THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Szilard engine
A one-molecule thought experiment that extracts k_BT ln 2 of work per measurement, exposing the cost of information.
Tangent space
At each point p of a smooth n-manifold M, the n-dimensional vector space T_p M of all tangent vectors at p. Tangent vectors transform as ∂x^μ/∂x'^ν under coordinate change — the prototype of contravariant index behaviour. The disjoint union of all tangent spaces is the tangent bundle TM.
tautochrone
Curve where descent time is independent of starting point; the cycloid.
telescope
Optical instrument that gathers light and magnifies distant objects; from Newton's 1668 reflector to the James Webb Space Telescope.
Temperature
The intensity of thermal motion — the quantity that equalises when two bodies touch, and that decides which way heat flows.
terminal velocity
The steady speed at which a falling body's drag exactly cancels gravity, leaving zero net force.
Tesla
The SI unit of magnetic flux density. One tesla equals one weber per square metre, or one newton per ampere-metre. Symbol: T.
The two postulates
Einstein's 1905 axiomatic foundation for special relativity: (1) the laws of physics take the same form in all inertial frames; (2) the speed of light c is the same in all inertial frames, independent of the motion of the source. Everything else follows.
Thermal efficiency
The fraction of the heat supplied to an engine that emerges as useful work, η = W/Q_h.
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.
Thermometer
An instrument that gives temperature a number by letting a measurable physical property come to equilibrium with the thing measured.
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.
tidal force
The differential gravitational pull across an extended body; stretches along the line to the attractor and compresses perpendicular to it.
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.
Toroid
A coil wound into a doughnut shape. Confines its magnetic field almost entirely to the interior of the doughnut: B = μ₀ N I / (2πr).
torque
The rotational analogue of force: τ = r × F; equals the rate of change of angular momentum.
Total internal reflection (TIR)
The 100% reflection of light at an interface from a denser to a less dense medium when the angle of incidence exceeds the critical angle θ_c = arcsin(n₂/n₁). The basis of optical fibres, binoculars, and retroreflectors.
Transformer
A two-coil magnetic device that converts AC voltage up or down by the turn ratio: V₂/V₁ = N₂/N₁. The enabler of the electrical power grid.
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 Doppler effect
The relativistic frequency shift observed when the source's velocity is purely perpendicular to the line of sight at the moment of emission. Reduces to f = f₀/γ — pure time dilation, with no classical Doppler contribution. The cleanest experimental test of time dilation.
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.
Turbulence
Fluid motion organised into nested vortices across a vast range of scales. The last unsolved problem of classical physics.
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).