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.
Singularity
A place where the classical geometry of spacetime breaks down — defined by what is missing, not by what is there.
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 Derived by Snell 1621 (unpublished), Descartes 1637 (published).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.
Specific heat capacity
The heat required to raise one unit mass of a substance by one degree — large for water, small for metals.
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.
Spin
The intrinsic angular momentum of a particle — and, in statistical physics, the two-valued variable that stands in for it.
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).
State function
A property whose value depends only on the current state of a system, not on the path taken to reach it — internal energy, temperature, pressure, entropy.
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.
Strain
The dimensionless fractional length change a gravitational wave imprints on space: ΔL/L.
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.
Surface gravity
The acceleration at a black hole's horizon, which plays the role of its temperature.
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.
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.
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.
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.