THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Birkhoff's theorem
Any spherically symmetric vacuum solution of Einstein's equations must be static and equal to the Schwarzschild metric.
Boltzmann distribution
p_i ∝ exp(−E_i/k_BT): the probability of a microstate falls off exponentially with its energy.
Boltzmann entropy formula (S = k log W)
Entropy is Boltzmann's constant times the logarithm of the number of microstates: S = k_B ln Ω.
Boltzmann factor
exp(−E/k_BT) — the exponential weight that sets how likely a state of energy E is at temperature T, and the engine of statistical mechanics.
Born rigidity
Max Born's 1909 definition of relativistic rigidity: a body is Born-rigid if its proper length stays constant during acceleration. A truly rigid rod must have its trailing end accelerate faster than its leading end so that length contraction cancels exactly — the constraint that Bell's two-rocket setup violates.
Bound charge
Charge that cannot move freely through a material because it is stuck inside individual atoms or molecules — yet still rearranges locally when the medium is polarized.
Boundary conditions (EM)
The matching rules at an interface between two media: the normal component of D jumps by the free surface charge; the tangential component of E is continuous.
Boyle's law
At fixed temperature the pressure and volume of a gas are inversely proportional: PV is constant.
Brewster's angle
θ_B = arctan(n₂/n₁), the angle at which reflected light from a dielectric interface is perfectly s-polarised because the p-polarised Fresnel reflection coefficient r_p vanishes. Brewster 1815.
Buoyancy
The upward force on an object immersed in a fluid, equal to the weight of the fluid the object displaces.
Caloric theory
The discredited eighteenth-century idea that heat is a weightless, conserved fluid called caloric that flows from hot bodies to cold.
Calorimetry
The measurement of heat — classically by dropping a hot body into insulated water and reading the final temperature.
Canonical ensemble
A system at fixed temperature, volume and particle number, free to exchange energy with a heat bath.
Capacitance
The ratio of charge stored on a conductor (or between two conductors) to the voltage that stored it. C = Q/V. Units: farads.
Carnot cycle
The idealised, fully reversible engine cycle of two isotherms and two adiabats that sets the efficiency ceiling for all heat engines.
Carnot efficiency
The maximum possible efficiency of any heat engine running between two temperatures: η = 1 − T_c/T_h.
center of mass
The mass-weighted average position of a system; its motion obeys Newton's laws as if all the mass were concentrated there.
Central force
A force directed along the line connecting two bodies, depending only on their separation. Gravity and Coulomb attraction both qualify.
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.
Charles's law
At fixed pressure the volume of a gas is proportional to its absolute temperature — the line that, extended, points at absolute zero.
Chirp mass
The specific combination of two orbiting masses that controls how fast a gravitational-wave inspiral rises in pitch.
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.
Clausius inequality
For any thermodynamic cycle, ∮ dQ/T ≤ 0, with equality only for a reversible cycle.
Clausius statement
Heat does not pass spontaneously from a colder body to a hotter one.