THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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.
Magnetic susceptibility
The dimensionless ratio χ = M/H measuring how strongly a linear magnetic material is magnetised by an applied H-field. Negative for diamagnets, positive and small for paramagnets, large for ferromagnets.
Magnetization
The vector M = (magnetic dipole moment)/(volume) inside a magnetised material, measured in amperes per metre. The magnetic analogue of polarization density.
Malus's law
I = I₀ cos²θ. The transmitted intensity of linearly polarised light through an ideal polariser depends on the cosine-squared of the angle between the incident polarisation and the polariser's transmission axis.
Manifold
An n-dimensional space that locally looks Euclidean. Each point has a neighbourhood homeomorphic to ℝⁿ; a *smooth* manifold adds a differentiable structure compatible across overlapping coordinate patches. A sphere is a 2-manifold; spacetime in general relativity is a 4-manifold.
mass
The quantitative measure of a body's inertia; the m in F = ma.
Mass-energy equivalence
Einstein's 1905 result E = mc² — that mass and energy are the same physical quantity expressed in different units, with c² as the conversion factor. Binding energies and kinetic energies register on a balance as mass; the foundation of nuclear physics, fusion, fission, and particle production.
Maxwell stress tensor
T_ij = ε₀(E_iE_j − ½δ_ij E²) + (1/μ₀)(B_iB_j − ½δ_ij B²). The 3×3 symmetric tensor whose divergence gives the mechanical force per unit volume the electromagnetic field exerts on charges and currents.
Maxwell's equations
The four coupled partial differential equations (∇·E = ρ/ε₀, ∇·B = 0, ∇×E = −∂B/∂t, ∇×B = μ₀J + μ₀ε₀ ∂E/∂t) that fully describe classical electromagnetism. Every electromagnetic phenomenon below the quantum scale follows from them.
Meißner effect
The active expulsion of magnetic flux from the interior of a superconductor on cooling below T_c in an applied field. The signature that superconductivity is a distinct thermodynamic phase, not mere zero resistance.
Metric tensor
Symmetric (0,2) tensor g_{μν} that defines distances, angles, and proper times on a manifold. ds² = g_{μν} dx^μ dx^ν. In flat SR spacetime g = η = diag(+1, −1, −1, −1); in GR g_{μν}(x) varies with position and encodes all gravitational information.
Milankovitch cycles
The three astronomical cycles — eccentricity, obliquity, precession — that drive Earth's ice ages on 10,000- to 100,000-year timescales.
Mode
An allowed standing-wave pattern of a bounded system, labelled by an integer.
Moment arm
The perpendicular distance from a rotation axis to the line of action of a force. Torque = force × moment arm.
moment of inertia
The rotational analogue of mass: I = Σ m_i · r_i² (or ∫ r² dm for a continuous body).
momentum
Mass times velocity (a vector, p = m·v); conserved in any closed system.
monkey and the hunter
Classic thought experiment: a dart fired straight at a monkey that falls at the trigger still hits the monkey, because both are in the same free fall.