THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
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).
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.
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.
Plane wave
An EM wave whose phase is constant on planes perpendicular to the propagation direction k. Written E(r,t) = E₀ cos(k·r − ωt + φ), with ω = c|k| in vacuum. The simplest solution of the wave equation.
Poisson bracket
The antisymmetric bilinear {f, g} = Σ (∂f/∂q·∂g/∂p − ∂f/∂p·∂g/∂q). Every observable evolves as df/dt = {f, H}.
Polarization
The alignment of bound charges inside a dielectric — every atom or molecule turns into a tiny dipole that points along the local electric field.
Polarization axis
For a linearly polarised wave, the direction along which E oscillates. For a polariser, the transmission axis along which the incident E-component is passed. Set by the vector structure of the wave, not its scalar amplitude.
Polarization density
The vector P = (dipole moment)/(volume), measured in coulombs per square metre, that summarises how strongly a dielectric is polarized at each point.
potential energy
Energy stored in the configuration of a system against a conservative force, retrievable by reversing that configuration.
potential well
Region of potential energy that traps a system; shape determines oscillation character.
power
The rate at which work is done or energy is transferred: P = dW/dt, measured in watts (J/s).
Poynting vector
S = (1/μ₀)·E×B. The vector whose magnitude gives the energy-flux density (W/m²) of the electromagnetic field and whose direction gives the flow direction. Introduced by Poynting in 1884.
Poynting's theorem
∂u/∂t + ∇·S = −J·E. The local statement of energy conservation for the electromagnetic field: rate of change of field-energy density plus divergence of energy flux equals the negative of work done by fields on charges.
Precision Lorentz tests
The modern experimental program that constrains hypothetical Lorentz-violating extensions of special relativity to parts in 10⁻¹⁸ or better — Hughes-Drever magnetic-resonance comparisons, Kennedy-Thorndike interferometric asymmetries, and modern atomic-clock-comparison searches for any frame-dependence of fundamental physics.
Pressure
Force per unit area acting perpendicular to a surface. Scalar. Unit: pascal (Pa = N/m²).
principal axes
Three mutually perpendicular body-fixed axes about which the inertia tensor is diagonal; spinning about them produces no wobble.
Principle of least action
Of all paths a system could take between two fixed events, the one realised in nature is the path for which the action S is stationary.
Proper time
The time τ measured by a clock carried along a particle's world-line. Related to coordinate time by dτ = dt/γ, so dτ = √(1 − β²) dt; integrated along a timelike world-line gives the arc length in the Minkowski metric. Lorentz-invariant; the geometric content of time dilation.