THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
semi-major axis
Half the longest diameter of an ellipse; appears in Kepler's third law as T² ∝ a³.
separatrix
Phase-space boundary between qualitatively different motions.
shell theorem
A uniform spherical shell attracts an external particle as if all its mass were at the centre; it exerts zero net force on an internal particle.
simple harmonic oscillator
System with a linear restoring force F = −kx; its solution is a pure sinusoid.
Single-slit diffraction
The intensity pattern I(θ) = I₀ sinc²(πa sin θ/λ) produced when light of wavelength λ passes through a slit of width a. First minimum at sin θ = λ/a; central maximum carries most of the energy.
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 Derived by Snell 1621 (unpublished), Descartes 1637 (published).
Solenoid
A long, tightly wound helical coil of wire. Carrying a current, it produces a uniform magnetic field along its axis: B = μ₀ n I.
Sonic boom
The sharp pressure impulse heard when the Mach cone of a supersonic source sweeps past an observer.
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.
Synchrotron radiation
The electromagnetic radiation emitted by a relativistic charged particle following a curved trajectory in a magnetic field. Power scales as γ⁴ in circular motion; the spectrum is broad with characteristic frequency ω_c ∝ γ³c/R. Basis of synchrotron light sources and pulsar emission.
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.
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.