THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Clausius–Clapeyron relation
dP/dT = L/(TΔV): the slope of any coexistence curve, fixed entirely by a latent heat and a volume change.
Coefficient of performance
Heat moved per unit work paid — the figure of merit for any machine that pumps heat uphill.
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.
Coexistence curve
A line on the phase diagram along which two phases sit in equilibrium, neither one winning.
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.
Comoving Coordinates
Coordinate labels painted onto expanding space that stay fixed for objects riding the expansion.
Compressibility factor
Z = PV/nRT — the dimensionless number that reads 1 for an ideal gas and measures how far a real gas departs from it.
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.
Cosmic Censorship
Penrose's conjecture that nature always hides its singularities behind horizons — still unproven.
Cosmological Constant
A constant energy density of empty space, Einstein's Λ, that drives cosmic acceleration.
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 Density
The mean energy density that makes the universe spatially flat.
Critical exponent
The power in a power law near a critical point — a number that depends on dimension and symmetry, and on nothing else.
Critical point
The end of the liquid–vapour boundary, above which liquid and gas become a single indistinguishable supercritical fluid.
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.
Cryogenics
The science of the very cold — and of the machines without which there is nothing to study.
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.
Dark energy
The unknown component, about 68% of the universe, whose negative pressure drives the accelerating cosmic expansion.