Physics, drawn.

Physics is taught in equations and understood in pictures, and the pictures are usually the part left out. This is a collection of essays about the second kind — one idea at a time, illustrated to the point where the argument becomes visible.

Fig. 1 The field around a positive and a negative charge. Every line is traced by stepping along the local field direction, so the shape is a consequence of the inverse-square law rather than a drawing of what it ought to look like. The lines running off the edge do close on the negative charge — they simply do it outside the frame.

Nine fields

the divisions physics is conventionally cut into

Mechanics

Motion, force, and the quantities that refuse to change.

Waves

Oscillation, and everything that turns out to be an oscillation.

Optics

Light, and the small number of rules it obeys.

Electromagnetism

Charge, field, and the lines drawn between them.

Thermodynamics

Heat, disorder, and the one law with a direction in it.

Relativity

Space and time, drawn on the same axes.

Quantum

Where the continuous picture runs out, and what replaces it.

Fluids

Matter that will not hold a shape, and the forces that act in it anyway.

Astrophysics

Gravity read as geometry, and the laws carried where no laboratory can follow.

Start anywhere

one from each field, of 515

The pendulum's phase portrait. Angle plotted against angular velocity. Closed loops are swinging back and forth; the open curves above and below are rotating all the way round; the dashed curve between them is the separatrix.

The pendulum, and the small lie that makes it simple

A pendulum's period does not depend on how far it swings. This is one of the most useful false statements in physics, and it is worth knowing exactly how false.

A travelling wave, caught at one instant. A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.

A wave is a shape that travels, and nothing else does

In a wave on water, no water goes anywhere. What moves is the shape — and separating the two motions is the whole of wave physics.

4 figures $Refraction from n = 1 into n = 1.5. A ray crossing a boundary between media of refractive index 1 and 1.5, bending by the amount Snell's law requires.$ Optics

The bend at the boundary, and what it is really about

Light changes direction when it changes speed. Snell's law is the geometry of that statement, and it can be derived without knowing anything about light at all.

Electromagnetism

Field lines are a choice, not a discovery

Nothing in space is arranged in lines. The lines are a drawing convention — and an unusually good one, because three separate facts about the field survive the translation.

Molecular speeds at 4 temperatures. The distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.

The speeds in a still room

The air in a quiet room is not still. Every molecule in it is moving at hundreds of metres per second, and temperature is a single number summarising an entire distribution.

A spacetime diagram at β = 0.5. Position across, time up, in units where light travels at 45°. The shaded wedges are the future and past reachable by light; the tilted axes belong to an observer moving at 0.5 of the speed of light.

Two axes, one speed, and a diagram that does the arguing

Put position across and time up, insist that light travels at forty-five degrees for everyone, and nearly every result in special relativity becomes something to read off rather than derive.

The blackbody spectrum, against what classical physics predicted. Spectral exitance against wavelength for a blackbody at 3000, 4000, 5000 kelvin, in kilowatts per square metre per nanometre. Each curve peaks at the wavelength Wien's displacement law gives — 966 nm at 3000 K, 724 nm at 4000 K, 580 nm at 5000 K — and falls to nothing at short wavelengths.

The curve that would not come down

Classical physics predicted that a warm object radiates infinite power at short wavelengths. Every step of the derivation was correct, the prediction was absurd, and closing the gap required assuming that energy comes in lumps.

Three vessels, one pressure. Three vessels filled to the same depth of 3 m. The pressure on each base is 29.4 kPa — identical, because pressure is set by depth — while the weight of water each holds differs by a factor of 4.7. The base of the flaring vessel carries more force than the water standing over it weighs.

The pressure that only knows depth

A litre of water and a swimming pool press equally hard on a floor at the same depth. Pressure in a still fluid is a scalar with no direction of its own, it depends on how far down and on nothing else, and the shape of the container falls out of the arithmetic entirely.

Light crossing an accelerating box. A pulse crosses a box 6 m wide while the box accelerates at 9.81 m/s². The crossing takes 2·10⁻⁸ s, in which the far wall gains 1.96·10⁻⁷ m/s, so the pulse lands 1.96·10⁻¹⁵ m below the height it left at — and the path is a parabola. An observer sealed inside cannot tell that from a beam of light bending in a gravitational field, and the equivalence principle says there is nothing to tell. The sag is drawn 5.6·10¹⁴ times its true size.

The floor that cannot be told from gravity

Seal a laboratory, take away the windows, and no experiment inside it can distinguish standing in a gravitational field from accelerating through empty space. That is not a philosophical remark — it forces light to bend, forces clocks to disagree, and has a size at which it stops being true.

Recently added

40 essays, 16 September 2026

The ripple that counts the neighbours — waves
Below the gap, where there is nothing to absorb — waves
The drift a sound leaves behind — fluids
The oil that is a glass for a quarter of a millisecond — fluids
Whether a fluid can be made arbitrarily thin — fluids
A few cycles that are only mass and spin — astrophysics
The ring that does not come back — astrophysics
The field that points against the magnet it is in — electromagnetism
A potential that does not come back to itself — electromagnetism
The floor that does no work — mechanics
The wall that moves while the ball is in flight — mechanics
The rings that belong to the edge — optics
How accurate a mirror has to be — optics
Two states where the counting says three — quantum
The experiment that defines spin and cannot be done on it — quantum
A fridge with no work going into it — thermodynamics
An engine with one number in it — thermodynamics
The body that has no temperature when it moves — relativity
The count that no observer can disagree about — relativity
The bath that pushes back — relativity
The action that knows where every path ends — mechanics
The throw most likely to go in — mechanics
The orbit that ages less than a throw — relativity
The column that is hotter at the bottom — relativity
The reaction that cannot go all the way — thermodynamics
The glow that carries a voltage — thermodynamics
The outcomes identical photons refuse — quantum
The noise pushed below the floor — quantum
The fall that leaves the mass in the phase — quantum
The field outside that cannot find the core — electromagnetism
The solitons a hump already contains — waves
The coupler that does not care about the colour — waves
The crystal made of moments — optics
The walk that interference can stop — optics
The wave that holds a ship back — fluids
The twist that outlives the turbulence — astrophysics
The clocks that must all slow together — astrophysics
The like charges that pull together — fluids
The current no particle carries — electromagnetism
The circuit that forgets its charge — electromagnetism

Everything that has arrived, group by group

All 515 essays · every field · every ladder · every object named · every figure · what is taught wrongly · search

Threads running through

themes, not chapters

What stays the same

Conservation laws, and the habit of solving a problem by refusing to look at the middle of it.

The same equation again

A pendulum, a circuit, a molecule and a bridge, all obeying one differential equation and not knowing about each other.

Approximations that lie

The small-angle assumption, the frictionless plane, the point mass — where each is fine, and precisely where it stops being.

Fields, not forces

Replacing action at a distance with something that fills space, and what that buys.

The arrow of time

Nearly every law works equally well backwards. Almost nothing else does, and the gap between those facts is thermodynamics.

Where the model stops

Every picture in physics has a domain of validity, and the interesting physics usually lives at its edge.

Made into an instrument

The point at which a principle stops explaining something and starts measuring it — a critical angle sold as a refractometer, a Doppler shift weighing a planet, a null result testing a law.

Order out of the random

Enormous numbers of unpredictable particles producing quantities you can print on a dial.

The shape decides

A number that looks as though it should depend on the forces involved and turns out to depend only on the arrangement — a falloff exponent, a capacitance, a moment of inertia, the angle a rainbow has to be.

Who is measuring

Quantities that are not properties of the thing but of the thing and an observer: which events are simultaneous, how long something is, how fast it is going and whose second is being counted.

What happens at the edge

Quantities that live on a surface rather than in a volume, and conditions imposed at an edge that decide what the whole interior may do — a skin that costs energy per unit area, charge that sits entirely on the outside of a conductor, a clamped end that permits some frequencies and forbids the rest, a wall that quantises a box, and the interface where light has to change direction.

Only some values fit

Continuous objects producing discrete answers. A string that will sound some frequencies and not others, three permitted exponents, a speed no composition can exceed — the first sightings of quantisation, in a subject that has not reached it yet.