THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Abbe number
V_d = (n_d − 1)/(n_F − n_C), a dimensionless measure of optical dispersion in a material. High V_d (~65) means low dispersion (crown glasses); low V_d (~25) means high dispersion (flint glasses).
Abraham-Lorentz equation
The third-order equation of motion m·a = F_ext + (μ₀q²/6πc)·ȧ for a radiating classical point charge, combining Newton's second law with a jerk-proportional radiation-reaction force. Derived 1903–1904; harbours runaway solutions and acausal pre-acceleration.
Absolute zero
The lowest possible temperature, 0 K (−273.15 °C), where thermal motion reaches the minimum permitted by quantum mechanics.
AC frequency
The number of full cycles per second of an alternating current or voltage, measured in hertz (Hz). Standard power-grid frequencies are 50 Hz (most of the world) or 60 Hz (North America, parts of South America and Japan).
acceleration
The rate of change of velocity with respect to time; positive when speeding up, negative when slowing down.
Action
The time-integral of the Lagrangian along a trajectory: S = ∫ L dt = ∫ (T − V) dt. Units of energy × time.
Adiabatic demagnetisation
Cooling with disorder: turn a magnet down and the spins take their entropy back out of the temperature.
Adiabatic exponent
The ratio of heat capacities γ = C_p/C_v that governs adiabatic change: 5/3 for a monatomic gas, 7/5 for a diatomic one.
Adiabatic process
A change with no heat exchange, Q = 0; the gas cools as it expands and heats as it is compressed, following PVᵞ = const.
Aharonov-Bohm phase
The quantum-mechanical phase Φ = (q/ℏ) ∮ A·dℓ acquired by a charged particle traversing a closed loop, equal to (q/ℏ) times the enclosed magnetic flux. Periodic in the flux quantum Φ_0 = h/|q|; demonstrates that the four-potential is observable in quantum mechanics even where the field is zero.
Ampère's law
The line integral of B around a closed loop equals μ₀ times the enclosed current: ∮ B·dℓ = μ₀ I_enc. Magnetism's analogue of Gauss's law.
Amplitude response
The steady-state amplitude of a driven oscillator as a function of drive frequency — peaked near resonance.
angular acceleration
The rate of change of angular velocity: α = dω/dt; the rotational analogue of linear acceleration.
angular momentum
Rotational analogue of momentum: L = r × p for a particle, L = I·ω for a rigid body; conserved when external torque is zero.
Angular velocity
Rate of rotation, measured in radians per second: ω = dθ/dt. A vector aligned with the rotation axis (right-hand rule).
Anomalous magnetic moment
The deviation of the electron's gyromagnetic ratio from the Dirac value g = 2: a_e ≡ (g − 2)/2 = α/(2π) + O(α²) ≈ 0.00115965218... — the most precisely-tested prediction in physics, agreeing with experiment to 12 decimal places. Schwinger's 1948 calculation was the first triumph of QED.
Antenna gain
The dimensionless ratio G = 4π · (maximum radiation intensity)/(total radiated power) that quantifies how much an antenna concentrates its radiation in its peak direction relative to an isotropic radiator. Usually expressed in dBi (decibels over isotropic).
Antinode
A point on a standing wave where the oscillation reaches its full peak amplitude.
Arrhenius equation
k = A exp(−E_a/k_BT) — the law that ties a reaction's rate to temperature through the Boltzmann tail of molecules energetic enough to react.
Arrow of time
The one-way direction of macroscopic processes — set by increasing entropy, though the microscopic laws are time-symmetric.
Atmospheric pressure
The weight of the column of air above any point, at sea level ≈ 101.325 kPa or 760 mm Hg.
Avogadro's number
The count of molecules in one mole, 6.022 × 10²³ — the bridge between the gram-and-litre world and the molecule-by-molecule world.
Back-EMF
The EMF induced in an inductor or motor winding that opposes the change in current or rotation driving it. In a DC motor at steady state, back-EMF roughly equals the supply voltage minus the resistive drop.
Back-reaction
The effect of a radiating charge's own emitted field on its own motion — self-force. Usually small but produces measurable effects like the Abraham–Lorentz radiation-reaction force and the Lamb shift.
Barn-pole paradox
A textbook puzzle in which a pole longer than a barn at rest fits inside the barn at relativistic speed because length contraction shortens it in the barn frame, while in the pole frame the doors open and close non-simultaneously. Two observers, two stories, no contradiction — once the relativity of simultaneity is taken seriously.
Bekenstein–Hawking entropy
The entropy of a black hole, equal to one quarter of its horizon area in Planck units.
Bell's spaceship paradox
A thought experiment in which two identical rockets, accelerating identically in the launch frame, are connected by a thin string. The launch-frame distance between them is constant, but the string snaps. The resolution is that 'rigid' acceleration must Born-rigidly contract the rod, while two-rocket setups violate that constraint.
Bernoulli's principle
Along a streamline in an incompressible, inviscid fluid, p + ½ρv² + ρgh is conserved.
Bethe-Heitler formula
The 1934 quantum-mechanical bremsstrahlung cross-section derived by Hans Bethe and Walter Heitler, extending Kramers's classical formula to relativistic electrons and thin targets. Full treatment in a later QED branch.
Biot–Savart law
The integral that gives the magnetic field of a steady current: dB = (μ₀/4π) (I dℓ × r̂) / r². Magnetism's analogue of Coulomb's law.