A build-it-yourself book

From Newton
to M-Theory

Special relativity, general relativity, quantum mechanics, quantum field theory, the Standard Model and string theory — derived, not asserted. Nothing is stated that has not been built, and every step that is quoted rather than proved is marked as such.

Ask what stays the same when you change your point of view. Whatever survives is real; whatever does not was a fact about where you were standing.
37 / 76chapters built
564kwords
32kequations typeset
278plain-language passages

Above: the light cone, which no change of frame can move, and the hyperbolae of constant interval. Each marker is one event, shown from a continuously changing point of view. It slides, and never leaves its own curve. That is the whole thesis, drawn.

Three ways in

The same material, at three depths. They cross-reference each other, so you can move between them at any point.

The book

Chapters

The full derivations, with interactive figures, worked examples and problems whose solutions unfold when you want them. Start at the definition of a derivative.

Plain language

In Plain Terms

Every explanatory passage in the book, collected in order and readable as one continuous essay. No equations anywhere in it. It stands entirely on its own.

Reference

Math Ledger

Every mathematical object: where it was introduced, the question it was invented to answer, and every later chapter that spends it. Follow any symbol back to its origin.

The arc

Seven subjects, one idea — pick a symmetry, write the most general law invariant under it, then quantise. Each part is that sentence wearing different clothes.

Part 0
The Toolkit

Numbers describe a thing only relative to a choice. The useful description is the one in which a hard problem falls apart into independent pieces.

9 of 9 chapters
Part I
The Action Principle

Forces are the wrong primitive. Attach one number to each possible history, and nature selects the history where that number stops changing.

4 of 4 chapters
Part II
Special Relativity

The speed limit is built into the geometry, not the materials. Magnetism turns out to be electricity, seen from a moving frame.

6 of 6 chapters
Part III
General Relativity

Gravity is not a force but the shape of the arena. Free fall is the straightest available motion.

9 of 9 chapters
Part IV
Quantum Mechanics

“What state is this in” stops having a single answer. The mathematics was already built in Part 0.

9 of 20 chapters
Part V
Quantum Field Theory

Particles stop being fundamental. The field is; particles are its excitations, the way notes are excitations of a string.

11 chapters
Part VI
Gauge Theory

Demand a symmetry hold locally rather than globally, and a force appears to enforce it. Every force is that one demand.

8 chapters
Part VII
Strings and M-Theory

Gravity refuses the treatment that worked for everything else — followed by an honest account of what is known and what is conjecture.

9 chapters

How it is built

Written for someone who can grasp anything but wants the bricks laid one at a time.

Rule

Nothing asserted

No “it can be shown that”. Where a result is quoted rather than derived it carries a ⚑, so you always know what you are standing on.

Pacing

One step per line

Routine algebra folds into collapsible boxes, but the reasoning stays on the page. A reader who opens none of them can still follow every argument.

Figures

Only when they teach

Each interactive figure has to show something a static picture cannot, and most of them measure the result rather than illustrating it.