THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
beats
Amplitude modulation from superposition of two close frequencies; f_beat = |f₁ − f₂|.
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.
Big Bang Nucleosynthesis
The forging of the light elements in the first few minutes of the universe.
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.
Birefringence
The property of an optically anisotropic material to have different refractive indices for different polarisations of light. Splits an unpolarised beam into two refracted rays (ordinary and extraordinary).
Birkhoff's theorem
Any spherically symmetric vacuum solution of Einstein's equations must be static and equal to the Schwarzschild metric.
Blueshift
The compression of a wave's wavelength when source and observer move together.
Boltzmann constant (k_B)
The conversion factor between temperature and energy, k_B = 1.380649 × 10⁻²³ J/K.
Boltzmann distribution
p_i ∝ exp(−E_i/k_BT): the probability of a microstate falls off exponentially with its energy.
Boltzmann entropy formula (S = k log W)
Entropy is Boltzmann's constant times the logarithm of the number of microstates: S = k_B ln Ω.
Boltzmann factor
exp(−E/k_BT) — the exponential weight that sets how likely a state of energy E is at temperature T, and the engine of statistical mechanics.
Boost mixing of E and B
The phenomenon that under a Lorentz boost, electric and magnetic field components rotate into each other. A pure-E field in one frame becomes E and B in any boosted frame; a pure-B field becomes E and B; the two are not separate physical entities.
Born rigidity
Max Born's 1909 definition of relativistic rigidity: a body is Born-rigid if its proper length stays constant during acceleration. A truly rigid rod must have its trailing end accelerate faster than its leading end so that length contraction cancels exactly — the constraint that Bell's two-rocket setup violates.
Bound charge
Charge that cannot move freely through a material because it is stuck inside individual atoms or molecules — yet still rearranges locally when the medium is polarized.
Boundary conditions (EM)
The matching rules at an interface between two media: the normal component of D jumps by the free surface charge; the tangential component of E is continuous.
Boyle's law
At fixed temperature the pressure and volume of a gas are inversely proportional: PV is constant.
Bremsstrahlung
German for braking radiation — the continuous electromagnetic spectrum emitted when a charged particle decelerates in the Coulomb field of a nucleus. Produces the continuum background in X-ray tubes; cuts off sharply at the Duane-Hunt limit E_max = eU.
Brewster's angle
θ_B = arctan(n₂/n₁), the angle at which reflected light from a dielectric interface is perfectly s-polarised because the p-polarised Fresnel reflection coefficient r_p vanishes. Brewster 1815.
Brownian motion
The incessant random jitter of a small particle suspended in a fluid, driven by molecular collisions — the visible proof that atoms are real.
Buoyancy
The upward force on an object immersed in a fluid, equal to the weight of the fluid the object displaces.
Caloric theory
The discredited eighteenth-century idea that heat is a weightless, conserved fluid called caloric that flows from hot bodies to cold.
Calorie
A thermal unit of energy — the heat needed to raise one gram of water by one degree Celsius — equal to 4.186 joules.
Calorimetry
The measurement of heat — classically by dropping a hot body into insulated water and reading the final temperature.
Canonical ensemble
A system at fixed temperature, volume and particle number, free to exchange energy with a heat bath.
Capacitance
The ratio of charge stored on a conductor (or between two conductors) to the voltage that stored it. C = Q/V. Units: farads.
Capacitor charging
The exponential rise V(t) = V₀(1−e^(−t/τ)) of a capacitor's voltage as it is charged through a resistor. Half the energy delivered by the source ends up in the capacitor; half is dissipated in the resistor, regardless of R.
Carnot cycle
The idealised, fully reversible engine cycle of two isotherms and two adiabats that sets the efficiency ceiling for all heat engines.