THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
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.
Length contraction
The relativistic effect that an object of proper length L₀ measured in its rest frame appears contracted to L = L₀/γ along the direction of motion when measured by an observer in any inertial frame moving relative to the object. Symmetric; not a material compression; perpendicular dimensions unchanged.
Length contraction of current
The relativistic effect that a current-carrying lattice, viewed in the rest frame of its drift electrons, has its inter-ion spacing contracted by the Lorentz factor γ. Produces the net + charge density that explains magnetic attraction as relativistic electrostatics.
Lenz's law
The direction of an induced current is always such that its own magnetic field opposes the change in flux that caused the induction. Equivalently: the minus sign in Faraday's law is a consequence of energy conservation.
lever
A rigid bar pivoting about a fulcrum, trading applied force against distance to achieve mechanical advantage.
libration
Bounded oscillation within a potential well, as opposed to full rotation.
Light-cone
The locus of events null-separated from a chosen origin event in spacetime; geometrically a 4D double cone with apex at the origin. The boundary between causally accessible (timelike-interior) and causally inaccessible (spacelike-exterior) regions; the structure that encodes relativistic causality.
Line integral
The integral of a vector field along a curve, measuring the accumulated effect of the field's component tangent to the path.
Linear polarization
An EM wave in which E oscillates along a single fixed line perpendicular to k. Equivalent to a superposition of two circularly polarised waves of equal amplitude with opposite handedness.
Liouville's theorem
Under Hamiltonian flow, phase-space volume is exactly conserved. The foundation of classical statistical mechanics.
Lorentz force
The total electromagnetic force on a point charge: F = q(E + v×B). Bridges Maxwell's macroscopic fields to the motion of individual particles.
Lorentz invariants of the EM field
The two scalar quantities — E·B and |E|² − c²|B|² — that every observer agrees on, regardless of their motion. Constructed as tensor traces from F^{μν}; classify the field as 'electric-like', 'magnetic-like', or 'null'.
Lorentz transformation
The linear coordinate transformation between two inertial frames in special relativity. For a boost along +x at velocity v: t' = γ(t − vx/c²), x' = γ(x − vt), y' = y, z' = z. Replaces the Galilean transformation; reduces to it in the limit β → 0.
Lorentz transformation of fields
The closed-form rule by which the components of E and B transform under a Lorentz boost. Parallel components are unchanged; perpendicular components mix linearly with the perpendicular components of the OTHER field. Derived by Hendrik Lorentz in 1895.
Lorenz gauge
The gauge condition ∇·A + (1/c²)∂V/∂t = 0, which decouples Maxwell's equations for the scalar potential V and vector potential A into two separate wave equations with the same speed c. Named for Ludvig Lorenz (not Hendrik Lorentz).
Luminiferous aether
The hypothetical all-pervasive medium that nineteenth-century physics posited as the substrate in which light waves propagate. Searched for via interferometry from 1881 onward; never detected. Discarded by Einstein's 1905 special-relativity paper.
Lyapunov exponent
The exponential rate λ at which nearby trajectories of a dynamical system diverge. Positive λ means chaos.
Mach number
The ratio of a source's speed to the speed of sound in the surrounding medium.
Magnetic dipole
The smallest possible source of a magnetic field — a tiny current loop or a single particle's intrinsic spin. The magnetic equivalent of an electric dipole.
Magnetic domain
A microscopic region inside a ferromagnet in which all atomic moments point in the same direction. Bulk ferromagnets are partitioned into many such domains, averaging to zero or near-zero net magnetization at rest.
Magnetic energy density
The energy stored per unit volume of a magnetic field: u_B = B²/(2μ₀) in vacuum, u_B = ½ BH in linear matter. The magnetic counterpart of the electric field energy density ε₀E²/2.
Magnetic field
The vector field B that exerts a sideways force on moving charges and steady currents. Sourced by currents and intrinsic spin, never by isolated magnetic charges.
Magnetic moment
The vector m = IA n̂ that quantifies the strength and orientation of a magnetic dipole. Determines its torque, energy, and far-field structure in any external field.
Magnetic monopole
A hypothetical particle carrying isolated magnetic charge g, sourcing the dual field tensor *F^{μν} the way an electron sources F^{μν}. Predicted in 1931 by Dirac as quantum-mechanically consistent; force charge quantisation; arise naturally in grand-unified theories. Never observed despite sixty years of dedicated search.
Magnetic permeability
The factor μ that relates B to H in a linear magnetic material: B = μH. Vacuum has μ = μ₀; other materials are characterised by the relative permeability μ_r = μ/μ₀ = 1 + χ.