THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Invariant interval
The Lorentz-scalar combination s² = c²Δt² − Δx² − Δy² − Δz² between any two events. Invariant under Lorentz boosts and rotations; the special-relativistic analogue of Euclidean distance; its sign distinguishes timelike (s² > 0), spacelike (s² < 0), and null (s² = 0) separations.
inverse-square law
Force or intensity that falls as 1/r² with distance; the form of Newton's gravity and Coulomb's law.
Isentropic process
A reversible adiabatic process, during which the entropy stays constant.
Ising model
A lattice of ±1 spins that agree with their neighbours — the simplest model with a phase transition, and the most studied in physics.
Isobaric process
A change carried out at constant pressure — a horizontal line on a PV diagram, with work simply W = P ΔV.
Isochoric process
A change carried out at constant volume — a vertical line on a PV diagram, doing no work at all, so all heat goes into internal energy.
isochronism
Property of oscillating with a constant period regardless of amplitude; Galileo's 1583 discovery.
Isothermal process
A change at constant temperature, held by slow exchange with a heat reservoir; for an ideal gas ΔU = 0, so Q = W = nRT ln(V₂/V₁).
Johnson noise
The thermal voltage noise of any resistor, V² = 4k_BTRΔf, independent of the resistor's material.
Joule
The SI unit of energy — one newton acting through one metre — named for James Prescott Joule.
Joule–Thomson effect
Squeeze a gas through a plug and it changes temperature — but only cools if it is already cold enough.
KAM theorem
Most invariant tori of a near-integrable Hamiltonian system survive small perturbations. Proves the solar system is mostly stable.
Kelvin scale
The absolute temperature scale whose zero is the floor of thermal motion, making it the only scale on which temperature is a true ratio.
Kelvin–Planck statement
No cyclic engine can turn heat from a single reservoir entirely into work with no other effect.
kinematic equations
The three algebraic relations that describe motion under constant acceleration: v = v₀ + at, x = x₀ + v₀t + ½at², and v² = v₀² + 2a(x − x₀).
kinetic energy
The energy of a body in motion, ½·m·v², measured in joules.
kinetic friction
The friction force acting on a body that is already sliding; has fixed magnitude μ_k · N, independent of speed.
Kinetic theory of gases
The picture of a gas as countless tiny molecules in ceaseless motion, from which pressure and temperature emerge as statistical averages.
Kirchhoff's current law (KCL)
The sum of currents flowing into any node in a circuit equals the sum of currents flowing out. Equivalently: charge conservation applied to circuit junctions, ∇·J = 0 in steady state.
Kirchhoff's voltage law (KVL)
The sum of voltage drops around any closed loop in a circuit equals zero. Equivalently: the electrostatic field is conservative, ∮E·dℓ = 0 in the quasi-static limit.
Kolmogorov spectrum
E(k) ∝ ε^(2/3) k^(−5/3) — the universal inertial-range energy spectrum of fully developed turbulence.
Kramers formula
Hendrik Kramers's 1923 classical thick-target bremsstrahlung spectrum, dN/dE ∝ (E_max − E)/E, giving the continuous-continuum shape of an X-ray tube running at accelerating voltage U with E_max = eU. Full treatment in a later branch.
Lagrange points
Five equilibrium positions in the restricted three-body problem where gravitational and centrifugal forces balance.
Lagrangian
The scalar function L = KE − PE whose time-integral (the action) is minimised along the true path of a physical system.
Laminar flow
Orderly flow in parallel layers, without mixing across them. Characteristic of low Reynolds number.
Landauer's principle
Erasing one bit of information dissipates at least k_BT ln 2 of heat.
Larmor formula
The classical expression P = q²a²/(6πε₀c³) for the total electromagnetic power radiated by a non-relativistic point charge of acceleration a. Derived by Joseph Larmor in 1897; the foundational result of classical radiation theory.
Larmor power
The instantaneous total radiated power P = q²a²/(6πε₀c³) of an accelerating point charge, integrated over all solid angle. Synonym of the Larmor formula result; the quantity that appears as the rate of energy loss in radiation-reaction problems.
Laser cooling
Cooling atoms by shining light on them — down to a millionth of a degree.
Latent heat
The heat absorbed or released during a phase change at constant temperature — energy spent on bonds, not on warming.