THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Resistance
The ratio R = V/I for a conductor obeying Ohm's law. Measured in ohms (Ω). Determined by the conductor's geometry (R = ρℓ/A) and material resistivity ρ.
Rest energy
The energy E₀ = mc² that a massive particle has in its own rest frame, where its three-momentum vanishes and its four-momentum reduces to (mc, 0, 0, 0). The conversion factor between mass and energy; the floor below which a particle's total energy cannot drop.
restoring force
Force proportional to displacement and directed back toward equilibrium: F = −kx.
Retarded time
The earlier time t_r = t − |r − r_s(t_r)|/c at which a signal must have left a moving source in order to arrive at the observer at time t. Built into the retarded potentials and all causal electromagnetic radiation formulae.
Reynolds number
Dimensionless ratio Re = ρvL/η of inertial to viscous forces. Re ≪ 1: creeping flow. Re ≫ 1: turbulent.
RL time constant
τ = L/R. The characteristic time for current in an RL circuit to rise to 1−1/e ≈ 63% of its steady-state value, or decay to 1/e ≈ 37% of its initial value.
Roche limit
The minimum orbital distance at which tidal forces overcome self-gravity; closer than this, a moon is torn apart.
Rocket equation
Δv = u · ln(m₀ / m_f) — the velocity a rocket gains by expelling propellant, derived from momentum conservation.
Rolling without slipping
The kinematic constraint v = ω·R that locks a wheel's linear velocity to its rotation so the contact point is momentarily at rest.
Runaway solution
A solution of the Abraham-Lorentz equation in which a free charge's acceleration grows exponentially without bound, a ∝ exp(t/τ₀), without any external force or energy source. The most famous pathology of classical radiation-reaction theory.
Running coupling
The energy-dependent value α(E) of the QED fine-structure constant, increasing from α ≈ 1/137 at low energies to α ≈ 1/128 at the Z-pole and toward 1 at the Landau pole. The breakdown of perturbation theory at high energy is one of the doors from QED to deeper theory.
s-polarization
An EM wave incident on an interface with its electric field perpendicular to the plane of incidence (German senkrecht, "perpendicular"). Also called TE (transverse electric) polarisation. Reflection coefficient never vanishes except at grazing.
Self-energy divergence
The infinite electrostatic field energy U = (q²/8πε₀)·∫ dr/r² stored in the field of a point charge, diverging as 1/r at small radii. Root cause of the pathologies of classical radiation-reaction theory and the target of QED's mass-renormalisation procedure.
Self-inductance
The property of a coil that makes it oppose changes in its own current, characterised by L = Φ/I, where Φ is the flux the coil produces through itself. Units of henry (H = V·s/A).
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.
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.