THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Fresnel equations
The four amplitude coefficients (r_s, r_p, t_s, t_p) giving what fraction of a wave's amplitude reflects from or transmits through a dielectric interface, derived from Maxwell boundary conditions. r_p vanishes at Brewster's angle.
friction
Force that opposes relative motion between two surfaces in contact, converting kinetic energy into heat.
Friedmann Equations
The two differential equations that govern the expansion of a homogeneous, isotropic universe.
Fundamental postulate of statistical mechanics
The assumption that all accessible microstates of an isolated system in equilibrium are equally probable.
Galilean invariance
The principle that the laws of mechanics take the same form in all inertial frames related by Galilean transformations — uniform translation at constant velocity. The pre-relativistic statement of relativity, valid for low speeds.
Gas constant
R = 8.314 J/(mol·K) — the single proportionality constant that makes PV = nRT the same equation for every gas.
Gauge group
The Lie group whose local symmetry transformations leave a gauge theory's Lagrangian invariant. U(1) for electromagnetism (one phase parameter), SU(2) for the weak force (three parameters, three W-bosons), SU(3) for QCD (eight parameters, eight gluons). The Standard Model gauge group is SU(3)×SU(2)×U(1).
Gauge invariance
The principle that the equations of electromagnetism are unchanged under the gauge transformation A_μ → A_μ + ∂_μΛ for any scalar function Λ. Together with Noether's theorem, gauge invariance implies charge conservation. The template for every gauge theory in the Standard Model.
Gauge theory origins
The intellectual lineage from the 1865-1867 observation of gauge freedom in electromagnetism, through Hermann Weyl's 1918 unification attempt and 1929 retooling as a quantum-phase symmetry, to Yang-Mills 1954 and the Standard Model. The gauge principle is the template behind every fundamental force in nature.
Gauge transformation
A change A → A + ∇λ, V → V − ∂λ/∂t in the potentials that leaves all physical fields E and B unchanged. The freedom that defines what 'gauge' means.
Gaussian surface
An imaginary closed surface chosen to exploit symmetry when applying Gauss's law.
Generalised coordinates
Any set of independent variables that fully specifies a system's configuration. Not necessarily Cartesian.
Geodesic equation
d²x^μ/dλ² + Γ^μ_{αβ} (dx^α/dλ)(dx^β/dλ) = 0. The trajectory of a freely-falling particle in curved spacetime; the curve whose tangent is parallel-transported along itself. Generalises the Newtonian straight line. In GR, free-fall = geodesic motion.
Gibbs free energy
G = U − TS + PV, whose decrease decides whether a process runs spontaneously at constant temperature and pressure.
GPS clock correction
The combined SR + GR clock-rate correction applied by every GPS satellite firmware: kinematic time dilation slows the orbiting clock by ~7 μs/day, gravitational time dilation speeds it up by ~45 μs/day, net correction ~+38 μs/day. Without the correction, position fixes would drift roughly 11 km per day.
Gradient
A vector that points in the direction of steepest increase of a scalar field, with magnitude equal to the rate of that increase.
Grand canonical ensemble
A system free to exchange both energy and particles with a reservoir, at fixed temperature and chemical potential.
gravitational field
The vector field g(r) = −GM/r² r̂ giving the acceleration any test mass would experience at each point in space.
Gravitational Lensing
The bending of light by mass, turning galaxies and clusters into natural telescopes that magnify and multiply whatever lies behind them.
Gravitational redshift
Photons climbing out of a gravitational potential lose energy and frequency: Δν/ν = gh/c² for a tower of height h on Earth's surface; equivalently, clocks at lower potential tick slower than clocks at higher potential. A direct consequence of the equivalence principle, derivable without the field equations.
Gravitational wave
A propagating ripple in the curvature of spacetime, traveling at the speed of light.
gravity assist
Technique in which a spacecraft gains or loses speed by flying close to a planet, exchanging momentum through the planet's gravitational field.
Group velocity
The speed v_g = dω/dk at which a wave packet's envelope — and therefore its energy and information — propagates.
Group velocity (EM)
v_g = dω/dk. The speed at which a wave packet's envelope — and therefore its energy and information content — propagates. In a dispersive medium v_g differs from the phase velocity v_p = ω/k.
gyroscope
A rapidly spinning rotor on a gimbal or pivot, whose angular momentum resists reorientation — the workhorse of modern inertial navigation.
H-field
The auxiliary magnetic field H = B/μ₀ − M, in amperes per metre. Its circulation around a loop is determined by free currents only, ignoring bound currents inside magnetised matter.
Hamilton's equations
The first-order system q̇ = ∂H/∂p, ṗ = −∂H/∂q generating time evolution in phase space.
Hamiltonian
A scalar function H(q, p, t) whose partial derivatives, via Hamilton's equations, generate time evolution. For conservative systems, H = T + V.
Harmonic series
The ladder of integer-multiple frequencies that a bounded system supports above its fundamental.
Hawking radiation
The thermal glow emitted by a black hole's horizon, which makes black holes evaporate.