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.
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19 essays
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.
MechanicsThe angle that throws furthest, and why nobody notices
Forty-five degrees is the answer, and the maximum is so flat that a throw ten degrees off loses almost nothing. Both halves of that are worth drawing.
MechanicsThe slope, and the two directions that make it easy
An inclined plane looks like a harder problem than a flat one. Split the weight into two components chosen to suit the slope and it becomes an easier one.
MechanicsCollisions are easier than forces, and momentum is the reason
Nobody knows what happens inside a collision. Momentum conservation makes that ignorance irrelevant, which is the whole trick — and energy, deliberately, is not conserved.
WavesA 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.
WavesWhen two waves meet, they simply add
Waves pass through each other unchanged and their displacements add point by point. From that one impoverished-sounding rule comes interference, beats, and the evidence that light is a wave at all.
WavesOnly some notes fit, and that is where discreteness comes from
A string clamped at both ends can vibrate at some frequencies and not others. A continuous object producing a whole-number list is the oldest quantisation in physics.
OpticsThe 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.
OpticsWhat a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
OpticsThe angle past which light cannot leave
Snell's law asks for the sine of an angle greater than one, and no such angle exists. What happens instead is a perfect mirror made out of nothing but a change of speed.
ElectromagnetismField 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.
ElectromagnetismThe field before the lines were drawn on it
A field is a vector attached to every point of space. Drawing it as arrows on a grid is honest and ugly; drawing it as lines is beautiful and throws information away.
ElectromagnetismCounting what comes out, and never looking inside
Draw any closed surface. The field crossing it depends only on the charge enclosed — not on where that charge sits, not on its shape, not on anything outside.
ThermodynamicsThe 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.
ThermodynamicsEntropy is a count, and the arrow of time is arithmetic
Nothing in mechanics prefers a direction. Entropy is not a force pushing things toward disorder — it is the observation that some outcomes have vastly more ways of happening than others.
ThermodynamicsThe ceiling on every engine, set before it was designed
There is a maximum efficiency no heat engine can exceed, and it depends on nothing but two temperatures. Not the fuel, not the working substance, not the cleverness of the engineer.
RelativityTwo 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.
RelativityThe clock that has to slow, and why no clock can refuse
One constant speed and one right-angled triangle force a moving clock to tick slower. The argument is Pythagoras, which is what makes it inescapable rather than merely surprising.
RelativityNow is a choice of slicing
Two events happening at the same time is not a fact about the events. It is a fact about who is asking, and different observers slice spacetime at different angles.
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.
Order out of the random
Enormous numbers of unpredictable particles producing quantities you can print on a dial.