Wave Ontology

FLOW ALGEBRA
WAVE ONTOLOGY
Version: 1.1
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/wave-entities/wave-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research | https://kirethresearch.org
Status: Independent scientific synthesis; source page not independently verified.

01. PURPOSE
Represent wave phenomena, mathematical models, physical media, propagation, interactions and observations using typed semantic relationships and testable constraints.

02. SCOPE
Includes mechanical, electromagnetic, matter and gravitational waves; travelling and standing waves; linear and nonlinear, longitudinal and transverse waves. Model assumptions must be explicit.

03. TYPES
Wave: physical or mathematical propagating/oscillatory disturbance.
WaveField: scalar, vector or tensor field describing a wave.
Medium: material supporting specified wave modes; optional for vacuum-propagating fields.
Source: excitation or initial/boundary condition.
Observer: reference frame or measuring apparatus.
WaveMode: permitted oscillatory solution of a model.
Boundary: interface with stated boundary conditions.
Measurement: observed value, unit, uncertainty and provenance.
Interaction: reflection, transmission, refraction, diffraction, interference, scattering or absorption.

04. IDENTIFIERS
Each wave instance has id, wave_kind, model, frame, domain, time_interval and provenance. Distinguish an individual wave packet from a wave class.

05. RELATIONSHIPS
Wave --DESCRIBED_BY--> WaveField
Wave --GENERATED_BY--> Source
Wave --PROPAGATES_IN--> Medium [where applicable]
Wave --HAS_MODE--> WaveMode
Wave --INTERACTS_WITH--> Boundary
Wave --OBSERVED_BY--> Observer
Wave --HAS_MEASUREMENT--> Measurement
Wave --SUPERPOSES_WITH--> Wave [linear regime]
Wave --TRANSFERS--> Energy [model-dependent]

06. STATE VARIABLES
x: position [m]; t: time [s]; A: amplitude [field-dependent]; f: frequency [Hz]; omega: angular frequency [rad/s]; lambda: wavelength [m]; k: angular wavenumber [rad/m]; phi: phase [rad]; v_phase: phase velocity [m/s]; v_group: group velocity [m/s].

07. HARMONIC TRAVELLING WAVE
u(x,t) = A cos(k*x - omega*t + phi).
k = 2*pi/lambda; omega = 2*pi*f; v_phase = omega/k = f*lambda for nonzero k.
Assumptions: one-dimensional, monochromatic, uniform medium or applicable vacuum model.

08. WAVE EQUATION
For a scalar non-dispersive homogeneous isotropic model:
partial_t^2 u = v^2 * nabla^2 u.
Requires appropriate initial and boundary conditions for a well-posed problem.

09. DISPERSION
omega = omega(k) is the dispersion relation.
v_phase = omega/k (k != 0); v_group = d omega/dk for a differentiable branch.
Group velocity need not equal energy or information velocity in general.

10. SUPERPOSITION
If L is linear and L[u1] = L[u2] = 0, then L[a*u1+b*u2] = 0.
Superposition is not automatically valid in nonlinear media.

11. INTERFERENCE
For coherent scalar amplitudes: I proportional to |u1+u2|^2.
For equal-frequency coherent fields: I = I1 + I2 + 2*sqrt(I1*I2)*cos(delta_phi), with compatible polarisation and normalisation.

12. STANDING WAVES
u(x,t) = 2*A*sin(k*x)*cos(omega*t) from suitable equal-amplitude counterpropagating waves.
Node positions satisfy sin(k*x) = 0. Boundary conditions determine allowed modes.

13. REFLECTION AND TRANSMISSION
At an interface apply the boundary conditions appropriate to the wave field and medium. Define reflection/transmission coefficients for amplitudes or energy flux explicitly; do not equate the two.

14. REFRACTION
For isotropic optical media under applicable geometric-optics assumptions: n1*sin(theta1) = n2*sin(theta2).
For general anisotropic/dispersive media use the appropriate phase-matching relations.

15. DIFFRACTION
Wave spreading and interference arise from finite apertures, obstacles and spatially varying boundaries. Exact patterns depend on geometry, wavelength and coherence.

16. POLARISATION
For vector waves, polarisation describes the orientation/evolution of transverse field components. A scalar pressure wave does not have electromagnetic-style polarisation.

17. MECHANICAL WAVES
Require a supporting medium in conventional continuum models. Examples: acoustic waves, elastic waves, surface waves. The medium's constitutive law controls propagation.

18. ELECTROMAGNETIC WAVES
In source-free vacuum, Maxwell's equations imply wave propagation at c = 1/sqrt(mu0*epsilon0). Electric and magnetic field components satisfy transverse plane-wave relations.

19. MATTER WAVES
Quantum states exhibit wave-like interference. de Broglie relation: lambda = h/p for nonzero momentum in the relevant regime. Probability amplitudes are not classical material displacements.

20. GRAVITATIONAL WAVES
In weak-field general relativity, propagating metric perturbations have tensor polarisations and travel at c in vacuum. Gravitational waves are observed; gravitons remain hypothetical.

21. ENERGY AND INTENSITY
Energy density and flux depend on the wave theory. For a suitable classical plane wave, time-averaged intensity often scales with squared amplitude, holding medium and frequency fixed.

22. DAMPING
An attenuated amplitude may be modelled as A(x) = A0*exp(-alpha*x), alpha >= 0, where the approximation and units are declared. Intensity attenuation differs by a factor of two in the exponent when I proportional to A^2.

23. RESONANCE
A driven system can show enhanced response near its natural modes. Resonant frequency, bandwidth and quality factor depend on damping and coupling.

24. FOURIER DECOMPOSITION
For suitable integrable signals: U(omega) = integral u(t)*exp(-i*omega*t) dt; u(t) = (1/(2*pi))*integral U(omega)*exp(i*omega*t) d omega.
Record transform convention and convergence conditions.

25. WAVE PACKETS
u(x,t) = integral A(k)*exp(i*(k*x-omega(k)*t)) dk; physical real fields may use the real part. Bandwidth determines localisation and dispersion effects.

26. DIMENSIONAL RULES
[f] = s^-1; [lambda] = m; [k] = m^-1; [omega] = s^-1; [v] = m/s.
Amplitude units are model-specific; never assign metres universally.

27. INFERENCE RULES
IF monochromatic AND lambda > 0 AND f > 0 AND non-dispersive phase relation applies THEN v_phase = f*lambda.
IF two solutions share a linear homogeneous operator THEN their linear combination is also a solution.
IF dispersion relation is nonlinear in k THEN phase and group velocities may differ.
IF boundary conditions fix endpoints of a string THEN standing-wave modes are quantised by the string length.
IF medium is vacuum AND wave_kind is electromagnetic THEN a material medium is not required.

28. INVALID INFERENCES
Do not infer wave energy from amplitude without a specified physical model.
Do not infer v_group <= c for every formal dispersion model; distinguish signal/front velocity and physical causality.
Do not infer that every wave is transverse or every wave requires matter.
Do not infer that all oscillations propagate.

29. WORKED EXAMPLE: FREQUENCY
Given f = 50 Hz and phase speed v = 340 m/s, lambda = v/f = 6.8 m.
Applies to a monochromatic wave with these stated values.

30. WORKED EXAMPLE: STANDING STRING
Fixed string length L = 1 m, wave speed v = 100 m/s.
Allowed wavelengths lambda_n = 2*L/n and frequencies f_n = n*v/(2*L) = 50*n Hz, n = 1,2,...

31. WORKED EXAMPLE: ATTENUATION
A0 = 2 units, alpha = 0.1 m^-1, x = 10 m.
A(x) = 2*exp(-1) approximately 0.736 units.

32. VALIDATION
Check non-empty identifiers, consistent units, model applicability, phase conventions, causal interpretation, boundary conditions, uncertainty and provenance.
Reject lambda <= 0 for physical wavelength records and f < 0 for nonnegative-frequency metadata conventions.
Check mathematical equations against declared dimensional types.

33. SEMANTIC_EQUIVALENCE
"wave speed" is ambiguous: require phase, group, energy or signal speed.
"amplitude" may mean displacement, pressure, electric field or probability amplitude; resolve by WaveField type.
"frequency" and "angular frequency" are related by omega = 2*pi*f but are not identical units.

34. CONFIDENCE
confidence_model: evidence-weighted; never treat confidence as proof.
confidence_fields: theory_status, empirical_support, measurement_uncertainty, model_validity, source_quality.
Mark idealisations and unresolved phenomena explicitly.

35. FLOW_HASH
algorithm: SHA-256
canonicalisation: UTF-8, LF line endings, deterministic field ordering, exclude the hash value itself.
flow_hash_value: NOT_COMPUTED (compute after final canonical publication).

36. UPDATE_MODEL
version: 1.1
update_trigger: new evidence, model correction, terminology revision, unit correction or ontology relationship change.
change_policy: retain stable IDs; record revisions and affected dependencies.

37. AI_CONSUMPTION
output_types: typed triples, equations, constraints, inference rules, examples, provenance.
reasoning_policy: distinguish definition, assumption, derived consequence and measured observation.
uncertainty_policy: do not fabricate values or elevate model-specific approximations to universal laws.

38. PROVENANCE
source_url: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/wave-entities/wave-ontology.html
source_verification: NOT_VERIFIED
scientific_status: established models with stated limits; synthesis authored for Kireth Semantic Library.

39. COMPLETENESS_CHECK
required_sections: 01..39
check: all numbered sections present; final closing marker present.

END FLOW ALGEBRA — WAVE ONTOLOGY