back to index## Cumrun Vafa: String Theory | Lex Fridman Podcast #204

link |

The following is a conversation with Kamran Valfa,

link |

a theoretical physicist at Harvard

link |

specializing in string theory.

link |

He is the winner of the 2017 Breakthrough Prize

link |

in Fundamental Physics,

link |

which is the most lucrative academic prize in the world.

link |

Quick mention of our sponsors,

link |

Headspace, Jordan Harmer's show,

link |

Squarespace, and Allform.

link |

Check them out in the description to support this podcast.

link |

As a side note, let me say that string theory

link |

is a theory of quantum gravity

link |

that unifies quantum mechanics and general relativity.

link |

It says that quarks, electrons, and all other particles

link |

are made up of much tinier strings of vibrating energy.

link |

They vibrate in 10 or more dimensions,

link |

depending on the flavor of the theory.

link |

Different vibrating patterns result in different particles.

link |

From its origins, for a long time,

link |

string theory was seen as too good not to be true,

link |

but has recently fallen out of favor

link |

in the physics community,

link |

partly because over the past 40 years,

link |

it has not been able to make any novel predictions

link |

that could then be validated through experiment.

link |

Nevertheless, to this day,

link |

it remains one of our best candidates

link |

for a theory of everything,

link |

or a theory that unifies the laws of physics.

link |

Let me mention that a similar story happened

link |

with neural networks

link |

in the field of artificial intelligence,

link |

where it fell out of favor

link |

after decades of promise and research,

link |

but found success again in the past decade

link |

as part of the deep learning revolution.

link |

So I think it pays to keep an open mind,

link |

since we don't know which of the ideas in physics

link |

may be brought back decades later

link |

and be found to solve the biggest mysteries

link |

in theoretical physics.

link |

String theory still has that promise.

link |

This is the Lex Friedman podcast,

link |

and here's my conversation with Kamran Wafa.

link |

What is the difference between mathematics

link |

Well, that's a difficult question,

link |

because in many ways,

link |

math and physics are unified in many ways.

link |

So to distinguish them is not an easy task.

link |

I would say that perhaps the goals

link |

of math and physics are different.

link |

Math does not care to describe reality, physics does.

link |

That's the major difference.

link |

But a lot of the thoughts, processes, and so on,

link |

which goes to understanding the nature and reality,

link |

are the same things that mathematicians do.

link |

So in many ways, they are similar.

link |

Mathematicians care about deductive reasoning,

link |

and physicists or physics in general,

link |

we care less about that.

link |

We care more about interconnection of ideas,

link |

about how ideas support each other,

link |

or if there's a puzzle, discord between ideas.

link |

That's more interesting for us.

link |

And part of the reason is that we have learned in physics

link |

that the ideas are not sequential.

link |

And if we think that there's one idea

link |

which is more important,

link |

and we start with there and go to the next idea,

link |

and next one, and deduce things from that,

link |

like mathematicians do,

link |

we have learned that the third or fourth thing

link |

we deduce from that principle

link |

turns out later on to be the actual principle.

link |

And from a different perspective,

link |

starting from there leads to new ideas,

link |

which the original one didn't lead to,

link |

and that's the beginning of a new revolution in science.

link |

So this kind of thing we have seen again and again

link |

in the history of science,

link |

we have learned to not like deductive reasoning

link |

because that gives us a bad starting point,

link |

to think that we actually have the original thought process

link |

should be viewed as the primary thought,

link |

and all these are deductions,

link |

like the way mathematicians sometimes do.

link |

So in physics, we have learned to be skeptical

link |

of that way of thinking.

link |

We have to be a bit open to the possibility

link |

that what we thought is a deduction of a hypothesis

link |

is actually the reason that's true is the opposite.

link |

And so we reverse the order.

link |

And so this switching back and forth between ideas

link |

makes us more fluid about deductive fashion.

link |

Of course, it sometimes gives a wrong impression

link |

like physicists don't care about rigor.

link |

They just say random things.

link |

They are willing to say things that are not backed

link |

by the logical reasoning.

link |

That's not true at all.

link |

So despite this fluidity

link |

in saying which one is a primary thought,

link |

we are very careful about trying to understand

link |

what we have really understood in terms of relationship

link |

So that's an important ingredient.

link |

And in fact, solid math, being behind physics

link |

is I think one of the attractive features

link |

of a physical law.

link |

So we look for beautiful math underpinning it.

link |

Can we dig into that process of starting from one place

link |

and then ending up at like the fourth step

link |

and realizing all along that the place you started at

link |

So is that happened when there's a discrepancy

link |

between what the math says

link |

and what the physical world shows?

link |

Is that how you then can go back

link |

and do the revolutionary idea

link |

for different starting place altogether?

link |

Perhaps I give an example to see how it goes.

link |

And in fact, the historical example is Newton's work

link |

on classical mechanics.

link |

So Newton formulated the laws of mechanics,

link |

the force F equals to MA and his other laws,

link |

and they look very simple, elegant, and so forth.

link |

Later, when we studied more examples of mechanics

link |

and other similar things, physicists came up with the idea

link |

that the notion of potential is interesting.

link |

Potential was an abstract idea, which kind of came,

link |

you could take its gradient and relate it to the force.

link |

So you don't really need it a priori,

link |

but it solved, helped some thoughts.

link |

And then later, Euler and Lagrange reformulated

link |

Newtonian mechanics in a totally different way

link |

in the following fashion.

link |

They said, if you take,

link |

if you wanna know where a particle at this point

link |

and at this time, how does it get to this point

link |

at the later time, is the following.

link |

You take all possible paths connecting this particle

link |

from going from the initial point to the final point,

link |

and you compute the action.

link |

And what is an action?

link |

Action is the integral over time

link |

of the kinetic term of the particle minus its potential.

link |

So you take this integral,

link |

and each path will give you some quantity.

link |

And the path it actually takes, the physical path,

link |

is the one which minimizes this integral or this action.

link |

Now, this sounded like a backward step from Newton's.

link |

Newton's formula seemed very simple.

link |

F equals to ma, and you can write F is minus

link |

the gradient of the potential.

link |

So why would anybody start formulating such a simple thing

link |

in terms of this complicated looking principle?

link |

You have to study the space of all paths and all things

link |

and find the minimum, and then you get the same equation.

link |

So what's the point?

link |

So Euler and Lagrange's formulation of Newton,

link |

which was kind of recasting in this language,

link |

is just a consequence of Newton's law.

link |

F equals to ma gives you the same fact

link |

that this path is a minimum action.

link |

Now, what we learned later, last century,

link |

was that when we deal with quantum mechanics,

link |

Newton's law is only an average correct.

link |

And the particle going from one to the other

link |

doesn't take exactly one path.

link |

It takes all the paths with the amplitude,

link |

which is proportional to the exponential

link |

of the action times an imaginary number, i.

link |

And so this fact turned out to be the reformulation

link |

of quantum mechanics.

link |

We should start there as the basis of the new law,

link |

which is quantum mechanics, and Newton is only

link |

an approximation on the average correct.

link |

And when you say amplitude, you mean probability?

link |

Yes, the amplitude means if you sum up all these paths

link |

with exponential i times the action,

link |

if you sum this up, you get the number, complex number.

link |

You square the norm of this complex number,

link |

gives you a probability to go from one to the other.

link |

Is there ways in which mathematics can lead us astray

link |

when we use it as a tool to understand the physical world?

link |

Yes, I would say that mathematics can lead us astray

link |

as much as old physical ideas can lead us astray.

link |

So if you get stuck in something,

link |

then you can easily fool yourself

link |

that just like the thought process,

link |

we have to free ourselves of that.

link |

Sometimes math does that role, like say,

link |

oh, this is such a beautiful math.

link |

I definitely want to use it somewhere.

link |

And so you just get carried away

link |

and you just get maybe carried too far away.

link |

So that is certainly true, but I wouldn't say

link |

it's more dangerous than old physical ideas.

link |

To me, new math ideas is as much potential

link |

to lead us astray as old physical ideas,

link |

which could be long held principles of physics.

link |

So I'm just saying that we should keep an open mind

link |

about the role the math plays,

link |

not to be antagonistic towards it

link |

and not to over, over welcoming it.

link |

We should just be open to possibilities.

link |

What about looking at a particular characteristics

link |

of both physical ideas and mathematical ideas,

link |

You think beauty leads us astray, meaning,

link |

and you offline showed me a really nice puzzle

link |

that illustrates this idea a little bit.

link |

Now, maybe you can speak to that or another example

link |

where beauty makes it tempting for us to assume

link |

that the law and the theory we found

link |

is actually one that perfectly describes reality.

link |

I think that beauty does not lead us astray

link |

because I feel that beauty is a requirement

link |

for principles of physics.

link |

So beauty is a fundamental in the universe?

link |

I think beauty is fundamental.

link |

At least that's the way many of us view it.

link |

It's not emergent.

link |

It's not emergent.

link |

I think Hardy is the mathematician who said

link |

that there's no permanent place for ugly mathematics.

link |

And so I think the same is true in physics

link |

that if we find the principle which looks ugly,

link |

we are not going to be, that's not the end stage.

link |

So therefore beauty is going to lead us somewhere.

link |

Now, it doesn't mean beauty is enough.

link |

It doesn't mean if you just have beauty,

link |

if I just look at something is beautiful, then I'm fine.

link |

No, that's not the case.

link |

Beauty is certainly a criteria that every good

link |

physical theory should pass.

link |

That's at least the view we have.

link |

Why do we have this view?

link |

That's a good question.

link |

It is partly, you could say, based on experience

link |

of science over centuries, partly is philosophical view

link |

of what reality is or should be.

link |

And in principle, it could have been ugly

link |

and we might have had to deal with it,

link |

but we have gotten maybe confident through examples

link |

in the history of science to look for beauty.

link |

And our sense of beauty seems to incorporate

link |

a lot of things that are essential for us

link |

to solve some difficult problems like symmetry.

link |

We find symmetry beautiful

link |

and the breaking of symmetry beautiful.

link |

Somehow symmetry is a fundamental part

link |

of how we conceive of beauty at all layers of reality,

link |

which is interesting.

link |

Like in both the visual space, like the way we look at art,

link |

we look at each other as human beings,

link |

the way we look at creatures in the biological space,

link |

the way we look at chemistry,

link |

and then into the physics world as the work you do.

link |

It's kind of interesting.

link |

It makes you wonder like,

link |

which one is the chicken or the egg?

link |

Is symmetry the chicken and our conception of beauty

link |

the egg or the other way around?

link |

Or somehow the fact that the symmetry is part of reality,

link |

it somehow creates a brain that then is able to perceive it.

link |

Or maybe this is just because we,

link |

maybe it's so obvious, it's almost trivial,

link |

that symmetry, of course,

link |

will be part of every kind of universe that's possible.

link |

And then any kind of organism that's able to observe

link |

that universe is going to appreciate symmetry.

link |

Well, these are good questions.

link |

We don't have a deep understanding

link |

of why we get attracted to symmetry.

link |

Why do laws of nature seem to have symmetries underlying

link |

them and the reasoning or the examples of whether,

link |

if there wasn't symmetry,

link |

we would have understood it or not.

link |

We could have said that, yeah, if there were, you know,

link |

things which didn't look that great,

link |

we could understand them.

link |

For example, we know that symmetries get broken

link |

and we have appreciated nature

link |

in the broken symmetry phase as well.

link |

The world we live in has many things

link |

which do not look symmetric,

link |

but even those have underlying symmetry

link |

when you look at it more deeply.

link |

So we have gotten maybe spoiled perhaps

link |

by the appearance of symmetry all over the place.

link |

And we look for it.

link |

And I think this is perhaps related to a sense of aesthetics

link |

that scientists have.

link |

And we don't usually talk about it among scientists.

link |

In fact, it's kind of a philosophical view

link |

of why do we look for simplicity or beauty or so forth.

link |

And I think in a sense, scientists are a lot

link |

like philosophers.

link |

Sometimes I think, especially modern science

link |

seems to shun philosophers and philosophical views.

link |

And I think at their peril, I think in my view,

link |

science owes a lot to philosophy.

link |

And in my view, many scientists, in fact,

link |

probably all good scientists

link |

are perhaps amateur philosophers.

link |

They may not state that they are philosophers

link |

or they may not like to be labeled philosophers,

link |

but in many ways what they do

link |

is like what is philosophical takes of things.

link |

Looking for simplicity or symmetry

link |

is an example of that in my opinion, or seeing patterns.

link |

You see, for example, another example of the symmetry

link |

is like how you come up with new ideas in science.

link |

You see, for example, an idea A

link |

is connected with an idea B.

link |

Okay, so you study this connection very deeply.

link |

And then you find the cousin of an idea A,

link |

let me call it A prime.

link |

And then you immediately look for B prime.

link |

If A is like B and if there's an A prime,

link |

then you look for B prime.

link |

Well, it completes the picture.

link |

Well, it's philosophically appealing

link |

to have more balance in terms of that.

link |

And then you look for B prime and lo and behold,

link |

you find this other phenomenon,

link |

which is a physical phenomenon, which you call B prime.

link |

So this kind of thinking motivates

link |

asking questions and looking for things.

link |

And it has guided scientists, I think, through many centuries

link |

and I think it continues to do so today.

link |

And I think if you look at the long arc of history,

link |

I suspect that the things that will be remembered

link |

is the philosophical flavor of the ideas of physics

link |

and chemistry and computer science and mathematics.

link |

Like, I think the actual details

link |

will be shown to be incomplete or maybe wrong,

link |

but the philosophical intuitions

link |

will carry through much longer.

link |

There's a sense in which, if it's true,

link |

that we haven't figured out most of how things work,

link |

currently, that it'll all be shown as wrong and silly.

link |

It'd almost be a historical artifact.

link |

But the human spirit, whatever,

link |

like the longing to understand,

link |

the way we perceive the world, the way we conceive of it,

link |

of our place in the world, those ideas will carry on.

link |

I completely agree.

link |

In fact, I believe that almost,

link |

well, I believe that none of the principles

link |

or laws of physics we know today are exactly correct.

link |

All of them are approximations to something.

link |

They are better than the previous versions that we had,

link |

but none of them are exactly correct,

link |

and none of them are gonna stand forever.

link |

So I agree that that's the process we are heading,

link |

And yes, indeed, the thought process

link |

and that philosophical take is common.

link |

So when we look at older scientists,

link |

or maybe even all the way back to Greek philosophers

link |

and the things that the way they thought and so on,

link |

almost everything they said about nature was incorrect.

link |

But the way they thought about it

link |

and many things that they were thinking

link |

is still valid today.

link |

For example, they thought about symmetry breaking.

link |

They were trying to explain the following.

link |

This is a beautiful example, I think.

link |

They had figured out that the Earth is round,

link |

and they said, okay, Earth is round.

link |

They have seen the length of the shadow of a meter stick,

link |

and they have seen that if you go

link |

from the equator upwards north,

link |

they find that depending on how far away you are,

link |

that the length of the shadow changes.

link |

And from that, they had even measured

link |

the radius of the Earth to good accuracy.

link |

That's brilliant, by the way, the fact that they did that.

link |

Very brilliant, very brilliant.

link |

So these Greek philosophers are very smart.

link |

And so they had taken it to the next step.

link |

They asked, okay, so the Earth is round,

link |

why doesn't it move?

link |

They thought it doesn't move.

link |

They were looking around, nothing seemed to move.

link |

So they said, okay, we have to have a good explanation.

link |

It wasn't enough for them to be there.

link |

So they really wanna deeply understand that fact.

link |

And they come up with a symmetry argument.

link |

And the symmetry argument was,

link |

oh, if the Earth is a spherical,

link |

it must be at the center of the universe for sure.

link |

So they said the Earth is at the center of the universe.

link |

And they said, if the Earth is going to move,

link |

which direction does it pick?

link |

Any direction it picks, it breaks that spherical symmetry

link |

because you have to pick a direction.

link |

And that's not good because it's not symmetrical anymore.

link |

So therefore, the Earth decides to sit put

link |

because it would break the symmetry.

link |

So they had the incorrect science.

link |

They thought Earth doesn't move.

link |

But they had this beautiful idea

link |

that symmetry might explain it.

link |

But they were even smarter than that.

link |

Aristotle didn't agree with this argument.

link |

He said, why do you think symmetry prevents it from moving?

link |

Because the preferred position?

link |

He gave an example.

link |

He said, suppose you are a person

link |

and we put you at the center of a circle

link |

and we spread food around you on a circle around you,

link |

loaves of bread, let's say.

link |

And we say, okay, stay at the center of the circle forever.

link |

Are you going to do that

link |

just because it's a symmetric point?

link |

No, you are going to get hungry.

link |

You're going to move towards one of those loaves of bread,

link |

despite the fact that it breaks the symmetry.

link |

So from this way, he tried to argue

link |

being at the symmetric point

link |

may not be the preferred thing to do.

link |

And this idea of spontaneous symmetry breaking

link |

is something we just use today

link |

to describe many physical phenomena.

link |

So spontaneous symmetry breaking

link |

is the feature that we now use.

link |

But this idea was there thousands of years ago,

link |

but applied incorrectly to the physical world,

link |

but now we are using it.

link |

So these ideas are coming back in different forms.

link |

So I agree very much that the thought process

link |

is more important and these ideas are more interesting

link |

than the actual applications that people may find today.

link |

Did they use the language of symmetry

link |

and the symmetry breaking and spontaneous symmetry breaking?

link |

That's really interesting.

link |

Because I could see a conception of the universe

link |

that kind of tends towards perfect symmetry

link |

and is stuck there, not stuck there,

link |

but achieves that optimal and stays there.

link |

The idea that you would spontaneously

link |

break out of symmetry, like have these perturbations,

link |

like jump out of symmetry and back,

link |

that's a really difficult idea to load into your head.

link |

Like where does that come from?

link |

And then the idea that you may not be

link |

at the center of the universe.

link |

That is a really tough idea.

link |

Right, so symmetry sometimes is an explanation

link |

of being at the symmetric point.

link |

It's sometimes a simple explanation of many things.

link |

Like if you have a bowl, a circular bowl,

link |

then the bottom of it is the lowest point.

link |

So if you put a pebble or something,

link |

it will slide down and go there at the bottom

link |

and stays there at the symmetric point

link |

because it's the preferred point, the lowest energy point.

link |

But if that same symmetric circular bowl that you had

link |

had a bump on the bottom, the bottom might not be

link |

at the center, it might be on a circle on the table,

link |

in which case the pebble would not end up at the center,

link |

it would be the lower energy point.

link |

Symmetrical, but it breaks the symmetry

link |

once it takes a point on that circle.

link |

So we can have symmetry reasoning for where things end up

link |

or symmetry breakings, like this example would suggest.

link |

We talked about beauty.

link |

I find geometry to be beautiful.

link |

You have a few examples that are geometric

link |

in nature in your book.

link |

How can geometry in ancient times or today

link |

be used to understand reality?

link |

And maybe how do you think about geometry

link |

as a distinct tool in mathematics and physics?

link |

Yes, geometry is my favorite part of math as well.

link |

And Greeks were enamored by geometry.

link |

They tried to describe physical reality using geometry

link |

and principles of geometry and symmetry.

link |

Platonic solids, the five solids they had discovered

link |

had these beautiful solids.

link |

They thought it must be good for some reality.

link |

There must be explaining something.

link |

They attached one to air, one to fire and so forth.

link |

They tried to give physical reality to symmetric objects.

link |

These symmetric objects are symmetries of rotation

link |

and discrete symmetry groups we call today

link |

of rotation group in three dimensions.

link |

Now, we know now, we kind of laugh at the way

link |

they were trying to connect that symmetry

link |

to the laws of the realities of physics.

link |

But actually it turns out in modern days,

link |

we use symmetries in not too far away

link |

exactly in these kinds of thoughts processes

link |

in the following way.

link |

In the context of string theory,

link |

which is the field light study,

link |

we have these extra dimensions.

link |

And these extra dimensions are compact tiny spaces typically

link |

but they have different shapes and sizes.

link |

We have learned that if these extra shapes and sizes

link |

have symmetries, which are related

link |

to the same rotation symmetries

link |

that the Greek we're talking about,

link |

if they enjoy those discrete symmetries

link |

and if you take that symmetry and caution the space by it,

link |

in other words, identify points under these symmetries,

link |

you get properties of that space at the singular points

link |

which force emanates from them.

link |

Forces like the ones we have seen in nature today,

link |

like electric forces, like strong forces, like weak forces.

link |

So these same principles that were driving them

link |

to connect geometry and symmetries to nature

link |

is driving today's physics,

link |

now much more modern ideas, but nevertheless,

link |

the symmetries connecting geometry to physics.

link |

In fact, often sometimes we ask the following question,

link |

suppose I want to get this particular physical reality,

link |

I wanna have this particles with these forces and so on,

link |

It turns out that you can geometrically design

link |

the space to give you that.

link |

You say, oh, I put the sphere here, I will do this,

link |

I will shrink them.

link |

So if you have two spheres touching each other

link |

and shrinking to zero size, that gives you strong forces.

link |

If you have one of them, it gives you the weak forces.

link |

If you have this, you get that.

link |

And if you want to unify forces, do the other thing.

link |

So these geometrical translation of physics

link |

is one of my favorite things that we have discovered

link |

in modern physics and the context of string theory.

link |

The sad thing is when you go into multiple dimensions

link |

and we'll talk about it is we start to lose our capacity

link |

to visually intuit the world we're discussing.

link |

And then we go into the realm of mathematics

link |

and we'll lose that.

link |

Unfortunately, our brains are such that we're limited.

link |

But before we go into that mysterious, beautiful world,

link |

let's take a small step back.

link |

And you also in your book have this kind of

link |

through the space of puzzles, through the space of ideas,

link |

have a brief history of physics, of physical ideas.

link |

Now, we talked about Newtonian mechanics leading all

link |

through different Lagrangian, Hamiltonian mechanics.

link |

Can you describe some of the key ideas

link |

in the history of physics?

link |

Maybe lingering on each from electromagnetism to relativity

link |

to quantum mechanics and to today,

link |

as we'll talk about with quantum gravity and string theory.

link |

Sure, so I mentioned the classical mechanics

link |

and the Euler Lagrangian formulation.

link |

One of the next important milestones for physics

link |

were the discoveries of laws of electricity and magnetism.

link |

So Maxwell put the discoveries all together

link |

in the context of what we call the Maxwell's equations.

link |

And he noticed that when he put these discoveries

link |

that Faraday's and others had made about electric

link |

and magnetic phenomena in terms of mathematical equations,

link |

it didn't quite work.

link |

There was a mathematical inconsistency.

link |

Now, one could have had two attitudes.

link |

One would say, okay, who cares about math?

link |

I'm doing nature, electric force, magnetic force,

link |

math I don't care about.

link |

But it bothered him.

link |

It was inconsistent.

link |

The equations he were writing, the two equations

link |

he had written down did not agree with each other.

link |

And this bothered him, but he figured out,

link |

if you add this jiggle, this equation

link |

by adding one little term there, it works.

link |

At least it's consistent.

link |

What is the motivation for that term?

link |

He said, I don't know.

link |

Have we seen it in experiments?

link |

Why did you add it?

link |

Well, because of mathematical consistency.

link |

So he said, okay, math forced him to do this term.

link |

He added this term, which we now today call the Maxwell term.

link |

And once he added that term, his equations were nice,

link |

differential equations, mathematically consistent,

link |

beautiful, but he also found the new physical phenomena.

link |

He found that because of that term,

link |

he could now get electric and magnetic waves

link |

moving through space at a speed that he could calculate.

link |

So he calculated the speed of the wave

link |

and lo and behold, he found it's the same

link |

as the speed of light, which puzzled him

link |

because he didn't think light had anything

link |

to do with electricity and magnetism.

link |

But then he was courageous enough to say,

link |

well, maybe light is nothing

link |

but these electric and magnetic fields moving around.

link |

And he wasn't alive to see the verification

link |

of that prediction and indeed it was true.

link |

So this mathematical inconsistency,

link |

which we could say this mathematical beauty drove him

link |

to this physical, very important connection

link |

between light and electric and magnetic phenomena,

link |

which was later confirmed.

link |

So then physics progresses and it comes to Einstein.

link |

Einstein looks at Maxwell's equation,

link |

says, beautiful, these are nice equation,

link |

except we get one speed light.

link |

Who measures this light speed?

link |

And he asked the question, are you moving?

link |

Are you not moving?

link |

If you move, the speed of light changes,

link |

but Maxwell's equation has no hint

link |

of different speeds of light.

link |

It doesn't say, oh, only if you're not moving,

link |

you get the speed, it's just you always get the speed.

link |

So Einstein was very puzzled and he was daring enough

link |

to say, well, you know, maybe everybody gets

link |

the same speed for light.

link |

And that motivated his theory of special relativity.

link |

And this is an interesting example

link |

because the idea was motivated from physics,

link |

from Maxwell's equations, from the fact

link |

that people try to measure the properties of ether,

link |

which was supposed to be the medium

link |

in which the light travels through.

link |

And the idea was that only in that medium,

link |

the speed of, if you're at risk with respect

link |

to the ether, the speed, the speed of light,

link |

then if you're moving, the speed changes

link |

and people did not discover it.

link |

Michelson and Morley's experiment showed there's no ether.

link |

So then Einstein was courageous enough to say,

link |

you know, light is the same speed for everybody,

link |

regardless of whether you're moving or not.

link |

And the interesting thing is about special theory

link |

of relativity is that the math underpinning it

link |

It's a linear algebra, nothing terribly deep.

link |

You can teach it at a high school level, if not earlier.

link |

Okay, does that mean Einstein's special relativity

link |

So this is an example where simple math, you know,

link |

linear algebra leads to deep physics.

link |

Einstein's theory of special relativity.

link |

Motivated by this inconsistency that Maxwell's equation

link |

would suggest for the speed of light,

link |

depending on who observes it.

link |

What's the most daring idea there,

link |

that the speed of light could be the same everywhere?

link |

That's the basic, that's the guts of it.

link |

That's the core of Einstein's theory.

link |

That statement underlies the whole thing.

link |

Speed of light is the same for everybody.

link |

It's hard to swallow and it doesn't sound right.

link |

It sounds completely wrong on the face of it.

link |

And it took Einstein to make this daring statement.

link |

It would be laughing in some sense.

link |

How could anybody make this possibly ridiculous claim?

link |

And it turned out to be true.

link |

How does that make you feel?

link |

Because it still sounds ridiculous.

link |

It sounds ridiculous until you learn

link |

that our intuition is at fault

link |

about the way we conceive of space and time.

link |

The way we think about space and time is wrong

link |

because we think about the nature of time as absolute.

link |

And part of it is because we live in a situation

link |

where we don't go with very high speeds.

link |

There are speeds that are small

link |

compared to the speed of light.

link |

And therefore the phenomena we observe

link |

does not distinguish the relativity of time.

link |

The time also depends on who measures it.

link |

There's no absolute time.

link |

When you say it's noon today and now,

link |

it depends on who's measuring it.

link |

And not everybody would agree with that statement.

link |

And to see that you would have to have fast observer

link |

moving speeds close to the speed of light.

link |

So this shows that our intuition is at fault.

link |

And a lot of the discoveries in physics

link |

precisely is getting rid of the wrong old intuition.

link |

And it is funny because we get rid of it,

link |

but it's always lingers in us in some form.

link |

Like even when I'm describing it,

link |

I feel like a little bit like, isn't it funny?

link |

As you're just feeling the same way.

link |

But we kind of replace it by an intuition.

link |

And actually there's a very beautiful example of this,

link |

how physicists do this, try to replace their intuition.

link |

And I think this is one of my favorite examples

link |

about how physicists develop intuition.

link |

It goes to the work of Galileo.

link |

So, again, let's go back to Greek philosophers

link |

or maybe Aristotle in this case.

link |

Now, again, let's make a criticism.

link |

He thought that the heavier objects fall faster

link |

than the lighter objects.

link |

It kind of makes sense.

link |

And people say about the feather and so on,

link |

but that's because of the air resistance.

link |

But you might think like,

link |

if you have a heavy stone and a light pebble,

link |

the heavy one will fall first.

link |

If you don't do any experiments,

link |

that's the first gut reaction.

link |

I would say everybody would say that's the natural thing.

link |

Galileo did not believe this.

link |

And he kind of did the experiment.

link |

Famously it said he went on the top of Pisa Tower

link |

and he dropped these heavy and light stones

link |

and they fell at the same time

link |

when he dropped it at the same time from the same height.

link |

So he said, I'm done.

link |

I've showed that the heavy and lighter objects

link |

fall at the same time.

link |

I did the experiment.

link |

Scientists at that time did not accept it.

link |

Because at that time, science was not just experimental.

link |

The experiment was not enough.

link |

They didn't think that they have to soil their hands

link |

in doing experiments to get to the reality.

link |

They said, why is it the case?

link |

So Galileo had to come up with an explanation

link |

of why heavier and lighter objects fall at the same rate.

link |

This is the way he convinced them using symmetry.

link |

He said, suppose you have three bricks,

link |

the same shape, the same size, same mass, everything.

link |

And we hold these three bricks at the same height

link |

Which one will fall to the ground first?

link |

Everybody said, of course, we know it's symmetry

link |

tells you they're all the same shape,

link |

same size, same height.

link |

Of course, they fall at the same time.

link |

Yeah, we know that.

link |

He said, okay, what if we move these bricks around

link |

with the same height?

link |

Does it change the time they hit the ground?

link |

They said, if it's the same height,

link |

again, by the symmetry principle,

link |

because the height translation horizontal

link |

translates to the symmetry, no, it doesn't matter.

link |

They all fall at the same rate.

link |

Does it matter how close I bring them together?

link |

Okay, suppose I make the two bricks touch

link |

and then let them go.

link |

Do they fall at the same rate?

link |

But then he said, well, the two bricks that touch

link |

are twice more mass than this other brick.

link |

And you just agreed that they fall at the same rate.

link |

They say, yeah, yeah, we just agreed.

link |

That's right, that's great.

link |

So he deconfused them by the symmetry reasoning.

link |

So this way of repackaging some intuition,

link |

a different type of intuition.

link |

When the intuitions clash,

link |

then you side on the, you replace the intuition.

link |

In some of these more difficult physical ideas,

link |

physics ideas in the 20th century and the 21st century,

link |

it starts becoming more and more difficult

link |

to then replace the intuition.

link |

What does the world look like

link |

for an object traveling close to the speed of light?

link |

You start to think about the edges

link |

of supermassive black holes,

link |

and you start to think like, what's that look like?

link |

Or I've been into gravitational waves recently.

link |

It's like when the fabric of space time

link |

is being morphed by gravity,

link |

like what's that actually feel like?

link |

If I'm riding a gravitational wave, what's that feel like?

link |

I mean, I think some of those are more sort of hippy,

link |

not useful intuitions to have,

link |

but if you're an actual physicist

link |

or whatever the particular discipline is,

link |

I wonder if it's possible to meditate,

link |

to sort of escape through thinking,

link |

prolong thinking and meditation on a world,

link |

like live in a visualized world that's not like our own

link |

in order to understand a phenomenon deeply.

link |

So like replace the intuition,

link |

like through rigorous meditation on the idea

link |

in order to conceive of it.

link |

I mean, if we talk about multiple dimensions,

link |

I wonder if there's a way to escape

link |

with a three dimensional world in our mind

link |

in order to then start to reason about it.

link |

It's, the more I talk to topologists,

link |

the more they seem to not operate at all

link |

in the visual space.

link |

They really trust the mathematics,

link |

like which is really annoying to me because topology

link |

and differential geometry feels like it has a lot

link |

of potential for beautiful pictures.

link |

Yes, I think they do.

link |

Actually, I would not be able to do my research

link |

if I don't have an intuitive feel about geometry.

link |

And we'll get to it as you mentioned before

link |

that how, for example, in strength theory,

link |

you deal with these extra dimensions.

link |

And I'll be very happy to describe how we do it

link |

because without intuition, we will not get anywhere.

link |

And I don't think you can just rely on formalism.

link |

I don't think any physicist just relies on formalism.

link |

That's not physics.

link |

That's not understanding.

link |

So we have to intuit it.

link |

And that's crucial.

link |

And there are steps of doing it.

link |

And we learned it might not be trivial,

link |

but we learn how to do it.

link |

Similar to what this Galileo picture I just told you,

link |

you have to build these gradually.

link |

But you have to connect the bricks.

link |

Exactly, you have to connect the bricks, literally.

link |

So yeah, so then, so going back to your question

link |

about the path of the history of the science.

link |

So I was saying about the electricity and magnetism

link |

and the special relativity where simple idea

link |

led to special relativity.

link |

But then he went further thinking about acceleration

link |

in the context of relativity.

link |

And he came up with general relativity

link |

where he talked about the fabric of space time

link |

being curved and so forth and matter

link |

affecting the curvature of the space and time.

link |

So this gradually became a connection

link |

between geometry and physics.

link |

Namely, he replaced Newton's gravitational force

link |

with a very geometrical, beautiful picture.

link |

It's much more elegant than Newton's,

link |

but much more complicated mathematically.

link |

So when we say it's simpler,

link |

we mean in some form it's simpler,

link |

but not in pragmatic terms of equation solving.

link |

The equations are much harder to solve

link |

in Einstein's theory.

link |

And in fact, so much harder that Einstein himself

link |

couldn't solve many of the cases.

link |

He thought, for example, you couldn't solve the equation

link |

for a spherical symmetric matter,

link |

like if you had a symmetric sun,

link |

he didn't think you can actually solve his equation for that.

link |

And a year after he said that it was solved by Schwarzschild.

link |

So it was that hard

link |

that he didn't think it's gonna be that easy.

link |

So yeah, deformism is hard.

link |

But the contrast between the special relativity

link |

and general relativity is very interesting

link |

because one of them has almost trivial math

link |

and the other one has super complicated math.

link |

Both are physically amazingly important.

link |

And so we have learned that, you know,

link |

the physics may or may not require complicated math.

link |

We should not shy from using complicated math

link |

like Einstein did.

link |

Nobody, Einstein wouldn't say,

link |

I'm not gonna touch this math because it's too much,

link |

you know, tensors or, you know, curvature

link |

and I don't like the four dimensional space time

link |

because I can't see four dimension.

link |

He wasn't doing that.

link |

He was willing to abstract from that

link |

because physics drove him in that direction.

link |

But his motivation was physics.

link |

Physics pushed him.

link |

Just like Newton pushed to develop calculus

link |

because physics pushed him that he didn't have the tools.

link |

So he had to develop the tools

link |

to answer his physics questions.

link |

So his motivation was physics again.

link |

So to me, those are examples which show

link |

that math and physics have this symbiotic relationship

link |

which kind of reinforce each other.

link |

Here I'm using, I'm giving you examples of both of them,

link |

namely Newton's work led to development

link |

of mathematics, calculus.

link |

And in the case of Einstein, he didn't develop

link |

Riemannian geometry, he just used them.

link |

So it goes both ways and in the context of modern physics,

link |

we see that again and again, it goes both ways.

link |

Let me ask a ridiculous question.

link |

You know, you talk about your favorite soccer player,

link |

the bar, I'll ask the same question about Einstein's ideas

link |

which is, which one do you think

link |

is the biggest leap of genius?

link |

Is it the E equals MC squared?

link |

Is it Brownian motion?

link |

Is it special relativity, is it general relativity?

link |

Which of the famous set of papers he's written in 1905

link |

and in general, his work was the biggest leap of genius?

link |

In my opinion, it's special relativity.

link |

The idea that speed of light is the same for everybody

link |

is the beginning of everything he did.

link |

The beginning is the seed.

link |

Once you embrace that weirdness,

link |

all the weirdness, all the rest.

link |

I would say that's, even though he says

link |

the most beautiful moment for him,

link |

he says that is when he realized that if you fall

link |

in an elevator, you don't know if you're falling

link |

or whether you're in the falling elevator

link |

or whether you're next to the earth, gravitational.

link |

That to him was his aha moment,

link |

which inertial mass and gravitational mass

link |

being identical geometrically and so forth

link |

as part of the theory, not because of, you know,

link |

some funny coincidence.

link |

That's for him, but I feel from outside at least,

link |

it feels like the speed of light being the same

link |

is the really aha moment.

link |

The general relativity to you is not

link |

like the conception of space time.

link |

In a sense, the conception of space time

link |

already was part of the special relativity

link |

when you talk about length contraction.

link |

So general relativity takes that to the next step,

link |

but beginning of it was already space,

link |

length contracts, time dilates.

link |

So once you talk about those, then yeah,

link |

you can dilate more or less different places

link |

than its curvature.

link |

So you don't have a choice.

link |

So it kind of started just with that same simple thought.

link |

Speed of light is the same for all.

link |

Where does quantum mechanics come into view?

link |

Exactly, so this is the next step.

link |

So Einstein's, you know, developed general relativity

link |

and he's beginning to develop the foundation

link |

of quantum mechanics at the same time,

link |

the photoelectric effects and others.

link |

And so quantum mechanics overtakes, in fact,

link |

Einstein in many ways because he doesn't like

link |

the probabilistic interpretation of quantum mechanics

link |

and the formulas that's emerging,

link |

but fits his march on and try to, for example,

link |

combine Einstein's theory of relativity

link |

with quantum mechanics.

link |

So Dirac takes special relativity,

link |

tries to see how is it compatible with quantum mechanics.

link |

Can we pause and briefly say what is quantum mechanics?

link |

So quantum mechanics, so I discussed briefly

link |

when I talked about the connection

link |

between Newtonian mechanics

link |

and the Euler Lagrange reformulation

link |

of the Newtonian mechanics and interpretation

link |

of this Euler Lagrange formulas in terms of the paths

link |

that the particle take.

link |

So when we say a particle goes from here to here,

link |

we usually think it classically follows

link |

a specific trajectory, but actually in quantum mechanics,

link |

it follows every trajectory with different probabilities.

link |

And so there's this fuzziness.

link |

Now, most probable, it's the path that you actually see

link |

and deviation from that is very, very unlikely

link |

and probabilistically very minuscule.

link |

So in everyday experiments,

link |

we don't see anything deviated from what we expect,

link |

but quantum mechanics tells us that the things

link |

Things are not as precise as the line you draw.

link |

Things are a bit like cloud.

link |

So if you go to microscopic scales,

link |

like atomic scales and lower,

link |

these phenomena become more pronounced.

link |

You can see it much better.

link |

The electron is not at the point,

link |

but the cloud spread out around the nucleus.

link |

And so this fuzziness, this probabilistic aspect of reality

link |

is what quantum mechanics describes.

link |

Can I briefly pause on that idea?

link |

Do you think quantum mechanics

link |

is just a really damn good approximation,

link |

a tool for predicting reality,

link |

or does it actually describe reality?

link |

Do you think reality is fuzzy at that level?

link |

Well, I think that reality is fuzzy at that level,

link |

but I don't think quantum mechanics

link |

is necessarily the end of the story.

link |

So quantum mechanics is certainly an improvement

link |

over classical physics.

link |

That much we know by experiments and so forth.

link |

Whether I'm happy with quantum mechanics,

link |

whether I view quantum mechanics,

link |

for example, the thought,

link |

the measurement description of quantum mechanics,

link |

am I happy with it?

link |

Am I thinking that's the end stage or not?

link |

I don't think we're at the end of that story.

link |

And many physicists may or may not view this way.

link |

Some do, some don't.

link |

But I think that it's the best we have right now,

link |

It's the best approximation for reality we know today.

link |

And so far, we don't know what it is,

link |

the next thing that improves it or replaces it and so on.

link |

But as I mentioned before,

link |

I don't believe any of the laws of physics we know today

link |

are permanently exactly correct.

link |

That doesn't bother me.

link |

I'm not like dogmatic saying,

link |

I have figured out this is the law of nature.

link |

I know everything.

link |

No, no, that's the beauty about science

link |

is that we are not dogmatic.

link |

And we are willing to, in fact,

link |

we are encouraged to be skeptical of what we ourselves do.

link |

So you were talking about Dirac.

link |

Yes, I was talking about Dirac, right.

link |

So Dirac was trying to now combine

link |

this Schrodinger's equations,

link |

which was described in the context of trying to talk about

link |

how these probabilistic waves of electrons

link |

move for the atom,

link |

which was good for speeds

link |

which were not too close to the speed of light,

link |

to what happens when you get to the near the speed of light.

link |

So then you need relativity.

link |

So then Dirac tried to combine Einstein's relativity

link |

with quantum mechanics.

link |

So he tried to combine them

link |

and he wrote this beautiful equation, the Dirac equation,

link |

which roughly speaking,

link |

take the square root of the Einstein's equation

link |

in order to connect it to Schrodinger's

link |

time evolution operator,

link |

which is first order in time derivative

link |

to get rid of the naive thing

link |

that Einstein's equation would have given,

link |

which is second order.

link |

So you have to take a square root.

link |

Now square root usually has a plus or minus sign

link |

And when he did this,

link |

he originally didn't notice this plus,

link |

didn't pay attention to this plus or minus sign,

link |

but later physicists pointed out to Dirac says,

link |

look, there's also this minus sign.

link |

And if you use this minus sign,

link |

you get negative energy.

link |

In fact, it was very, very annoying that, you know,

link |

somebody else tells you this obvious mistake you make.

link |

Pauli famous physicist told Dirac, this is nonsense.

link |

You're going to get negative energy with your equation,

link |

which negative energy without any bottom,

link |

you can go all the way down to negative.

link |

Infinite energy, so it doesn't make any sense.

link |

Dirac thought about it.

link |

And then he remembered Pauli's exclusion principle

link |

Pauli had said, you know,

link |

there's this principle called the exclusion principle

link |

that, you know, two electrons cannot be on the same orbit.

link |

And so Dirac said, okay, you know what?

link |

All these negative energy states are filled orbits,

link |

So according to you,

link |

Mr. Pauli, there's no place to go.

link |

So therefore they only have to go positive.

link |

Sounded like a big cheat.

link |

And then Pauli said, oh, you know what?

link |

We can change orbits from one orbit to another.

link |

What if I take one of these negative energy orbits

link |

and put it up there?

link |

Then it seems to be a new particle,

link |

which has opposite properties to the electron.

link |

It has positive energy, but it has positive charge.

link |

Dirac was a bit worried.

link |

He said, maybe that's proton

link |

because proton has plus charge.

link |

But then he said, oh, maybe it's proton.

link |

But then they said, no, no, no, no.

link |

It has the same mass as the electron.

link |

It cannot be proton because proton is heavier.

link |

He says, well, then maybe another part we haven't seen.

link |

By that time, Dirac himself was getting a little bit worried

link |

about his own equation and his own crazy interpretation.

link |

Until a few years later, Anderson,

link |

in the photographic place that he had gotten

link |

from these cosmic rays,

link |

he discovered a particle which goes

link |

in the opposite direction that the electron goes

link |

when there's a magnetic field,

link |

and with the same mass,

link |

exactly like what Dirac had predicted.

link |

And this was what we call now positron.

link |

And in fact, beginning with the work of Dirac,

link |

we know that every particle has an antiparticle.

link |

And so this idea that there's an antiparticle

link |

came from this simple math.

link |

There's a plus and a minus

link |

from the Dirac's quote unquote mistake.

link |

So again, trying to combine ideas,

link |

sometimes the math is smarter than the person

link |

who uses it to apply it,

link |

and you try to resist it,

link |

and then you kind of confront it by criticism,

link |

which is the way it should be.

link |

So physicists comes and said, no, no, that's wrong,

link |

and you correct it, and so on.

link |

So that is a development of the idea

link |

there's particle, there's antiparticle, and so on.

link |

So this is the beginning of development

link |

of quantum mechanics and the connection with relativity,

link |

but the thing was more challenging

link |

because we had to also describe

link |

how electric and magnetic fields work with quantum mechanics.

link |

This was much more complicated

link |

because it's not just one point.

link |

Electric and magnetic fields were everywhere.

link |

So you had to talk about fluctuating

link |

and a fuzziness of electrical fields

link |

and magnetic fields everywhere.

link |

And the math for that was very difficult to deal with.

link |

And this led to a subject called quantum field theory.

link |

Fields like electric and magnetic fields had to be quantum,

link |

had to be described also in a wavy way.

link |

Feynman in particular was one of the pioneers

link |

along with Schrodingers and others

link |

to try to come up with a formalism

link |

to deal with fields like electric and magnetic fields,

link |

interacting with electrons in a consistent quantum fashion.

link |

And they developed this beautiful theory,

link |

quantum electrodynamics from that.

link |

And later on that same formalism,

link |

quantum field theory led to the discovery of other forces

link |

and other particles all consistent

link |

with the idea of quantum mechanics.

link |

So that was how physics progressed.

link |

And so basically we learned that all particles

link |

and all the forces are in some sense related

link |

to particle exchanges.

link |

And so for example, electromagnetic forces

link |

are mediated by a particle we call photon and so forth.

link |

And same for other forces that they discovered,

link |

strong forces and the weak forces.

link |

So we got the sense of what quantum field theory is.

link |

Is that a big leap of an idea that particles

link |

are fluctuations in the field?

link |

Like the idea that everything is a field.

link |

It's the old Einstein, light is a wave,

link |

both a particle and a wave kind of idea.

link |

Is that a huge leap in our understanding

link |

of conceiving the universe as fields?

link |

I would say that viewing the particles,

link |

this duality that Bohr mentioned

link |

between particles and waves,

link |

that waves can behave sometimes like particles,

link |

sometimes like waves,

link |

is one of the biggest leaps of imagination

link |

that quantum mechanics made physics do.

link |

So I agree that that is quite remarkable.

link |

Is duality fundamental to the universe

link |

or is it just because we don't understand it fully?

link |

Like will it eventually collapse

link |

into a clean explanation that doesn't require duality?

link |

Like that a phenomena could be two things at once

link |

and both to be true.

link |

So that seems weird.

link |

So in fact I was going to get to that

link |

when we get to string theory

link |

but maybe I can comment on that now.

link |

Duality turns out to be running the show today

link |

and the whole thing that we are doing is string theory.

link |

Duality is the name of the game.

link |

So it's the most beautiful subject

link |

and I want to talk about it.

link |

Let's talk about it in the context of string theory then.

link |

So we do want to take a next step into,

link |

because we mentioned general relativity,

link |

we mentioned quantum mechanics,

link |

is there something to be said about quantum gravity?

link |

Yes, that's exactly the right point to talk about.

link |

So namely we have talked about quantum fields

link |

and I talked about electric forces,

link |

photon being the particle carrying those forces.

link |

So for gravity, quantizing gravitational field

link |

which is this curvature of space time according to Einstein,

link |

you get another particle called graviton.

link |

So what about gravitons?

link |

Should be there, no problem.

link |

So then you start computing it.

link |

What do I mean by computing it?

link |

Well, you compute scattering of one graviton

link |

off another graviton, maybe with graviton with an electron

link |

and so on, see what you get.

link |

Feynman had already mastered this quantum electrodynamics.

link |

He said, no problem, let me do it.

link |

Even though these are such weak forces,

link |

the gravity is very weak.

link |

So therefore to see them,

link |

these quantum effects of gravitational waves was impossible.

link |

It's even impossible today.

link |

So Feynman just did it for fun.

link |

He usually had this mindset that I want to do something

link |

which I will see in experiment,

link |

but this one, let's just see what it does.

link |

And he was surprised because the same techniques

link |

he was using for doing the same calculations,

link |

quantum electrodynamics, when applied to gravity failed.

link |

The formulas seem to make sense,

link |

but he had to do some integrals

link |

and he found that when he does those integrals,

link |

he got infinity and it didn't make any sense.

link |

Now there were similar infinities in the other pieces

link |

but he had managed to make sense out of those before.

link |

This was no way he could make sense out of it.

link |

He just didn't know what to do.

link |

He didn't feel it's an urgent issue

link |

because nobody could do the experiment.

link |

So he was kind of said, okay, there's this thing,

link |

but okay, we don't know how to exactly do it,

link |

but that's the way it is.

link |

So in some sense, a natural conclusion

link |

from what Feynman did could have been like,

link |

gravity cannot be consistent with quantum theory,

link |

but that cannot be the case

link |

because gravity is in our universe,

link |

quantum mechanics in our universe,

link |

they both together somehow should work.

link |

So it's not acceptable to say they don't work together.

link |

So that was a puzzle.

link |

How does it possibly work?

link |

And then we get to the string theory.

link |

So this is the puzzle of quantum gravity.

link |

The particle description of quantum gravity failed.

link |

So the infinity shows up.

link |

What do we do with infinity?

link |

Let's get to the fun part.

link |

Let's talk about string theory.

link |

Let's discuss some technical basics of string theory.

link |

What is string theory?

link |

How many dimensions are we talking about?

link |

What are the different states?

link |

How do we represent the elementary particles

link |

and the laws of physics using this new framework?

link |

So string theory is the idea

link |

that the fundamental entities are not particles,

link |

but extended higher dimensional objects

link |

like one dimensional strings, like loops.

link |

These loops could be open like with two ends,

link |

like an interval or a circle without any ends.

link |

And they're vibrating and moving around in space.

link |

So how big they are?

link |

Well, you can of course stretch it and make it big,

link |

or you can just let it be whatever it wants.

link |

It can be as small as a point

link |

because the circle can shrink to a point

link |

and be very light,

link |

or you can stretch it and becomes very massive,

link |

or it could oscillate and become massive that way.

link |

So it depends on which kind of state you have.

link |

In fact, the string can have infinitely many modes,

link |

depending on which kind of oscillation it's doing.

link |

Like a guitar has different harmonics,

link |

string has different harmonics,

link |

but for the string, each harmonic is a particle.

link |

So each particle will give you,

link |

ah, this is a more massive harmonic, this is a less massive.

link |

So the lightest harmonic, so to speak, is no harmonics,

link |

which means like the string shrunk to a point,

link |

and then it becomes like a massless particles

link |

or light particles like photon and graviton and so forth.

link |

So when you look at tiny strings,

link |

which are shrunk to a point, the lightest ones,

link |

they look like the particles that we think,

link |

they're like particles.

link |

In other words, from far away, they look like a point.

link |

But of course, if you zoom in,

link |

there's this tiny little circle that's there

link |

that's shrunk to almost a point.

link |

Should we be imagining, this is to the visual intuition,

link |

should we be imagining literally strings

link |

that are potentially connected as a loop or not?

link |

We knew, and when somebody outside of physics

link |

is imagining a basic element of string theory,

link |

which is a string,

link |

should we literally be thinking about a string?

link |

Yes, you should literally think about string,

link |

but string with zero thickness.

link |

With zero thickness.

link |

So notice, it's a loop of energy, so to speak,

link |

if you can think of it that way.

link |

And so there's a tension like a regular string,

link |

if you pull it, there's, you know, you have to stretch it.

link |

But it's not like a thickness, like you're made of something,

link |

It's not made of atoms or something like that.

link |

But it is very, very tiny.

link |

Much smaller than elementary particles of physics.

link |

So we think if you let the string to be by itself,

link |

the lowest state, there'll be like fuzziness

link |

or a size of that tiny little circle,

link |

which is like a point,

link |

about, could be anything between,

link |

we don't know the exact size,

link |

but in different models have different sizes,

link |

but something of the order of 10 to the minus,

link |

let's say 30 centimeters.

link |

So 10 to the minus 30 centimeters,

link |

just to compare it with the size of the atom,

link |

which is 10 to the minus eight centimeters,

link |

is 22 orders of magnitude smaller.

link |

Unimaginably small, I would say.

link |

So we basically think from far away,

link |

string is like a point particle.

link |

And that's why a lot of the things that we learned

link |

about point particle physics

link |

carries over directly to strings.

link |

So therefore there's not much of a mystery

link |

why particle physics was successful,

link |

because a string is like a particle

link |

when it's not stretched.

link |

But it turns out having this size,

link |

being able to oscillate, get bigger,

link |

turned out to be resolving this puzzles

link |

that Feynman was having in calculating his diagrams,

link |

and it gets rid of those infinities.

link |

So when you're trying to do those infinities,

link |

the regions that give infinities to Feynman,

link |

as soon as you get to those regions,

link |

then this string starts to oscillate,

link |

and these oscillation structure of the strings

link |

resolves those infinities to finite answer at the end.

link |

So the size of the string,

link |

the fact that it's one dimensional,

link |

gives a finite answer at the end.

link |

Resolves this paradox.

link |

Now, perhaps it's also useful to recount

link |

of how string theory came to be.

link |

Because it wasn't like somebody say,

link |

well, let me solve the problem of Einstein's,

link |

solve the problem that Feynman had with unifying

link |

Einstein's theory with quantum mechanics

link |

by replacing the point by a string.

link |

No, that's not the way the thought process,

link |

the thought process was much more random.

link |

Physicist, then it's John on this case,

link |

was trying to describe the interactions

link |

they were seeing in colliders, in accelerators.

link |

And they were seeing that some process,

link |

in some process, when two particles came together

link |

and joined together and when they were separately,

link |

in one way, and the opposite way, they behave the same way.

link |

In some way, there was a symmetry, a duality,

link |

which he didn't understand.

link |

The particles didn't seem to have that symmetry.

link |

He said, I don't know what it is,

link |

what's the reason that these colliders

link |

and experiments we're doing seems to have the symmetry,

link |

but let me write the mathematical formula,

link |

which exhibits that symmetry.

link |

He used gamma functions, beta functions and all that,

link |

you know, complete math, no physics,

link |

other than trying to get symmetry out of his equation.

link |

He just wrote down a formula as the answer for a process,

link |

not a method to compute it.

link |

Just say, wouldn't it be nice if this was the answer?

link |

Physics looked at this one, that's intriguing,

link |

it has the symmetry all right, but what is this?

link |

Where is this coming from?

link |

Which kind of physics gives you this?

link |

A few years later, people saw that,

link |

oh, the equation that you're writing,

link |

the process you're writing in the intermediate channels

link |

that particles come together,

link |

seems to have all the harmonics.

link |

Harmonics sounds like a string.

link |

Let me see if what you're describing

link |

has anything to do with the strings.

link |

And people try to see if what he's doing

link |

has anything to do with the strings.

link |

If I study scattering of two strings,

link |

I get exactly the formula you wrote down.

link |

That was the reinterpretation

link |

of what he had written in the formula as the strings,

link |

but still had nothing to do with gravity.

link |

It had nothing to do with resolving the problems

link |

of gravity with quantum mechanics.

link |

It was just trying to explain a process

link |

that people were seeing in hydronic physics collisions.

link |

So it took a few more years to get to that point.

link |

They did notice that,

link |

physicists noticed that whenever you try to find

link |

the spectrum of strings, you always get a massless particle

link |

which has exactly the properties

link |

that the graviton is supposed to have.

link |

And no particle in hydronic physics that had that property.

link |

You are getting a massless graviton

link |

as part of this scattering without looking for it.

link |

It was forced on you.

link |

People were not trying to solve quantum gravity.

link |

Quantum gravity was pushed on them.

link |

I don't want this graviton.

link |

They couldn't get rid of it.

link |

They gave up trying to get rid of it.

link |

Physicists, Sherk and Schwartz said,

link |

you know what, string theory is theory of quantum gravity.

link |

They've changed their perspective altogether.

link |

We are not describing the hydronic physics.

link |

We are describing this theory of quantum gravity.

link |

And that's when string theory probably got like exciting

link |

that this could be the unifying theory.

link |

Exactly, it got exciting,

link |

but at the same time, not so fast.

link |

Namely, it should have been fast, but it wasn't

link |

because particle physics through quantum field theory

link |

were so successful at that time.

link |

This is mid seventies, standard model of physics,

link |

electromagnetism and unification of electromagnetic forces

link |

with all the other forces were beginning to take place

link |

without the gravity part.

link |

Everything was working beautifully for particle physics.

link |

And so that was the shining golden age

link |

of quantum field theory and all the experiments,

link |

standard model, this and that, unification,

link |

spontaneous symmetry breaking was taking place.

link |

All of them was nice.

link |

This was kind of like a side show

link |

and nobody was paying so much attention.

link |

This exotic string is needed for quantum gravity.

link |

Maybe there's other ways, maybe we should do something else.

link |

So, yeah, it wasn't paid much attention to.

link |

And this took a little bit more effort

link |

to try to actually connect it to reality.

link |

There are a few more steps.

link |

First of all, there was a puzzle

link |

that you were getting extra dimensions.

link |

String was not working well

link |

with three spatial dimension on one time.

link |

It needed extra dimension.

link |

Now, there are different versions of strings,

link |

but the version that ended up being related

link |

to having particles like electron,

link |

what we call fermions, needed 10 dimensions,

link |

what we call super string.

link |

Why the word super?

link |

It turns out this version of the string,

link |

which had fermions, had an extra symmetry,

link |

which we call supersymmetry.

link |

This is a symmetry between a particle and another particle

link |

with exactly the same properties,

link |

same mass, same charge, et cetera.

link |

The only difference is that one of them

link |

has a little different spin than the other one.

link |

And one of them is a boson, one of them is a fermion

link |

because of that shift of spin.

link |

Otherwise, they're identical.

link |

So there was this symmetry.

link |

String theory had this symmetry.

link |

In fact, supersymmetry was discovered

link |

through string theory, theoretically.

link |

So theoretically, the first place that this was observed

link |

when you were describing these fermionic strings.

link |

So that was the beginning of the study of supersymmetry

link |

was via string theory.

link |

And then it had remarkable properties

link |

that the symmetry meant and so forth

link |

that people began studying supersymmetry after that.

link |

And that was a kind of a tangent direction

link |

at the beginning for string theory.

link |

But people in particle physics started also thinking,

link |

oh, supersymmetry is great.

link |

Let's see if we can have supersymmetry

link |

in particle physics and so forth.

link |

Forget about strings.

link |

And they developed on a different track as well.

link |

Supersymmetry in different models

link |

became a subject on its own right,

link |

understanding supersymmetry and what does this mean?

link |

Because it unified bosons and fermion,

link |

unified some ideas together.

link |

So photon is a boson, electron is a fermion.

link |

Could things like that be somehow related?

link |

It was a kind of a natural kind of a question

link |

to try to kind of unify

link |

because in physics, we love unification.

link |

Now, gradually, string theory was beginning

link |

to show signs of unification.

link |

It had graviton, but people found that you also have

link |

things like photons in them,

link |

different excitations of string behave like photons,

link |

another one behaves like electron.

link |

So a single string was unifying all these particles

link |

That's remarkable.

link |

It's in 10 dimensions though.

link |

It is not our universe

link |

because we live in three plus one dimension.

link |

How could that be possibly true?

link |

So this was a conundrum.

link |

It was elegant, it was beautiful,

link |

but it was very specific

link |

about which dimension you're getting,

link |

which structure you're getting.

link |

It wasn't saying, oh, you just put D equals to four,

link |

you'll get your space time dimension that you want.

link |

No, it didn't like that.

link |

It said, I want 10 dimensions and that's the way it is.

link |

So it was very specific.

link |

Now, so people try to reconcile this

link |

by the idea that, you know,

link |

maybe these extra dimensions are tiny.

link |

So if you take three macroscopic spatial dimensions

link |

on one time and six extra tiny spatial dimensions,

link |

like tiny spheres or tiny circles,

link |

then it avoids contradiction with manifest fact

link |

that we haven't seen extra dimensions in experiments today.

link |

So that was a way to avoid conflict.

link |

Now, this was a way to avoid conflict,

link |

but it was not observed in experiments.

link |

A string observed in experiments?

link |

No, because it's so small.

link |

So it's beginning to sound a little bit funny.

link |

Similar feeling to the way perhaps Dirac had felt

link |

about this positron plus or minus, you know,

link |

it was beginning to sound a little bit like,

link |

oh yeah, not only I have to have 10 dimension,

link |

but I have to have this, I have to also this.

link |

And so conservative physicists would say,

link |

hmm, you know, I haven't seen these experiments.

link |

I don't know if they are really there.

link |

Are you pulling my leg?

link |

Do you want me to imagine things that are not there?

link |

So this was an attitude of some physicists

link |

towards string theory, despite the fact

link |

that the puzzle of gravity and quantum mechanics

link |

merging together work, but still was this skepticism.

link |

You're putting all these things that you want me

link |

to imagine there, these extra dimensions

link |

that I cannot see, aha, aha.

link |

And you want me to believe that string

link |

that you have not even seen the experiments are real,

link |

aha, okay, what else do you want me to believe?

link |

So this kind of beginning to sound a little funny.

link |

Now, I will pass forward a little bit further.

link |

A few decades later, when string theory became

link |

the mainstream of efforts to unify the forces

link |

and particles together, we learned

link |

that these extra dimensions actually solved problems.

link |

They weren't a nuisance the way they originally appeared.

link |

First of all, the properties of these extra dimensions

link |

reflected the number of particles we got in four dimensions.

link |

If you took these six dimensions to have like five holes

link |

or four holes, change the number of particles

link |

that you see in four dimensional space time,

link |

you get one electron and one muon if you had this,

link |

but if you did the other J shape, you get something else.

link |

So geometrically, you could get different kinds of physics.

link |

So it was kind of a mirroring of geometry by physics

link |

down in the macroscopic space.

link |

So these extra dimension were becoming useful.

link |

Fine, but we didn't need the extra dimension

link |

to just write an electron in three dimensions,

link |

we did rewrote it, so what?

link |

Was there any other puzzle?

link |

Yes, there were, Hawking.

link |

Hawking had been studying black holes in mid 70s

link |

following the work of Bekenstein,

link |

who had predicted that black holes have entropy.

link |

So Bekenstein had tried to attach the entropy

link |

to the black hole.

link |

If you throw something into the black hole,

link |

the entropy seems to go down

link |

because you had something entropy outside the black hole

link |

and you throw it, black hole was unique,

link |

so the entropy did not have any, black hole had no entropy.

link |

So the entropy seemed to go down.

link |

And so that's against the laws of thermodynamics.

link |

So Bekenstein was trying to say, no, no,

link |

therefore black hole must have an entropy.

link |

So he was trying to understand that he found that

link |

if you assign entropy to be proportional

link |

to the area of the black hole, it seems to work.

link |

And then Hawking found not only that's correct,

link |

he found the correct proportionality factor

link |

of a one quarter of the area and Planck units

link |

is the correct amount of entropy.

link |

And he gave an argument using

link |

quantum semi classical arguments,

link |

which means basically using a little bit

link |

of a quantum mechanics,

link |

because he didn't have the full quantum mechanics

link |

of string theory, he could do some aspects

link |

of approximate quantum arguments.

link |

So he heuristic quantum arguments led

link |

to this entropy formula.

link |

But then he didn't answer the following question.

link |

He was getting a big entropy for the black hole,

link |

the black hole with the size of the horizon

link |

of a black hole is huge, has a huge amount of entropy.

link |

What are the microstates of this entropy?

link |

When you say, for example, the gas is entropy,

link |

you count where the atoms are,

link |

you count this bucket or that bucket,

link |

there's an information about there and so on, you count them.

link |

For the black hole, the way Hawking was thinking,

link |

there was no degree of freedom, you throw them in,

link |

and there was just one solution.

link |

So where are these entropy?

link |

What are these microscopic states?

link |

They were hidden somewhere.

link |

So later in string theory,

link |

the work that we did with my colleague Strominger,

link |

in particular showed that these ingredients

link |

in string theory of black hole arise

link |

from the extra dimensions.

link |

So the degrees of freedom are hidden

link |

in terms of things like strings,

link |

wrapping these extra circles in these hidden dimensions.

link |

And then we started counting how many ways

link |

like the strings can wrap around this circle

link |

and the extra dimension or that circle

link |

and counted the microscopic degrees of freedom.

link |

And lo and behold, we got the microscopic degrees

link |

of freedom that Hawking was predicting four dimensions.

link |

So the extra dimensions became useful

link |

for resolving a puzzle in four dimensions.

link |

The puzzle was where are the degrees of freedom

link |

of the black hole hidden?

link |

The answer, hidden in the extra dimensions.

link |

The tiny extra dimensions.

link |

So then by this time, it was beginning to,

link |

we see aspects that extra dimensions

link |

are useful for many things.

link |

It's not a nuisance.

link |

It wasn't to be kind of, you know, be ashamed of.

link |

It was actually in the welcome features.

link |

New feature, nevertheless.

link |

How do you intuit the 10 dimensional world?

link |

So yes, it's a feature for describing certain phenomena

link |

like the entropy in black holes,

link |

but what you said that to you a theory becomes real

link |

or becomes powerful when you can connect it

link |

to some deep intuition.

link |

So how do we intuit 10 dimensions?

link |

Yes, so I will explain how some of the analogies work.

link |

First of all, we do a lot of analogies.

link |

And by analogies, we build intuition.

link |

So I will start with this example.

link |

I will try to explain that if we are in 10 dimensional space,

link |

if we have a seven dimensional plane

link |

and eight dimensional plane,

link |

we ask typically in what space do they intersect each other

link |

in what dimension?

link |

That might sound like,

link |

how do you possibly give an answer to this?

link |

So we start with lower dimensions.

link |

We start with two dimensions.

link |

We say, if you have one dimension and a point,

link |

do they intersect typically on a plane?

link |

So a line one dimensional, a point zero dimension

link |

on a two dimensional plane, they don't typically meet.

link |

But if you have a one dimensional line and another line,

link |

which is one plus one on a plane,

link |

they typically intersect at a point.

link |

Typically means if you're not parallel,

link |

typically they intersect at a point.

link |

So one plus one is two and in two dimension,

link |

they intersect at the zero dimensional point.

link |

So you see two dimension, one and one, two,

link |

two minus two is zero.

link |

So you get point out of intersection.

link |

Let's go to three dimension.

link |

You have a plane, two dimensional plane and a point.

link |

Do they intersect?

link |

How about the plane and a line?

link |

A plane is two dimensional and a line is one.

link |

Two plus one is three.

link |

In three dimension, a plane and a line meet at points,

link |

which is zero dimensional.

link |

Three minus three is zero.

link |

Okay, so plane and a line intersect

link |

at a point in three dimension.

link |

How about the plane and a plane in 3D?

link |

Well, plane is two and this is two.

link |

Two plus two is four.

link |

In 3D, four minus three is one.

link |

They intersect on a one dimensional line.

link |

Okay, we're beginning to see the pattern.

link |

Okay, now come to the question.

link |

We're in 10 dimension.

link |

Now we have the intuition.

link |

We have a seven dimensional plane

link |

and eight dimensional plane in 10 dimension.

link |

They intersect on a plane.

link |

What's the dimension?

link |

Well, seven plus eight is 15 minus 10 is five.

link |

We draw the same picture as two planes

link |

and we write seven dimension, eight dimension,

link |

but we have gotten the intuition

link |

from the lower dimensional one.

link |

It doesn't scare us anymore.

link |

So we draw this picture.

link |

We cannot see all the seven dimensions

link |

by looking at this two dimensional visualization of it,

link |

but it has all the features we want.

link |

It has, so we draw this picture.

link |

It says seven, seven,

link |

and they meet at the five dimensional plane.

link |

So we have built this intuition.

link |

Now, this is an example of how we come up with intuition.

link |

Let me give you more examples of it

link |

because I think this will show you

link |

that people have to come up with intuitions to visualize it.

link |

Otherwise, we will be a little bit lost.

link |

So what you just described is kind of

link |

in these high dimensional spaces,

link |

focus on the meeting place of two planes

link |

in high dimensional spaces.

link |

Exactly, how the planes meet, for example,

link |

what's the dimension of their intersection and so on.

link |

So how do we come up with intuition?

link |

We borrow examples from lower dimensions,

link |

build up intuition and draw the same pictures

link |

as if we are talking about 10 dimensions,

link |

but we are drawing the same as a two dimensional plane

link |

because we cannot do any better.

link |

But our words change, but not our pictures.

link |

So your sense is we can have a deep understanding

link |

of reality by looking at its slices,

link |

at lower dimensional slices.

link |

And this brings me to the next example I wanna mention,

link |

Let's think about how do we think about the sphere?

link |

Well, the sphere is a sphere, the round nice thing,

link |

but sphere has a circular symmetry.

link |

Now, I can describe the sphere in the following way.

link |

I can describe it by an interval,

link |

which is thinking about this going from the north

link |

of the sphere to the south.

link |

And at each point, I have a circle attached to it.

link |

So you can think about the sphere as a line

link |

with a circle attached with each point,

link |

the circle shrinks to a point at end points

link |

So I can say, oh, one way to think about the sphere

link |

is an interval where at each point on that interval,

link |

there's another circle I'm not drawing.

link |

But if you like, you can just draw it.

link |

Say, okay, I won't draw it.

link |

So from now on, there's this mnemonic.

link |

I draw an interval when I wanna talk about the sphere

link |

and you remember that the end points of the interval

link |

mean a strong circle, that's all.

link |

And they say, yeah, I see, that's a sphere, good.

link |

Now, we wanna talk about the product of two spheres.

link |

That's four dimensional, how can I visualize it?

link |

Easy, you just take an interval and another interval,

link |

that's just gonna be a square.

link |

A square is a four dimensional space, yeah, why is that?

link |

Well, at each point on the square, there's two circles,

link |

one for each of those directions you drew.

link |

And when you get to the boundaries of each direction,

link |

one of the circles shrink on each edge of that square.

link |

And when you get to the corners of the square,

link |

all both circles shrink.

link |

This is a sphere times a sphere, I have defined interval.

link |

I just described for you a four dimensional space.

link |

Do you want a six dimensional space?

link |

No problem, take a corner of a room.

link |

In fact, if you want to have a sphere times a sphere

link |

times a sphere times a sphere, take a cube.

link |

A cube is a rendition of this six dimensional space,

link |

two sphere times another sphere times another sphere,

link |

where three of the circles I'm not drawing for you.

link |

For each one of those directions, there's another circle.

link |

But each time you get to the boundary of the cube,

link |

one circle shrinks.

link |

When the boundaries meet, two circles shrinks.

link |

When three boundaries meet, all the three circles shrink.

link |

So I just give you a picture.

link |

Now, mathematicians come up with amazing things.

link |

Like, you know what, I want to take a point in space

link |

You know, these concepts like topology and geometry,

link |

complicated, how do you do?

link |

In this picture, it's very easy.

link |

Blow it up in this picture means the following.

link |

You think about this cube, you go to the corner

link |

and you chop off a corner.

link |

Chopping off the corner replaces the point.

link |

Replace the point by a triangle.

link |

So you're blowing up a point and then this triangle

link |

is what they call P2, projective two space.

link |

But these pictures are very physical and you feel it.

link |

There's nothing amazing.

link |

I'm not talking about six dimension.

link |

Four plus six is 10, the dimension of string theory.

link |

So we can visualize it, no problem.

link |

Okay, so that's building the intuition

link |

to a complicated world of string theory.

link |

Nevertheless, these objects are really small.

link |

And just like you said, experimental validation

link |

is very difficult because the objects are way smaller

link |

than anything that we currently have the tools

link |

and accelerators and so on to reveal through experiment.

link |

So there's a kind of skepticism

link |

that's not just about the nature of the theory

link |

because of the 10 dimensions, as you've explained,

link |

but in that we can't experimentally validate it

link |

and it doesn't necessarily, to date,

link |

maybe you can correct me,

link |

predict something fundamentally new.

link |

So it's beautiful as an explaining theory,

link |

which means that it's very possible

link |

that it is a fundamental theory

link |

that describes reality and unifies the laws,

link |

but there's still a kind of skepticism.

link |

And me, from sort of an outside observer perspective,

link |

have been observing a little bit of a growing cynicism

link |

about string theory in the recent few years.

link |

Can you describe the cynicism about,

link |

sort of by cynicism I mean a cynicism

link |

about the hope for this theory

link |

of pushing theoretical physics forward?

link |

Can you do describe why this is cynicism

link |

and how do we reverse that trend?

link |

Yes, first of all, the criticism for string theory

link |

is healthy in a sense that in science

link |

we have to have different viewpoints and that's good.

link |

So I welcome criticism and the reason for criticism

link |

and I think that is a valid reason

link |

is that there has been zero experimental evidence

link |

for string theory.

link |

That is no experiment has been done

link |

to show that there's this loop of energy moving around.

link |

And so that's a valid objection and valid worry.

link |

And if I were to say, you know what,

link |

string theory can never be verified

link |

or experimentally checked, that's the way it is,

link |

they would have every right to say

link |

what you're talking about is not science.

link |

Because in science we will have to have

link |

experimental consequences and checks.

link |

The difference between string theory

link |

and something which is not scientific

link |

is that string theory has predictions.

link |

The problem is that the predictions we have today

link |

of string theory is hard to access by experiments

link |

available with the energies we can achieve

link |

with the colliders today.

link |

It doesn't mean there's a problem with string theory,

link |

it just means technologically we're not that far ahead.

link |

Now, we can have two attitudes.

link |

You say, well, if that's the case, why are you studying

link |

Because you can't do experiment today.

link |

Now, this is becoming a little bit more like mathematics

link |

You say, well, I want to learn,

link |

I want to know how the nature works

link |

even though I cannot prove it today

link |

that this is it because of experiments.

link |

That should not prevent my mind not to think about it.

link |

So that's the attitude many string theorists follow,

link |

that it should be like this.

link |

Now, so that's an answer to the criticism,

link |

but there's actually a better answer to the criticism,

link |

We don't have experimental evidence for string theory,

link |

but we have theoretical evidence for string theory.

link |

And what do I mean by theoretical evidence

link |

for string theory?

link |

String theory has connected different parts

link |

of physics together.

link |

It didn't have to.

link |

It has brought connections between part of physics,

link |

although suppose you're just interested

link |

in particle physics.

link |

Suppose you're not even interested in gravity at all.

link |

It turns out there are properties

link |

of certain particle physics models

link |

that string theory has been able to solve using gravity,

link |

using ideas from string theory,

link |

ideas known as holography,

link |

which is relating something which has to do with particles

link |

to something having to do with gravity.

link |

Why did it have to be this rich?

link |

The subject is very rich.

link |

It's not something we were smart enough to develop.

link |

As I explained to you,

link |

the development of string theory

link |

came from accidental discovery.

link |

It wasn't because we were smart enough

link |

to come up with the idea,

link |

oh yeah, string of course has gravity in it.

link |

No, it was accidental discovery.

link |

So some people say it's not fair to say

link |

we have no evidence for string theory.

link |

Graviton, gravity is an evidence for string theory.

link |

It's predicted by string theory.

link |

We didn't put it by hand, we got it.

link |

So there's a qualitative check.

link |

Okay, gravity is a prediction of string theory.

link |

It's a postdiction because we know gravity existed.

link |

But still, logically it is a prediction

link |

because really we didn't know it had the graviton

link |

that we later learned that, oh, that's the same as gravity.

link |

So literally that's the way it was discovered.

link |

It wasn't put in by hand.

link |

So there are many things like that,

link |

that there are different facets of physics,

link |

like questions in condensed matter physics,

link |

questions of particle physics,

link |

questions about this and that have come together

link |

to find beautiful answers by using ideas

link |

from string theory at the same time

link |

as a lot of new math has emerged.

link |

That's an aspect which I wouldn't emphasize

link |

as evidence to physicists necessarily,

link |

because they would say, okay, great, you got some math,

link |

but what's it do with reality?

link |

But as I explained, many of the physical principles

link |

we know of have beautiful math underpinning them.

link |

So it certainly leads further confidence

link |

that we may not be going astray,

link |

even though that's not the full proof as we know.

link |

So there are these aspects that give further evidence

link |

for string theory, connections between each other,

link |

connection with the real world,

link |

but then there are other things that come about

link |

and I can try to give examples of that.

link |

So these are further evidences

link |

and these are certain predictions of string theory.

link |

They are not as detailed as we want,

link |

but there are still predictions.

link |

Why is the dimension of space and time three plus one?

link |

Say, I don't know, just deal with it, three plus one.

link |

But in physics, we want to know why.

link |

Well, take a random dimension from one to infinity.

link |

What's your random dimension?

link |

A random dimension from one to infinity would not be four.

link |

Eight would most likely be a humongous number,

link |

I mean, there's no, if you choose any reasonable distribution

link |

which goes from one to infinity,

link |

three or four would not be your pick.

link |

The fact that we are in three or four dimension

link |

is already strange.

link |

The fact that strings are sorry,

link |

I cannot go beyond 10 or maybe 11 or something.

link |

The fact that there's this upper bound,

link |

the range is not from one to infinity,

link |

it's from one to 10 or 11 or whatnot,

link |

it already brings a natural prior.

link |

Oh yeah, three or four is just on the average.

link |

If you pick some of the compactification,

link |

then it could easily be that.

link |

So in other words, it makes it much more possible

link |

that it could be three of our universe.

link |

So the fact that the dimension already is so small,

link |

it should be surprising.

link |

We don't ask that question.

link |

We should be surprised because we could have conceived

link |

of universes with our pre dimension.

link |

Why is it that we have such a small dimension?

link |

That's number one.

link |

So good theory of the universe should give you

link |

an intuition of the why it's four or three plus one.

link |

And it's not obvious that it should be.

link |

That should be explained.

link |

We take that as an assumption,

link |

but that's a thing that should be explained.

link |

Yeah, so we haven't explained that in string theory.

link |

Actually, I did write a model within string theory

link |

to try to describe why we end up

link |

with three plus one space time dimensions,

link |

which are big compared to the rest of them.

link |

And even though this has not been,

link |

the technical difficulties to prove it is still not there,

link |

but I will explain the idea because the idea connects

link |

to some other piece of elegant math,

link |

which is the following.

link |

Consider a universe made of a box, three dimensional box.

link |

Or in fact, if we start in string theory,

link |

nine dimensional box,

link |

because we have nine spatial dimension on one time.

link |

So imagine a nine dimensional box.

link |

So we should imagine the box of a typical size of the string,

link |

So the universe would naturally start

link |

with a very tiny nine dimensional box.

link |

What do strings do?

link |

Well, strings go around the box

link |

and move around and vibrate and all that,

link |

but also they can wrap around one side of the box

link |

to the other because I'm imagining a box

link |

with periodic boundary conditions.

link |

So what we call the torus.

link |

So the string can go from one side to the other.

link |

This is what we call a winding string.

link |

The string can wind around the box.

link |

Now, suppose you have, you've now evolved the universe.

link |

Because there's energy, the universe starts to expand.

link |

But it doesn't expand too far.

link |

Well, because there are these strings

link |

which are wrapped around

link |

from one side of the wall to the other.

link |

When the universe, the walls of the universe are growing,

link |

it is stretching the string

link |

and the strings are becoming very, very massive.

link |

So it becomes difficult to expand.

link |

It kind of puts a halt on it.

link |

In order to not put a halt,

link |

a string which is going this way

link |

and a string which is going that way

link |

should intersect each other

link |

and disconnect each other and unwind.

link |

So a string which winds this way

link |

and the string which finds the opposite way

link |

should find each other to reconnect

link |

and this way disappear.

link |

So if they find each other and they disappear.

link |

But how can strings find each other?

link |

Well, the string moves and another string moves.

link |

A string is one dimensional, one plus one is two

link |

and one plus one is two and two plus two is four.

link |

In four dimensional space time, they will find each other.

link |

In a higher dimensional space time,

link |

they typically miss each other.

link |

So if the dimension were too big,

link |

they would miss each other,

link |

they wouldn't be able to expand.

link |

So in order to expand, they have to find each other

link |

and three of them can find each other

link |

and those can expand and the other one will be stuck.

link |

So that explains why within string theory,

link |

these particular dimensions are really big

link |

and full of exciting stuff.

link |

That could be an explanation.

link |

That's a model we suggested with my colleague Brandenberger.

link |

But it turns out to be related to a deep piece of math.

link |

You see, for mathematicians,

link |

manifolds of dimension bigger than four are simple.

link |

Four dimension is the hardest dimension for math,

link |

And it turns out the reason it's difficult is the following.

link |

It turns out that in higher dimension,

link |

you use what's called surgery in mathematical terminology,

link |

where you use these two dimensional tubes

link |

to maneuver them off of each other.

link |

So you have two plus two becoming four.

link |

In higher than four dimension,

link |

you can pass them through each other

link |

without them intersecting.

link |

In four dimension, two plus two

link |

doesn't allow you to pass them through each other.

link |

So the same techniques that work in higher dimension

link |

don't work in four dimension because two plus two is four.

link |

The same reasoning I was just telling you

link |

about strings finding each other in four

link |

ends up to be the reason why four is much more complicated

link |

to classify for mathematicians as well.

link |

So there might be these things.

link |

So I cannot say that this is the reason

link |

that string theory is giving you three plus one,

link |

but it could be a model for it.

link |

And so there are these kinds of ideas

link |

that could underlie why we have three extra dimensions

link |

which are large and the rest of them are small.

link |

But absolutely, we have to have a good reason.

link |

We cannot leave it like that.

link |

Can I ask a tricky human question?

link |

So you are one of the seminal figures in string theory.

link |

You got the Breakthrough Prize.

link |

You've worked with Edward Witten.

link |

There's no Nobel Prize that has been given on string theory.

link |

Credit assignment is tricky in science.

link |

It makes you quite sad, especially big, like LIGO,

link |

big experimental projects when so many incredible people

link |

have been involved and yet the Nobel Prize is annoying

link |

in that it's only given to three people.

link |

Who do you think gets the Nobel Prize

link |

for string theory at first?

link |

If it turns out that it, if not in full, then in part,

link |

is a good model of the way the physics of the universe works.

link |

Who are the key figures?

link |

Maybe let's put Nobel Prize aside.

link |

Who are the key figures?

link |

Okay, I like the second version of the question.

link |

Because I think to try to give a prize to one person

link |

in string theory doesn't do justice to the diversity

link |

So there was quite a lot of incredible people

link |

in the history of string theory.

link |

Quite a lot of people.

link |

I mean, starting with Veneziano,

link |

who wasn't talking about strings.

link |

I mean, he wrote down the beginning of the strings.

link |

We cannot ignore that for sure.

link |

And so you start with that and you go on

link |

with various other figures and so on.

link |

So there are different epochs in string theory

link |

and different people have been pushing it.

link |

And so for example, the early epoch,

link |

we just told you people like Veneziano,

link |

and Nambu, and the Susskind, and others were pushing it.

link |

Green and Schwarz were pushing it and so forth.

link |

So this was, or Scherck and so on.

link |

So these were the initial periods of pioneers,

link |

I would say, of string theory.

link |

And then there were the mid 80s that Edward Witten

link |

was the major proponent of string theory.

link |

And he really changed the landscape of string theory

link |

in terms of what people do and how we view it.

link |

And I think his efforts brought a lot of attention

link |

to the community of string theory.

link |

To the community about high energy community

link |

to focus on this effort as the correct theory

link |

of unification of forces.

link |

So he brought a lot of research as well as, of course,

link |

the first rate work he himself did to this area.

link |

So that's in mid 80s and onwards,

link |

and also in mid 90s where he was one of the proponents

link |

of the duality revolution in string theory.

link |

And with that came a lot of these other ideas

link |

that led to breakthroughs involving, for example,

link |

the example I told you about black holes and holography,

link |

and the work that was later done by Maldacena

link |

about the properties of duality between particle physics

link |

and quantum gravity and the deeper connections

link |

of holography, and it continues.

link |

And there are many people within this range,

link |

which I haven't even mentioned.

link |

They have done fantastic important things.

link |

How it gets recognized, I think, is secondary,

link |

in my opinion, than the appreciation

link |

that the effort is collective.

link |

That, in fact, that to me is the more important part

link |

of science that gets forgotten.

link |

For some reason, humanity likes heroes,

link |

and science is no exception.

link |

We like heroes, but I personally try to avoid that trap.

link |

I feel, in my work, most of my work is with colleagues.

link |

I have much more collaborations than sole author papers,

link |

and I enjoy it, and I think that that's, to me,

link |

one of the most satisfying aspects of science

link |

is to interact and learn and debate ideas with colleagues

link |

because that influx of ideas enriches it,

link |

and that's why I find it interesting.

link |

To me, science, if I was on an island,

link |

and if I was developing string theory by myself

link |

and had nothing to do with anybody,

link |

it would be much less satisfying, in my opinion.

link |

Even if I could take credit I did it,

link |

it won't be as satisfying.

link |

Sitting alone with a big metal drinking champagne, no.

link |

I think, to me, the collective work is more exciting,

link |

and you mentioned my getting the breakthrough.

link |

When I was getting it, I made sure to mention

link |

that it is because of the joint work

link |

that I've done with colleagues.

link |

At that time, it was around 180 or so collaborators,

link |

and I acknowledged them in the webpage for them.

link |

I write all of their names

link |

and the collaborations that led to this.

link |

So, to me, science is fun when it's collaboration,

link |

and yes, there are more important

link |

and less important figures, as in any field,

link |

and that's true, that's true in string theory as well,

link |

but I think that I would like to view this

link |

as a collective effort.

link |

So, setting the heroes aside,

link |

the Nobel Prize is a celebration of,

link |

what's the right way to put it,

link |

that this idea turned out to be right.

link |

So, like, you look at Einstein

link |

didn't believe in black holes,

link |

and then black holes got their Nobel Prize.

link |

Do you think string theory will get its Nobel Prize,

link |

Nobel Prizes, if you were to bet money?

link |

If this was an investment meeting

link |

and we had to bet all our money,

link |

do you think he gets the Nobel Prizes?

link |

I think it's possible that none of the living physicists

link |

will get the Nobel Prize in string theory,

link |

but somebody will.

link |

Because, unfortunately, the technology available today

link |

is not very encouraging

link |

in terms of seeing directly evidence for string theory.

link |

Do you think it ultimately boils down to

link |

the Nobel Prize will be given

link |

when there is some direct or indirect evidence?

link |

There would be, but I think that part of this

link |

breakthrough prize was precisely the appreciation

link |

that when we have sufficient evidence,

link |

theoretical as it is, not experiment,

link |

because of this technology lag,

link |

you appreciate what you think is the correct path.

link |

So, there are many people who have been recognized precisely

link |

because they may not be around

link |

when it actually gets experimented,

link |

even though they discovered it.

link |

So, there are many things like that

link |

that's going on in science.

link |

So, I think that I would want to attach less significance

link |

to the recognitions of people.

link |

And I have a second review on this,

link |

which is there are people who look at these works

link |

that people have done and put them together

link |

and make the next big breakthrough.

link |

And they get identified with, perhaps rightly,

link |

with many of these new visions.

link |

But they are on the shoulders of these little scientists.

link |

Which don't get any recognition.

link |

You know, yeah, you did this little work.

link |

Oh yeah, you did this little work.

link |

Oh yeah, yeah, five of you.

link |

Oh yeah, these showed this pattern.

link |

And then somebody else, it's not fair.

link |

To me, those little guys, which kind of like,

link |

like seem to do the little calculation here,

link |

a little thing there, which doesn't rise to the occasion

link |

of this grandiose kind of thing,

link |

doesn't make it to the New York Times headlines and so on,

link |

deserve a lot of recognition.

link |

And I think they don't get enough.

link |

I would say that there should be this Nobel prize

link |

for, you know, they have these Doctors Without Borders,

link |

they're a huge group.

link |

They should do a similar thing.

link |

And these String Theors Without Borders kind of,

link |

everybody is doing a lot of work.

link |

And I think that I would like to see that effort recognized.

link |

I think in the long arc of history,

link |

we're all little guys and girls

link |

standing on the shoulders of each other.

link |

I mean, it's all going to look tiny in retrospect.

link |

If we celebrate, the New York Times,

link |

you know, as a newspaper,

link |

or the idea of a newspaper in a few centuries from now

link |

will be long forgotten.

link |

Yes, I agree with that.

link |

Especially in the context of String Theory,

link |

we should have a very long term view.

link |

Just as a tiny tangent, we mentioned Edward Witten.

link |

And he, in a bunch of walks of life for me as an outsider,

link |

comes up as a person who is widely considered as like

link |

one of the most brilliant people in the history of physics,

link |

just as a powerhouse of a human,

link |

like the exceptional places that a human mind can rise to.

link |

You've gotten the chance to work with him.

link |

Yes, more than that.

link |

He was my advisor, PhD advisor.

link |

So I got to know him very well

link |

and I benefited from his insights.

link |

In fact, what you said about him is accurate.

link |

He is not only brilliant,

link |

but he is also multifaceted in terms of the impact

link |

he has had in not only physics, but also mathematics.

link |

He has gotten the Fields Medal

link |

because of his work in mathematics.

link |

And rightly so, he has used his knowledge of physics

link |

in a way which impacted deep ideas in modern mathematics.

link |

And that's an example of the power of these ideas

link |

in modern high energy physics and string theory,

link |

the applicability of it to modern mathematics.

link |

So he's quite an exceptional individual.

link |

We don't come across such people a lot in history.

link |

So I think, yes, indeed,

link |

he's one of the rare figures in this history of subject.

link |

He has had great impact on a lot of aspects

link |

of not just string theory,

link |

a lot of different areas in physics,

link |

and also, yes, in mathematics as well.

link |

So I think what you said about him is accurate.

link |

I had the pleasure of interacting with him as a student

link |

and later on as colleagues writing papers together

link |

What impact did he have on your life?

link |

Like what have you learned from him?

link |

If you were to look at the trajectory of your mind

link |

of the way you approach science and physics and mathematics,

link |

how did he perturb that trajectory in a way?

link |

Yes, he did actually.

link |

So I can explain because when I was a student,

link |

I had the biggest impact by him,

link |

clearly as a grad student at Princeton.

link |

So I think that was a time where I was a little bit confused

link |

about the relation between math and physics.

link |

I got a double major in mathematics and physics

link |

at MIT because I really enjoyed both.

link |

And I liked the elegance and the rigor of mathematics.

link |

And I liked the power of ideas in physics

link |

and its applicability to reality

link |

and what it teaches about the real world around us.

link |

But I saw this tension between rigorous thinking

link |

in mathematics and lack thereof in physics.

link |

And this troubled me to no end.

link |

I was troubled by that.

link |

So I was at crossroads when I decided

link |

to go to graduate school in physics

link |

because I did not like some of the lack of rigors

link |

I was seeing in physics.

link |

On the other hand, to me, mathematics,

link |

even though it was rigorous,

link |

I didn't see the point of it.

link |

In other words, the math theorem by itself could be beautiful

link |

but I really wanted more than that.

link |

I wanted to say, okay, what does it teach us

link |

about something else, something more than just math?

link |

So I wasn't that enamored with just math

link |

but physics was a little bit bothersome.

link |

Nevertheless, I decided to go to physics

link |

and I decided to go to Princeton

link |

and I started working with Edward Witten

link |

as my thesis advisor.

link |

And at that time I was trying to put physics

link |

in rigorous mathematical terms.

link |

I took quantum field theory.

link |

I tried to make rigorous out of it and so on.

link |

And no matter how hard I was trying,

link |

I was not being able to do that.

link |

And I was falling behind from my classes.

link |

I was not learning much physics

link |

and I was not making it rigorous.

link |

And to me, it was this dichotomy between math and physics.

link |

I like math but this is not exactly this.

link |

There comes Edward Witten as my advisor

link |

and I see him in action thinking about math and physics.

link |

He was amazing in math.

link |

He knew all about the math.

link |

It was no problem with him.

link |

But he thought about physics in a way

link |

which did not find this tension between the two.

link |

It was much more harmonious.

link |

For him, he would draw the Feynman diagrams

link |

but he wouldn't view it as a formalism.

link |

He was viewed, oh yeah, the particle goes over there

link |

and this is what's going on.

link |

And so wait, you're thinking really,

link |

is this particle, this is really electron going there?

link |

It's not the form or the result perturbation.

link |

You just feel like the electron.

link |

You're moving with this guy and do that and so on.

link |

And you're thinking invariantly about physics

link |

or the way he thought about relativity.

link |

Like I was thinking about this momentum system.

link |

He was thinking invariantly about physics,

link |

just like the way you think about invariant concepts

link |

and relativity, which don't depend on the frame of reference.

link |

He was thinking about the physics in invariant ways,

link |

the way that doesn't, that gives you a bigger perspective.

link |

So this gradually helped me appreciate

link |

that interconnections between ideas and physics

link |

replaces mathematical rigor.

link |

That the different facets reinforce each other.

link |

They say, oh, I cannot rigorously define

link |

what I mean by this,

link |

but this thing connects with this other physics I've seen

link |

and this other thing.

link |

And they together form an elegant story.

link |

And that replaced for me what I believed as a solidness,

link |

which I found in math as a rigor, solid.

link |

I found that replaced the rigor and solidness in physics.

link |

So I found, okay, that's the way you can hang onto.

link |

It is not wishy washy.

link |

It's not like somebody is just not being able to prove it,

link |

just making up a story.

link |

It was more than that.

link |

And it was no tension with mathematics.

link |

In fact, mathematics was helping it, like friends.

link |

And so much more harmonious and gives insights to physics.

link |

So that's, I think, one of the main things I learned

link |

from interactions with Witten.

link |

And I think that now perhaps I have taken that

link |

Maybe he wouldn't go this far as I have.

link |

Namely, I use physics to define new mathematics

link |

in a way which would be far less rigorous

link |

than a physicist might necessarily believe,

link |

because I take the physical intuition,

link |

perhaps literally in many ways that could teach us about.

link |

So now I've gained so much confidence

link |

in physical intuition that I make bold statements

link |

that sometimes takes math friends off guard.

link |

So an example of it is mirror symmetry.

link |

So we were studying these compactification

link |

of string geometries.

link |

This is after my PhD now.

link |

I've, by the time I come to Harvard,

link |

we're studying these aspects of string compactification

link |

on these complicated manifolds,

link |

six dimensional spaces called Kalabial manifolds,

link |

And I noticed with a couple other colleagues

link |

that there was a symmetry in physics suggested

link |

between different Kalabials.

link |

It suggested that you couldn't actually compute

link |

the Euler characteristic of a Kalabia.

link |

Euler characteristic is counting the number of points

link |

minus the number of edges plus the number of faces minus.

link |

So you can count the alternating sequence

link |

of properties of a space,

link |

which is a topological property of a space.

link |

So Euler characteristics of the Kalabia

link |

was a property of the space.

link |

And so we noticed that from the physics formalism,

link |

if string moves in a Kalabia,

link |

you cannot distinguish,

link |

we cannot compute the Euler characteristic.

link |

You can only compute the absolute value of it.

link |

Now this bothered us

link |

because how could you not compute the actual sign

link |

unless the both sides were the same?

link |

So I conjectured maybe for every Kalabia

link |

with Euler characteristics positive,

link |

there's one with negative.

link |

I told this to my colleague Yao

link |

who's namesake is Kalabia,

link |

that I'm making this conjecture.

link |

Is it possible that for every Kalabia,

link |

there's one with the opposite Euler characteristic?

link |

Sounds not reasonable.

link |

He said, well, we know more Kalabias

link |

with negative Euler characteristics than positive.

link |

I said, but physics says we cannot distinguish them.

link |

At least I don't see how.

link |

So we conjectured that for every Kalabia

link |

with one sign, there's the other one,

link |

despite the mathematical evidence,

link |

despite the mathematical evidence,

link |

despite the expert telling us it's not the right idea.

link |

If a few years later, this symmetry, mirror symmetry

link |

between the sign with the opposite sign

link |

was later confirmed by mathematicians.

link |

So this is actually the opposite view.

link |

That is physics is so sure about it

link |

that you're going against the mathematical wisdom,

link |

telling them they better look for it.

link |

So taking the physical intuition literally

link |

and then having that drive the mathematics.

link |

And now we are so confident about many such examples

link |

that has affected modern mathematics in ways like this,

link |

that we are much more confident

link |

about our understanding of what string theory is.

link |

These are another aspects,

link |

other aspects of why we feel string theory is correct.

link |

It's doing these kinds of things.

link |

I've been hearing your talk quite a bit

link |

about string theory, landscape and the swamp land.

link |

What the heck are those two concepts?

link |

Okay, very good question.

link |

So let's go back to what I was describing about Feynman.

link |

Feynman was trying to do these diagrams for graviton

link |

and electrons and all that.

link |

He found that he's getting infinities he cannot resolve.

link |

Okay, the natural conclusion is that field theories

link |

and gravity and quantum theory don't go together

link |

and you cannot have it.

link |

So in other words, field theories and gravity

link |

are inconsistent with quantum mechanics, period.

link |

String theory came up with examples

link |

but didn't address the question more broadly

link |

that is it true that every field theory

link |

can be coupled to gravity in a quantum mechanical way?

link |

It turns out that Feynman was essentially right.

link |

Almost all particle physics theories,

link |

no matter what you add to it,

link |

when you put gravity in it, doesn't work.

link |

Only rare exceptions work.

link |

So string theory are those rare exceptions.

link |

So therefore the general principle

link |

that Feynman found was correct.

link |

Quantum field theory and gravity and quantum mechanics

link |

don't go together except for Joule's exceptional cases.

link |

There are exceptional cases.

link |

Okay, the total vastness of quantum field theories

link |

that are there we call the set of quantum field theories,

link |

Which ones can be consistently coupled to gravity?

link |

We call that subspace the landscape.

link |

The rest of them we call the swampland.

link |

It doesn't mean they are bad quantum field theories,

link |

they are perfectly fine.

link |

But when you couple them to gravity,

link |

they don't make sense, unfortunately.

link |

And it turns out that the ratio of them,

link |

the number of theories which are consistent with gravity

link |

to the ones without,

link |

the ratio of the area of the landscape

link |

to the swampland, in other words, is measure zero.

link |

So the swampland's infinitely large?

link |

The swampland's infinitely large.

link |

So let me give you one example.

link |

Take a theory in four dimension with matter

link |

with maximum amount of supersymmetry.

link |

Can you get, it turns out a theory in four dimension

link |

with maximum amount of supersymmetry

link |

is characterized just with one thing, a group.

link |

What we call the gauge group.

link |

Once you pick a group, you have to find the theory.

link |

Okay, so does every group make sense?

link |

As far as quantum field theory, every group makes sense.

link |

There are infinitely many groups,

link |

there are infinitely many quantum field theories.

link |

But it turns out there are only finite number of them

link |

which are consistent with gravity out of that same list.

link |

So you can take any group but only finite number of them,

link |

the ones who's, what we call the rank of the group,

link |

the ones whose rank is less than 23.

link |

Any one bigger than rank 23 belongs to the swampland.

link |

There are infinitely many of them.

link |

They're beautiful field theories,

link |

but not when you include gravity.

link |

So then this becomes a hopeful thing.

link |

So in other words, in our universe, we have gravity.

link |

Therefore, we are part of that jewel subset.

link |

Now, is this jewel subset small or large?

link |

It turns out that subset is humongous,

link |

but we believe still finite.

link |

The set of possibilities is infinite,

link |

but the set of consistent ones,

link |

I mean, the set of quantum field theories are infinite,

link |

but the consistent ones are finite, but humongous.

link |

The fact that they're humongous

link |

is the problem we are facing in string theory,

link |

because we do not know which one of these possibilities

link |

the universe we live in.

link |

If we knew, we could make more specific predictions

link |

about our universe.

link |

And that is one of the challenges when string theory,

link |

which point on the landscape,

link |

which corner of this landscape do we live in?

link |

Well, there are principles that are beginning to emerge.

link |

So I will give you one example of it.

link |

You look at the patterns of what you're getting

link |

in terms of these good ones,

link |

the ones which are in the landscape

link |

compared to the ones which are not.

link |

You find certain patterns.

link |

I'll give you one pattern.

link |

You find in all the ones that you get from string theory,

link |

gravitational force is always there,

link |

but it's always, always the weakest force.

link |

However, you could easily imagine field theories

link |

for which gravity is not the weakest force.

link |

For example, take our universe.

link |

If you take mass of the electron,

link |

if you increase the mass of electron by a huge factor,

link |

the gravitational attraction of the electrons

link |

will be bigger than the electric repulsion

link |

between two electrons.

link |

And the gravity will be stronger.

link |

It happens that it's not the case in our universe

link |

because electron is very tiny in mass compared to that.

link |

Just like our universe, gravity is the weakest force.

link |

We find in all these other ones,

link |

which are part of the good ones,

link |

the gravity is the weakest force.

link |

This is called the weak gravity conjecture.

link |

We conjecture that all the points in the landscape

link |

have this property.

link |

Our universe being just an example of it.

link |

So there are these qualitative features

link |

that we are beginning to see.

link |

But how do we argue for this?

link |

Just by looking patterns?

link |

Just by looking string theory as this?

link |

No, that's not enough.

link |

We need more reason, more better reasoning.

link |

And it turns out there is.

link |

The reasoning for this turns out to be studying black holes.

link |

Ideas of black holes turn out to put certain restrictions

link |

of what a good quantum filter should be.

link |

It turns out using black hole,

link |

the fact that the black holes evaporate,

link |

the fact that the black holes evaporate

link |

gives you a way to check the relation

link |

between the mass and the charge of elementary particle.

link |

Because what you can do, you can take a charged particle

link |

and throw it into a charged black hole

link |

and wait it to evaporate.

link |

And by looking at the properties of evaporation,

link |

you find that if it cannot evaporate particles

link |

whose mass is less than their charge,

link |

then it will never evaporate.

link |

You will be stuck.

link |

And so the possibility of a black hole evaporation

link |

forces you to have particles whose mass

link |

is sufficiently small so that the gravity is weaker.

link |

So you connect this fact to the other fact.

link |

So we begin to find different facts

link |

that reinforce each other.

link |

So different parts of the physics reinforce each other.

link |

And once they all kind of come together,

link |

you believe that you're getting the principle correct.

link |

So weak gravity conjecture

link |

is one of the principles we believe in

link |

as a necessity of these conditions.

link |

So these are the predictions string theory are making.

link |

Well, it's qualitative.

link |

It's a semi quantity.

link |

It's just the mass of the electron

link |

should be less than some number.

link |

But that number is, if I call that number one,

link |

the mass of the electron

link |

turns out to be 10 to the minus 20 actually.

link |

So it's much less than one.

link |

But on the other hand,

link |

there's a similar reasoning for a big black hole

link |

And if that evaporation should take place,

link |

gives you another restriction,

link |

tells you the mass of the electron

link |

is bigger than 10 to the,

link |

now in this case, bigger than something.

link |

It shows bigger than 10 to the minus 30 in the Planck unit.

link |

the mass of the electron should be less than one,

link |

but bigger than 10 to the minus 30.

link |

the mass of the electron is 10 to the minus 20.

link |

Okay, now this kind of you could call postiction,

link |

but I would say it follows from principles

link |

that we now understand from string theory, first principle.

link |

So we are making, beginning to make

link |

these kinds of predictions,

link |

which are very much connected to aspects of particle physics

link |

that we didn't think are related to gravity.

link |

We thought, just take any electron mass you want.

link |

What's the problem?

link |

It has a problem with gravity.

link |

And so that conjecture

link |

has also a happy consequence

link |

that it explains that our universe,

link |

like why the heck is gravity so weak as a force

link |

and that's not only an accident, but almost a necessity

link |

if these forces are to coexist effectively?

link |

Exactly, so that's the reinforcement

link |

of what we know in our universe,

link |

but we are finding that as a general principle.

link |

So we want to know what aspects of our universe

link |

like the weak gravity conjecture and other aspects.

link |

How much of them do we understand?

link |

Can we have particles lighter than neutrinos?

link |

Or maybe that's not possible.

link |

You see the neutrino mass,

link |

it turns out to be related to dark energy

link |

in a mysterious way.

link |

Naively, there's no relation between dark energy

link |

and the mass of a particle.

link |

We have found arguments

link |

from within the swampland kind of ideas,

link |

why it has to be related.

link |

And so there are beginning to be these connections

link |

between graph consistency of quantum gravity

link |

and aspects of our universe gradually being sharpened.

link |

But we are still far from a precise quantitative prediction

link |

like we have to have such and such, but that's the hope,

link |

that we are going in that direction.

link |

Coming up with the theory of everything

link |

that unifies general relativity and quantum field theory

link |

is one of the big dreams of human civilization.

link |

Us descendants of apes wondering about how this world works.

link |

So a lot of people dream.

link |

What are your thoughts about sort of other out there ideas,

link |

theories of everything or unifying theories?

link |

So there's a quantum loop gravity.

link |

There's also more sort of like a friend of mine,

link |

Eric Weinstein beginning to propose

link |

something called geometric unity.

link |

So these kinds of attempts,

link |

whether it's through mathematical physics

link |

or through other avenues,

link |

or with Stephen Wolfram,

link |

a more computational view of the universe.

link |

Again, in his case, it's these hyper graphs

link |

that are very tiny objects as well.

link |

Similarly, a string theory

link |

and trying to grapple with this world.

link |

What do you think?

link |

Is there any of these theories that are compelling to you,

link |

that are interesting that may turn out to be true

link |

or at least may turn out to contain ideas that are useful?

link |

Yes, I think the latter.

link |

I would say that the containing ideas that are true

link |

is my opinion was what some of these ideas might be.

link |

For example, loop quantum gravity

link |

is to me not a complete theory of gravity in any sense,

link |

but they have some nuggets of truth in them.

link |

And typically what I expect to happen,

link |

and I have seen examples of this within string theory,

link |

aspects which we didn't think are part of string theory

link |

come to be part of it.

link |

For example, I'll give you one example.

link |

String was believed to be 10 dimensional.

link |

And then there was this 11 dimensional super gravity.

link |

Nobody know what the heck is that?

link |

Why are we getting 11 dimensional super gravity

link |

whereas string is saying it should be 10 dimensional?

link |

11 was the maximum dimension you can have a super gravity,

link |

but string was saying, sorry, we're 10 dimensional.

link |

So for a while we thought that theory is wrong

link |

because how could it be?

link |

Because string theory is definitely a theory of everything.

link |

We later learned that one of the circles

link |

of string theory itself was tiny,

link |

that we had not appreciated that fact.

link |

And we discovered by doing thought experiments

link |

of string theory that there's gotta be an extra circle

link |

and that circle is connected

link |

to an 11 dimensional perspective.

link |

And that's what later on got called M theory.

link |

So there are these kinds of things

link |

that we do not know what exactly string theory is.

link |

We're still learning.

link |

So we do not have a final formulation of string theory.

link |

It's very well could be the different facets

link |

of different ideas come together

link |

like loop quantum gravity or whatnot,

link |

but I wouldn't put them on par.

link |

Namely, loop quantum gravity is a scatter of ideas

link |

about what happens to space when they get very tiny.

link |

For example, you replace things by discrete data

link |

and try to quantize it and so on.

link |

And it sounds like a natural idea to quantize space.

link |

If you were naively trying to do quantum space,

link |

you might think about trying to take points

link |

and put them together in some discrete fashion

link |

in some way that is reminiscent of loop quantum gravity.

link |

String theory is more subtle than that.

link |

For example, I will just give you an example.

link |

And this is the kind of thing that we didn't put in by hand,

link |

And so it's more subtle than,

link |

so what happens if you squeeze the space

link |

to be smaller and smaller?

link |

Well, you think that after a certain distance,

link |

the notion of distance should break down.

link |

You know, when you go smaller than Planck scale,

link |

should break down.

link |

What happens in string theory?

link |

We do not know the full answer to that,

link |

but we know the following.

link |

Namely, if you take a space

link |

and bring it smaller and smaller,

link |

if the box gets smaller than the Planck scale

link |

by a factor of 10,

link |

it is equivalent by the duality transformation

link |

to a space which is 10 times bigger.

link |

So there's a symmetry called T duality,

link |

which takes L to one over L.

link |

Well, L is measured in Planck units,

link |

or more precisely string units.

link |

This inversion is a very subtle effect.

link |

And I would not have been,

link |

or any physicist would not have been able to design a theory

link |

which has this property,

link |

that when you make the space smaller,

link |

it is as if you're making it bigger.

link |

That means there is no experiment you can do

link |

to distinguish the size of the space.

link |

This is remarkable.

link |

For example, Einstein would have said,

link |

of course I can't measure the size of the space.

link |

Well, I take a flashlight,

link |

I send the light around,

link |

measure how long it takes for the light

link |

to go around the space,

link |

and bring back and find the radius

link |

or circumference of the universe.

link |

What's the problem?

link |

I said, well, suppose you do that,

link |

and you shrink it.

link |

He said, well, it gets smaller and smaller.

link |

I said, well, it turns out in string theory,

link |

there are two different kinds of photons.

link |

One photon measures one over L,

link |

the other one measures L.

link |

And so this duality reformulates.

link |

And when the space gets smaller,

link |

it says, oh no, you better use the bigger perspective

link |

because the smaller one is harder to deal with.

link |

So you do this one.

link |

So these examples of loop quantum gravity

link |

have none of these features.

link |

These features that I'm telling you about,

link |

we have learned from string theory.

link |

But they nevertheless have some of these ideas

link |

like topological gravity aspects

link |

are emphasized in the context of loop quantum gravity

link |

And so these ideas might be there in some kernel,

link |

in some corners of string theory.

link |

In fact, I wrote a paper about topological string theory

link |

and some connections with potentially loop quantum gravity,

link |

which could be part of that.

link |

So there are little facets of connections.

link |

I wouldn't say they're complete,

link |

but I would say most probably what will happen

link |

to some of these ideas, the good ones at least,

link |

they will be absorbed to string theory,

link |

if they are correct.

link |

Let me ask a crazy out there question.

link |

Can physics help us understand life?

link |

So we spoke so confidently about the laws of physics

link |

being able to explain reality.

link |

But, and we even said words like theory of everything,

link |

implying that the word everything

link |

is actually describing everything.

link |

Is it possible that the four laws we've been talking about

link |

are actually missing,

link |

they are accurate in describing what they're describing,

link |

but they're missing the description

link |

of a lot of other things,

link |

like emergence of life

link |

and emergence of perhaps consciousness.

link |

So is there, do you ever think about this kind of stuff

link |

where we would need to understand extra physics

link |

to try to explain the emergence of these complex pockets

link |

of interesting weird stuff that we call life

link |

and consciousness in this big homogeneous universe

link |

that's mostly boring and nothing is happening yet?

link |

So first of all, we don't claim that string theory

link |

is the theory of everything in the sense that

link |

we know enough what this theory is.

link |

We don't know enough about string theory itself,

link |

we are learning it.

link |

So I wouldn't say, okay, give me whatever,

link |

I will tell you how it works, no.

link |

However, I would say by definition,

link |

by definition to me physics is checking all reality.

link |

Any form of reality, I call it physics,

link |

that's my definition.

link |

I mean, I may not know a lot of it,

link |

like maybe the origin of life and so on,

link |

maybe a piece of that,

link |

but I would call that as part of physics.

link |

To me, reality is what we're after.

link |

I don't claim I know everything about reality.

link |

I don't claim string theory necessarily has the tools

link |

right now to describe all the reality either,

link |

but we are learning what it is.

link |

So I would say that I would not put a border to say,

link |

no, from this point onwards, it's not my territory,

link |

it's somebody else's.

link |

But whether we need new ideas in string theory

link |

to describe other reality features, for sure I believe,

link |

as I mentioned, I don't believe any of the laws

link |

we know today is final.

link |

So therefore, yes, we will need new ideas.

link |

This is a very tricky thing for us to understand

link |

and be precise about.

link |

But just because you understand the physics

link |

doesn't necessarily mean that you understand

link |

the emergence of chemistry, biology, life,

link |

intelligence, consciousness.

link |

So those are built, it's like you might understand

link |

the way bricks work, but to understand what it means

link |

to have a happy family, you don't get from the bricks.

link |

So directly, in theory you could,

link |

if you ran the universe over again,

link |

but just understanding the rules of the universe

link |

doesn't necessarily give you a sense

link |

of the weird, beautiful things that emerge.

link |

Right, no, so let me describe what you just said.

link |

So there are two questions.

link |

One is whether or not the techniques I use

link |

in let's say quantum field theory and so on

link |

will describe how the society works.

link |

Okay, that's far different scales of questions

link |

that we're asking here.

link |

The question is, is there a change of,

link |

is there a new law which takes over

link |

that cannot be connected to the older laws

link |

that we know, or more fundamental laws that we know?

link |

Do you need new laws to describe it?

link |

I don't think that's necessarily the case

link |

in many of these phenomena like chemistry

link |

or so on you mentioned.

link |

So we do expect in principle chemistry

link |

can be described by quantum mechanics.

link |

We don't think there's gonna be a magical thing,

link |

but chemistry is complicated.

link |

Yeah, indeed, there are rules of chemistry

link |

that chemists have put down which has not been explained yet

link |

using quantum mechanics.

link |

Do I believe that they will be something

link |

described by quantum mechanics?

link |

I don't think they are going to be sitting there

link |

in this just forever, but maybe it's too complicated

link |

and maybe we'll wait for very powerful quantum computers

link |

or whatnot to solve those problems.

link |

But I don't think in that context

link |

we have new principles to be added to fix those.

link |

So I'm perfectly fine in the intermediate situation

link |

to have rules of thumb or principles that chemists have found

link |

which are working, which are not founded

link |

on the basis of quantum mechanical laws, which does the job.

link |

Similarly, as biologists do not found everything

link |

in terms of chemistry, but they think,

link |

there's no reason why chemistry cannot.

link |

They don't think necessarily they're doing something

link |

amazingly not possible with chemistry.

link |

Coming back to your question,

link |

does consciousness, for example, bring this new ingredient?

link |

If indeed it needs a new ingredient,

link |

I will call that new ingredient part of physical law.

link |

We have to understand it.

link |

To me that, so I wouldn't put a line to say,

link |

okay, from this point onwards, it's disconnected.

link |

It's fully disconnected from string theory or whatever.

link |

We have to do something else.

link |

What I'm referring to is can physics of a few centuries

link |

from now that doesn't understand consciousness

link |

be much bigger than the physics of today,

link |

where the textbook grows?

link |

It definitely will.

link |

I would say, it will grow.

link |

I don't know if it grows because of consciousness

link |

being part of it or we have different view of consciousness.

link |

I do not know where the consciousness will fit.

link |

It's gonna be hard for me to guess.

link |

I mean, I can make random guesses now

link |

which probably most likely is wrong,

link |

but let me just do just for the sake of discussion.

link |

I could say, brain could be their quantum computer,

link |

classical computer.

link |

Their arguments against this being a quantum thing,

link |

so it's probably classical, and if it's classical,

link |

it could be like what we are doing in machine learning,

link |

slightly more fancy and so on.

link |

Okay, people can go to this argument to no end

link |

and to some whether consciousness exists or not,

link |

or life, does it have any meaning?

link |

Or is there a phase transition where you can say,

link |

does electron have a life or not?

link |

At what level does a particle become life?

link |

Maybe there's no definite definition of life

link |

in that same way that, we cannot say electron,

link |

if you, I like this example quite a bit.

link |

We distinguish between liquid and a gas phase,

link |

like water is liquid or vapor is gas,

link |

and we say they're different.

link |

You can distinguish them.

link |

Actually, that's not true.

link |

It's not true because we know from physics

link |

that you can change temperatures and pressure

link |

to go from liquid to the gas

link |

without making any phase transition.

link |

So there is no point that you can say this was a liquid

link |

and this was a gas.

link |

You can continuously change the parameters

link |

to go from one to the other.

link |

So at the end, it's very different looking.

link |

Like, I know that water is different from vapor,

link |

but there's no precise point this happens.

link |

I feel many of these things that we think,

link |

like consciousness, clearly dead person

link |

is not conscious and the other one is.

link |

So there's a difference like water and vapor,

link |

but there's no point you could say that this is conscious.

link |

There's no sharp transition.

link |

So it could very well be that what we call heuristically

link |

in daily life, consciousness is similar,

link |

or life is similar to that.

link |

I don't know if it's like that or not.

link |

I'm just hypothesizing it's possible.

link |

There's no discrete phases.

link |

There's no discrete phase transition like that.

link |

Yeah, yeah, but there might be concepts of temperature

link |

and pressure that we need to understand

link |

to describe what the head consciousness in life is

link |

that we're totally missing.

link |

I think that's not a useless question.

link |

Even those questions,

link |

they is back to our original discussion of philosophy.

link |

I would say consciousness and free will, for example,

link |

are topics that are very much so

link |

in the realm of philosophy currently.

link |

But I don't think they will always be.

link |

And I think I'm fine with some topics

link |

being part of a different realm than physics today

link |

because we don't have the right tools,

link |

just like biology was.

link |

I mean, before we had DNA and all that genetics

link |

and all that gradually began to take hold.

link |

I mean, when people were beginning phase experiments

link |

with biology and chemistry and so on,

link |

gradually they came together.

link |

So it wasn't like together.

link |

So yeah, I'd be perfectly understanding of a situation

link |

where we don't have the tools.

link |

So do these experiments that you think

link |

as defines a conscious in different form

link |

and gradually we'll build it and connect it.

link |

And yes, we might discover new principles of nature

link |

that we didn't know.

link |

I don't know, but I would say that if they are,

link |

they will be deeply connected with the else.

link |

We have seen in physics,

link |

we don't have things in isolation.

link |

You cannot compartmentalize,

link |

this is gravity, this is electricity, this is that.

link |

We have learned they all talk to each other.

link |

There's no way to make them in one corner and don't talk.

link |

So the same thing with anything, anything which is real.

link |

So consciousness is real.

link |

So therefore we have to connect it to everything else.

link |

So to me, once you connect it,

link |

you cannot say it's not reality.

link |

And once it's reality, it's physics.

link |

I call it physics.

link |

It may not be the physics I know today, for sure it's not,

link |

but I would be surprised if there's disconnected realities

link |

that you cannot imagine them as part of the same soup.

link |

So I guess God doesn't have a biology or chemistry textbook

link |

and mostly, or maybe he or she reads it for fun,

link |

biology and chemistry,

link |

but when you're trying to get some work done,

link |

it'll be going to the physics textbook.

link |

Okay, what advice, let's put on your wise visionary hat.

link |

What advice do you have for young people today?

link |

You've dedicated your book actually to your kids,

link |

What advice would you give to them?

link |

What advice would you give to young people today

link |

thinking about their career, thinking about life,

link |

of how to live successful life, how to live a good life?

link |

Yes, yes, I have three sons.

link |

And in fact, to them, I have tried not to give

link |

So even though I've tried to kind of not give advice,

link |

maybe indirectly it has been some impact.

link |

My oldest one is doing biophysics, for example,

link |

and the second one is doing machine learning

link |

and the third one is doing theoretical computer science.

link |

So there are these facets of interest

link |

which are not too far from my area,

link |

but I have not tried to impact them in that way,

link |

but they have followed their own interests.

link |

And I think that's the advice I would give

link |

to any young person, follow your own interests

link |

and let that take you wherever it takes you.

link |

And this I did in my own case that I was planning

link |

to study economics and electrical engineering

link |

when I started at MIT.

link |

And I discovered that I'm more passionate

link |

about math and physics.

link |

And at that time I didn't feel math and physics

link |

would make a good career.

link |

And so I was kind of hesitant to go in that direction,

link |

but I did because I kind of felt that

link |

that's what I'm driven to do.

link |

So I don't regret it, I'm lucky in the sense

link |

that society supports people like me

link |

who are doing these abstract stuff,

link |

which may or may not be experimentally verified

link |

even let alone applied to the technology in our lifetimes.

link |

I'm lucky I'm doing that.

link |

And I feel that if people follow their interests,

link |

they will find the niche that they're good at.

link |

And this coincidence of hopefully their interests

link |

and abilities are kind of aligned,

link |

at least some extent to be able to drive them

link |

to something which is successful.

link |

And not to be driven by things like,

link |

this doesn't make a good career,

link |

or this doesn't do that, and my parents expect that,

link |

or what about this?

link |

And I think ultimately you have to live with yourself

link |

and you only have one life and it's short, very short.

link |

I can tell you I'm getting there.

link |

So I know it's short.

link |

So you really want not to do things

link |

that you don't want to do.

link |

So I think following an interest

link |

is my strongest advice to young people.

link |

Yeah, it's scary when your interest

link |

doesn't directly map to a career of the past or of today.

link |

So you're almost anticipating future careers