THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Boost mixing of E and B
The phenomenon that under a Lorentz boost, electric and magnetic field components rotate into each other. A pure-E field in one frame becomes E and B in any boosted frame; a pure-B field becomes E and B; the two are not separate physical entities.
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.
Bremsstrahlung
German for braking radiation — the continuous electromagnetic spectrum emitted when a charged particle decelerates in the Coulomb field of a nucleus. Produces the continuum background in X-ray tubes; cuts off sharply at the Duane-Hunt limit E_max = eU.
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.
Capacitance
The ratio of charge stored on a conductor (or between two conductors) to the voltage that stored it. C = Q/V. Units: farads.
Capacitor charging
The exponential rise V(t) = V₀(1−e^(−t/τ)) of a capacitor's voltage as it is charged through a resistor. Half the energy delivered by the source ends up in the capacitor; half is dissipated in the resistor, regardless of R.
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.
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.
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.
Continuous symmetry
A symmetry that depends on a continuous parameter — the kind Noether's theorem turns into conservation laws.