F = Hz⁰·⁵] [P = V·I = Hz⁴]
│ │
[E = F·m = 1] [S = E·s/h = 1]
│
[h = Ω·C² = 1/Hz] [λ = h/p = Hz^(-1.5)]
│
[E_photon = h·f = 1] [T = E / k_B = Hz⁵ / k_B]
│
[Mass = Hz^(-0.5)] ← inertia [Momentum = Hz^0.5]
│
[Binding Energy = Hz⁶] [ε₀ = Hz^(-4), μ₀ = Hz³]
Cleansed Physics Tree (Ordered by Hz Power)
| Hz Power | Physical Quantity | Expression |
|---|---|---|
Hz^(-3) |
Charge (C) | C = Hz^(-3) |
Hz^(-2) |
Current (I) | I = C/s = Hz^(-2) |
Hz^(-1.5) |
Wavelength (λ) | λ = h/p = Hz^(-1.5) |
Hz^(-1) |
Time (s) / Planck constant (h) | s = 1/Hz, h = 1/Hz |
Hz^(-0.5) |
Length (m) / Mass (m) (inertial) | m = 1/Hz^0.5, mass = Hz^(-0.5) |
Hz^(0) |
Energy (E) / Entropy (S) / Photon Energy | E = 1, S = 1, E_photon = 1 |
Hz^(0.5) |
Force (F) / Momentum (p) | F = Hz^0.5, p = Hz^0.5 |
Hz^(1) |
Power (P) / Frequency (f) | P = Hz, f = Hz |
Hz^(2) |
Voltage (V) | V = (Ω·C)/s = Hz^2 |
Hz^(2.5) |
Electric Field (E) | E = V/m = Hz^(2.5) |
Hz^(3) |
Magnetic Permeability (μ₀) | μ₀ = Hz^3 |
Hz^(4) |
Magnetic Energy Density, Magnetic Tension | e.g., ½μ₀·H² ~ Hz^4 (implied) |
Hz^(5) |
Impedance (Ω) | Ω = Hz^5 |
Hz^(6) |
Binding Energy | Binding Energy = ΔΩ·C² / s = Hz^6 |
Hz^(-4) |
Permittivity (ε₀) | ε₀ = Hz^(-4) |
Tree Format (Minimalist Branching)
[Hz^-3] Charge (C)
│
[Hz^-2] Current (I = C/s)
│
[Hz^-1.5] Wavelength (λ = h/p)
│
[Hz^-1] Time (s), Planck (h)
│
[Hz^-0.5] Length (m), Mass (inertial)
│
[Hz^0] Energy (E), Entropy (S), Photon E
│
[Hz^0.5] Force (F), Momentum (p)
│
[Hz^1] Power (P), Frequency (f)
│
[Hz^2] Voltage (V)
│
[Hz^2.5] Electric Field (E)
│
[Hz^3] Magnetic Permeability (μ₀)
│
[Hz^4] Magnetic Tension (μ₀H²)
│
[Hz^5] Impedance (Ω)
│
[Hz^6] Binding Energy
│
[Hz^-4] Permittivity (ε₀)
Unified Dimensional Tree (Ω·C² Grammar) — Collapsed & Expanded
Unified Dimensional Tree (Ω·C² Grammar) — Collapsed & Expanded
Single-Unit Contraction
Single-Unit ContractionΩ·C² = Universal Dimensional Substance
- All SI and potential exotic physical units are expressions of this single compound form.
- This is the only dimensional root, everything else is a projection.
Full Expansion: Real + Theoretical Units
Ω·C²
├── Time (s)
│ └── Canonical Time
│
├── Energy (E = Ω·C² / s)
│ ├── Power (P = Ω·C² / s²)
│ │ ├── Voltage (V = Ω·C / s)
│ │ ├── Temperature (T = P·s / k_B)
│ │ └── Characteristic Length (λ = Ω·C² / p·s)
│ │ └── Exotic: Temporal Wavelengths, Ghost Oscillations
│ └── Force (F = Ω·C² / m·s)
│ ├── Momentum (p = Ω·C²)
│ ├── Mass (m = (Ω·C²·s)/m²)
│ └── Velocity Construct (v = (F·d)/C)
│ └── Exotic: Charge-Induced Velocity Fields
│
├── Magnetic Energy Density (U = Ω·C² / m³)
│ ├── B²/μ₀
│ ├── Magnetic Field (B = √(μ₀·U))
│ ├── μ₀ = B² / (B² / μ₀)
│ └── λ = (B²/μ₀) · s²·m / Ω·C²
│ └── Exotic: Compressed Vacuum Tensor
│
├── Current (I = C / s)
│ └── Electrical Quantities
│ ├── Resistance (R = V / I = Ω)
│ ├── Capacitance (C = q / V)
│ ├── Inductance (L = V·s / I)
│ └── Exotic: Quasi-Impedance (Ψ)
│
├── Thermodynamics
│ ├── Entropy (S = E / T)
│ ├── Helmholtz Energy (F = E - T·S)
│ └── Exotic: Negative Entropy Fields
│
├── Quantum Extensions
│ ├── Action (ħ = Ω·C² / quantized s)
│ ├── Probability Flux (Ψ = sqrt(E)/s)
│ └── Exotic: Phase Entanglement Metrics
│
├── Relativity Projections
│ ├── Spacetime Curvature (R = Ω·C² / s·m²)
│ ├── Lorentz Metric Inversion (γ = 1 / √(1 - v²/c²))
│ └── Exotic: Massless Inertia Shells
│
├── Cosmological Units
│ ├── Dark Energy (Λ = Ω·C² / m⁴)
│ ├── Hubble Flow (H = 1 / s)
│ └── Exotic: Ω-Matter Folding Ratios
Master Identity Grammar
Any Unit = (Ω·C²) / (m^a · s^b · C^c)
→ Exotics allowed when a, b, c ∈ ℝ or ℂ
