Definition
A wave is a propagating χ-mode—an oscillation traveling through the α-field:
All waves are χ-modes. Different types differ in what's oscillating, but all propagate through the α-field.
Wave Properties
| Property | Symbol | Meaning |
|---|---|---|
| Wavelength | λ | Spatial period of χ-mode |
| Frequency | f | Temporal oscillation rate |
| Amplitude | A | Maximum χ-mode displacement |
| Phase | φ | Position in oscillation cycle |
| Speed | v | λf = ω/k |
All follow from χ-mode dynamics in the α-field.
Types of χ-Mode Waves
Electromagnetic: Photon χ-modes, oscillating electric and magnetic fields
Sound: Mechanical χ-modes in matter, pressure oscillations
Gravitational: α-field ripples, ψ-curvature waves
Matter waves: Quantum χ-modes with λ = h/p
All are χ-modes propagating through different aspects of the α-field.
Wave Equation
The wave equation in SCU:
Solutions are propagating χ-modes. This emerges from Master Equation 1 in the appropriate limit.
Interference
When χ-modes overlap, they add:
Constructive: Phases align → larger amplitude
Destructive: Phases oppose → smaller amplitude
Interference reveals that χ-modes are waves, not particles.
Diffraction
χ-modes bend around obstacles:
Diffraction occurs when wavelength is comparable to obstacle size. It's χ-modes spreading as they propagate.
Standing Waves
When χ-modes reflect and combine:
Standing waves have fixed nodes. They're the basis for resonant structures—atoms, musical instruments, optical cavities.
The Double Slit
Single χ-modes pass through both slits:
Interference creates bands even for single photons/electrons. This shows particles ARE χ-modes—extended oscillations, not point objects.
Gravitational Waves
Ripples in the α-field itself:
LIGO detects these as length changes ~10⁻²¹. They carry energy because ψ-curvature propagates.
Wave-Particle Duality Resolved
Traditional puzzle: How can something be both wave and particle?
SCU answer: Everything is χ-modes. χ-modes:
- Propagate as waves (interference, diffraction)
- Transfer energy discretely (quantized oscillation)
No duality—consistent behavior of resonant χ-modes.
The Key Insight
A wave is not a disturbance in some medium.
A wave IS a propagating χ-mode:
- Electromagnetic waves = photon χ-modes
- Sound waves = mechanical χ-modes
- Gravitational waves = α-field ripples
- Matter waves = quantum χ-modes
- All obey χ-mode dynamics in the α-field
When you see a wave, you're seeing the α-field oscillate. When light interferes, χ-modes are adding. When particles diffract, their wave nature shows.
The universe is made of oscillations propagating through the chronometric field. Everything is waves.