THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
Chandler wobble
A 433-day periodic wobble of the Earth's rotation axis with a few-metre amplitude at the surface, due to free rigid-body precession.
Chaos
Deterministic dynamics with sensitive dependence on initial conditions — nearby trajectories diverge exponentially.
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.
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.
Compton shift
The wavelength shift Δλ = (h/m_e c)(1 − cos θ) of light scattered off electrons, where θ is the scattering angle. Angle-dependent, independent of the incident wavelength; first measured by Arthur Compton in 1923 with X-rays on graphite — the experiment that established photons as mechanically legitimate particles.
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.
Constructive interference
The superposition of two or more coherent waves in phase, producing an amplitude (and intensity) greater than any single wave. Condition: path-length difference = mλ for integer m.