# A theory of everything | Garrett Lisi

Whoa, dude. (Laughter) Check out those killer equations. Sweet. Actually, for the next 18 minutes

I’m going to do the best I can to describe the beauty

of particle physics without equations. It turns out there’s a lot

we can learn from coral. A coral is a very beautiful

and unusual animal. Each coral head consists

of thousands of individual polyps. These polyps are continually

budding and branching into genetically identical neighbors. If we imagine this

to be a hyperintelligent coral, we can single out an individual

and ask him a reasonable question. We can ask how exactly

he got to be in this particular location compared to his neighbors — if it was just chance,

or destiny, or what? Now, after admonishing us

for turning the temperature up too high, he would tell us that our question

was completely stupid. These corals can be kind of mean, you see, and I have surfing scars to prove that. But this polyp would continue and tell us that his neighbors were

quite clearly identical copies of him. That he was in all

these other locations as well, but experiencing them

as separate individuals. For a coral, branching

into different copies is the most natural thing in the world. Unlike us, a hyperintelligent coral would be uniquely prepared

to understand quantum mechanics. The mathematics of quantum mechanics very accurately describes

how our universe works. And it tells us our reality is continually

branching into different possibilities, just like a coral. It’s a weird thing for us humans

to wrap our minds around, since we only ever get

to experience one possibility. This quantum weirdness was first described by Erwin Schrödinger and his cat. The cat likes this version better. (Laughter) In this setup, Schrödinger is in a box

with a radioactive sample that, by the laws of quantum mechanics,

branches into a state in which it is radiated

and a state in which it is not. (Laughter) In the branch in which

the sample radiates, it sets off a trigger that releases poison

and Schrödinger is dead. But in the other branch of reality,

he remains alive. These realities are experienced

separately by each individual. As far as either can tell,

the other one doesn’t exist. This seems weird to us, because each of us

only experiences an individual existence, and we don’t get to see other branches. It’s as if each of us,

like Schrödinger here, are a kind of coral

branching into different possibilities. The mathematics

of quantum mechanics tells us this is how the world

works at tiny scales. It can be summed up in a single sentence: Everything that can happen, does. That’s quantum mechanics. But this does not mean everything happens. The rest of physics is about describing

what can happen and what can’t. What physics tells us

is that everything comes down to geometry and the interactions

of elementary particles. And things can happen only if

these interactions are perfectly balanced. Now I’ll go ahead and describe

how we know about these particles, what they are and how this balance works. In this machine,

a beam of protons and antiprotons are accelerated to near the speed of light and brought together in a collision,

producing a burst of pure energy. This energy is immediately converted

into a spray of subatomic particles, with detectors and computers

used to figure out their properties. This enormous machine — the Large Hadron Collider

at CERN in Geneva — has a circumference of 17 miles

and, when it’s operating, draws five times as much power

as the city of Monterey. We can’t predict specifically what particles will be produced

in any individual collision. Quantum mechanics tells us

all possibilities are realized. But physics does tell us

what particles can be produced. These particles must have

just as much mass and energy as is carried in

by the proton and antiproton. Any particles more massive

than this energy limit aren’t produced, and remain invisible to us. This is why this new

particle accelerator is so exciting. It’s going to push

this energy limit seven times beyond what’s ever been done before, so we’re going to get to see

some new particles very soon. But before talking

about what we might see, let me describe the particles

we already know of. There’s a whole zoo

of subatomic particles. Most of us are familiar with electrons. A lot of people in this room

make a good living pushing them around. (Laughter) But the electron also has

a neutral partner called the neutrino, with no electric charge

and a very tiny mass. In contrast, the up and down quarks

have very large masses, and combine in threes to make

the protons and neutrons inside atoms. All of these matter particles

come in left- and right-handed varieties, and have antiparticle partners

that carry opposite charges. These familiar particles also have less familiar

second and third generations, which have the same charges as the first

but have much higher masses. These matter particles all interact

with the various force particles. The electromagnetic force

interacts with electrically charged matter via particles called photons. There is also a very weak force called, rather unimaginatively,

the weak force … (Laughter) that interacts

only with left-handed matter. The strong force acts between quarks which carry a different kind of charge,

called color charge, and come in three different varieties:

red, green and blue. You can blame Murray Gell-Mann

for these names — they’re his fault. Finally, there’s the force of gravity, which interacts with matter

via its mass and spin. The most important thing

to understand here is that there’s a different kind of charge

associated with each of these forces. These four different forces

interact with matter according to the corresponding charges

that each particle has. A particle that hasn’t been seen yet,

but we’re pretty sure exists, is the Higgs particle, which gives masses

to all these other particles. The main purpose

of the Large Hadron Collider is to see this Higgs particle,

and we’re almost certain it will. But the greatest mystery

is what else we might see. And I’m going to show you

one beautiful possibility towards the end of this talk. Now, if we count up

all these different particles using their various spins and charges, there are 226. That’s a lot of particles

to keep track of. And it seems strange that nature would have

so many elementary particles. But if we plot them out

according to their charges, some beautiful patterns emerge. The most familiar charge

is electric charge. Electrons have an electric charge, a negative one, and quarks have

electric charges in thirds. So when two up quarks and a down quark

are combined to make a proton, it has a total

electric charge of plus one. These particles also have antiparticles,

which have opposite charges. Now, it turns out the electric charge is actually a combination

of two other charges: hypercharge and weak charge. If we spread out

the hypercharge and weak charge and plot the charges of particles

in this two-dimensional charge space, the electric charge

is where these particles sit along the vertical direction. The electromagnetic

and weak forces interact with matter according to their hypercharge

and weak charge, which make this pattern. This is called

the unified electroweak model, and it was put together back in 1967. The reason most of us

are only familiar with electric charge and not both of these

is because of the Higgs particle. The Higgs, over here on the left,

has a large mass and breaks the symmetry

of this electroweak pattern. It makes the weak force very weak

by giving the weak particles a large mass. Since this massive Higgs sits along

the horizontal direction in this diagram, the photons of electromagnetism

remain massless and interact with electric charge

along the vertical direction in this charge space. So the electromagnetic and weak forces are described by this pattern

of particle charges in two-dimensional space. We can include the strong force

by spreading out its two charge directions and plotting the charges

of the force particles in quarks along these directions. The charges of all known particles can be plotted in

a four-dimensional charge space, and projected down to two dimensions

like this so we can see them. Whenever particles interact,

nature keeps things in a perfect balance along all four of these charge directions. If a particle and an antiparticle collide, it creates a burst of energy

and a total charge of zero in all four charge directions. At this point, anything can be created as long as it has the same energy

and maintains a total charge of zero. For example, this weak force particle

and its antiparticle can be created in a collision. In further interactions,

the charges must always balance. One of the weak particles could decay

into an electron and an antineutrino, and these three

still add to zero total charge. Nature always keeps a perfect balance. So these patterns of charges

are not just pretty. They tell us what interactions

are allowed to happen. And we can rotate this charge space

in four dimensions to get a better look

at the strong interaction, which has this nice hexagonal symmetry. In a strong interaction,

a strong force particle, such as this one, interacts with a colored quark,

such as this green one, to give a quark with a different

color charge — this red one. And strong interactions

are happening millions of times each second in every atom of our bodies, holding the atomic nuclei together. But these four charges

corresponding to three forces are not the end of the story. We can also include two more charges

corresponding to the gravitational force. When we include these, each matter particle

has two different spin charges, spin-up and spin-down. So they all split and give a nice pattern

in six-dimensional charge space. We can rotate this pattern

in six dimensions and see that it’s quite pretty. Right now, this pattern

matches our best current knowledge of how nature is built at the tiny scales

of these elementary particles. This is what we know for certain. Some of these particles

are at the very limit of what we’ve been able to reach

with experiments. From this pattern we already know the particle physics

of these tiny scales — the way the universe works

at these tiny scales is very beautiful. But now I’m going to discuss

some new and old ideas about things we don’t know yet. We want to expand this pattern

using mathematics alone, and see if we can get our hands

on the whole enchilada. We want to find

all the particles and forces that make a complete picture

of our universe. And we want to use this picture

to predict new particles that we’ll see when experiments

reach higher energies. So there’s an old idea in particle physics that this known pattern of charges, which is not very symmetric, could emerge from a more perfect pattern

that gets broken — similar to how the Higgs particle

breaks the electroweak pattern to give electromagnetism. In order to do this,

we need to introduce new forces with new charge directions. When we introduce a new direction, we get to guess what charges

the particles have along this direction, and then we can rotate it

in with the others. If we guess wisely,

we can construct the standard charges in six charge dimensions

as a broken symmetry of this more perfect pattern

in seven charge dimensions. This particular choice

corresponds to a grand unified theory introduced by Pati and Salam in 1973. When we look at this new unified pattern, we can see a couple of gaps

where particles seem to be missing. This is the way

theories of unification work. A physicist looks for larger,

more symmetric patterns that include the established

pattern as a subset. The larger pattern allows us

to predict the existence of particles that have never been seen. This unification model

predicts the existence of these two new force particles, which should act a lot

like the weak force, only weaker. Now, we can rotate this set

of charges in seven dimensions and consider an odd fact

about the matter particles: the second and third generations of matter have exactly the same charges

in six-dimensional charge space as the first generation. These particles are not

uniquely identified by their six charges. They sit on top of one another

in the standard charge space. However, if we work

in eight-dimensional charge space, then we can assign

unique new charges to each particle. Then we can spin these in eight dimensions and see what the whole pattern looks like. Here we can see the second

and third generations of matter now, related to the first generation

by a symmetry called “triality.” This particular pattern

of charges in eight dimensions is actually part of the most beautiful

geometric structure in mathematics. It’s a pattern of the largest

exceptional Lie group, E8. This Lie group is a smooth,

curved shape with 248 dimensions. Each point in this pattern

corresponds to a symmetry of this very complex and beautiful shape. One small part of this E8 shape

can be used to describe the curved space-time

of Einstein’s general relativity, explaining gravity. Together with quantum mechanics, the geometry of this shape

could describe everything about how the universe works

at the tiniest scales. The pattern of this shape living

in eight-dimensional charge space is exquisitely beautiful, and it summarizes thousands

of possible interactions between these elementary particles, each of which is just a facet

of this complicated shape. As we spin it, we can see

many of the other intricate patterns contained in this one. And with a particular rotation, we can look down through this pattern

in eight dimensions along a symmetry axis and see all the particles at once. It’s a very beautiful object, and as with any unification, we can see some holes where new particles

are required by this pattern. There are 20 gaps

where new particles should be, two of which have been filled

by the Pati-Salam particles. From their location in this pattern,

we know that these new particles should be scalar fields

like the Higgs particle, but have color charge

and interact with the strong force. Filling in these new particles

completes this pattern, giving us the full E8. This E8 pattern has

very deep mathematical roots. It’s considered by many to be the most

beautiful structure in mathematics. It’s a fantastic prospect that this object

of great mathematical beauty could describe the truth

of particle interactions at the smallest scales imaginable. And this idea that nature is described

by mathematics is not at all new. In 1623, Galileo wrote this: “Nature’s grand book,

which stands continually open to our gaze, is written in the language of mathematics. Its characters are triangles,

circles and other geometrical figures, without which it is humanly impossible

to understand a single word of it; without these, one is wandering around

in a dark labyrinth.” I believe this to be true, and I’ve tried

to follow Galileo’s guidance in describing the mathematics

of particle physics using only triangles, circles

and other geometrical figures. Of course, when other physicists

and I actually work on this stuff, the mathematics

can resemble a dark labyrinth. But it’s reassuring that at the heart

of this mathematics is pure, beautiful geometry. Joined with quantum mechanics, this mathematics describes our universe

as a growing E8 coral, with particles interacting

at every location in all possible ways according to a beautiful pattern. And as more of the pattern

comes into view using new machines like the Large Hadron Collider, we may be able to see whether nature

uses this E8 pattern or a different one. This process of discovery is

a wonderful adventure to be involved in. If the LHC finds particles

that fit this E8 pattern, that will be very, very cool. If the LHC finds new particles,

but they don’t fit this pattern — well, that will be very interesting,

but bad for this E8 theory. And, of course, bad for me personally. (Laughter) Now, how bad would that be? Well, pretty bad. (Laughter) But predicting how nature works

is a very risky game. This theory and others like it

are long shots. One does a lot of hard work

knowing that most of these ideas probably won’t end up

being true about nature. That’s what doing

theoretical physics is like: there are a lot of wipeouts. In this regard, new physics theories

are a lot like start-up companies. As with any large investment, it can be emotionally difficult

to abandon a line of research when it isn’t working out. But in science,

if something isn’t working, you have to toss it out

and try something else. Now, the only way to maintain sanity and achieve happiness

in the midst of this uncertainty is to keep balance

and perspective in life. I’ve tried the best I can

to live a balanced life. (Laughter) I try to balance my life equally

between physics, love and surfing — my own three charge directions. (Laughter) This way, even if the physics

I work on comes to nothing, I still know I’ve lived a good life. And I try to live in beautiful places. For most of the past ten years

I’ve lived on the island of Maui, a very beautiful place. Now, it’s one of the greatest mysteries

in the universe to my parents how I managed to survive all that time without engaging in anything

resembling full-time employment. (Laughter) I’m going to let you in on that secret. This was a view

from my home office on Maui. And this is another, and another. And you may have noticed

that these beautiful views are similar, but in slightly different places. That’s because this used to be

my home and office on Maui. (Laughter) I’ve chosen a very unusual life. But not worrying about rent allowed me to spend my time

doing what I love. Living a nomadic existence

has been hard at times, but it’s allowed me

to live in beautiful places and keep a balance in my life

that I’ve been happy with. It allows me to spend a lot of my time

hanging out with hyperintelligent coral. But I also greatly enjoy

the company of hyperintelligent people. So I’m very happy

to have been invited here to TED. Thank you very much. (Applause) Chris Anderson: Stay here one second. (Applause) I probably understood two percent of that, but I still absolutely loved it. So I’m going to sound dumb. Your theory of everything — Garrett Lisi: I’m used to coral. CA: That’s right. The reason it’s got

a few people at least excited is because, if you’re right, it brings

gravity and quantum theory together. So are you saying that we should

think of the universe, at its heart — that the smallest things that there are, are somehow an E8 object of possibility? I mean, is there a scale to it,

at the smallest scale, or …? GL: Well, right now

the pattern I showed you that corresponds to what we know

about elementary particle physics — that already corresponds

to a very beautiful shape. And that’s the one

that I said we knew for certain. And that shape

has remarkable similarities — and the way it fits into this E8 pattern,

which could be the rest of the picture. And these patterns of points

that I’ve shown for you actually represent symmetries

of this high-dimensional object that would be warping

and moving and dancing over the space-time that we experience. And that would be what explains all these

elementary particles that we see. CA: But a string theorist,

as I understand it, explains electrons in terms

of much smaller strings vibrating — I know, you don’t like string theory —

vibrating inside it. How should we think

of an electron in relation to E8? GL: Well, it would be one

of the symmetries of this E8 shape. So what’s happening is, as the shape

is moving over space-time, it’s twisting. And the direction it’s twisting

as it moves is what particle we see. So it would be — CA: The size of the E8 shape,

how does that relate to the electron? I feel like I need that for my picture.

Is it bigger? Is it smaller? GL: As far as we know,

electrons are point particles, so this would be going down

to the smallest possible scales. So the way these things are explained

in quantum field theory is, all possibilities are expanding

and developing at once. And this is why

I use the analogy to coral. And — in this way, the way that E8 comes in is it will be as a shape that’s attached

at each point in the space-time. And, as I said,

the way the shape twists — the directional along which way

the shape is twisting as it moves over this curved surface — is what the elementary particles

are, themselves. So through quantum field theory, they manifest themselves as points

and interact that way. I don’t know if I’ll be able

to make this any clearer. (Laughter) CA: It doesn’t really matter. It’s evoking a kind of sense of wonder, and I certainly

want to understand more of this. But thank you so much for coming.

That was absolutely fascinating. (Applause)