THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Thermal equilibrium
The state two bodies reach when net heat flow between them has stopped and they share a single temperature.
Thermodynamic work
Energy transferred by a system pushing its boundary against a force — for a gas, W = ∫P dV, the area under its path on a PV diagram.
Thin lens
An idealised lens thin enough to neglect the thickness for ray tracing. Obeys the thin-lens equation 1/f = 1/s_o + 1/s_i and the lensmaker's equation 1/f = (n−1)(1/R₁ − 1/R₂).
Third law of thermodynamics
The entropy of a perfect crystal goes to zero at absolute zero — and absolute zero cannot be reached in finitely many steps.
Threshold energy
The minimum incoming-particle energy required to produce a given set of final-state particles in a collision, consistent with conservation of four-momentum. Computed cleanly in the centre-of-momentum frame as the total rest energy of the products; in the lab frame, requires extra kinetic energy to satisfy momentum balance.
Time dilation
The relativistic effect that a clock measured by an inertial observer in motion ticks slower than an identical clock at rest in that observer's frame, by the Lorentz factor γ = 1/√(1 − β²). Symmetric between frames; not an illusion; verified by muon decay, atomic clocks, and GPS.
Timelike
A separation between two events with invariant interval s² > 0 — meaning a sub-c signal can connect them. Timelike-separated events have a frame-independent temporal order; proper time Δτ = √(s²)/c elapses on a clock travelling between them.
torque
The rotational analogue of force: τ = r × F; equals the rate of change of angular momentum.
Transmission line
A pair of conductors (coax, twisted pair, stripline) carrying signals whose wavelength is comparable to or shorter than the line length. Governed by the telegrapher's equations rather than Kirchhoff's laws.
Transverse electromagnetic wave
An EM plane wave in which both E and B oscillate perpendicular to the propagation direction k, and perpendicular to each other. The Gauss-law constraints ∇·E = 0 and ∇·B = 0 force the transverse structure in vacuum.
Transverse-traceless gauge
The coordinate choice that strips a gravitational wave down to its two physical degrees of freedom.
Trapped Surface
A closed 2-surface from which even outward-aimed light is converging — the robust signature that collapse has become irreversible.
Triple point
The single pressure and temperature at which solid, liquid, and gas of a substance coexist in equilibrium.
Turns ratio
n = N₁/N₂, the ratio of primary to secondary turn counts in a transformer. Sets the voltage step (V₁/V₂ = n), the current step (I₁/I₂ = 1/n), and the impedance step (Z_reflected = n²·Z_load).
Unitarity
The principle that quantum time evolution preserves probability and never destroys information.
Universality
The principle that critical behaviour depends only on dimensionality and symmetry — never on what the system is made of.
Vapour-compression cycle
The loop inside every real refrigerator — and the reason it boils something.
vector
A quantity with both magnitude and direction; represented as an arrow and added tip-to-tail.
Vector potential
The vector field A whose curl gives the magnetic field: B = ∇×A. Lets you compute B from a scalar-like integral over the source currents.
velocity
The rate of change of position with respect to time; a vector in 2D and 3D, a signed scalar in 1D.
vis viva equation
v² = GM(2/r − 1/a) — gives the orbital speed at any distance r for an orbit with semi-major axis a.
Viscosity
A fluid's internal resistance to shear. For Newtonian fluids, shear stress = η·(du/dy). Unit: Pa·s.
Voltage divider
Two resistors in series between a voltage source and ground, with the output voltage taken at the midpoint. V_out = V_in · R₂/(R₁+R₂). The simplest non-trivial circuit.
Vortex
A coherent region of swirling fluid — the basic building block of turbulent and near-turbulent flow.
Wave equation
The linear PDE whose solutions are any right-mover plus any left-mover at speed v.
Wave packet
A localised wave formed by superposing many plane-wave components with a narrow band of wavenumbers.
Waveguide mode
A specific transverse field pattern that propagates along a waveguide without distortion, characterised by a propagation constant β and a cutoff frequency below which the mode is evanescent.
Wavelength
The spatial period of a wave — distance crest to crest, symbol λ.
Wavelength (EM)
The spatial period λ of an EM plane wave, the distance between successive points of equal phase. Related to frequency by λ = c/f in vacuum, λ = c/(nf) in a medium. Ranges from kilometres (longwave radio) to femtometres (gamma).
Wavenumber
k = 2π/λ, the spatial angular frequency of a wave, measured in rad/m. The wavevector k has magnitude k and direction along propagation. In spectroscopy, wavenumber often means k̃ = 1/λ in cm⁻¹.