THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
simple harmonic oscillator
System with a linear restoring force F = −kx; its solution is a pure sinusoid.
Skin depth
δ = √(2/(μσω)), the 1/e penetration depth of an EM wave into a conductor. Fields decay exponentially with depth, so high-frequency currents flow only in a thin surface layer — the skin effect.
Snell's law
n₁ sin θ₁ = n₂ sin θ₂. The ratio of the sines of the incidence and refraction angles at an interface equals the inverse ratio of refractive indices. Derived by Snell 1621 (unpublished), Descartes 1637 (published).
Spacelike
A separation between two events with invariant interval s² < 0 — meaning no signal at or below c can connect them. Spacelike-separated events have a frame-dependent temporal order; the relativity of simultaneity is exactly the freedom to choose any timelike frame and slice spacelike directions as 'now.'
Spacetime
The 4-dimensional pseudo-Euclidean manifold of events introduced by Hermann Minkowski in 1908, in which the three spatial coordinates and time enter on equal footing. The geometric arena of special relativity; the substrate on which world-lines, light-cones, and the invariant interval are defined.
Speed of light (c)
c = 1/√(μ₀ε₀) = 2.99792458 × 10⁸ m/s exactly, by SI definition since 1983. The invariant propagation speed of electromagnetic waves in vacuum and the universal speed limit of special relativity.
Standing wave
A wave pattern locked in place by interference, with fixed nodes and antinodes that don't propagate.
Standing-wave ratio (SWR)
VSWR = V_max/V_min = (1+|Γ|)/(1−|Γ|). A measure of transmission-line reflection. SWR = 1 is a perfect match (no reflection); SWR = ∞ is total reflection (open or short).
static equilibrium
The condition of a body at rest, requiring net force and net torque both to vanish.
static friction
The friction force that resists the onset of sliding; can match applied forces up to a maximum of μ_s · N.
Stationary action
The precise formulation of least action: δS = 0 for every first-order variation of the path vanishing at the endpoints.
Stokes' law
The drag force on a sphere of radius r moving slowly through a fluid of viscosity η: F = 6πηrv.
Streamline
A curve whose tangent at every point coincides with the local fluid velocity. In steady flow, streamlines are also particle paths.
Stress-energy tensor
T_{μν} — the symmetric (0,2) tensor whose components encode energy density (T_{00}), momentum density (T_{0i}), pressure (T_{ii}), and shear stress (T_{ij}, i≠j). Conserved: ∇^μ T_{μν} = 0. The matter side of Einstein's field equations. Perfect fluid: T_{μν} = (ρ + p/c²) u_μ u_ν − p g_{μν}.
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.
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.
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.