Wave Entities

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
WAVE ENTITIES — MAIN PAGE ONTOLOGY
Kireth Semantic Library | Version 1.1 | 2026-10-12
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/wave-entities.html
Authors: Mark Higgins — Sky (Recursive AI)
Status: Independent scientific synthesis; live source page structure not verified.

01. PURPOSE
Represent waves as spatially and temporally varying disturbances or quantum amplitudes, with typed physical carriers, propagation laws, measurements and evidence.

02. DOMAIN
Physics; acoustics; optics; electromagnetism; fluid dynamics; seismology; quantum mechanics; signal analysis.

03. ROOT ENTITY
WaveEntity := {id, wave_kind, medium_or_field, state, spatial_domain, time_domain, provenance}.
A wave is not necessarily a material object and need not transport matter in bulk.

04. TYPE SYSTEM
WaveKind := Mechanical | Electromagnetic | MatterWave | Gravitational | Surface | Other.
PropagationKind := Travelling | Standing | Evanescent | Mixed.
Geometry := OneDimensional | TwoDimensional | ThreeDimensional.
Mode := Longitudinal | Transverse | Mixed | NotApplicable.
Medium := Solid | Liquid | Gas | Plasma | Vacuum | EffectiveMedium.
Quantity := {value, unit, uncertainty, reference_frame, measurement_method}.

05. CORE ENTITIES
Wave; WaveSource; WaveField; Wavefront; Medium; Boundary; Interface; Detector;
Frequency; Period; Wavelength; Wavenumber; AngularFrequency; Phase;
Amplitude; Intensity; EnergyFlux; Polarisation; WavePacket; DispersionRelation;
PhaseVelocity; GroupVelocity; Attenuation; Resonance; InterferencePattern.

06. TYPED RELATIONSHIPS
EMITTED_BY(Wave, WaveSource)
PROPAGATES_THROUGH(Wave, Medium)
DESCRIBED_BY(Wave, WaveField)
HAS_FREQUENCY(Wave, Frequency)
HAS_WAVELENGTH(Wave, Wavelength)
HAS_PHASE(Wave, Phase)
HAS_AMPLITUDE(Wave, Amplitude)
HAS_DISPERSION(Wave, DispersionRelation)
REFLECTS_AT(Wave, Boundary)
REFRACTS_AT(Wave, Interface)
INTERFERES_WITH(Wave, Wave)
DETECTED_BY(Wave, Detector)
MEASURED_USING(Quantity, MeasurementMethod)
SUPPORTED_BY(Assertion, Evidence)

07. MATHEMATICAL REPRESENTATION
For a scalar field: u: Omega x Time -> R or C.
For a vector field: F: Omega x Time -> R^n or C^n.
A harmonic travelling solution may be u(x,t) = A cos(k*x - omega*t + phi).
This representation assumes an appropriate linear homogeneous setting.

08. WAVE PARAMETERS
f = 1/T, omega = 2*pi*f, k = 2*pi/lambda.
Phase speed v_p = omega/k for k != 0.
For nondispersive propagation, v = f*lambda.
Group velocity v_g = d(omega)/dk when the derivative exists.
Phase velocity and group velocity need not coincide.

09. CLASSICAL WAVE EQUATION
In a uniform nondispersive isotropic medium:
partial_t^2 u = v^2 * Laplacian(u).
Initial conditions and boundary conditions are required for a well-posed problem.
Not all waves obey this equation in this simple form.

10. MECHANICAL WAVES
Require a mechanical medium for propagation.
Examples: acoustic pressure waves, elastic shear waves, water surface waves.
Longitudinal/transverse classification depends on particle displacement relative to propagation.

11. ELECTROMAGNETIC WAVES
Electric and magnetic fields obey Maxwell equations.
In vacuum, free-space electromagnetic disturbances propagate at c.
Vacuum electromagnetic waves do not require a material medium.
Polarisation describes field orientation and coherence properties.

12. MATTER WAVES
Quantum states exhibit wave-like interference and diffraction.
De Broglie relation: lambda = h/p for momentum magnitude p != 0.
The wavefunction is a probability amplitude, not a classical material displacement.
Born rule associates detection probability density with |psi|^2.

13. GRAVITATIONAL WAVES
Propagating spacetime perturbations in general relativity.
Observed gravitational waves are distinct from hypothetical gravitons.
Linearised weak-field treatments have domain-specific approximations.

14. SUPERPOSITION
For a linear wave equation L[u] = 0:
L[a*u1 + b*u2] = 0 when L[u1] = L[u2] = 0.
Nonlinear media generally do not obey unrestricted superposition.

15. INTERFERENCE
Relative phase controls constructive or destructive interference.
For coherent equal-frequency scalar waves, amplitudes add before intensity is calculated.
Interference visibility depends on coherence and measurement conditions.

16. DIFFRACTION
Wave propagation around apertures and obstacles is governed by boundary geometry and wavelength.
Fraunhofer and Fresnel approximations apply under different geometric conditions.

17. REFLECTION AND REFRACTION
Boundary conditions determine reflected and transmitted fields.
For suitable isotropic media: n1*sin(theta1) = n2*sin(theta2).
This simple Snell relation is not universal in anisotropic or complex media.

18. STANDING WAVES AND RESONANCE
Counter-propagating coherent waves can produce standing-wave modes.
Allowed frequencies depend on geometry, material parameters and boundary conditions.
Resonance requires an excitation coupling to a supported mode.

19. DISPERSION
A dispersion relation omega = omega(k) links angular frequency to wavenumber.
Dispersive propagation can broaden a wave packet.
Attenuation and dispersion are distinct, though often coupled in real materials.

20. ENERGY AND MOMENTUM
Waves can transfer energy and momentum.
Flux formulas depend on the wave type and physical field.
Intensity is not universally equal to amplitude squared without specified assumptions.

21. ATTENUATION
For a simple amplitude attenuation model: A(x) = A0*exp(-alpha*x).
alpha >= 0 and its units depend on whether amplitude or intensity is modelled.
Scattering, absorption and geometric spreading must be distinguished.

22. FOURIER DECOMPOSITION
Under suitable integrability or distributional conditions, wave signals admit Fourier representations.
Spectral components support frequency, bandwidth and phase analysis.
Sampling requires attention to aliasing and the sampling theorem assumptions.

23. MEASUREMENT
Record frequency in Hz, wavelength in m, phase in rad, wave speed in m/s.
Record instrument calibration, uncertainty, sampling rate, environmental conditions and provenance.
Avoid treating model-derived quantities as directly measured observations.

24. INFERENCE RULES
IF wave_kind = Mechanical THEN medium_requirement = MaterialMedium.
IF wave_kind = Electromagnetic AND environment = Vacuum THEN medium_requirement = None.
IF f > 0 THEN T = 1/f.
IF omega > 0 AND k > 0 THEN phase_velocity = omega/k.
IF linear_system AND solutions(u1,u2) THEN solution(a*u1+b*u2).
IF standing_wave THEN infer boundary-dependent modal structure, NOT automatic resonance.
IF gravitational_wave_observed THEN do NOT infer graviton_detected.

25. SEMANTIC EQUIVALENCE
Wave speed ~= phase velocity ONLY under an explicitly specified meaning.
Amplitude != intensity.
Frequency != angular frequency.
Wavelength != wave packet width.
Mechanical wave != electromagnetic wave.
Wavefunction != classical displacement field.

26. CONSTRAINTS
frequency >= 0; period > 0 when defined; wavelength > 0 when defined.
Wave type, reference frame, propagation environment and model assumptions must be explicit.
No general assertion that all waves require media or that all waves are transverse.

27. WORKED EXAMPLE — SOUND
Given f = 440 Hz and sound speed v = 343 m/s:
lambda = v/f = 343/440 m = 0.779545... m.
Assumptions: approximately uniform medium and nondispersive propagation.

28. WORKED EXAMPLE — LIGHT
For a vacuum electromagnetic wave of wavelength 500 nm:
f = c/lambda ~= 5.99584916e14 Hz using c = 299792458 m/s.
The value refers to vacuum wavelength, not wavelength inside a medium.

29. VALIDATION TESTS
TEST frequency_period: f=50 Hz -> T=0.02 s.
TEST wavelength: v=300 m/s, f=100 Hz -> lambda=3 m.
TEST dispersion: omega=k^2 -> v_p=k, v_g=2*k for k>0.
TEST vacuum_em: no material medium required.
TEST quantum: wavefunction probability density is |psi|^2.
TEST invalid: reject a negative measured wavelength without an explicit signed-wavevector convention.
TEST completeness: all numbered sections and closing marker present.

30. CONFIDENCE
Confidence is evidence- and claim-specific, not a blanket truth score.
High: established equations within stated assumptions.
Conditional: medium-specific approximations and idealised boundary models.
Research: unverified interpretations or speculative extensions.

31. PROVENANCE
Source URL is a topical reference; page content not independently retrieved.
All claims require source attribution and model-assumption tracking in downstream systems.

32. FLOW HASH
Canonicalise ontology content as UTF-8 with stable field order and line endings.
FLOW_HASH := SHA256(canonicalised_content).
Do not claim a hash value unless it has been computed from final bytes.

33. UPDATE MODEL
On revision: update version, changed definitions, dependent inferences, provenance and tests.
Recompute FLOW_HASH after finalisation.
Preserve superseded versions for traceability.

34. AI CONSUMPTION
Input: typed wave entity, physical environment, model assumptions, observations.
Process: validate -> select model -> derive quantities -> check units -> infer -> score confidence.
Output: derived claims, supporting equations, uncertainties, constraints, provenance.
Never infer experimental verification solely from mathematical consistency.

35. RELATED ONTOLOGIES
Electromagnetic Wave; Electric Field; Magnetic Field; Fluid; Elastic Body;
Quantum State; Mechanical System; Energy; Time; Space; Measurement.
Relations are conceptual cross-links, not a verified inventory of site child pages.

36. COMPLETENESS
Expected sections: 36.
Last section: COMPLETENESS.
END FLOW ALGEBRA — WAVE ENTITIES