THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Centrifugal force
The outward fictitious force that appears in a rotating reference frame, with magnitude Ω²r.
centripetal force
The net inward force that keeps a body moving on a circular path: F_c = m·v²/r = m·ω²·r.
Characteristic impedance
Z₀ = √(L/C) for a lossless transmission line. The ratio of voltage to current in a travelling wave propagating along the line. Standard values: 50 Ω (RF), 75 Ω (video), 100 Ω (differential digital), 377 Ω (free space).
Charge invariance
The principle that electric charge is a Lorentz scalar — every inertial observer measures the same total charge in a given closed volume, regardless of relative motion. The one quantity in classical electrodynamics that no boost can mix away.
Christiaan Huygens
Dutch physicist and astronomer (1629–1695) who proposed the wave theory of light in Traité de la lumière (1678) and formulated the Huygens construction of secondary wavelets. Full physicist entry in a later session.
Christoffel symbols
The connection coefficients Γ^ρ_{μν} = (1/2) g^{ρσ}(∂_μ g_{νσ} + ∂_ν g_{μσ} − ∂_σ g_{μν}) computed from the metric. Not tensors — they don't transform tensorially — but appear in covariant derivatives and the geodesic equation. Define the unique torsion-free metric-compatible Levi-Civita connection.
Circular polarization
An EM wave whose E-vector rotates in a circle at frequency ω as the wave propagates, tracing a helix in space. Left- and right-handed variants are the two independent polarisation states.
Classical limit of QED
The high-occupation-number limit of quantum electrodynamics in which Maxwell's equations are recovered exactly as the expectation value of the photon field operator in a coherent state with |α|² → ∞. The classical theory is incomplete but consistent: every successor theory (QED, gauge unification, beyond) has had to learn to speak Maxwell.
coefficient of restitution
A dimensionless number e between 0 and 1 characterising how elastic a collision is: ratio of post-collision to pre-collision relative speed.
Coherence length
L_c = c·τ_c ≈ λ²/Δλ, the path-length difference beyond which two parts of a light beam stop being able to interfere. Governs the maximum usable path difference in interferometers and holography.
Coherent state
An eigenstate |α⟩ of the photon annihilation operator â with complex eigenvalue α, possessing a Poisson photon-number distribution ⟨n⟩ = |α|², σ_n = |α|, σ_n/⟨n⟩ = 1/|α|. In the |α|² → ∞ limit the relative quantum fluctuation vanishes and ⟨α|Ê|α⟩ approaches the classical EM field exactly. The bridge from QED to classical electromagnetism.
Conjugate momentum
The momentum paired with a generalised coordinate q, defined as p = ∂L/∂q̇.
conservation of energy
The total energy of an isolated system — mechanical, thermal, chemical, radiated — is constant over time.
Constraint
A restriction on the motion of a system — a surface, wire, or fixed distance. In Lagrangian mechanics, absorbed into coordinate choice.
Continuous symmetry
A symmetry that depends on a continuous parameter — the kind Noether's theorem turns into conservation laws.
Coriolis force
The fictitious force -2m Ω×v that deflects moving objects in a rotating reference frame.
Coulomb gauge
The gauge condition ∇·A = 0. Reduces the equation for the scalar potential V to the instantaneous Poisson equation, and leaves only the vector potential A subject to a wave equation. Convenient for non-relativistic electrostatics.
Covariant derivative
The generalisation of the partial derivative to curved manifolds, ∇_μ V^ν = ∂_μ V^ν + Γ^ν_{μρ} V^ρ. Unlike ∂_μ V^ν (which is not a tensor on a curved space), the covariant derivative is a (1,1) tensor — the Christoffel correction Γ exactly cancels the non-tensorial transformation behaviour of the partial derivative.
Critical angle
θ_c = arcsin(n₂/n₁), the angle of incidence above which total internal reflection occurs at an interface from n₁ to n₂ < n₁. For water–air, θ_c ≈ 48.6°; for glass–air, θ_c ≈ 42°; for diamond–air, θ_c ≈ 24.4°.
Critical temperature
The temperature T_c below which a superconductor exhibits zero resistance and the Meißner effect. Ranges from 1.2 K (aluminium) to 135 K (cuprate high-T_c materials) to above 250 K in hydride compounds under pressure.
Cross product
The vector a × b perpendicular to both a and b, with magnitude |a||b|sin θ. The operation that produces torque and angular momentum.
Curie temperature
The critical temperature T_c above which a ferromagnet loses its spontaneous magnetization and becomes an ordinary paramagnet. 1043 K for iron, 627 K for nickel, 1388 K for cobalt.
Curl
A vector operation ∇× that measures how much a vector field circulates around a point. Nonzero curl means the field has rotational structure; zero curl means it is conservative.
Current density
The vector J = nqv giving the charge passing per unit time through a unit area perpendicular to the flow direction. Units: amperes per square metre.
cycloid
Curve traced by a point on a rolling circle; solves both tautochrone and brachistochrone.
damping
Energy dissipation causing oscillation amplitude to decay exponentially.
derivative
The instantaneous rate of change of one quantity with respect to another; geometrically, the slope of the tangent line to a curve.
Dielectric
An insulating material that can be polarized but does not conduct — its bound charges shift locally in response to a field while no current flows.
Dielectric constant
The dimensionless ratio κ = ε/ε₀ of a material's permittivity to that of vacuum. Tells you how much a dielectric amplifies a capacitor's storage capacity.
Dirac quantization condition
The 1931 Dirac result that the existence of a single magnetic monopole anywhere in the universe forces electric charge to be quantised in integer multiples of e = 2πℏ/(g μ₀ c), where g is the magnetic charge. Turns the empirical fact of charge quantisation into a theoretical consequence.