THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Einstein equivalence principle
The form of the equivalence principle Einstein needed for general relativity: WEP + local Lorentz invariance + local position invariance. Inside any sufficiently small freely falling laboratory, the laws of physics reduce to special relativity, and any deviation would be measurable by a sensitive enough experiment.
Einstein field equations
G_{μν} = (8πG/c⁴) T_{μν}. Ten coupled nonlinear partial differential equations relating spacetime geometry (left) to matter-energy distribution (right). The defining equations of general relativity. Published November 1915 by Einstein; near-simultaneously derived by Hilbert via the Einstein-Hilbert action.
Einstein tensor
G_{μν} = R_{μν} − (1/2) R g_{μν}. The unique divergence-free combination of Ricci and metric — ∇^μ G_{μν} = 0, a consequence of the contracted Bianchi identities. The geometric side of Einstein's field equations G_{μν} = (8πG/c⁴) T_{μν}.
elastic collision
A collision in which total kinetic energy is conserved as well as total momentum.
Electric charge
The fundamental conserved quantity that produces electric forces. Comes in ± signs. Measured in coulombs.
Electric field
The force per unit charge that a test charge would feel at a given point. A vector field filling all of space. Units: newtons per coulomb, equivalently volts per metre.
Electric potential
The electrostatic potential energy per unit charge at a point. A scalar field measured in volts. V = −∫E·dℓ from a reference point.
Electric susceptibility
The dimensionless coefficient χ_e in P = ε₀χ_e E that measures how easily a dielectric polarizes in response to an applied electric field.
Electromagnetic duality
The symmetry E → cB, cB → −E (equivalently F^{μν} → *F^{μν}) that maps the source-free Maxwell equations to themselves. In a universe with magnetic monopoles, the duality extends to interchanging electric and magnetic charges/currents, restoring perfect E↔B symmetry to the field equations.
Electromagnetic field
The unified field consisting of both the electric field E and the magnetic field B (equivalently, the antisymmetric tensor F^μν). Classical electromagnetism is the study of its dynamics. Full treatment across §07–§08.
Electromagnetic field tensor
The rank-2 antisymmetric 4×4 tensor F^{μν} that packages the three components of E and three components of B into one Lorentz-covariant object, with F^{0i} = E_i/c and F^{ij} = -ε_{ijk} B_k. Also called the Faraday tensor.
Electromagnetic induction
The generation of an electromotive force in a circuit whenever the magnetic flux through it changes. Discovered by Faraday and Henry in 1831, it is the foundation of every electric generator, transformer, and inductive sensor ever built.
Electromagnetic spectrum
The full range of frequencies (or equivalently wavelengths) of EM radiation, from kilohertz radio to zettahertz gamma rays. All regions are the same physical phenomenon — classical EM waves — differing only in ω.
Electromagnetic wave
A self-sustaining coupled oscillation of electric and magnetic fields that propagates through vacuum at c = 1/√(μ₀ε₀). E, B, and k are mutually perpendicular. Maxwell's synthesis identified light itself as an electromagnetic wave.
Electromagnetic wave equation
The second-order PDE ∇²E = (1/c²)∂²E/∂t² (and identically for B), derived from Maxwell's equations in source-free vacuum. Its plane-wave solutions propagate at c = 1/√(μ₀ε₀).
Electromotive force (EMF)
The work per unit charge done by a source on charges as they move around a closed circuit, measured in volts. Despite the name, EMF is not a force; it is the energy-per-charge a battery, generator, or induction process supplies.
ellipse
Closed curve where the sum of distances from any point to two foci is constant.
elliptic integral
Integral involving square root of cubic/quartic polynomial; gives the exact period of a large-angle pendulum.
Elliptical polarization
The general polarisation state of a single-frequency EM wave: the E-vector traces an ellipse per cycle. Linear and circular polarisations are the two degenerate limits.
EM Lagrangian density
The Lorentz-invariant scalar L = −¼F_{μν}F^{μν} − A_μJ^μ from which all of classical electromagnetism follows. Euler-Lagrange recovers Maxwell's equations; gauge invariance via Noether gives charge conservation. The cleanest sentence in physics.
Energy cascade
Richardson's picture: energy injected at large scales is handed down, eddy by eddy, to smaller scales until viscosity dissipates it as heat.
Eötvös parameter
The dimensionless ratio η = (m_g − m_i)/m_i quantifying the fractional difference between gravitational and inertial mass for a given material. Eötvös's torsion-balance experiments constrained η ≲ 10⁻⁹; modern Eöt-Wash and MICROSCOPE measurements push the bound to ≲ 10⁻¹⁵.
epicycle
Small circle whose center moves along a larger one; Ptolemy's device for saving uniform circular motion.
equatorial bulge
The excess of the Earth's equatorial radius over its polar radius (about 21 km), caused by the centrifugal deformation of rotation.
Equipotential
A surface on which the electric potential is constant. No work is done moving a charge along an equipotential, and the electric field is everywhere perpendicular to it.
Equivalence principle
Einstein's foundational GR axiom: no local experiment can distinguish a freely falling laboratory in a gravitational field from an inertial laboratory in flat spacetime. Comes in three increasingly strong forms — weak (m_g = m_i), Einstein (WEP + local Lorentz invariance + local position invariance), and strong (extends to self-gravitating bodies).
escape velocity
The minimum speed needed to escape a gravitational field: v_esc = √(2GM/r). For Earth's surface, ~11.2 km/s.
Euler angles
Three angles specifying the orientation of a rigid body in space relative to a fixed reference frame.
Euler-Lagrange equations
d/dt(∂L/∂q̇) = ∂L/∂q — the differential form of stationary action, equivalent to Newton's second law.
Far-field zone
The region r ≫ λ surrounding an oscillating source where the field is an outgoing spherical wave with amplitude ∝ 1/r and time-averaged Poynting flux that transports energy irreversibly outward. Also called the radiation zone, Fraunhofer zone, or wave zone.