THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Past hypothesis
The premise that the universe began in an extraordinarily low-entropy state, which grounds the thermodynamic arrow of time.
pendulum clock
Mechanical clock regulated by a swinging pendulum; first accurate timekeeper, built by Huygens in 1656.
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.
Penrose Process
Extracting energy from a spinning black hole by feeding it negative energy.
Perihelion Precession
The slow rotation of an elliptical orbit's long axis, whose general-relativistic part first confirmed Einstein's theory through Mercury.
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 transition
A change from one phase to another — melting, boiling, sublimation — that occurs at a definite temperature and pressure and absorbs or releases latent heat.
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.
Phonon
A quantum of lattice vibration — the particle-like packet of sound and heat that carries thermal energy through a solid.
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.
Planck scale
The length, time, and energy where gravity and quantum mechanics must merge — and where general relativity expects to fail.
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.