THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
Piezoelectricity
The appearance of an electric voltage across certain crystals when they are mechanically squeezed — and the converse: the same crystals deform when a voltage is applied.
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.
Poincaré recurrence
In a bounded Hamiltonian system, almost every trajectory returns arbitrarily close to its starting state — given enough time.
Poiseuille flow
Steady laminar flow through a cylindrical pipe driven by a pressure drop. Volumetric flow rate Q = πR⁴Δp/(8ηL).
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.
precession
The slow conical sweep of a spinning body's axis of rotation when a torque acts perpendicular to its angular momentum.
Precession of the equinoxes
The slow 26,000-year conical sweep of Earth's rotation axis, which makes the equinoxes drift through the zodiac.
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.
projectile motion
Motion of an object fired into the air under gravity alone; the trajectory is a parabola in vacuum.
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.
quadrant
Pre-telescope astronomical instrument for measuring the angular position of stars and planets.
quality factor
Quality factor Q = ω₀/γ; number of oscillations before energy drops to 1/e.
Quality factor (Q)
Dimensionless number Q = ω₀L/R = 1/(ω₀RC) = (1/R)·√(L/C) for an RLC circuit, measuring how sharply resonant the response is. Equivalently Q = 2π · (energy stored) / (energy lost per cycle).
Radiation pattern
The angular distribution of an antenna's far-field radiated power as a function of direction, dP/dΩ(θ, φ). For a short dipole the pattern is the sin²θ doughnut; for arrays and apertures it is the magnitude-squared Fourier transform of the current distribution.
Radiation pressure
The mechanical pressure an electromagnetic wave exerts on a surface it strikes: I/c for absorbers, 2I/c for perfect reflectors, where I is the intensity in W/m². Discovered in principle by Maxwell (1871), measured by Lebedev (1901).