Illustrated Physics
physics, drawn
Concept

Conservation law — where it appears

A statement that some quantity — energy, momentum, angular momentum, charge — keeps its total value however a system evolves. By Noether's theorem each follows from a symmetry of the laws, and each lets a motion be found without solving it in full.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Why the meander has to move west. A line of fluid columns at 45° pushed into a meander 3,000 km long and 300 km in amplitude, seen from above with north up and east to the right. Columns pushed north find the planet spinning faster beneath them and turn clockwise; columns pushed south turn anticlockwise. Each turning column drives the fluid north on one side of it and south on the other, and the arrows are that flow, from integrating the columns' spin along the line: it peaks at 2.32 m/s, a quarter of a wavelength west of each crest, so the columns just west of a crest are carried north and the crest itself is rebuilt further west. The dashed meander is the same pattern 2 days later, moved 638 km west at β/k² = 3.69 m/s. Nothing in the argument depends on which way the meander was first pushed.

The wave that can only travel west

A column of air or water on a spinning planet keeps one quantity as it moves: its total spin divided by its depth. Carry it north, where the planet's own spin about the local vertical is larger, and it must turn the other way to compensate. That single bookkeeping rule makes a wave that exists nowhere else — one whose crests can only ever move west — and the same rule holds the jet stream's meanders still over the mountains, makes the ocean take decades to notice a change in the wind, and pins the Gulf Stream to the western side of the Atlantic.

mechanics · Circular motion Pushed forward, and left at rest. The path of an electron, initially at rest, overtaken by a 6-cycle pulse of linearly polarised light travelling to the right, for peak field strengths a₀ = 0.5, 1, 2, where a₀ = 1 is the strength at which the electron's quiver becomes relativistic; lengths in wavelengths of the light, the vertical axis along the electric field. While the pulse passes, the electron quivers across the beam and is pushed along it. When the pulse has gone it is at rest again — not moving, with none of the light's energy — but displaced forward by 0.14, 0.56, 2.25 wavelengths respectively, a distance growing as a₀². The quiver's width grows only as a₀: at a₀ = 2 the electron is pushed forward several times further than it swings sideways.

The light that moves an electron and pays it nothing

A pulse of light strong enough to throw an electron forward at a large fraction of the speed of light passes over it, and the electron is left exactly as it was found — at rest, with none of the light's energy — except that it is somewhere else. The reason is two quantities the electron cannot change while a plane wave is passing, and the same two quantities fix the figure eight it traces inside the wave and the angle at which it leaves a real, focused beam carrying the energy it managed to keep.

relativity · Relativistic dynamics

Named alongside it

The objects these essays reach for when they reach for this one.

Canonical momentumCoriolis effectDispersion relationFigure eight orbitLaser accelerationLawson woodward theoremThe Lorentz factorPlane wavePonderomotive forcePotential vorticityRossby waveRotating frame

All concepts