Electromagnetic Field Ontology

FLOW ALGEBRA
ELECTROMAGNETIC FIELD ONTOLOGY
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/electromagnetic-entities/electromagnetic-field-ontology.html
Status: Independent scientific synthesis; source page not independently verified.

01. PURPOSE
Represent electromagnetic fields as typed, measurable, dynamical physical entities with rigorous equations, relations, provenance and inference constraints.

02. ONTOLOGY IDENTITY
ontology_id: KR:PhysicalEntities:ElectromagneticField
parent: KR:ElectromagneticEntities
related: ElectricField, MagneticField, ElectricCharge, ElectricCurrent, ElectromagneticWave, MagneticFlux, Voltage
scope: Classical electromagnetism in SI units; qualified links to relativistic and quantum theories.

03. CORE DEFINITION
An electromagnetic field is a spacetime-dependent physical field whose classical electric and magnetic components obey Maxwell's equations and couple to electric charges and currents.
Representation: F = (E(x,t), B(x,t)) in a chosen inertial frame.
E: electric field, V/m or N/C.
B: magnetic flux density, tesla (T).

04. TYPED ENTITIES
ElectromagneticField: PhysicalField
ElectricField: VectorField
MagneticFluxDensity: AxialVectorField
ChargeDensity: ScalarField
CurrentDensity: VectorField
ElectromagneticPotential: FourPotential
ScalarPotential: ScalarField
VectorPotential: VectorField
FieldTensor: AntisymmetricRankTwoTensor
Medium: MaterialEntity
Permittivity: ConstitutiveParameter
Permeability: ConstitutiveParameter
PoyntingVector: EnergyFluxVector
FieldEnergyDensity: EnergyDensity
BoundarySurface: GeometricEntity
ReferenceFrame: SpacetimeFrame
Observation: MeasurementEvent

05. RELATIONSHIP TYPES
HAS_COMPONENT(ElectromagneticField, ElectricField)
HAS_COMPONENT(ElectromagneticField, MagneticFluxDensity)
SOURCED_BY(ElectromagneticField, ChargeCurrentDistribution)
SATISFIES(ElectromagneticField, MaxwellEquation)
INTERACTS_WITH(ElectromagneticField, ChargedParticle)
PROPAGATES_THROUGH(ElectromagneticWave, Medium)
MEASURED_BY(FieldQuantity, Instrument)
EXPRESSED_IN(FieldQuantity, SIUnit)
TRANSFORMS_UNDER(ElectromagneticField, LorentzTransformation)
DERIVED_FROM(FieldTensor, FourPotential)
SUBJECT_TO(ElectromagneticField, BoundaryCondition)

06. TYPING RULES
HAS_COMPONENT(F,E) requires F:ElectromagneticField and E:ElectricField.
HAS_COMPONENT(F,B) requires B:MagneticFluxDensity.
SOURCED_BY(F,J) requires J:ChargeCurrentDistribution.
All numeric field assertions require units, coordinate frame and applicable time.

07. MAXWELL EQUATIONS — VACUUM SI
nabla dot E = rho/epsilon_0
nabla dot B = 0
nabla cross E = -partial B/partial t
nabla cross B = mu_0 J + mu_0 epsilon_0 partial E/partial t
These equations apply to macroscopic classical vacuum fields with charge density rho and current density J.

08. CONTINUITY EQUATION
partial rho/partial t + nabla dot J = 0
Inference: Maxwell equations imply local charge conservation when fields and sources are sufficiently regular.

09. ELECTROMAGNETIC FORCE
F = q(E + v cross B)
Applicable to a point charge q with velocity v in the selected reference frame.
Power delivered to point charge: P = q E dot v.
The magnetic contribution does no instantaneous work on a point charge.

10. POTENTIAL REPRESENTATION
B = nabla cross A
E = -nabla phi - partial A/partial t
Gauge transformation: A' = A + nabla chi; phi' = phi - partial chi/partial t.
Gauge-related potentials generate the same E and B.

11. ELECTROMAGNETIC WAVES
In source-free homogeneous vacuum:
nabla^2 E - (1/c^2) partial^2 E/partial t^2 = 0
nabla^2 B - (1/c^2) partial^2 B/partial t^2 = 0
c = 1/sqrt(mu_0 epsilon_0).
For a plane wave in vacuum: E perpendicular B, and |E| = c|B|.

12. ENERGY DENSITY AND FLUX
u = (epsilon_0/2)|E|^2 + (1/(2 mu_0))|B|^2
S = (1/mu_0) E cross B
Poynting theorem: partial u/partial t + nabla dot S = -J dot E.
Interpretation: local electromagnetic energy conservation.

13. FIELD MOMENTUM
Momentum density in vacuum: g = S/c^2 = epsilon_0 E cross B.
Electromagnetic stress is represented by the Maxwell stress tensor.
Conservation statements require specified material and boundary terms.

14. MATERIAL MEDIA
Macroscopic fields: D = epsilon_0 E + P; H = B/mu_0 - M.
Macroscopic equations: nabla dot D = rho_free;
nabla cross H = J_free + partial D/partial t.
Constitutive laws depend on medium; D = epsilon E and B = mu H only under suitable linear isotropic assumptions.

15. BOUNDARY CONDITIONS
n dot (B_2 - B_1) = 0
n cross (E_2 - E_1) = 0 for finite regular fields without singular magnetic surface currents.
n dot (D_2 - D_1) = sigma_free
n cross (H_2 - H_1) = K_free
n points from medium 1 to medium 2.

16. RELATIVISTIC REPRESENTATION
Electric and magnetic fields are frame-dependent components of the electromagnetic field tensor F_mu_nu.
F_mu_nu = partial_mu A_nu - partial_nu A_mu.
Lorentz transformations mix electric and magnetic components.
Invariant scalars (sign convention dependent): E dot B and E^2 - c^2 B^2.

17. QUANTUM DOMAIN BOUNDARY
Quantum electrodynamics quantises the electromagnetic field.
Photons are quantum excitations; classical Maxwell fields are not interchangeable with individual photons.
Do not infer discrete photon counts solely from a classical field amplitude.

18. FIELD CLASSIFICATION
Electrostatic: partial E/partial t = 0 under specified stationary conditions.
Magnetostatic: partial B/partial t = 0 under specified stationary conditions.
Time-varying: at least one component changes with time.
Radiative: propagating field carries energy to distant regions.
Near-field: source-proximate field components may include nonradiative energy storage.

19. INFERENCE RULES
R1: POINT_CHARGE(q) and FIELD(E,B) and VELOCITY(v) -> LORENTZ_FORCE(q*(E+v cross B)).
R2: SOURCE_FREE_VACUUM and MAXWELL_VALID -> WAVE_EQUATIONS_VALID.
R3: POTENTIALS(phi,A) -> FIELDS(-grad(phi)-dt(A), curl(A)).
R4: GAUGE_TRANSFORM(phi,A,chi) -> SAME_PHYSICAL_FIELDS.
R5: FIELD(E,B) and VACUUM -> ENERGY_DENSITY(u) and ENERGY_FLUX(S).
R6: MAXWELL_VALID and REGULAR_SOURCES -> CHARGE_CONTINUITY.
R7: MATERIAL_RESPONSE_KNOWN -> APPLY_CONSTITUTIVE_LAW; otherwise UNKNOWN.
R8: FRAME_CHANGE -> TRANSFORM_FIELD_TENSOR; do not hold E and B separately invariant.

20. RULE GUARDS
No field magnitude without location, time and frame.
No claim of superluminal signal propagation from phase velocity alone.
No use of vacuum constitutive laws for arbitrary anisotropic materials.
No inference of magnetic monopoles from classical Maxwell equations.
Do not conflate B with H or charge density with current density.

21. WORKED EXAMPLE — POINT CHARGE
For a stationary point charge q in vacuum, away from r=0:
E(r) = [q/(4*pi*epsilon_0)] r_hat/r^2.
B = 0 in its rest frame.
The source at r=0 is represented distributionally by rho = q delta^3(r).

22. WORKED EXAMPLE — PLANE WAVE
E = E0 cos(kz-omega*t) x_hat.
B = (E0/c) cos(kz-omega*t) y_hat.
Propagation is in +z; omega = c*k in vacuum.
Time-averaged flux: <S> = (epsilon_0*c*E0^2/2) z_hat.

23. WORKED EXAMPLE — CHARGED PARTICLE
q = 1 C; E = (2,0,0) N/C; v = (0,3,0) m/s; B = (0,0,4) T.
v cross B = (12,0,0) N/C per coulomb.
F = (14,0,0) N.
Illustrative numerical values only, not a practical experimental configuration.

24. DIMENSIONAL VALIDATION
[E] = N/C = V/m.
[B] = T = N*s/(C*m).
[S] = W/m^2.
[u] = J/m^3.
All derived values must pass unit checks.

25. SEMANTIC EQUIVALENCE
Electric field strength ~= E (when context unambiguous).
Magnetic flux density ~= B.
Electromagnetic field tensor ~= Faraday tensor.
NOT_EQUIVALENT(MagneticFieldStrength_H, MagneticFluxDensity_B).
NOT_EQUIVALENT(ElectromagneticField, ElectromagneticWave).
NOT_EQUIVALENT(ClassicalField, Photon).

26. KNOWLEDGE GRAPH TRIPLES
ElectromagneticField --hasComponent--> ElectricField
ElectromagneticField --hasComponent--> MagneticFluxDensity
ElectromagneticField --governedBy--> MaxwellEquations
ElectromagneticField --actsOn--> ElectricCharge
ElectromagneticWave --carries--> Energy
FieldTensor --transformsUnder--> LorentzTransformation
MagneticFluxDensity --measuredIn--> Tesla
ElectricField --measuredIn--> VoltPerMetre

27. CONFIDENCE MODEL
CONFIDENCE:
  foundational_maxwell_equations: high_within_classical_domain
  classical_wave_propagation: high_within_assumptions
  material_constitutive_prediction: conditional_on_material_model
  quantum_interpretation: model_dependent
  unverified_page_alignment: unknown
Confidence refers to claims and their domain, not an invented probability of truth.

28. VALIDATION TESTS
TEST01: div(B)=0 for regular vacuum plane wave -> PASS.
TEST02: E and B plane-wave amplitudes obey E0=c*B0 -> PASS.
TEST03: charge continuity from Maxwell equations -> PASS.
TEST04: q(E+v cross B) dimensions equal newtons -> PASS.
TEST05: potential gauge transformation preserves fields -> PASS.
TEST06: material constitutive relation absent -> BLOCK unsupported prediction.
TEST07: all source claims distinguish established classical laws from model assumptions -> REQUIRED.
TEST08: document contains closing marker -> REQUIRED.

29. PROVENANCE AND SOURCE MODEL
SOURCE_PAGE: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/electromagnetic-entities/electromagnetic-field-ontology.html
SOURCE_ACCESS: not independently verified
SYNTHESIS_BASIS: established classical electromagnetism and standard theoretical terminology
CLAIM_PROVENANCE: assign sources and measurement conditions when data are ingested

30. FLOW HASH SPECIFICATION
FLOW_HASH:
  algorithm: SHA-256
  input: canonical UTF-8 content with normalised LF line endings
  exclude: any stored hash value field to prevent circularity
  output: 64-character lowercase hexadecimal digest
  status: specification_only; compute on publication

31. UPDATE MODEL
UPDATE_MODEL:
  version: 1.1
  revision_policy: semantic_versioning
  on_change: validate_equations, regenerate_hash, record_provenance, review_cross_links
  preserve: previous_version, change_log, scientific_domain_qualifiers

32. AI CONSUMPTION
AI_CONSUMPTION:
  preferred_representation: typed_knowledge_graph_plus_equations
  reasoning_mode: guarded_symbolic_inference
  units: SI
  coordinate_frame: mandatory_for_observations
  uncertainty: mandatory_for_measured_values
  unsupported_claim_policy: abstain_or_qualify
  source_page_alignment: unverified

33. COMPLETENESS CHECK
Required: identity, typed entities, typed relations, Maxwell equations, force law,
potentials, waves, energy, materials, relativity, guarded inference,
examples, validation, provenance, confidence, FLOW_HASH, UPDATE_MODEL,
AI_CONSUMPTION and final marker.
Status: COMPLETE for this independent synthesis.

END FLOW ALGEBRA — ELECTROMAGNETIC FIELD ONTOLOGY