THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
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–Boltzmann distribution
The probability distribution of molecular speeds in a gas at thermal equilibrium — the first statistical law in the history of physics.
Maxwell's demon
A hypothetical molecule-sorting being that seems to violate the second law — until the entropy cost of its memory is counted.
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.
Mean free path
The average distance a molecule travels between collisions — short enough that a gas molecule is hit billions of times a second.
Mean-field theory
The approximation that each part of a system feels the average of the others — right above four dimensions, wrong in three.
Mechanical equivalent of heat
The fixed conversion factor between mechanical work and heat — 4.186 joules per calorie — that proved heat is a form of energy.
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.
Microcanonical ensemble
An isolated system at fixed energy, volume and particle number, with every accessible microstate equally likely.
Microstate
A complete specification of every degree of freedom of a system — every molecule's position and velocity at once.
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.
Molar heat capacity
The heat to raise one mole of a substance by one degree — the per-atom measure that reveals the Dulong–Petit regularity.
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.
Monte Carlo method
Computing a thermodynamic average by taking a random walk through configuration space, weighted by the Boltzmann factor.
Mössbauer effect
Recoilless gamma-ray emission and absorption by nuclei bound in a solid lattice. The lattice absorbs the recoil momentum collectively, leaving the gamma-ray energy unbroadened by Doppler — producing emission lines narrow enough to resolve frequency shifts at parts-per-quadrillion precision. The technique that made the Pound-Rebka 1960 gravitational redshift measurement feasible.
Most-probable speed
v_mp = √(2k_BT/m) — the speed at the peak of the Maxwell–Boltzmann distribution, the slowest of its three characteristic speeds.
Motional EMF
The EMF induced in a conductor moving through a magnetic field, driven by the magnetic part of the Lorentz force on free charges inside the conductor. Equals (v × B) · ℓ for a straight rod of length ℓ moving with velocity v in field B.
Multi-messenger astronomy
Observing a single cosmic event through more than one fundamental channel — light, gravitational waves, neutrinos, or cosmic rays — at the same time.
Multiplicity (Ω)
The number of microstates that realise a given macrostate — the quantity whose logarithm is entropy.
Mutual inductance
The coupling between two separated coils: M = Φ₁₂/I₂, the flux that coil 2's current produces through coil 1 per unit coil-2 current. The operating principle of every transformer.