The following is a conversation with Kamran Vafa, a theoretical physicist at Harvard specializing

in strength theory.

He is the winner of the 2017 Breakthrough Prize in Fundamental Physics, which is the

most lucrative academic prize in the world.

Quick mention of our sponsors, Headspace, Jordan Harmergeshow, Squarespace, and Alform.

Check them out in the description to support this podcast.

As a side note, let me say that strength theory is a theory of quantum gravity that

unifies quantum mechanics and general relativity.

It says that quarks, electrons, and all other particles are made up of much tinier strings

of vibrating energy.

They vibrate in 10 or more dimensions, depending on the flavor of the theory.

Different vibrating patterns result in different particles.

From its origins, for a long time, strength theory was seen as too good not to be true,

but has recently fallen out of favor in the physics community, partly because over the

past 40 years, it has not been able to make any novel predictions that could then be validated

through experiment.

Nevertheless, to this day, it remains one of our best candidates for a theory of everything,

or a theory that unifies the laws of physics.

Let me mention that a similar story happened with neural networks in the field of artificial

intelligence, where it fell out of favor after decades of promise and research, but found

success, again, in the past decade, as part of the deep learning revolution.

So I think it pays to keep an open mind, since we don't know which of the ideas in

physics may be brought back decades later and be found to solve the biggest mysteries

in theoretical physics.

Strength theory still has that promise.

This is the Lex Friedman podcast, and here's my conversation with Kamran Vafa.

What is the difference between mathematics and physics?

Well, that's a difficult question, because in many ways, math and physics are unified

in many ways.

So to distinguish them is not an easy task.

I would say that perhaps the goals of math and physics are different.

Math does not care to describe reality.

Physics does.

It's a major difference, but a lot of the thoughts, processes, and so on, which goes

to understanding the nature and reality are the same things that mathematicians do.

So in many ways, they are similar.

Mathematicians care about deductive reasoning, and physicists or physics in general, we care

less about that.

We care more about interconnection of ideas, about how ideas support each other, or if

there's a puzzle discord between ideas, that's more interesting for us.

And part of the reason is that we have learned in physics that the ideas are not sequential,

and if we think that there's one idea which is more important, and we start with there

and go to the next idea and next one and deduce things from that like mathematicians do, we

have learned that the third or fourth thing we deduce from that principle turns out later

on to be the actual principle, and from a different perspective, starting from there

leads to new ideas which the original one didn't lead to, and that's the beginning of

a new revolution in science.

So this kind of thing we have seen again and again in the history of science, we have learned

to not like deductive reasoning, because that gives us a bad starting point to think that

we actually have the original thought process should be viewed as the primary thought, and

all these are deductions, like the way mathematicians sometimes do.

So in physics, we have learned to be skeptical of that way of thinking.

We have to be a bit open to the possibility that what we thought is a deduction of a hypothesis

actually the reason that's true is the opposite, and so we reverse the order.

And so this switching back and forth between ideas makes us more fluid about deductive fashion.

Of course, it sometimes gives a wrong impression like physicists don't care about rigor, they

just say random things, they are willing to say things that are not backed by the logical

reasoning, that's not true at all.

So despite this fluidity in saying which one is the primary thought, we are very careful

about trying to understand what we have really understood in terms of relationship between

ideas.

So that's an important ingredient, and in fact, solid math, being behind physics is,

I think, one of the attractive features of a physical law.

So we look for beautiful math underpinning it.

Can we dig into that process of starting from one place and then ending up at the fourth

step and realizing all along that the place you started at was wrong?

So is that happened when there's a discrepancy between what the math says and what the physical

world shows?

Is that how you then can go back and do the revolutionary idea for a different starting

place altogether?

Perhaps I'll give an example to see how it goes, and in fact, the historical example

is Newton's work on classical mechanics.

So Newton formulated the laws of mechanics, you know, the force F equals to MA and his

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

Later, when we studied more examples of mechanics and other similar things, physicists came up

with the idea that the notion of potential is interesting.

Potential was an abstract idea, which kind of came.

You could take its gradient and relate it to the force, so you don't really need a

tapiri, but it solved, helped some thoughts.

And then later, Euler and Lagrange reformulated Newtonian mechanics in a totally different

way in the following fashion.

They said, if you want to know where a particle at this point and at this time, how does it

get to this point at the later time, is the following.

You take all possible paths connecting this particle from going from the initial point

to the final point, and you compute the action on what is an action.

Action is the integral over time of the kinetic term of the particle minus its potential.

So you take this integral, and each path will give you some quantity, and the path it actually

takes, the physical path, is the one which minimizes this integral or this action.

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

Newton's formula seemed very simple.

F equals to MA, and you can write F is minus the gradient of the potential.

So why would anybody start formulating such a simple thing in terms of this complicated

looking principle?

You have to study the space of all paths and all things and find the minimum, and then

you get the same equation.

So what's the point?

So Euler and Lagrange's formulation of Newton, which was kind of a recasting in this language,

is just a consequence of Newton's law.

F equals to MA gives you the same fact that this path is a minimal action.

Now what we learned later, last century, was that when we deal with quantum mechanics,

Newton's law is only an average correct.

And the particle going from one to the other doesn't take exactly one path.

It takes all the paths with the amplitude, which is proportional to the exponential of

the action times an imaginary number, I.

And so this fact turned out to be the reformulation of quantum mechanics.

We should start there as the basis of the new law, which is quantum mechanics.

And Newton is only an approximation on the average correct.

When we say amplitude, you mean probability?

Yes.

The amplitude means if you sum up all these paths with the exponential I times the action,

if you sum this up, you get the number, complex number, you square the norm of this complex

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

Is there ways in which mathematics can lead us astray when we use it as a tool to understand

the physical world?

Yes.

I would say that mathematics can lead us astray as much as all physical ideas can lead us astray.

So if you get stuck in something, then you can easily fool yourself that just like the

thought process, we have to free ourselves of that.

Sometimes math does that role, like say, oh, this is such a beautiful math, I definitely

want to use it somewhere.

And so you just get carried away and you just get maybe carried too far away.

So that is certainly true.

But I wouldn't say it's more dangerous than old physical ideas.

To me, new math ideas is as much potential to lead us astray as old physical ideas,

which could be long held principles of physics.

So I'm just saying that we should keep an open mind about the role the math plays, not

to be antagonistic towards it, and not to over, over welcoming it.

We should just be open to possibilities.

What about looking at a particular characteristics of both physical ideas and mathematical ideas,

which is beauty?

Do you think beauty leads us astray?

Meaning, and you offline showed me a really nice puzzle that illustrates this idea a little

bit.

Now, maybe you can speak to that or another example where beauty makes it tempting for

us to assume that the law and the theory we found is actually one that perfectly describes

reality.

I think that beauty does not lead us astray, because I feel that beauty is a requirement

for principles of physics.

So beauty is fundamental in the universe?

I think beauty is fundamental, at least that's the way many of us view it.

It's not emergent.

It's not emergent.

I think Hardy is the mathematician who said that there's no permanent place for ugly mathematics.

And so I think the same is true in physics, that if we find a principle which looks ugly,

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

So therefore, beauty is going to lead us somewhere.

Now, it doesn't mean beauty is enough.

It doesn't mean if you just have beauty, if I just look at something as beautiful, then

I'm fine.

No, that's not the case.

Beauty is certainly a criteria that every good physical theory should pass.

That's at least the view we have.

Why do we have this view?

That's a good question.

It is partly, you could say, based on experience of science over centuries.

Partly is a philosophical view of what reality is or should be.

And in principle, it could have been ugly and we might have had to deal with it, but

we have gotten maybe confident through examples after examples in the history of science to

look for beauty.

And our sense of beauty seems to incorporate a lot of things that are essential for us

to solve some difficult problems like symmetry.

We find symmetry beautiful and the breaking of symmetry beautiful.

Somehow symmetry is a fundamental part of how we conceive of beauty at all layers of

reality, which is interesting.

In both the visual space, the way we look at art, we look at each other as human beings,

the way we look at creatures in the biological space, the way we look at chemistry and then

to the physics world as the work you do is kind of interesting.

It makes you wonder like, which one is the chicken or the egg?

Is symmetry the chicken and our conception of beauty the egg or the other way around?

Or somehow the fact that the symmetry is part of reality, it somehow creates a brain that

then is able to perceive it or maybe it's so obvious, it's almost trivial, that symmetry

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

And then any kind of organism that's able to observe that universe is going to appreciate

symmetry.

Well, these are good questions.

We don't have a deep understanding of why we get attracted to symmetry.

Why do laws of nature seem to have symmetries underlying them?

And the reasoning or the examples of whether if there wasn't symmetry, we would have understood

it or not.

We could have said that, yeah, if there were things which didn't look that great, we could

understand them.

For example, we know that symmetries get broken and we have appreciated nature in the broken

symmetry phase as well.

The world we live in has many things which do not look symmetric, but even those have

underlying symmetry when you look at it more deeply.

So we have gotten maybe spoiled perhaps by the appearance of symmetry all over the place

and we look for it.

And I think this is perhaps related to the sense of aesthetics that scientists have.

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

In fact, it's kind of a philosophical view of why do we look for simplicity or beauty

or so forth.

And I think in a sense, scientists are a lot like philosophers.

Sometimes I think especially modern science seems to shun philosophers and philosophical

views.

And I think at their peril.

I think in my view, science owes a lot to philosophy.

And in my view, many scientists, in fact probably all good scientists are perhaps amateur philosophers.

They may not state that they are philosophers or they may not like to be labeled philosophers,

but in many ways what they do is like what is philosophical takes of things.

Looking for simplicity or symmetry is an example of that in my opinion or seeing patterns.

You see, for example, another example of the symmetry is like how you come up with no ideas

in science.

You see, for example, an idea A is connected with an idea B. Okay, so you study this connection

very deeply.

And then you find the cousin of an idea A, let me call it A prime.

And then you immediately look for B prime.

If A is like B and if there's an A prime, then you look for B prime.

Why?

Well, it completes the picture.

Why? Well, it's philosophically appealing to have more balance in terms of that.

And then you look for B prime and lo and behold, you find this other phenomenon, which is a

physical phenomenon, which you call B prime.

So this kind of thinking motivates asking questions and looking for things.

And it has guided scientists, I think, through many centuries and I think it continues to

do so today.

And I think if you look at the long arc of history, I suspect that the things that will

be remembered is the philosophical flavor of the ideas of physics and chemistry and computer

science and mathematics.

Like I think the actual details will be shown to be incomplete or maybe wrong, but the philosophical

intuitions will carry through much longer.

There's a sense in which if it's true that we haven't figured out most of how things

work currently, that it'll all be shown as wrong and silly, almost be a historical artifact.

But the human spirit, whatever, like the longing to understand the way we perceive the world,

the way we conceive of it, of our place in the world, those ideas will carry on.

I completely agree.

In fact, I believe that almost, well, I believe that none of the principles or laws of physics

we know today are exactly correct.

All of them are approximations to something.

They're better than the previous versions of what we had, but none of them are exactly

correct and none of them are going to stand forever.

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

And yes, indeed, the thought process and that philosophical take is common.

So when we look at older scientists or maybe even all the way back to Greek philosophers

and the things that the way they thought and so on, almost everything they said about nature

was incorrect.

But the way they thought about it and many things that they were thinking is still valid

today.

For example, they thought about symmetry breaking.

They were trying to explain the following.

This is a beautiful example, I think.

They had figured out that the Earth is round and they said, okay, Earth is round.

They have seen the length of the shadow of a meter stick and they have seen that if you

go from the equator upwards north, they find that depending on how far away you are, the

length of the shadow changes.

And from that, they had even measured the radius of the Earth to good accuracy.

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

Very brilliant.

So these Greek philosophers were very smart and so they had taken it to the next step.

They asked, okay, so the Earth is round.

Why doesn't it move?

They thought it doesn't move.

They were looking around, nothing seemed to move.

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

It wasn't enough for them to be there.

So they really want to deeply understand that fact.

They come up with a symmetry argument.

And the symmetry argument was, oh, if the Earth is a spherical, it must be at the center

of the universe, for sure.

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

And they said, you know, if the Earth is going to move, which direction does it pick?

Any direction it picks, it breaks that spherical symmetry because you have to pick a direction.

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

So therefore, the Earth decides to sit put because it would break the symmetry.

So they had the incorrect science, they thought Earth doesn't move.

And they, but they had this beautiful idea that symmetry might explain it, but they were

even smarter than that.

Aristotle didn't agree with this argument.

He said, why do you think symmetry prevents it from moving because it's a preferred position?

Not so.

He gave an example.

He said, suppose you are a person and we put you at the center of a circle and we spread

food around you on a circle around you, loaves of bread, let's say, and we say, okay, stay

at the center of the circle forever.

Are you going to do that just because it's a symmetric point?

No, you are going to get hungry, you're going to move towards one of those loaves of bread,

despite the fact that it breaks the symmetry.

So from this way, he tried to argue being at the symmetric point may not be the preferred

thing to do.

And this idea of spontaneous symmetry breaking is something we just use today to describe

many physical phenomena.

So spontaneous symmetry breaking is the feature that we now use, but this idea was there thousands

of years ago, but applied incorrectly to the physical world, but now we are using it.

So these ideas are coming back in different forms.

So I agree very much that the thought process is more important and these ideas are more

interesting than the actual applications that people may find today.

Did they use the language of symmetry and the symmetry breaking and spontaneous symmetry

break?

That's really interesting because I could see a conception of the universe that kind

of tends towards perfect symmetry and is stuck there, not stuck there, but achieves that

optimal and stays there.

The idea that you would spontaneously break out of symmetry, like have these perturbations,

jump out of symmetry and back, that's a really difficult idea to load into your head.

Where does that come from?

And then the idea that you may not be at the center of the universe, that is a really

tough idea.

So symmetry sometimes an explanation of being at the symmetric point is sometimes a simple

explanation of many things like if you have a ball, a circular ball, then the bottom of

it is the lowest point, so if you put a pebble or something, it will slide down and go there

at the bottom and stays there at the symmetric point because the preferred point, the lowest

energy point.

But if that same symmetric circular ball that you had had a bump on the bottom, the bottom

might not be at the center, it might be on a circle on the table, in which case the pebble

would not end up at the center, will be the lower energy point, symmetrical, but it breaks

a symmetry once it picks a point on that circle.

So we can have symmetry reasoning for where things end up or symmetry breakings, like

this example would suggest.

We talked about beauty, I find geometry to be beautiful.

You have a few examples that are geometric in nature in your book.

How can geometry in ancient times or today be used to understand reality?

And maybe how do you think about geometry as a distinct tool in mathematics and physics?

Yes, geometry is my favorite part of math as well, and Greeks were enamored by geometry.

They tried to describe physical reality using geometry and principles of geometry and symmetry.

Platonic solids, the five solids they had discovered had these beautiful solids.

They thought it must be good for some reality.

There must be explaining something.

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

They tried to give physical reality to symmetric objects.

These symmetric objects are symmetries of rotation and discrete symmetry groups we call

today of rotation group in three dimensions.

Now we know, now we kind of laugh at the way they were trying to connect that symmetry

to the realities of physics, but actually it turns out in modern days we use symmetry

in not too far away, exactly in these kind of thought processes in the following way.

In the context of string theory, which is the field light study, we have these extra

dimensions, and these extra dimensions are compact tiny spaces typically, but they have

different shapes and sizes.

We have learned that if these extra shapes and sizes have symmetries which are related

to the same rotation symmetries that the Greek were talking about, if they enjoy those

discrete symmetries, and if you take that symmetry and caution the space by that, in

other words, identify points under these symmetries, you get properties of that space at the singular

points which force emanates from them.

What forces?

Forces like the ones we have seen in nature today, like electric forces, like strong forces,

like weak forces.

These same principles that were driving them to connect geometry and symmetries to nature

is driving today's physics, now much more modern ideas, but nevertheless the symmetries

connecting geometry to physics.

In fact, often sometimes we ask the following question.

Suppose I want to get this particular physical reality, I want to have these particles with

these forces and so on, what do I do?

It turns out that you can geometrically design the space to give you that.

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

So if you have two spheres touching each other and shrinking to zero size, that gives you

strong forces.

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

If you have this, you get that, and if you want to unify forces, do the other thing.

So these geometrical translation of physics is one of my favorite things that we have

discovered in modern physics in the context of strength theory.

The sad thing is when you go into multiple dimensions and we'll talk about it is we start

to lose our capacity to visually intuit the world we're discussing, and then we go into

the realm of mathematics, and we'll lose that.

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

But before we go into that mysterious, beautiful world, let's take a small step back.

You also in your book have this kind of through the space of puzzles, through the space of

ideas have a brief history of physics, of physical ideas.

Now we talked about Newtonian mechanics, leading all through different Lagrangian, Hamiltonian

mechanics.

Can you describe some of the key ideas in the history of physics, maybe lingering on

each from electromagnetism to relativity to quantum mechanics and to today, as we'll talk

about with quantum gravity and strength theory?

So I mentioned the classical mechanics and the Euler Lagrangian formulation.

One of the next important milestones for physics were the discoveries of laws of electricity

and magnetism.

So Maxwell put the discoveries all together in the context of what we call the Maxwell's

equations.

And he noticed that when he put these discoveries that Faraday's and others had made about electric

and magnetic phenomena in terms of mathematical equations, it didn't quite work.

There was a mathematical inconsistency.

Now, you know, one could have two attitudes, one say, okay, who cares about math?

I'm doing nature, you know, electric force, magnetic force, math, I don't care about.

But it bothered him.

It was inconsistent.

The equations he were writing, the two equations he had written down did not agree with each

other.

And this bothered him.

But he figured out, you know, if you add this jiggle, this equation by adding one little

term there, it works.

At least it's consistent.

What is the motivation for that term?

He said, I don't know.

Have we seen it in experiments?

No.

Why did you add it?

Well, because of mathematical consistency.

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

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

And once he added that term, his equations were nice, you know, differential equations,

mathematically consistent, beautiful.

But he also found a new physical phenomena.

He found that because of that term, he could now get electric and magnetic waves moving

through space at a speed that he could calculate.

So he calculated the speed of the wave.

And lo and behold, he found it's the same as the speed of light, which puzzled him because

he didn't think light had anything to do with electricity and magnetism.

But then he was courageous enough to say, well, maybe light is nothing but these electric

and magnetic fields moving around.

And he wasn't alive to see the verification of that prediction, and indeed it was true.

So this mathematical inconsistency, which we could say, you know, this mathematical beauty

drove him to this physical, very important connection between light and electric and

magnetic phenomena, which was later confirmed.

So then physics progresses, and it comes to Einstein.

Einstein looks at Maxwell's equation, says, beautiful, these are nice equations, except

we get one speed light.

Who measures this light speed?

And he asks the question, are you moving?

Are you not moving?

If you move, the speed of light changes, but Maxwell's equation has no hint of different

speeds of light.

It doesn't say, oh, only if you're not moving, you get the speed.

It's just you always get the speed.

So Einstein was very puzzled, and he was daring enough to say, well, you know, maybe everybody

gets the same speed for light.

And that motivated his theory of special relativity.

And this is an interesting example, because the idea was motivated from physics, from

Maxwell's equations, from the fact that people tried to measure the properties of ether,

which was supposed to be the medium in which the light travels through.

And the idea was that only in that medium, the speed of light, if you're at rest with

respect to the ether, the speed of light, and if you're moving, the speed changes,

and people did not discover it.

So Michael Sonan Morley's experiment showed there is no ether.

So then Einstein was courageous enough to say, you know, light is the same speed for everybody

regardless of whether you're moving or not.

And the interesting thing is about special theory of relativity is that the math underpinning

it is very simple.

It's a linear algebra, nothing terribly deep.

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

Okay.

So does that mean Einstein's special relativity is boring?

Not at all.

So this is an example where simple math, you know, linear algebra leads to deep physics.

Einstein's theory of special relativity, motivated by this inconsistency at Maxwell's equation

would suggest for the speed of light depending on who observes it.

What's the most daring idea there, that the speed of light could be the same everywhere?

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

That's the core of Einstein's theory.

That statement underlies the whole thing.

Speed of light is the same for everybody, it's hard to swallow and doesn't sound right.

It sounds completely wrong on the face of it.

And it took Einstein to make this daring statement.

It would be laughing in some sense.

How could anybody make this possibly ridiculous claim and it turned out to be true?

How does that make you feel?

Because it still sounds ridiculous.

It sounds ridiculous until you learn that our intuition is at fault about the way we

conceive of space and time.

The way we think about space and time is wrong, because we think about the nature of time

as absolute.

And part of it is because we live in a situation where we don't go with very high speeds.

There are speeds that are small compared to the speed of light.

And therefore the phenomena we observe does not distinguish the relativity of time.

The time also depends on who measures it.

There's no absolute time.

When you say it's noon today, now, it depends on who's measuring it and not everybody would

agree with that statement and to see that, you would have to have fast observer moving

speeds close to the speed of light.

So this shows that our intuition is at fault.

And a lot of the discoveries in physics precisely is getting rid of the wrong old intuition.

And it is funny because we get rid of it, but it's always lingers in us in some form.

Even when I'm describing it, I feel like a little bit funny as you're just feeling the

same way.

It is.

It is.

But we kind of replace it by an intuition.

And actually there's a very beautiful example of this, how physicists do this, try to replace

their intuition.

And I think this is one of my favorite examples about how physicists develop intuition.

It goes to the work of Galileo.

So again, let's go back to Greek philosophers or maybe Aristotle in this case.

Now again, let's make a criticism.

He thought that objects, the heavier objects fall faster than the lighter objects.

Makes sense.

It kind of makes sense.

And you know, people say about feather and so on, but that's because of the air resistance.

But you might think like if you have a heavy stone and a light pebble, the heavy one will

fall first.

If you don't, you know, do any experiments, that's the first gut reaction.

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

Galileo did not believe this.

And he kind of did the experiment.

Obviously it said he went on the top of Pisa Tower and he dropped, you know, these heavy

and light stones and they fell at the same time when he dropped it at the same time from

the same height.

Okay, good.

So he said, I'm done.

You know, I've showed that the heavy and lighter objects fall at the same time.

I did the experiment.

Scientists at that time did not accept it.

Why was that?

Because at that time science was not just experimental.

The experiment was not enough.

They didn't think that they have to sort their hands in doing experiments to get to the reality.

They said, why is it the case?

So Galileo had to come up with an explanation of why heavier and lighter objects fall at

the same rate.

This is the way he convinced them using symmetry.

He said, suppose you have three bricks, the same shape, the same size, same mass, everything.

And we hold these three bricks at the same height and drop them.

Which one will fall to the ground first?

Everybody said, of course, we know that symmetry tells you, you know, they're all the same

shapes, same size, same height.

Of course they fall at the same time.

Yeah, we know that next, next, this trivia.

He said, okay, what if we move these bricks around with the same height?

Does it change the time they hit the ground?

They said, if it's the same height again by the symmetry principle because the height

translation, horizontal translation is a symmetry, no, it doesn't matter.

They all fall at the same rate.

Good.

Does it matter how close I bring them together?

No, it doesn't.

Okay.

Suppose I make the two bricks touch and then let them go.

Do they fall at the same rate?

Yes, they do.

But then he said, well, the two bricks that touch are twice more mass than this other

brick.

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

They say, yeah, yeah, we just agreed.

That's right.

That's great.

Yes.

So he deconfused them by the symmetry reasoning.

So this way of repackaging some intuition, a different intuition, when the intuitions

clash, then you, then you slide on the, you replace the intuition.

That's brilliant.

I, in some of these diff, more difficult physical ideas, physics ideas in the 20th century

and the 21st century, it starts becoming more and more difficult to then replace the intuition.

You know, what, what does the world look like for an object traveling close to the speed

of light?

You start to think about like the edges of supermassive black holes and you start to

think like, what, what's that look like?

Or a, I've been read into gravitational ways or something.

It's like when the fabric of space time is being morphed by gravity, like what's that

actually feel like?

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

I mean, I think some of those are more sort of hippie, not useful intuitions to have.

But if you're an actual physicist or whatever the particular discipline is, I wonder if

it's possible to meditate, to sort of escape through thinking, prolonged thinking and meditation

on a war on a world like live in a visualized world that's not like our own in order to

understand a phenomenon deeply.

Or like replace the intuition, like through rigorous meditation on the idea in order to

conceive of it.

I mean, if we talk about multiple dimensions, I wonder if there's a way to escape with a

three dimensional world in our mind in order to then start to reason about it.

It's, the more I talk to topologists, the more they seem to not operate at all in the visual

space.

They really trust the mathematics.

Like which is really annoying to me because topology and differential geometry feels like

it has a lot of potential for beautiful pictures.

Yes.

I think they do.

Actually, I would not be able to do my research if I don't have an intuitive feel about geometry.

And we'll get to it as you mentioned before, that's how, for example, in string theory,

you deal with these extra dimensions and I'll be very happy to describe how we do it because

with that intuition, we will not get anywhere and I don't think you can just rely on formalism.

I don't.

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

That's not physics.

That's not understanding.

So we have to intuit it and that's crucial and there are steps of doing it and we learned

it might not be trivial, but we learn how to do it.

Similar to what this Galileo picture I just told you, you have to build these gradually.

But you have to connect the bricks.

Yeah, exactly.

You have to connect the bricks, literally, so yeah, so then, so going back to your question

about the path of the history of the science, so I was saying about the electrician magnetism

and the special relativity where simple idea led to special relativity, but then he went

further thinking about acceleration in the context of relativity and he came up with

general relativity, where he talked about, you know, the fabric of space, time being

curved and so forth and matter affecting the curvature of the space and time.

So this gradually became a connection between geometry and physics, namely he replaced Newton's,

you know, gravitational force with a very geometrical beautiful picture.

It's much more elegant than Newton's, but much more complicated mathematically.

So when we say simpler, we mean in some form it's simpler, but not in pragmatic terms of

equation solving.

The equations are much harder to solve in Einstein's theory.

And in fact, so much, so much harder that Einstein himself couldn't solve many of his,

many of the cases he thought, for example, he couldn't solve the equation for a spherical

symmetric matter, like, like if you had a symmetric sun, he didn't think you can actually

write the solve his equation for that.

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

So it was, it was that hard that he didn't think it's going to be that easy.

So yeah, the formism is hard.

But the contrast between the special relativity and general relativity is very interesting

because one of them has almost trivial math and the other one has super complicated math.

Both are physically amazingly important.

And so, so we have learned that, you know, the physics may or may not require complicated

math.

We should not shy from using complicated math like Einstein did.

Nobody, Einstein wouldn't say, I'm not going to touch this math because it's too much,

you know, tensors or, you know, curvature and I don't like the four dimensional space

time because I can't see four dimension, he wasn't doing that.

He was willing to abstract from that because physics drove him in that direction.

But his motivation was physics, physics pushed him just like Newton pushed to develop calculus

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

So he had to develop the tools to answer his physics questions.

So his motivation was physics again.

So to me, those are examples would show that math and physics have this symbiotic relationship

which kind of reinforced each other.

Here I'm using, I'm giving you examples of both of them, namely Newton's work led to

development of mathematics, calculus.

And in the case of Einstein, he didn't develop the Riemannian geometry, just use them.

So, so it goes both ways.

And in the context of modern physics, we see that again and again, it goes both ways.

Let me ask a ridiculous question, you know, you talk about your favorite soccer player

to bar.

I'll ask the same question about Einstein's ideas, which is, which one do you think is

the biggest leap of genius?

Is it the E equals MC squared?

Is it Brownian motion?

Is it special relativity?

Is it general relativity?

Which of the famous set of papers he's written in 1905 and in general, his work was the biggest

leap of genius.

In my opinion is special relativity.

The idea that speed of light is the same for everybody is the beginning of everything

he did.

The beginning is the beginning.

It's the beginning.

Once you embrace that weirdness, all the weirdness, I would say that's, that's, even

though he says the most beautiful moment for him, he says that is when he realized that

if you fall in an elevator, you don't know if you're falling or whether you're in the

falling elevator or whether you're next to the earth gravitational.

That to him was his aha moment, which inertial mass and gravitational mass being identical

geometrically and so forth as part of the theory, not because of some funny coincidence.

That's for him.

But I feel from outside, at least, it feels like the speed of light being the same is

the really aha moment.

The general relativity to you is not like a conception of space time.

In a sense, the conception of space time already was part of the special relativity when we

talked about length contraction.

So general relativity takes that to the next step, but beginning of it was already space

length contracts, time dilates.

So once you talk about those, then yeah, you can dilate more or less different places

than it's curvature.

So you don't have a choice.

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

Speed of light is the same for all.

Where does quantum mechanics come into view?

Exactly.

So this is the next step.

So Einstein's developed general relativity and he's beginning to develop the foundation

of quantum mechanics at the same time.

The photoelectric effects on others.

And so quantum mechanics overtakes, in fact, Einstein in many ways, because he doesn't

like the probabilistic interpretation of quantum mechanics and the formulas that's emerging.

What fits his march on?

And try to, for example, combine Einstein's theory of relativity with quantum mechanics.

So Dirac takes special relativity, tries to see how is it compatible with quantum mechanics.

Can we pause and briefly say what is quantum mechanics?

Oh yes, sure.

So quantum mechanics, so I discussed briefly when I talked about the connection between

Newtonian mechanics and the Euler Lagrange formulation of the Newtonian mechanics and

interpretation of this Euler Lagrange formulas in terms of the paths that the particle take.

So when we say a particle goes from here to here, we usually think it, classically, follows

a specific trajectory, but actually in quantum mechanics, it follows every trajectory with

different probabilities.

And so there's this fuzziness.

Now most probable, it's the path that you actually see and the deviation from that is

very, very unlikely and probabilistically very minuscule.

So in everyday experiments, we don't see anything deviated from what we expect.

But quantum mechanics tells us that things are more fuzzy.

Things are not as precise as the line you draw.

Things are a bit like cloud.

So if you go to microscopic scales, like atomic scales, and though these phenomena become

more pronounced, you can see it much better.

The electron is not at the point, but the cloud spread out around the nucleus.

And so this fuzziness, this probabilistic aspect of reality is what quantum mechanics

describes.

Can I briefly pause on that idea?

Do you think this is quantum mechanics is just a really damn good approximation, a tool

for predicting reality, or does it actually describe reality?

Do you think reality is fuzzy at that level?

Well, I think that reality is fuzzy at that level, but I don't think quantum mechanics

is necessarily the end of the story.

So quantum mechanics is certainly an improvement over classical physics.

That much we know by experiments and so forth.

Whether I'm happy with quantum mechanics, whether I view quantum mechanics, for example,

the thought, the measurement description of quantum mechanics, am I happy with it?

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

I don't.

I don't think we're at the end of that story, and many physicists may or may not view this

way.

Some do, some don't.

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

It's the best approximation for reality we know today, and so far, we don't know what

it is, the next thing that improves it, replaces it, and so on.

But as I mentioned before, I don't believe any of the laws of physics we know today are

currently exactly correct.

It doesn't bother me.

I'm not like dogmatic, saying, I have figured out this is the law of nature.

I know everything.

No.

No, that's the beauty about science that we are not dogmatic.

And we are willing to, in fact, we are encouraged to be skeptical of what we ourselves do.

So you were talking about Dirac.

Yes, I was talking about Dirac.

Right.

So Dirac was trying to now combine this Schrodinger's equations, which was described in the context

of trying to talk about how these probabilistic waves of electrons move for the atom, which

was good for speeds which were not too close to the speed of light, to what happens when

you get to the near the speed of light.

So then you need relativity.

So then Dirac tried to combine Einstein's relativity with quantum mechanics.

So he tried to combine them, and he wrote this beautiful equation, the Dirac equation,

which roughly speaking, take the square root of the Einstein's equation in order to connect

it to Schrodinger's time evolution operator, which is first order in time derivative, to

get rid of the naive thing that Einstein's equation would have given, which is second

order.

So you have to take a square root.

Now, square root usually has a plus or minus sign when you take it.

And when he did this, he originally didn't notice this, didn't pay attention to this

plus or minus sign, but later physicists pointed out to Dirac, says, look, there's also this

minus sign.

And if you use this minus sign, you get negative energy.

In fact, it was very, very annoying that, you know, somebody else tells you this obvious

mistake you make.

Pauly, famous physicist, told Dirac, this is nonsense, you're going to get negative

energy with your equation, which negative energy without any bottom, you can go all

the way down to negative infinite energy.

So it doesn't make any sense.

Dirac thought about it.

And then he remembered Pauly's exclusion principle.

Just before him, Pauly had said, you know, there's this principle called the exclusion

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

And so Dirac said, okay, you know what, all these negative energy states are filled orbits

occupied.

So according to you, Mr. Pauly, there's no place to go.

So therefore, they only have to go positive.

Sounded like a big cheat.

And then Pauly said, oh, you know what, we can change orbits from one orbit to another.

What if I take one of these negative energy orbits and put it up there?

Then it seems to be a new particle, which has opposite properties to the electron, has

positive energy, but it has positive charge.

What is that?

Dirac was a bit worried, he said, maybe that's proton because proton has plus charge.

He wasn't sure.

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

But then they said, no, no, no, it has the same mass as the electron cannot be proton

because proton is heavier.

Dirac was stuck.

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

By that time, Dirac himself was getting a little bit worried about his own equation

and his own crazy interpretation.

After a few years later, Anderson, in the photographic place that he had gotten from

these cosmic rays, he discovered a particle which goes in the opposite direction that

the electron goes when there's a magnetic field and with the same mass, exactly like

what Dirac had predicted.

And this was what we call now positron.

And in fact, beginning with the work of Dirac, we know that every particle has an anti particle.

And so this idea that there's an anti particle came from the simple math, you know, there's

a plus and a minus from the Dirac's quote unquote mistake.

So again, trying to combine ideas, sometimes the math is smarter than the person who uses

them to apply it and you try to resist it and then you kind of confronted by criticism,

which is the way it should be.

So physicists comes and said, no, no, that's wrong and you corrected and so on.

So that is a development of the idea there's particle, there's anti particle and so on.

So this is the beginning of development of quantum mechanics and the connection with

relativity.

But the thing was more challenging because we had to also describe how electric and

magnetic fields work with quantum mechanics.

This was much more complicated because it's not just one point, electric and magnetic

fields were everywhere.

So you had to talk about fluctuating and a fuzziness of electrical field and magnetic

fields everywhere.

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

And this led to a subject called quantum field theory.

Fields like electric and magnetic fields had to be quantum, had to be described also in

a wavy way.

Fine men in particular was one of the pioneers along with Schringer's and others to try to

come up with a formalism to deal with fields like electric and magnetic fields interacting

with electrons in a consistent quantum fashion and they developed this beautiful theory quantum

electrodynamics from that and later on that same formalism quantum field theory led to

the discovery of other forces and other particles all consistent with the idea of quantum mechanics.

So that was how physics progressed.

And so basically we learned that all particles and all the forces are in some sense related

to particle exchanges.

And so for example, electromagnetic forces are mediated by a particle we call photon.

And so forth and the same for other forces that they discovered strong forces and the

weak forces.

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

Is that a big leap of an idea that particles are fluctuations in the field?

Like the idea that everything is a field is the old Einstein light is a wave, both a particle

and a wave kind of idea.

Is that a huge leap in our understanding of conceiving the universe's fields?

I would say so.

I would say that viewing the particles, this duality that Bohr mentioned between particles

and waves that waves can behave sometimes like particles, sometimes like waves is one

of the biggest leaps of imagination that quantum mechanics made physicists do.

So I agree that that is quite remarkable.

Is duality fundamental to the universe or is it just because we don't understand it

fully?

Like will eventually collapse into a clean explanation that doesn't require duality?

Like that a phenomena could be two things at once and both to be true.

That seems weird.

So in fact, I was going to get to that when we get to string theory, but maybe I can comment

on that now.

Duality turns out to be running the show today and the whole thing that we are doing in string

theory, duality is the name of the game.

So it's the most beautiful subject and I want to talk about it.

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

So we do want to take a next step into, because we mentioned general relativity, we mentioned

quantum mechanics.

Is there something to be said about quantum gravity?

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

So namely, we have talked about quantum fields and I talked about electric forces, photon

being the particle carrying those forces.

So for gravity, quantizing gravitational field, which is this curvature of space time

according to Einstein, you get another particle called graviton.

So what about gravitons?

Should be there.

No problem.

So then you start computing it.

What do I mean by computing it?

Well you compute scattering of one graviton off another graviton, maybe with graviton

with an electron and so on, see what you get.

Even had already mastered this quantum electrodynamics, he said, no problem, let me do it.

Even though these are such weak forces, the gravity is very weak.

So therefore to see them, these quantum effects of gravitational waves was impossible.

It's even impossible today.

So Feynman just did it for fun.

He usually had this mindset that I want to do something which I will see in experiment,

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

And he was surprised because the same techniques he was using for doing the same calculations

quantum electrodynamics when applied to gravity failed.

The formulas seemed to make sense, but he had to do some integrals and he found that

when he does those integrals, he got infinity.

And it didn't make any sense.

Now there were similar infinities in the other pieces that, but he had managed to make sense

out of those before.

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

He just didn't know what to do.

He didn't feel as an urgent issue because nobody could do the experiment.

So he was kind of said, okay, there's this thing, but okay, we don't know how to exactly

do it, but that's the way it is.

So in some sense, a natural conclusion from what Feynman did could have been like gravity

cannot be consistent with quantum theory, but that cannot be the case because gravity

is in our universe.

Quantum mechanics in our universe, they both together somehow should work.

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

So that was a puzzle.

How does it possibly work?

It was left open.

And then we get to the string theory.

So this is the puzzle of quantum gravity.

The particle description of quantum gravity failed.

So the infinity shows up.

What do we do?

What do we do with infinity?

Let's get to the fun part.

Let's talk about string theory.

Yes.

Let's discuss some technical basics of string theory.

What is string theory?

What is the string?

How many dimensions are we talking about?

What are the different states?

How do we represent the elementary particles and the laws of physics using this new framework?

So string theory is the idea that the fundamental entities are not particles, but extended higher

dimensional objects, like one dimensional strings, like loops.

These loops could be open, like two ends, like an interval, or a circle without any ends.

And they're vibrating and moving around in space.

So how big they are?

Well, you can, of course, stretch it and make it big, or you can just let it be whatever

it wants.

It can be as small as a point because the circle can shrink to a point and be very light.

Or you can stretch it and it becomes very massive, or it could oscillate and become massive

that way.

It depends on which kind of state you have.

In fact, this string can have infinitely many modes, depending on which kind of oscillation

it's doing.

Like a guitar has different harmonics, string has different harmonics, but for the string,

each harmonic is a particle.

So each particle will give you, ah, this is a more massive harmonic, this is a less mass.

So the lightest harmonic, so to speak, is no harmonics, which means the string shrunk

to a point.

And then it becomes like a massless particles, or light particles, like photon and graviton,

and so forth.

So when you look at tiny strings, which are shrunk to a point, the lightest ones, they

look like the particles that we think they are like particles.

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

But of course, if you zoom in, there's this tiny little circle that's there that's shrunk

to almost a point.

Should we be imagining, this is through the visual intuition, should we be imagining literally

strings that are potentially connected as a loop or not?

Between you and when somebody outside of physics is imagining a basic element of string theory,

which is a string, should we literally be thinking about a string?

Yes.

You should literally think about string, but string with zero thickness.

With zero thickness.

So now it's a loop of energy, so to speak, if you can't think of it that way.

And so there's a tension, like a regular string, if you pull it, you have to stretch it.

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

It's just energy.

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

But it is very, very tiny.

Very tiny.

Much smaller than elementary particles of physics.

Much smaller.

So we think if you let the string to be by itself, the lowest state, there will be like

a fuzziness or a size of that tiny little circle, which is like a point, about, could

be anything between, we don't know exact size, but in different models have different sizes,

but something of the order of 10 to the minus, let's say 30 centimeters.

So 10 to the minus 30 centimeters, just to compare with the size of the atom, which is

10 to the minus eight centimeters, is 22 orders of magnitude smaller.

So unimaginably small, I would say.

Very small.

So we basically think from far away, string is like a point particle.

And that's why a lot of the things that we learned about point particle physics carries

over directly to strings.

So therefore, there's not much of a mystery why particle physics was successful, because

a string is like a particle when it's not stretched.

But it turns out having this size, being able to oscillate, get bigger, turned out to be

resolving these puzzles that Feynman was having in calculating his diagrams, and it gets rid

of those infinities.

So when you're trying to do those infinities, the regions that give infinities to Feynman,

as soon as you get to those regions, then this string starts to oscillate, and these

oscillation structure of the strings resolves those infinities to finite answer at the end.

So the size of the string, the fact that it's one dimensional, gives a finite answer at

the end, resolves this paradox.

Now perhaps it's also useful to recount of how string theory came to be, because it wasn't

like somebody say, well, let me solve the problem of Einstein's, solve the problem that Feynman

had with unifying Einstein's theory with quantum mechanics by replacing the point by a string.

No.

That's not the way the thought process.

The thought process was much more random.

Physicists, Venetian in this case, was trying to describe the interactions they were seeing

in colliders, in accelerators.

And they were seeing that some process, in some process, when two particles came together

and joined together and when they were separately in one way, and the opposite way, they behaved

the same way.

In some way, there was a symmetry, duality, which she didn't understand.

The particles didn't seem to have that symmetry.

He said, I don't know what it is, what's the reason that these colliders and experiments

we're doing seems to have the symmetry, but let me write the mathematical formula, which

exhibits that symmetry.

He used gamma functions, beta functions, and all that, complete math, no physics, other

than trying to get symmetry out of his equation.

He just wrote down a formula as the answer for a process, not a method to compute it.

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

Yes.

Physics looked at this formula, that's intriguing, it has this symmetry, all right, but what

is this?

Where is this coming from?

Which kind of physics gives you this?

I don't know.

A few years later, people saw that, oh, the equation that you're writing, the process

that you're writing in the intermediate channels that particles come together, seems to have

all the harmonics.

Harmonics sounds like a string.

Let me see what you're describing has anything to do with the strings, and people try to

see what he's doing has anything to do with the strings.

Yeah, indeed.

If I study scattering of two strings, I get exactly the formula you wrote down.

That was the reinterpretation of what he had written in the formula as a string, but

still had nothing to do with gravity.

It had nothing to do with resolving the problems of gravity with quantum mechanics.

It was just trying to explain a process that people were seeing in hadronic physics collisions.

So it took a few more years to get to that point, they noticed that, physicists noticed

that whenever you try to find the spectrum of strings, you always get a massless particle

which has exactly properties that the graviton is supposed to have, and no particle in hadronic

physics that had that property.

You are getting a massless graviton as part of this scattering without looking for it.

It was forced on you.

People were not trying to solve quantum gravity.

Quantum gravity was pushed on them.

I don't want this graviton.

Get rid of it.

They couldn't get rid of it.

They gave up trying to get rid of it.

Physicists, Sheridan Short said, you know what, string theory is theory of quantum gravity.

They've changed the perspective altogether.

We are not describing the hadronic physics, we are describing the theory of quantum gravity.

And that's one string theory probably got like exciting that this could be the unifying

theory.

Exactly.

It got exciting, but at the same time not so fast.

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

Because particle physics through quantum field theory were so successful at that time.

This is mid-'70s.

Standard model of physics, electromagnetism and unification of electromagnetic forces

with all the other forces were beginning to take place without the gravity part.

Everything was working beautifully for particle physics.

And so that was the shining golden age of quantum field theory and all the experiments,

solid model, this and that, unification, spontaneous symmetry breaking was taking place.

All of them was nice.

This was kind of like a side true and nobody was paying so much attention.

This exotic string is needed for quantum gravity.

Maybe there's other ways.

Maybe we should do something else.

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

And this took a little bit more effort to try to actually connect it to reality.

There were a few more steps.

First of all, there was a puzzle that you were getting extra dimensions.

String was not working well with three spatial dimensions on one time.

It needed extra dimension.

Now there are different versions of strings, but the version that ended up being related

to having particles like electron, what we call fermions, needed 10 dimensions, what

we call super string.

Now why super?

Why the word super?

It turns out this version of the string, which had fermions, had an extra symmetry,

which we call supersymmetry.

This is a symmetry between a particle and another particle with exactly the same property,

same mass, same charge, etc.

The only difference is that one of them has a little different spin than the other one.

One of them is a boson, one of them is a fermion because of that shift of spin.

Otherwise, they're identical.

So there was this symmetry.

String theory had the symmetry.

In fact, supersymmetry was discovered through string theory, theoretically.

So theoretically, the first place that this was observed when you were describing these

fermionic strings.

So that was the beginning of the study of supersymmetry was via string theory.

And then it had remarkable properties that the symmetry meant and so forth that people

began studying supersymmetry after that.

And that was a kind of a tangent direction at the beginning for string theory, but people

in particle physics started also thinking, oh, supersymmetry is great.

Let's see if we can have supersymmetry in particle physics and so forth.

Forget about strings and they developed on a different track as well.

Supersymmetry in different models became a subject on its own right, understanding supersymmetry

and what does this mean?

Because it unified bosons and fermions, unified some ideas together.

So photon is a boson, electron is a fermion, could things like that be somehow related?

It was a kind of a natural kind of a question to try to kind of unify because in physics

we love unification.

Now gradually string theory was beginning to show signs of unification.

It had graviton, but people found that they also have things like photons in them.

Different excitations of string behave like photons.

Another one behaves like electron.

So a single string was unifying all these particles into one object.

That's remarkable.

It's in ten dimensions though.

It is not our universe because we live in three plus one dimension.

How could that be possibly true?

So this was a conundrum.

It was elegant.

It was beautiful, but it was very specific about which dimension you're getting, which

structure you're getting.

It wasn't saying, oh, you just put D equals to four, you'll get your space time dimension

that you want.

No, it didn't like that.

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

So it was very specific.

Now so people try to reconcile this by the idea that maybe these extra dimensions are

tiny.

So if you take three macroscopic spatial dimensions at one time and six extra tiny spatial dimensions,

like tiny spheres or tiny circles, then it avoids contradiction with manifest fact that

we haven't seen extra dimensions in experiments today.

So that was a way to avoid conflict.

Now this was a way to avoid conflict, but it was not observed in experiments.

Having observed in experiments, no, because it's so small.

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

Similar feeling to the way perhaps Dirac had felt about this positron plus or minus, you

know, it was beginning to sound a little bit like, oh yeah, not only you have to have ten

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

And so conservative physicists would say, hmm, you know, I haven't seen these experiments.

I don't know if they are really there.

Are you pulling my leg?

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

So this was an attitude of some physicists just towards string theory, despite the fact

that the puzzle of gravity and quantum mechanics merging together work, but still was a skepticism.

You're putting all these things that you want me to imagine, there are these extra dimensions

that I cannot see.

And you want me to believe that string that you have not even seen experiments are real.

Okay, what else do you want me to believe?

So it was kind of beginning to sound a little funny.

Now, I will pass forward a little bit further, if you decades later, when string theory became

the mainstream of efforts to unify the forces and particles together, we learned that these

extra dimensions actually solved problems.

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

First of all, the properties of these extra dimensions reflected the number of particles

we got in four dimensions.

If you took these six dimensions to have like six, five holes or four holes, it changed

the number of particles that you see in four dimensional space time, you get one electron

and one muon if you had this, but if you did the other J shape, you get something else.

So geometrically, you could get different kinds of physics.

So it was kind of a mirroring of geometry by physics down in the macroscopic space.

So these extra dimension were becoming useful.

Fine, but we didn't need extra dimensions to just write an electron in three dimensions.

We did rewrote it, so what?

Was there any other puzzle?

Yes, there were.

Hawking.

Hawking had been studying black holes in mid seventies, following the work of Beckenstein,

what predicted that black holes have entropy.

So Beckenstein had tried to attach entropy to the black hole.

If you throw something into the black hole, the entropy seems to go down because you had

something entropy outside the black hole and you throw it.

The black hole was unique, so the entropy did not have any black hole at no entropy.

So the entropy seemed to go down.

And so that's against the laws of thermodynamics.

So Beckenstein was trying to say, no, no, therefore black hole must have an entropy.

So he was trying to understand that he found that if you assign entropy to be proportional

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

And then Hawking found not only that's correct, he found the correct proportionality factor

of factor of one quarter of the area and Planck units is the correct amount of entropy.

And he gave an argument using semi classical arguments, which means basically using a little

bit of quantum mechanics because he didn't have the full quantum mechanics of string

there.

He could do some aspects of approximate quantum arguments.

So he risked quantum arguments that led to this entropy formula.

But then he didn't answer the following question.

He was getting a big entropy for the black hole, the black hole with the size of a horizon

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

What are the microstates of this entropy?

When you say, for example, the gas of entropy, you count where the atoms are, you count this

bucket or that bucket, there's that information about there and so on, you count them.

For the black hole, the way Hawking was thinking, there was no degree of freedom.

You throw them in and there was just one solution.

So where are these entropy?

What are these microscopic states?

They were hidden somewhere.

So later in string theory, the work that we did with my colleague Stromiger in particular

showed that these ingredients in string theory of black hole arise from the extra dimensions.

So the degrees of freedom are hidden in terms of things like strings, wrapping these extra

circles in this hidden dimensions.

And then we started counting how many ways like the strings can wrap around this circle

and the extra dimension or that circle and counted the microscopic degrees of freedom.

And lo and behold, we got the microscopic degrees of freedom that Hawking was predicting

four dimensions.

So the extra dimensions became useful for resolving a puzzle in four dimensions.

The puzzle was, where are the degrees of freedom of the black hole hidden?

The answer, hidden in the extra dimensions, the tiny extra dimensions.

So then by this time, it was beginning to, we see aspects that extra dimensions are

useful for many things.

That's not a nuisance.

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

It was actually in the welcome features, new feature, nevertheless.

How do you intuit the 10 dimensional world?

So yes, it's a feature for describing certain phenomena like the entropy in black holes.

But what you said that to you, a theory becomes real or becomes powerful when you can connect

it to some deep intuition.

So how do we intuit 10 dimensions?

Yes.

So I will explain how some of the analogies work.

First of all, we do a lot of analogies.

And by analogies, we build intuition.

So I will start with this example.

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

plane and eight dimensional plane, we ask typically in what space do they intersect

each other in what dimension?

That might sound like, how do you possibly give an answer to this?

So we start with lower dimensions.

We start with two dimensions.

We say if you have one dimension and a point, do they intersect typically on a plane?

The answer is no.

So a line one dimensional, a point zero dimension on a two dimensional plane, they don't typically

meet.

But if you have a one dimensional line and another line, which is one plus one on a plane,

they typically intersect at a point.

That means if you're not parallel, typically they intersect at a point.

So one plus one is two.

And in two dimension, they intersect at a zero dimensional point.

So you see two dimension, one and one two, two minus two is zero.

So we get point out of intersection, okay?

Let's go to three dimension.

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

Do they intersect?

No, two and zero.

How about a plane and a line?

A plane is two dimensional and a line is one, two plus one is three, in three dimension,

a plane and a line meet at points, which is zero dimensional, three minus three is zero.

Okay?

So plane and a line intersect at a point in three dimension.

How about a plane and a plane in 3D?

A plane is two and this is two, two plus two is four.

In 3D, four minus three is one, they intersect on a one dimensional line.

Okay?

We're beginning to see the pattern.

Okay.

Now come to the question.

We're in ten dimensions.

Now we have the intuition.

One dimensional plane and eight dimensional plane in ten dimension.

They intersect on a plane.

What's the dimension?

What's seven plus eight is 15 minus 10 is five.

We draw the same picture as two planes and we write seven dimension, eight dimension,

but we have gotten the intuition from the lower dimensional one, what to expect.

It doesn't scare us anymore.

So we draw this picture.

We cannot see all the seven dimensions by looking at this two dimensional visualization

of it, but it has all the features we want.

It has, so we draw this picture, it says seven, seven and they meet at the five dimensional

plane.

It says five.

So we have, we have built this intuition now.

This is an example of how we come up with intuition.

Let me give you more examples of it because I think this will show you that people have

to come up with intuitions to visualize that otherwise we will be a little bit lost.

So what you just described is kind of in these high dimensional spaces, focus on the

meeting place of two planes in high dimensional spaces.

Exactly.

How the planes meet, for example, what's the dimension of their intersection and so

on.

So how do we come up with intuition?

We borrow examples from lower dimensions, build up intuition and draw the same pictures

as if we are talking about 10 dimensions, but we are drawing the same as a two dimensional

plane because we cannot do any better.

But our, our, our words change, but not our pictures.

So your sense is we can have a deep understanding of reality by looking at its, at, at slices,

a lower dimensional slices.

Exactly.

Exactly.

And this, this is the, brings me to the next example I want to mention, which is sphere.

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

Well, the sphere is a sphere, you know, the round nice thing, but sphere has a circular

symmetry.

Now I can't describe the sphere in the following way.

I can describe it by an interval, which is think about this going from the north of the

sphere to the south.

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

So you can think about the sphere as a line with a circle attached with each point, the

circle shrinks to a, the circle shrinks to a point at end points of the interval.

So I can say, oh, one way to think about the sphere is an interval where at each point

on that interval, there's another circle I'm not drawing.

But if you like, you can just draw it, say, okay, I want to draw it.

So from now on, there's this mnemonic, I draw an interval when I want to talk about the

sphere.

And you remember that the end points of the interval mean a strong circle.

That's all.

And then you say, yeah, I see, that's a sphere.

Good.

Now we want to talk about the product of two spheres.

That's four dimensional.

How can I visualize it?

Easy.

You just take an interval and another interval, that's just going to be a square.

Square is a four dimensional space.

Yeah.

Why is that?

Well, at each point on the square, there's two circles, one for each of those directions

you drew.

And when you get to the boundaries of each direction, one of the circle shrinks on each

edge of that square.

And when you get to the corners of the square, all both circle shrinks, this is a sphere

time the sphere.

I have divine interval.

I just described for you a four dimensional space.

Do you want a six dimensional space?

No problem.

Take the, take a corner of a room.

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

a sphere.

Take a cube.

A cube is a rendition of this six dimensional space, two sphere times another sphere times

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

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

But each time you get to the boundary of the cube, one circle shrinks.

When the boundaries meet two circle shrinks, when three boundaries meet all the three

circle shrinks.

So I just give you a picture.

Now, mathematicians come up with amazing things like, you know what?

I want to take a point in space and blow it up.

You know, these concepts like topology and geometry, complicated.

How do you do?

In this picture, it's very easy.

Blow it up.

In this picture, means the following.

You think about this cube, you go to the corner and you chop off a corner.

Chopping off the corner replaces the point, it's a point by a triangle.

That's called blowing up a point.

And then this triangle is what they call P2, projective two space.

But these pictures are very physical and you feel it.

There's nothing amazing.

I'm not talking about six dimensions.

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

So we can visualize it, no problem.

Okay, so that's building the intuition to a complicated world of string theory.

Nevertheless, these objects are really small.

And just like you said, experimental validation is very difficult because the objects are

way smaller than anything that we currently have the tools and accelerators and so on

to reveal through experiment.

So there's a kind of skepticism that's not just about the nature of the theory because

of the ten dimensions as you've explained, but in that we can't experimentally validate

it and it doesn't necessarily to date, maybe you can correct me, predict something fundamentally

new.

So it's beautiful as an explaining theory, which means that it's very possible that it

is a fundamental theory that describes reality and unifies the laws, but there's still a

kind of skepticism and me from sort of an odd side observer perspective have been observing

a little bit of a growing cynicism about string theory in the recent few years.

Can you describe the cynicism about sort of by cynicism, I mean a cynicism about the

hope for this theory of pushing theoretical physics forward.

Can you do describe why the cynicism and how do we reverse that trend?

First of all, the criticism for string theory is healthy in a sense that in science, we

have to have different viewpoints and that's good, so I welcome criticism.

And the reason for criticism and I think that is a valid reason is that there has been

zero experimental evidence for string theory, that is no experiment has been done to show

that there's this loop of energy moving around.

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

And if I were to say, you know what, string theory can never be verified or experimentally

checked, that's the way it is, they would have every right to say what you're talking

about is not science because in science, we will have to have experimental consequences

and checks.

The difference between string theory and something which is not scientific is that string theory

has predictions.

The problem is that the predictions we have today of string theory is hard to access by

experiments available with the energies we can achieve with the colliders today.

It doesn't mean there's a problem with string theory, it just means technologically we're

not that far ahead.

Now, we can have two attitudes, you say, well, if that's the case, why are you studying this

subject because you can't do experiment today.

Now this is becoming a little bit more like mathematics in that sense, you say, well,

I want to learn, I want to know what the nature works, even though I cannot prove it today

that this is it because of experiments.

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

So that's the attitude many string theories follow that that should be like this.

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

criticism, I would say.

We don't have experimental evidence for string theory, but we have theoretical evidence for

string theory.

And what do I mean by theoretical evidence for string theory?

String theory has connected different parts of physics together.

It didn't have to.

It has brought connections between part of physics, although suppose you're just interested

in particle physics.

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

It turns out there are part properties of certain particle physics models that string

theory has been able to solve using gravity, using ideas from string theory, ideas known

as holography, which is relating something which has to do with particles to something

having to do with gravity.

Why did it have to be this rich?

The subject is very rich.

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

It came at us.

I want to explain to you the development of string theory came from accidental discovery.

It wasn't because we were smart enough to come up with the idea of string, of course,

as gravity.

No.

It was accidental discovery.

So some people say it's not fair to say we have no evidence for string theory.

Graviton, gravity, is an evidence for string theory.

It's predicted by string theory.

We didn't put it by hand.

We got it.

So there's a qualitative check that, okay, gravity is a prediction of string theory.

It's a post fiction because we know gravity existed, but still, logically, it is a prediction

because really, we didn't know it had, it's a graviton that we later learned that, oh,

that's the same as gravity.

So literally, that's the way it was discovered.

It wasn't put in by hand.

So there are many things like that that there are different facets of physics, like questions

in condensed matter physics, questions of particle physics, questions about this and

that has come together to find beautiful answers by using ideas from string theory at the same

time as a lot of new math has emerged.

That's an aspect which I wouldn't emphasize as evidence to physicists necessarily because

they would say, okay, great, you got some math, but what does it do with reality?

But as I explained, many of the physical principles we know of have beautiful math underpinning

them.

That certainly leads further confidence that we may not be going astray, even though that's

not the foolproof as we know.

So there are these aspects that give further evidence for string theory, connections between

each other, connection with the real world, but then there are other things that come

about and I can try to give examples of that.

So these are further evidences and these are certain predictions of string theory.

They are not as detailed as we want, but there are still predictions.

Why is the dimension of space on time 3 plus 1?

Say, I don't know, just deal with it, 3 plus 1, but in physics we want to know why.

Well, take a random dimension from 1 to infinity, what's your random dimension?

A random dimension from 1 to infinity would not be 4.

It would most likely be a humongous number if not infinity.

I mean, there's no, if you choose any reasonable distribution which goes from 1 to infinity,

3 or 4 would not be your pick.

The fact that we are in 3 or 4 dimension is already strange.

The fact that strings is, sorry, I cannot go beyond 10 or maybe 11 or something.

The fact that they're just upper bound, the range is not from 1 to infinity, it's from

1 to 10 or 11 or whatnot.

It already brings a natural prior, oh yeah, 3 or 4 is, you know, it's just on the average.

If you pick some of the compactifications, then it could easily be that.

So in other words, it makes it much more possible that it could be 3 of our universe.

So the fact that the dimension already is so small, it should be surprising.

We don't ask that question.

We should be surprised because we could have conceived of universes with our predimension.

Why is it that we have such a small dimension?

That's number one.

So, oh, so, so good theory of the universe should give you an intuition of the why it's

4 or 3 plus 1 and it's not obvious that it should be, that they, that should be explained.

We take that as an assumption, but that's a thing that should be explained.

Yeah.

So we haven't explained that in string theory.

Actually, I did write a model within string theory to try to describe why we end up with

3 plus 1 space time dimensions, which are big compared to the rest of them.

And even though this has not been, the technical difficulties to prove it is still not there,

but I will explain the idea because the idea connects to some other piece of elegant math,

which is the following.

Consider a universe made of a box, a three dimensional box, or in fact, if we set a string

theory, nine dimensional box, because we have nine spatial dimensional on time.

So imagine a nine dimensional box.

So we should imagine the box of a typical size of the string, which is small.

So the universe would naturally small start with a very tiny nine dimensional box.

What do strings do?

Well, strings go, you know, go around the box and move around and vibrate and all that,

but also they can wrap around the one side of the box to the other because I'm imagining

a box with periodic boundary conditions, so what we call the torus.

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

This is what we call a winding string.

The string can wind around the box.

Now, suppose you have, you now evolve the universe because there's energy, the universe

starts to expand, but it doesn't, it doesn't expand too far.

Why is it?

Well, because there are these strings which are wrapped around from one side of the wall

to the other.

When the universe, the walls of the universe are growing, it is stretching the string and

the strings are becoming very, very massive.

So it becomes difficult to expand.

It kind of puts a halt on it.

In order to not put a halt, a string which is going this way and a string which is going

that way should, should intersect each other and disconnect each other and unwind.

So a string which is winds this way and the string which finds the opposite way should

find each other to, to, to reconnect and this way disappear.

So if they find each other and they, they, they disappear, but how can strings find each

other?

Well, the string moves and the other string moves, a string is one dimensional, one plus

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

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

In a higher dimensional space time, they typically miss each other.

Oh, interesting.

So if the dimensions were too big, they would miss each other.

They wouldn't be able to expand.

So in order to expand, they have to find each other and three of them can find each other

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

So that, that explains why within string theory, these particular dimensions are really big

and full of exciting stuff.

That could be an explanation.

That's the model we, we, we suggested with my colleague Brandenberger.

But it turns out we relate to the D piece of math.

You see, for mathematicians, manifolds of dimension bigger than four are simple.

Four dimension is the hardest dimension for math.

It turns out, and it turns out the reason it's difficult is the following.

It turns out that in higher dimension, you use, you use what's called surgery in mathematical

terminology where you use these two dimensional tubes to maneuver them off of each other.

So you have two plus two becoming four and higher than four dimension, you can pass them

through each other without them intersecting.

In four dimension, two plus two doesn't allow you to pass them through each other.

So the same techniques that work in higher dimension don't work in four dimension because

two plus two is four.

The same reasoning I was just telling you about strings finding each other in four ends

up to be the reason why four is much more complicated to classify for mathematicians

as well.

So, so there might be these, these things.

So I cannot say that this is the reason that string theory is, is giving you three plus

one, but it could be a model for it.

And so, so there are these kinds of ideas that could underlie why we have three extra

dimensions which are large and the rest of them are small, but absolutely, we have to

have a good reason.

We cannot leave it like that.

Can I ask a tricky human question?

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

You got the breakthrough prize.

You worked with Edward Witton.

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

You know, credit assignment is tricky in science.

It makes you quite sad, especially big, like LIGO, big experimental projects when so many

incredible people have been involved.

And yet the Nobel Prize is annoying in that it's only given to three people.

Who do you think gets the Nobel Prize for string theory at first?

If it turns out that it, if not in full, then in part is, is a good model of the way the

physics of the universe works.

Who are the key figures?

Maybe let's put Nobel Prize aside for the key figures.

Okay.

I like the second version of the question.

I think to try to give a prize to one person in string theory doesn't do justice to the

diversity of the subject.

That to me is.

There was quite a lot of incredible people in the history, quite a lot of people.

I mean, starting with Veneziano, who wasn't talking about strings, I mean, he wrote down

the, the beginning of the strings.

We cannot ignore that for sure.

And so, so you start with that and you go on with various other figures and so on.

So there are different epochs in string theory and different people have been pushing it

then.

So for example, the early epoch, we just told you people like, like Veneziano and Nambu

and the Soskin and others were pushing it green and shorts were pushing it and so forth.

So this was or shirk and so on.

So these were the initial periods of pioneers, I would say of string theory.

And then there were, there were the mid 80s that Edward Whitten was the major proponent

of string theory.

And he really changed the landscape of string theory in terms of what people do and how,

how we view it.

And I think his efforts brought a lot of attention to the community about high energy community

to focus on this effort as the correct theory of unification of forces.

So he brought a lot of research as well as of course the first rate work he himself did

to this area.

So that's in mid 80s and onwards and also in mid 90s where he was one of the proponents

of the duality revolution in string theory.

And with that came a lot of these other ideas that, you know, led to breakthroughs involving,

for example, the example I told you about black holes and holography and the work that

was later done by Maldesena about the properties of duality between particle physics and quantum

gravity and the connections, deeper connections of holography and it continues.

And there are many people within this range, which I haven't even mentioned, they have

done fantastic important things.

How it gets recognized, I think is secondary in my opinion than the appreciation that the

effort is collective, that in fact, that to me is the more important part of science

that gets forgotten.

For some reason, humanity likes heroes and science is no exception, we like heroes.

But I personally try to avoid that trap.

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

I have much more collaborations than sole author papers and I enjoy it.

And I think that that's to me one of the most satisfying aspects of science is to interact

and learn and debate ideas with colleagues because that influx of ideas enriches it.

And that's why I find it interesting.

To me, science, if I was in an island and if I was developing string theory by myself

and had nothing to do with anybody, it would be much less satisfying in my opinion.

Even if I could take credit, I did it.

It won't be as satisfying.

Sitting alone with a big metal drinking champagne?

No.

I think to me, the collective work is more exciting and you mentioned my getting the

breakthrough.

When I was getting it, I made sure to mention that it is because of the joint work that

I've done with colleagues at that time, it was around 180 or so collaborators and I acknowledged

them in the web page for them, I wrote all of their names and the collaborations that

led to this.

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

And yes, there are more important and less important figures as in any field.

And that's true, that's true in string theory as well.

But I think that I would like to view this as a collective effort.

So setting the heroes aside, the Nobel Prize is a celebration of, what's the right way

to put it, that this idea turned out to be right.

So like you look at Einstein didn't believe in black holes.

And then black holes got their Nobel Prize.

Do you think string theory will get its Nobel Prize, Nobel Prizes?

If you were to bet money, if this was like, if this was an investment meeting and we had

to bet all our money, do you think he gets the Nobel Prizes?

I think it's possible that none of the living physicists will get the Nobel Prize on string

theory, but somebody will because unfortunately the technology available today is not very

encouraging in terms of seeing directly evidence for string theory.

Do you think it ultimately boils down to the Nobel Prize will be given when there is some

direct or indirect evidence?

There would be, but I think that part of this breakthrough prize was precisely the appreciation

that when we have sufficient evidence, theoretical as it is, not experiment.

Because of this technology lag, you appreciate what you think is the correct path.

So there are many people who have been recognized precisely because they may not be around when

it actually gets experimented, even though they discovered it.

So there are many things like that that's going on in science.

So I think that I would want to attach less significance to the recognitions of people.

And I have a second review on this, which is there are people who look at these works

that people have done and put them together and make the next big breakthrough.

And they get identified with, perhaps rightly with many of these new visions, but they are

on the shoulders of these little scientists, which don't get any recognition, you know,

yeah, you did this little work, oh, yeah, you did this little work, oh, yeah, yeah, five

of you, oh, yeah, these show this pattern and then somebody else, it's not fair.

To me, to me, those little guys, which kind of like, like seem to do a little calculation

here, a little thing there, which is not doesn't doesn't rise to the occasion of this grandiose

kind of thing, doesn't make it to the New York Times headlines and so on deserve a lot

of recognition.

And I think they don't get enough.

I would say that there should be this Nobel Prize for, you know, they have these doctors

without borders, a huge group, they should be similar thing and the string tears without

borders kind of everybody is doing a lot of work.

And I think that I would like to see that efforts to recognize.

I think in the long arc of history, we're all little guys and girls standing on the

shoulders of each other.

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

We celebrate New York Times, you know, as a newspaper or the idea of a newspaper in a

few centuries from now will be long forgotten.

Yes, I agree with that.

Especially in the countries of string there, we should have very long term view.

Yes, exactly.

Just as a tiny tangent, we mentioned Edward Whitton and he in a bunch of walks of life

for me as an outsider comes up as a person who is widely considered as like one of the

most brilliant people in the history of physics, just as a powerhouse of a human.

Like the exceptional places that a human mind can rise to, you've gotten a chance to work

with him.

What's he like?

More than that, he was my advisor, a PhD advisor, so I got to know him very well and I benefited

from his insights.

In fact, what you said about him is accurate.

He's not only brilliant, but he's also multifaceted in terms of the impact he has had in not only

physics but also mathematics.

He's gotten the fields medal because of his work in mathematics and rightly so, he has

used his knowledge of physics in a way which impacted deep ideas in modern mathematics and

that's an example of the power of these ideas in modern high energy physics and string theory

that the applicability of it to modern mathematics.

He's quite an exceptional individual.

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

So I think, yes, indeed, he's one of the rare figures in this history of subject, he has

great impact on a lot of aspects of not just string theory, a lot of different areas in

physics and also, yes, in mathematics as well.

So I think what you said about him is accurate.

I had the pleasure of interacting with him as a student and later on as colleagues writing

papers together and so on.

What impact did he have on your life?

What have you learned from him?

If you were to look at the trajectory of your mind of the way you approach science and physics

and mathematics, how did he perturb that trajectory in a way?

Yes, he did actually.

So I can explain because when I was a student, I had the biggest impact by him clearly as

a grad student at Princeton.

So I think that was the time where I was a little bit confused about the relation between

math and physics.

I got a double major in mathematics and physics at MIT and because I really enjoyed both and

I liked the elegance and the rigor of mathematics and I liked the power of ideas in physics

and its applicability to reality and what it teaches about the real world around us.

But I saw this tension between rigorous thinking in mathematics and lack thereof in physics

and this troubled me to no end.