Is There a Theory of Everything? Here's the Scorecard.

Every cook knows the line: salt to taste. It's a fine instruction for soup. It's a strange one for the mass of the electron.

Physics has recipe cards too, and the first has about two dozen lines like that. The Standard Model of particle physics is the best recipe we have for every known particle and three of the four forces, and its results match experiments to many digits. But it has 19 numbers it can't explain: the mass of the electron, how strong the electric force is, how much the quarks mix, and the rest. Give the neutrinos their masses, and the mixing that comes with them, and it's about 26.¹ Nothing in the model says what any of them should be. Each one has to be measured and typed in by hand.

Gravity has its own card. Einstein's, from 1915, describes gravity as the bending of space and time, and it's superb. But it isn't a quantum card, and the two don't fit together where it matters: at the center of a black hole and at the start of the expansion of the universe, both have to apply at once.

A theory of everything would be one card, with gravity on it and no "to taste" anywhere. Every amount would come with its reason. Einstein spent the last thirty years of his life looking for a single field that would hold gravity and electromagnetism together, and never found it.² So is there one now?

In pictures, a theory of everything is one equation small enough for a T-shirt. The card is the better picture, because you can count the lines. A set of laws works like a recipe: it says what to do and how much, and a "to taste" line is a number it doesn't give. In physics, that's a number somebody had to measure and type in. The recipe is a drawing of something real, and the rest of this post makes it exact.

The short answer

Not a finished one yet. But a foundation exists, and nothing in it was dialed in.

The foundation starts from a job reality already does: telling one thing from another, and keeping a record of it. You're doing the first half right now, because reading this tells one letter from another, and so does every measurement. Known physics gives the reason for the second half, the record: the basic laws never destroy information, so every event leaves a trace that lasts.

Four laws come out of that job, each the only law that does its part of it:

• One price for a difference: J(x) = (x + 1/x) / 2 - 1, where x says how many times bigger one thing is than the other. Only that formula meets the requirements on a price.
• One ratio between levels: 1.618..., the golden ratio, written φ. Reality builds each level of structure out of earlier ones, and 1.618 is the only ratio when each level is a join of two earlier, different levels.
• Three dimensions of space. Two loops can link in three dimensions and in no other number.
• A shortest full cycle of 8 ticks, where a tick is one step in the writing of the record. Three yes-or-no directions give 2 × 2 × 2 = 8 corners of a cube to visit.

The rules of quantum odds come out of the same record: chances are squares, the numbers are complex, and in a game played by two far-apart labs, a shared record that each lab's measurement moves reaches exactly 2√2, the top score quantum physics allows.

Nobody set a dial anywhere in what's derived. (A dial is a number you can set to anything and still have a working world. "To taste" is a dial.) It's parameter-free as far as it's derived. What isn't derived yet is the step from this structure to the numbers we measure (how long a tick lasts in seconds, the strength of the electric force, the masses of the particles, which forces there are, how much dark energy and dark matter there is) and a complete quantum description of gravity. Those are open derivations, not dials.

And "everything" splits in two. The laws can be finished. The record of what actually happens can't, because every look at it adds an entry.

Why this matters: a card with "to taste" lines can describe the meal. It can't explain it. At every "to taste" line the explanation stops and a measurement takes over: that's the number, and nothing says why. A theory of everything is the claim that the explanation doesn't stop. That gives you a way to score any claim of one: count the lines that still say "to taste," and look for gravity. This post scores ours, line by line.

The route

Here's the whole answer in six steps. The rest of this post takes them one at a time and shows how we know each.

1. The test: no "to taste." A card of everything has no dials, and each line comes with its reason. The scorecard marks every line.
2. Four laws, no dial. One price, one ratio, three dimensions and eight ticks: each is what's left when you write down what telling things apart and keeping a record requires.
3. The quantum rules. Chances are squares, the numbers are complex, and a shared record moved from both labs reaches exactly 2√2.
4. The measured numbers aren't on the card. The scale, the strength of the electric force, the masses, the forces and the cosmological values are measured, not derived.
5. Quantum gravity isn't on the card. A complete quantum description of gravity isn't derived.
6. The laws aren't the record. Even a finished card wouldn't hold everything: no law picks the next entry, the start of the record is a premise, and every look adds an entry.

What the card stands on

The work comes from Recognition Science, the physics the Recognition Physics Research Institute develops. Two claims carry the rest, each with its reason. What You Are, Part 1 of the series The Universe Writes in Pen, develops them at length.

The smallest event is one thing told apart from another. A single yes or no. You're doing it right now: every perception and every measurement tells one thing from another. Telling two things apart needs information about both, and the least information there can be is one yes or no. So the smallest thing that can happen takes two things and one yes or no.

Reality keeps a permanent record, and nothing in it is ever erased. Every event leaves a complete trace, and the past still exists. The reason starts in known physics: the basic laws never destroy information. In quantum mechanics that's called unitarity: the present fixes the past exactly, and running the laws backward recovers every earlier state.³ That's why physicists treat the black hole information problem as a real problem: losing information would break the laws. Stephen Hawking's 1976 calculation said a black hole destroys the information that falls into it. That clashed with unitarity. Most physicists now expect the information to come back out in the radiation, and the open question is how.⁴

Our work adds a reason of its own: the record only grows. Each new entry is added with every earlier entry kept, and writing a new entry never alters an earlier one.⁵ The Universe Has No Delete Key develops this. What an entry is rests on a separate fact: each entry compares two things, and a comparison needs information about both, so every entry is written against what came before.

Counting comes out of the first claim too. Telling two things apart, again and again, is where the counting numbers and their rules come from.⁶ Is Math Invented or Discovered? builds them.

Step 1: The test is whether any line says "to taste"

A card of everything has no "to taste" lines, and every line comes with its reason.

A dial is a number you can set to anything and still have a working world. "To taste" is the cook's word for one. A forced number is the opposite: the only one that meets the requirements of its job, so there was nothing to set.

"To taste" isn't a flaw in a recipe. It's honesty: the card says plainly where it stops explaining. The scorecard does the same for ours.

Here's a dial. The electron's mass is known to better than one part in a billion.⁷ The Standard Model has a place for any value of it, so nothing in the model says why the mass is this one. Here's a forced number. Lasting structure needs pairs of loops that can't be pulled apart, as Step 2 explains. Two loops can link in three dimensions, can't link at all in two, and slip apart in four. So the 3 isn't set: it's the only number of dimensions that leaves the requirement standing.

That gives three marks for scoring a card:

1. No line says "to taste." Every number is forced, or follows from forced ones.
2. Every particle and force is on it, gravity included.
3. Each line comes with its reason: the conditions under which it's the only one.

Here's our card so far. A cyan check is a line on the card with no dial: a starting fact, or something derived from the facts. A magenta circle is a line that isn't written yet.

The first two checks are in "What the card stands on." The next four are Step 2, and the seventh is Step 3. The four circles are Steps 4 to 6.

Step 2: Four laws, each the only one that does its job

Four laws come out of the job of telling things apart and keeping a record. Each is the only law that does its part of the job.

The job has four parts, and each part leaves one option. One paragraph per part, with the post that works it through.

One price for a difference. Comparing two things of the same kind has a price, and the price measures how unbalanced they are. If one is x times the other, it's J(x) = (x + 1/x) / 2 - 1. Equal things (x = 1) cost 0. One twice the other (x = 2) costs (2 + 1/2) / 2 - 1 = 1/4, and so does one half the other (x = 1/2). The price has to be zero when the two match, grow as they differ, and come out the same whichever you name first, and this one does all three. Add the rule for how the prices of combined comparisons add, and one calibration (how sharply the price rises near a match), and exactly one formula is left.⁸ Without the calibration a whole family of prices survives. Who Set the Dials on the Universe? works through it.

One ratio between levels. Reality builds each level out of earlier levels, and two requirements fix the ratio between them. First, every level is the same multiple of the one below. (Why one multiple: a step up that treats a stack of things the way it treats each thing in it, and keeps every comparison, can only multiply by one number.) Second, the first new level is a join of two different earlier levels. (A join of two copies of the same level tells nothing apart, so it writes nothing and costs nothing.) Then the multiple r has to satisfy r × r = 1 + r, and exactly one positive number does: r = (1 + √5) / 2 = 1.618..., the golden ratio, φ. The ladder runs 1, 1.618, 2.618, 4.236, and each rung is the two below it, added. Let the first join be of equals and doubling gets in instead: 1, 2, 4, 8. Why Does the Golden Ratio Keep Showing Up? builds it rung by rung.⁹

Three dimensions. Lasting structure needs a connection that no smooth motion can undo, and linking is that connection: two rings of a chain can't be pulled apart without cutting one. Two loops can link in three dimensions and in no other number. In two dimensions loops can't wind around each other at all. In four or more, any two loops slide apart. The condition behind the 3 is that lasting pairs are joined by linking. Why Space Has Three Dimensions works through every case.¹⁰

Eight ticks. Each of the three directions carries one yes-or-no, so there are 2 × 2 × 2 = 8 combinations: the eight corners of a cube. A tick is one step in the writing of the record. On a full pass each tick flips one yes-or-no and the pass touches every corner. That takes at least 8 ticks, and 8 is enough: a route through all eight corners comes home in eight steps. The 8 counts ticks. It doesn't say how many seconds a tick lasts. It's also the number of electrons in a full outer shell for the atoms in the second and third rows of the periodic table: four seats (chemists call them orbitals), one round and one for each of the three directions, two electrons each, so 2 × (1 + 3) = 8. The two eights agree at three directions and at no other number. Why Chemistry Runs on Eight works through the meeting.¹¹

Notice what's missing from those four paragraphs: any measurement of the world. Nobody weighed an electron or measured a force to get these laws. That's the part worth sitting with. They're what's left when you write down what the job requires, and the requirements are written beside each law.

No dial. For each of the four, take one requirement away and a different law gets in. Keep them all and exactly one is left.

That's what "forced" means here: not that nothing else can be written down, but that nothing else meets the requirement. So there was nothing to set. It's parameter-free as far as it's derived. Every law above is derived with no fitted number, and its conditions are named beside it: the calibration for the price, a real first join for the ratio, linking for the three, a full pass for the eight. What isn't derived yet is an open derivation, not a dial.

Step 3: The rules of quantum odds come out of the same record

Chances are squares, the numbers are complex, and a shared record moved from both labs reaches exactly 2√2. Three results, each with its conditions.

Chances are squares. In the record, a quantum state is a row of eight slots, one for each corner of the cube. Each slot holds an amplitude: a number drawn as an arrow with a length. In 1926 Max Born gave the rule that a slot's chance is its length squared, and textbooks take it as a postulate. Take a photon meeting the front surface of a window head-on. Two of its eight slots are in use, bounce and pass. The bounce slot holds an arrow of length 0.2, so the chance of a bounce is 0.2 × 0.2 = 0.04: 4 photons in 100 bounce back, and the other 96 go through.

Why the square, and not something else? Five plain rules for reading a record leave only that rule. The chances total 1. None is negative. An empty slot has chance 0. The chances of separate slots add. And a slot of a given size has the same chance whoever its neighbors are. Four of the five are what it takes to be a chance at all. The fifth, the same-size rule, is the physical premise. No angle, no smooth curve and no calibration goes in. Is the Universe Rolling Dice? walks through it.¹²

The numbers are complex. An amplitude is a complex number: an arrow with a length and a direction. Here's why real numbers fall short. A tick shifts the eight slots one place around a ring, the ring of the eight-tick pass in Step 2. A steady pattern is one that a tick only rescales, and describing any state in terms of steady patterns takes eight of them. With real numbers there are two: all slots alike, and slots alternating plus and minus. With complex numbers there are all eight, each turning by a different number of eighths of a circle per tick.¹³ So the amplitudes are complex numbers, on one condition: that the tick's steady patterns are enough to describe every state.

The top score. Two labs far apart each get a card, 1 or 2, and answer yes or no. A round is won when the two answers fit a set rule. Any plan made in advance, answers fixed beforehand and carried along, wins at most 75 rounds in 100. Physicists score that as 2.

Quantum physics reaches about 85 in 100, a score of 2√2 = 2.83, and Tsirelson proved in 1980 that this is its ceiling. A shared record that both labs only read is a plan, so it stops at 2. A shared record that each lab's card moves, using the record's own basic move (flipping one yes-or-no mark, with its sign), reaches exactly 2√2.¹⁴ And a rule that asks only that no message gets through allows up to 4, a win every round.¹⁵

That's the number quantum physics already has, so a score like this can't tell the two apart: it's a match, not a new forecast. Entanglement Isn't Spooky. It's Shared. works through it.

Two conditions sit under this step, and both are premises: the same-size rule, and the demand that the tick's steady patterns describe every state.

Step 4: The measured numbers aren't on the card

The step from this structure to the numbers we measure isn't derived yet.

Here are the lines that step has to reach. Until a line is derived, it says "to taste" on our card too. Each is an open derivation, and none is a dial in what's derived.

• The scale. A tick is a step, not a length of time. No derivation yet says how many seconds one tick lasts, or how many joules one unit of price is. So the structure isn't yet read in seconds and joules.
• The strength of the electric force. The number physicists write α says how strongly light and electric charge couple. It's measured. It isn't derived.
• The masses. None of the fourteen particle numbers is derived: twelve masses (the electron, muon and tau, the six quarks, and the W, Z and Higgs) and two mass ratios (the ratio of the two neutrino mass splittings, and the proton's mass to the electron's). The premises behind the four laws, taken alone, don't fix the electron's mass: two worlds can obey all of them and have different electron masses. So the masses need a further layer of structure, and that layer isn't derived. What Is Everything Made Of? says where the work on masses stops.
• The forces. Which forces there are, the strong, the weak and the electromagnetic force, and why each has the structure it has. The Standard Model takes them as given, and they aren't derived here either.
• The cosmological values. How much dark energy and dark matter the universe holds isn't derived.
• Newton's constant, in everyday units. The number that says how strong gravity is, in meters and kilograms and seconds, is an input: measured, then put in.

So how can the derived part be parameter-free when none of this is derived? "Parameter-free" is a claim about what's derived, and only about that. Every derived line has no fitted number. A line that isn't derived isn't claimed: it says "to taste" until it is. It's a long list, and it's exact. A frontier you can list line by line is one you can work on.

Step 5: Quantum gravity isn't on the card

A complete quantum description of gravity isn't derived yet. We don't claim one.

Einstein's card describes gravity, and quantum physics describes the particles and the other three forces. At the center of a black hole and at the start of the expansion, both have to apply at once. Black holes are the sharp test. Hawking's 1976 calculation, above, said they destroy information. Most physicists now expect the information to come back out, and how it does is a question any complete description of gravity has to answer. Other programs, string theory the best known, are working on the same line, and no experiment has yet confirmed any of them. A complete quantum description of gravity is an open line on our card, not a written one.

Step 6: The laws aren't the record

Even a finished card wouldn't hold everything. The laws can be finished. The record can't.

A recipe card tells you how to cook. It doesn't hold the meals. In the drawing, the card is the laws and each plate is one entry in the record: one meal cooked, and kept. The card leaves three things out, and each one is a fact about the record.

Which entry comes next. The laws say what any next entry has to meet. They don't say which one comes, and nothing in the present does either: everything the present holds about the next entry is a set of exact odds. How the entry that gets written is selected isn't derived yet. Is the Universe Rolling Dice? says exactly where that stands, and Is Your Next Move Already Written? shows why no law and no forecast settles it.

Where the record starts. The laws work the same from any starting count: an endless past obeys every one of them. So that the record has a first page is a premise, not a result, and the step from the first entries to the hot, expanding universe that astronomers measure isn't derived. How Did the Universe Begin? says what's there and what isn't.

What's in the record. The record includes every look anyone takes at it. Looking is an event: a photo of your desk doesn't contain you looking at the photo.¹⁶ So each look adds an entry the record didn't hold. Your look at this sentence is one. No list of everything that happens is ever finished. Can We Ever Know Everything? works it through.

One more fact ties this back to the "to taste" lines. No measurement confirms an exact value. Say a scale reads 1,000 g, to a thousandth of a gram. A bar of 1,000.0001 g would have read the same. A scale a hundred times sharper can tell those two apart, and then a bar of 1,000.000001 g reads the same. However sharp the readings get, a bar a hair away still fits all of them. A reading can refute "the value is exactly c." It can never confirm it.¹⁷ An exact number comes from a derivation or a definition, never from readings. So a card with no "to taste" lines has to be written by derivation. A card of better measurements would still say "to taste" at the next digit.

So "everything" has two meanings. Everything the laws say is a finite card, and a finite card can be finished. Everything that happens is the record, and that can't be finished, because each look adds a line.

What's still open

Four things aren't on the card. Each is an open derivation, not a dial.

• The measured numbers. The scale (how many seconds one tick lasts, how many joules one unit of price is), the strength of the electric force, the fourteen particle numbers, which forces there are, the cosmological values, and Newton's constant in everyday units, which is an input.
• Quantum gravity. A complete quantum description of gravity isn't derived.
• The start. That the record has a first page is a premise, and the step from the first entries to the hot, expanding universe isn't derived.
• What picks each quantum result. The laws give exact odds. The step that says how the entry that gets written is selected isn't derived.

The whole trip, in one breath

A recipe card for the universe has a "to taste" line wherever a number was measured and typed in, and the Standard Model has about two dozen. A card of everything would have none, with gravity on the same card. Ours starts from telling one thing from another, which you're doing now, and a record that keeps every entry. That job leaves one price for a difference, one ratio between levels (1.618), three dimensions and a shortest full cycle of 8 ticks, each the only law that meets its requirements. Quantum odds come out of the same record: chances are squares, amplitudes are complex, and a shared record moved from two places reaches exactly 2√2. It's parameter-free as far as it's derived. The card isn't finished: the scale, the strength of the electric force, the masses, the forces, the cosmological values and a complete quantum description of gravity aren't derived. And a finished card still wouldn't be everything. No law picks the next entry, the start of the record is a premise, and every look adds an entry.

The laws are a card you can finish. The record is a story you never do. That's how reality is built.