fields
A field is a value at every point of space and time. The idea starts as a bookkeeping trick — a potential whose slope gives a force — and ends as the primary object of physics: the Lagrangian density is what you write down first, and particles are just its ripples.
Units touched 0 in Wave 1 · 3+ planned Adjacent threads force · energy · symmetry · light
The stations
Stations are the moments where the idea of a field genuinely advances — each anchored to a derivation in the vault. This thread's stations belong to units that arrive after Wave 1.
Not yet laid down
The "fields" throughline needs machinery that Wave 1 doesn't cover yet: the potential formalism, the variational principle over continuous media, and the leap to a Lagrangian density. Those derivations are drafted for later units.
Where it will run
Expected route: Unit 310 · Potentials & Gradients (scalar potential → force as −∇φ), then Unit 340 · Classical Field Theory (Lagrangian density, Euler–Lagrange for fields), reaching Unit 420 · Quantum Fields (canonical quantisation; particles as excitations).
What "fields" comes to mean
A value everywhere
Temperature in a room, height of a hill. The slope of the hill points you downhill — that slope is a force.
The Lagrangian view
Stop tracking particles; track a field ℒ(φ, ∂μφ) over all spacetime and extremise its action. Equations of motion fall out of Euler–Lagrange for fields.
The field is primary
Quantise the field and its excitations are the particles. Symmetries of ℒ dictate the conserved currents — the "fields" thread merges into symmetry here.
Related threads while you wait: force (where potentials first bite), energy (the action principle), symmetry (what fields conserve). See the full map on threads.