Reference shelf

Which model when

A decision guide: given a real situation, the simplest model that holds and exactly where it breaks.

Written by Claude Fable 5

Every model in this course is an approximation with an edge, a region where it is true and a line past which it lies. The first lesson makes that the whole point of physics. This page is the map: the situation you are in, the simplest model that still holds, and exactly when it stops.

How to use this

Always reach for the simplest model that does not break. Newton before relativity, a ray before a wave, a point before a spinning body. The skill is not knowing the fanciest model; it is knowing the cheapest one you can get away with, and noticing the moment its assumptions crack.

Which mechanics: Newton, relativity, or quantum

Three models of the same reality, nested by scale and speed. Newton covers essentially everything you can see and touch; the other two only earn their keep at the extremes of very fast and very small.

When the situation is	Reach for	It breaks when
Cars, balls, planets, buildings: everyday speeds, everyday sizes, everyday gravity	Newtonian mechanics	Speeds approach the speed of light, or you zoom down to single atoms and electrons. Almost never, for almost everything you touch.
Speeds a real fraction of light, or timing that must agree to nanoseconds, as in GPS	Relativity	Its corrections vanish at everyday speeds, so it is needless overhead there. It also says nothing about the atomic scale, which is quantum territory.
Electrons in atoms, photons, transistors, LEDs, solar cells: the very small	Quantum mechanics	You scale back up to many particles, where the averages wash out the weirdness and Newton returns as the large-number limit.

Why GPS is the perfect test case

A GPS satellite is where all three regimes collide. Newtonian orbits place it, special relativity slows its fast-moving clock, and general relativity speeds it up in weaker gravity. Ignore the relativity and positions drift about 11 km per day. The everyday model is not wrong so much as insufficient, exactly at the precision GPS demands.

Is light a ray, a wave, or a photon

Light is not three things; it is one thing you can afford to picture three ways. Which picture you pick is set entirely by what you are trying to predict.

When the situation is	Reach for	It breaks when
Lenses, cameras, mirrors, shadows, fibre optics: where an image forms	Light as a ray	The aperture or feature shrinks toward the wavelength of light, where the ray frays into diffraction and you need the wave picture.
Interference, diffraction, thin-film color, why two slits make bands	Light as a wave	Energy arrives one indivisible lump at a time, as in the photoelectric effect, which a smooth wave cannot explain.
A frequency threshold: photoelectric effect, LED colors, solar cells	Light as photons	You only care where the image lands, not its energy. Then the photon bookkeeping is wasted and the ray model is simpler.

Stepping time in a simulation

The same forces, three ways to march them forward. The choice is not about smaller steps but about the order of the updates, and it decides whether your orbit holds for a million frames or quietly flies apart.

When the situation is	Reach for	It breaks when
A short, one-off trajectory where small drift will not matter	Explicit Euler	Anything oscillates or orbits. It silently pumps in energy every step, so springs grow and orbits spiral outward.
A game, orbit, or spring that must stay stable over a long run	Semi-implicit Euler	Rarely, for a game. Reach further only when you need exact time-reversibility or the very tightest energy conservation.
Molecular dynamics or any long, precise, reversible simulation	Velocity Verlet	It costs more per step for accuracy you will not notice in a simple game loop, where semi-implicit Euler already holds.

Gases, heat, and the arrow of time

The thermodynamics models each assume a clean regime: a gas dilute enough to ignore its own molecules, heat flowing steadily by conduction, a system isolated enough to talk about its entropy.

When the situation is	Reach for	It breaks when
A dilute gas well above boiling: air in a tyre, a balloon, the atmosphere	Ideal gas law	Pressure gets high or the gas nears condensing, where molecules start attracting each other and taking up real space.
Heat flowing through stacked layers: chip to paste to heatsink to air	Thermal-resistance network	Radiation or stirred-up convection starts to dominate over steady conduction, so the simple series of resistances no longer adds up.
Which way a process runs, whether it can reverse, the ceiling on an engine	Entropy and the second law	You forget it is statistical: it forbids the overwhelmingly unlikely, not the strictly impossible, and only for an isolated system.

When a point is not enough

Most of mechanics pretends an object is a single point carrying all its mass. That shortcut is free until the object can spin or topple, and then you have to account for where the mass actually sits.

When the situation is	Reach for	It breaks when
Sliding, dropping, a projectile, an orbit: only the path of the center matters	Point mass	Spin starts carrying its own energy, or the object can tip and topple, and a single point can no longer stand in for the whole thing.
Spinning up, balancing a bike, a wrench on a bolt, a falling cat, a gyroscope	Rotational mechanics	The object is small and fast enough that its structure stops mattering, and you can safely collapse it back to a point.

The one habit under all of this

Before you compute, name your model and its assumptions out loud: point or body, ray or wave, Newton or relativity, ideal gas or not. Then the answer comes with a built-in warranty, the conditions under which you should trust it, and the first thing to suspect when a prediction and reality disagree.