The Last Equation  /  Archive copy Result 001 Derivation status: closed

WE FOUND IT.

There is nothing underneath.

§14.8FIG. 31LEMMA 6RUN 118/118RESIDUAL: 0NO FREE TERM REQUIRED

Checked by others. Twice.

§2.1
Gμν + Λgμν = 8πGc4 Tμν

gravity / 1915

§2.2
= −¼ FμνFμν + i ψ̄ D̸ ψ + ψ̄i yij ψj φ + h.c. + |Dμφ|2 V(φ)

almost everything else

FIG. 3
GRAVITY                         QUANTUM
  │                               │
  │                               │
  └────────────── ? ──────────────┘

This gap survived longer than several countries.

LEMMA 6

Lemma 6

The gap was never in the world. It was in the description.

Residual: 0  ·  no free term required

FIG. 31

Every earlier framework left something over: a term put in by hand, a constant nobody could derive, a limit where the arithmetic gave up and a footnote took over. Result 001 has none of these. The values that used to be measured are now consequences. The places that used to be undefined are now the only places anything could have been. We kept looking for the seam and there is no

§9.4
Gμν + Λgμν = 8πGc4 Tμν ──────▶ ──────▶ symbol 3 of 17

every prior result enters. fewer leave.

FIG. 12
quantum fields ────────●
                       │
curved spacetime ──────●────── ?
                       │
information ───────────●

Object 04  /  horizon

§11

WE CHECKED
THE HOLES FIRST.

rs = 2GM/c² OLD DESCRIPTION TERMINATES HERE HAWKING RADIATION HORIZON · OBJECT 04
  • Geometryrs = 2GM/c2Schwarzschild, 1916 · holds
  • EntropyS = kBc3A / 4GħBekenstein-Hawking, area law · holds
  • TemperatureTH = ħc3 / 8πGMkBHawking, 1974 · holds
  • Informationin → outthe arrows, finally, point somewhere · run 118/118
  • Singularityr = 0old description terminates here · replaced

The places where the old description became uncomfortable were the first places we looked.

§14.6

Corollary 14

Every physically possible event is contained in the solution space.

§14.7

Corollary 15

This includes observers deriving this equation.

§14.8

Corollary 16

This includes you reading it.

Yes. You too.

§17

The final form

17 symbols.

Everything else follows.

§18

Nothing special happened.

We expected something beautiful.

It wasn't.

We expected symmetry.

Not particularly.

We expected the constants to reveal themselves as inevitable.

They did.

We expected the universe to become less strange.

It became stranger in fewer symbols.

There is no
next equation.

Every earlier “fundamental” theory had something beneath it.

Molecules had atoms.

Atoms had nuclei.

Nuclei had quarks.

Forces had fields.

Space had geometry.

Geometry had

That's it.

We spent thousands of years asking what everything is made of.

Eventually we found out.

It did not explain
why there is anything.

Why this?

Why anything?

We found the answer
beneath everything.

Unfortunately, there was still a question beneath the answer.

Why this equation?

We don't know.

So there is still work to do.

One administrative problem remained

We wanted thelastequation.com.

Someone got there first.

A reminder that even after deriving the complete underlying structure of reality, some problems remain stubbornly outside theoretical physics.

They can keep it.

We found the other thing.

Open problemsStatus
quantum gravitysolved
black-hole informationsolved
fundamental constantsderived
unificationcomplete
why this rather than nothing...
thelastequation.comtaken

We can live with one of these.

See?
Anyway.

They got the domain.
We got the equation.

Anyway.

Fundamental physics appears to be handled.

Civilization is still shipping disposable lightbulbs, fourteen-step cancellation flows, software nobody asked for, and machines optimized to keep you looking at them.

Frankly, the harder problems may be ahead.

Some futures are worth building.

Some obviously aren't.

The universe turned out to be elegant.

We have fewer excuses.

See what's still unfinished →
The Last Equation
All fundamental questions resolved except the fundamental ones.
A needlessly ambitious project from Worth Building.
Results obvious.

What is real on this page: Einstein's field equations (1915); the Standard Model Lagrangian in its compressed form; the Schwarzschild radius (1916); the Bekenstein-Hawking entropy and the Hawking temperature (1974). What is not: the resolution. No final form has been found. The Standard Model still does not contain gravity, and general relativity and quantum theory are still not one framework. That gap is open. The question at the end would survive closing it. A Worth Building experiment.

worthbuilding.org