THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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 Conditions
The inequalities that demand 'gravity attracts' — the fuel the singularity theorems burn.
Ensemble
A conceptual collection of all microstates available to a system, weighted by probability — the bookkeeping device of statistical mechanics.
Enthalpy
H = U + PV, the energy bookkeeping appropriate to processes at constant pressure.
Entropy
The state function S with dS = dQ_rev/T — the quantity that stays constant on reversible paths and grows on every other.
Entropy of mixing
The entropy increase when distinct gases interdiffuse — positive even though no heat is added.
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.
Equipartition theorem
Every quadratic degree of freedom carries an average energy of ½k_BT — the theorem that fixes heat capacities, and whose failures opened the door to quantum mechanics.
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).
Ergosphere
The region outside a spinning black hole's horizon where standing still is impossible.
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.
Event Horizon
The one-way causal boundary of a black hole: the surface past which no signal can ever return to the outside universe.
Extensive quantity
A property that scales with the size of the system — double the system, double the quantity.
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.
Faraday's law
EMF = −dΦ_B/dt. The induced electromotive force in a closed loop equals the negative rate of change of magnetic flux through the loop. The first of Maxwell's time-dependent equations.
Fermat's principle
Light travels between two points along the path that takes the least time.
Field energy density
The energy stored per unit volume in an electric field: u = ½ε₀E². Measured in joules per cubic metre.
Field line
A curve whose tangent at every point is the direction of the electric field there. Lines begin on positive charges and end on negative ones.
Field momentum
g = ε₀ E×B = S/c². The momentum density carried by the electromagnetic field. Integrated over a volume, it gives the total mechanical momentum the field carries, separate from the momentum of charges and currents.
First law of thermodynamics
Energy conservation for systems that exchange heat and work: ΔU = Q − W. Energy is never created or destroyed, only transferred or stored.
FLRW Metric
The unique spacetime line element for a universe that is the same everywhere and in every direction.
Fluctuation–dissipation theorem
A system's spontaneous fluctuations and its dissipative response to a force are rigidly proportional, with k_BT the constant.
Flux
A scalar measure of how much of a vector field passes through a surface, weighted by the field's component normal to the surface.