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Introduction
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The Current Program (Round 3)
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Program History
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Hamilton's Principle
Newton's laws, Maxwell's equations, general relativity and the Standard Model are each formulated as an action via Hamilton's Principle. In every case the equations of motion are consequences rather than starting points. Conservation of energy, momentum and charge are not separate laws at all — Noether proved they follow from the action's symmetries. New models are now built by writing the action a symmetry permits and letting the dynamics follow. This is how electromagnetism and gravity were derived and how the nuclear forces were found. Hamilton's Principle alone survives the passage to quantum mechanics intact: the action becomes the phase carried by every possible history, and the classical path is simply where those phases fail to cancel. The action is the deepest thing physics knows.
- Stationary is not least — the long way round a great circle obeys the same rule at every point, and is plainly not the shortest. See the diagram.
- Why the rule holds at all — nature selects nothing. It sums over everything, and what looks like a choice is the residue left by interference.
- Start without the mathematics — every page carrying equations has a plain-language counterpart, linked from it and linking back.
Noether's 1st Theorem
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The Work of James Clerk Maxwell
On Physical Lines of Force
In four instalments between March 1861 and February 1862, James Clerk Maxwell
filled space with spinning cells and little rolling particles, to explain the mechanics behind magnetic fields. His machine was wrong. On the way to building it,
he wrote down the displacement current, derived the speed of light from two
electrical measurements that had nothing to do with optics, and founded field
theory.
A 65-page reading edition: Maxwell's argument in his own order and register, the modern equations derived from his results, and a plain-language explainer for every major idea.
- Start reading →
- Introduction — the story, and why the paper matters
- The explainers — plain language, no mathematics
- The missing term — the one addition that made radio possible
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