Themes
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.