THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Superposition principle
For any linear system, the sum of two solutions is also a solution: waves add, they don't collide.
symmetry
An operation under which a system is unchanged — in physics, the source of every conservation law via Noether's theorem.
Symplectic
The antisymmetric non-degenerate 2-form dq ∧ dp on phase space. Preserved exactly by Hamiltonian flow.
tautochrone
Curve where descent time is independent of starting point; the cycloid.
terminal velocity
The steady speed at which a falling body's drag exactly cancels gravity, leaving zero net force.
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.
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).
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.
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).
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.
Weak equivalence principle
The statement that gravitational mass equals inertial mass for any test particle, regardless of composition — equivalently, that all bodies in vacuum fall with identical acceleration. Galileo's Pisa-tower observation, Eötvös's torsion-balance precision result, and the MICROSCOPE 2017 satellite null result confirm it to ≲ 10⁻¹⁵.
work
The energy transferred to a body by a force acting over a distance: W = F · d · cos θ.
World-line
The locus of events in spacetime traced out by a particle as it moves; a 1D curve in the 4D manifold. Massive particles have timelike world-lines; photons have null world-lines; the proper time elapsed on the particle's clock is the arc length of its world-line in the Minkowski metric.