THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Newton's laws of motion
The three laws — inertia, F = ma, and equal-and-opposite reaction — that launched classical mechanics in 1687.
Newtonian fluid
A fluid whose shear stress is strictly proportional to its velocity gradient, with viscosity independent of shear rate.
Newtonian limit
The regime where Einstein's field equations reduce to Newton's: weak gravity (g_{μν} = η_{μν} + h_{μν}, |h| ≪ 1), slow sources (v ≪ c), static configuration. In this limit G_{00} ≈ −2∇²Φ/c² and T_{00} ≈ ρc², so EFE becomes ∇²Φ = 4πGρ — the Poisson equation of Newtonian gravity.
No-hair theorem
The statement that a stationary black hole is fully described by just three numbers: its mass, angular momentum, and electric charge.
Node
A point on a standing wave that never moves.
Noether's theorem
Every continuous symmetry of a physical system's action gives rise to a conserved quantity.
Non-abelian gauge theory
A gauge theory whose gauge group is non-commutative, so the gauge fields themselves carry charge under the group and the field strength tensor acquires a self-interaction term. Yang-Mills 1954 introduced the construction; QCD and the weak force are non-abelian; QED is the abelian exception.
nonlinear dynamics
Study of systems where output is not proportional to input; chaos, solitons, turbulence.
normal modes
Independent oscillation patterns of a coupled system; any motion is their superposition.
Null interval
A separation between two events with invariant interval s² = 0 — meaning a light signal exactly connects them. The world-lines of photons are null curves; the light-cone of any event is the locus of null-separated points; null separations sit on the boundary between timelike and spacelike.
Numerical aperture
NA = n sin θ_max. For a fibre, NA = √(n_core² − n_cladding²) gives the sine of the maximum acceptance half-angle. For a microscope objective, NA determines the diffraction-limited resolution λ/(2·NA).
Obliquity
The tilt angle between a planet's rotation axis and the perpendicular to its orbital plane.
Ohm's law
V = IR. For a metallic conductor at fixed temperature, the current through it is proportional to the voltage across it, with the proportionality constant R being the resistance.
Order parameter
The quantity that is non-zero in the ordered phase and zero in the disordered one — whose vanishing is the transition.
p-polarization
An EM wave incident on an interface with its electric field parallel to the plane of incidence (German parallel). Also called TM (transverse magnetic) polarisation. Reflection coefficient passes through zero at Brewster's angle.
parabola
Conic section given by a quadratic in one variable; the trajectory of a projectile under gravity alone.
Parallel transport
The operation that moves a vector along a curve while keeping it as parallel as possible — its covariant derivative along the curve vanishes: D V^μ/dλ = 0. On flat space this returns the same vector; on a curved space it generally rotates. The rotation around a closed loop is the holonomy and is a direct measure of curvature.
parallel-axis theorem
For any axis parallel to one through the centre of mass, I = I_CM + M·d² (also called Steiner's theorem).
Partition function
Z = Σ exp(−E_i/k_BT), the sum over states from which every thermodynamic quantity is obtained by differentiation.
Past hypothesis
The premise that the universe began in an extraordinarily low-entropy state, which grounds the thermodynamic arrow of time.
Penrose diagram
A conformally rescaled spacetime diagram that compresses the infinite ranges of time and space into a finite picture while keeping light rays at exactly 45 degrees.
Permittivity
The constant ε in D = εE that characterises how a medium permits the establishment of an electric field. SI unit: farad per metre.
Perpendicular axis theorem
For a planar body, I_z = I_x + I_y — the moment about an axis perpendicular to the plane equals the sum of moments about two in-plane axes.
Perpetual motion
A machine that runs forever or produces work from nothing — forbidden by the first or second law of thermodynamics.
Phase
A physically distinct, uniform state of matter — solid, liquid, or gas — set by the arrangement of its molecular bonds.
Phase diagram
A map of which state of matter a substance takes at each pressure and temperature.
phase portrait
Plot of position versus velocity showing the trajectory of a dynamical system.
Phase space
The 2N-dimensional space of (position, momentum) pairs in which every classical state is a single point.
Phase velocity
The speed v_p = ω/k at which an individual crest of a sinusoidal wave moves. Can exceed c; carries no information.
Phasor
A complex number representing the amplitude and phase of a sinusoidal quantity. Turns linear differential equations for AC circuits into algebraic equations: V = IZ in the frequency domain.