THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
Cosmic Microwave Background
The relic blackbody radiation released when the universe became transparent, now cooled to 2.725 K.
Cosmological Constant
A constant energy density of empty space, Einstein's Λ, that drives cosmic acceleration.
Cosmological redshift
The stretching of light's wavelength by the expansion of space, not by any motion of the source.
Coulomb (unit)
The SI unit of electric charge. One coulomb equals the charge carried by 6.24 × 10¹⁸ protons, or the charge that flows past a point in one second when the current is one ampere.
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 opalescence
The milky scattering of light by density fluctuations that grow to the wavelength of light near a critical point.
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.
Dark matter
Non-luminous, non-baryonic matter that outweighs ordinary atoms about five to one and binds galaxies and clusters together.
Debye temperature
The characteristic temperature above which a solid behaves classically and below which its heat capacity collapses toward zero.
Degrees of freedom
The independent ways a molecule can store energy — translation, rotation, vibration — each counted toward its heat capacity.
derivative
The instantaneous rate of change of one quantity with respect to another; geometrically, the slope of the tangent line to a curve.
Destructive interference
The superposition of two or more coherent waves in anti-phase, producing an amplitude (and intensity) less than the sum. Total cancellation requires equal amplitudes and a path-length difference of (m+½)λ.
Dewar flask
The double-walled vacuum vessel that made cryogenics a science — and your thermos.
Diamagnetism
The universal property of all matter to develop a weak magnetization *opposite* to an applied field. In most materials it is swamped by para- or ferromagnetism, but in closed-shell atoms it dominates.