The following is a conversation with Kamran Vafa, a theoretical physicist at Harvard specializing
in string 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 string 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 string 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.
String 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 it
a priori, 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, 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.
Then 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, 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 used 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.
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,
bump 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.
Right.
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, it will be the lower energy
point, symmetrical, but it breaks the 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, 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 symmetries 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 it, 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.
So 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 and 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 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, and 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?
Sure.
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 had 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 gigalus 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 the 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 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 equation, except we get one speed light.
Who measures this light speed?
And he asked 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
get 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 try 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, in that medium, the speed is speed of, if you're at
rest with respect to the ether, the speed is speed of light.
And if you're moving, the speed changes, and people did not discover it.
Michael Snell and 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.
We can teach it at a high school level, if not earlier.
Okay.
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, a question
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 it 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, you know, 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.
Like, even when I'm describing it, I feel like a little bit funny, as you're just feeling
the same way.
It is.
Yes.
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, you know, 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 the 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.
Famously, 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 heavier 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?
Why?
So, Galileo had to come up with an explanation of why heavier and lighter objects fought
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
shape, 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 the 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 de-confused 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 waves 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 phenomena deeply.
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 the 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 going back to your question about the path
of the history of the science, I was saying about the electricity and 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 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 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 it's 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 science theory.
And in fact, it's so much harder that Einstein himself couldn't solve many of the cases.
He thought, for example, you couldn't solve the equation for a spherical symmetric matter.
Like if you had a symmetric sun, he didn't think you can actually solve his equation
for that.
And a year after he said that it was solved by Schwarzschild.
So 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 we have learned that 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 tensors
or curvature and I don't like the four dimensional space time because I cannot see four dimensional.
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 reinforce each other.
Here 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 Riemannian geometry, just use them.
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 talk about your favorite soccer player at a 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 lambda c 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, it's special relativity.
The idea that speed of light is the same for everybody is the beginning of everything
he did.
The beginning is the same.
The beginning is the same.
But once you embrace that weirdness, all the weirdness, all the roughness.
I would say 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
field.
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 from outside, at least, 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 you
talk about length contraction.
So general relativity takes that to the next step.
But beginning of it was already space-link contracts, time dilates.
So once you talk about those, then yeah, you can dilate more or less different places
than its curvature.
So you don't have a choice.
So it 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.
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.
Both physicists 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 lower, these phenomena become more
pronounced.
You can see it much better.
The electron is not at the point, but the clouds 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 dogmatic.
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 before, 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, it 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.
Until 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, 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 physics comes and says, 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 formism 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 it eventually collapse into a clean explanation that doesn't require duality?
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 spacetime
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, 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 it's 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 massive.
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 a string, but string with zero thickness.
With zero thickness.
So now it's a loop of energy, so to speak, if you can 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 it with the size of the atom, which
is 10 to the minus eight centimeters is 22 orders of magnitude smaller.
So unimaginably small.
So very, 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.
And 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 this 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, would 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?
So 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, oh, 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 said, shirkan 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're describing this 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, et cetera.
The only difference is that one of them has a little different spin than the other one.
And 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 this 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 fermion, 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, you know, 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 I 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?
Or do you want me to imagine things that are not there?
So this was an attitude of some physicists 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 this kind of beginning to sound a little funny.
Now, I will, I will pass forward 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.
They're 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.
We wrote 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, who had
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 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 theory.
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 these 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, 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, 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, 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 you 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.
We have a seven dimensional plane and eight dimensional plane in ten dimension.
They intersect on a plane.
What's the dimension?
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 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 a 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 an 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 how 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 it.
So that's the attitude many string theories follow 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 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.
As I explained 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-section 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 have come together to find beautiful answers by using ideas from string theory
at the same time as a lot of new math has emerged.
Just 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.
So it certainly leads further confidence that we may not be going astray, even though that's
not the full proof 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 and time three plus one?
Say, I don't know, just deal with it, three plus one.
But in physics, we want to know why.
Well, take a random dimension from one to infinity, what's your random dimension?
A random dimension from one to infinity would not be four.
It would most likely be a humongous number if not infinity.
I mean, if you choose any reasonable distribution which goes from one to infinity, three or
four would not be your pick.
The fact that we are in three or four dimension is already strange.
The fact that string says, sorry, I cannot go beyond 10 or maybe 11 or something.
The fact that they're just upper bound, the range is not from one to infinity.
It's from one to 10 or 11 or whatnot.
It already brings a natural prior, oh yeah, three or four 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 three 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 pre-dimension.
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
four or three plus one, and it's not obvious that it should be that that should be explained
which take that as a, as an assumption, but that's a thing that should be explained.
Yes.
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
three plus one 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 dimension on one 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 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 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 reconnect and this way disappear.
So if they find each other and they disappear, but how can strings find each other?
Well, the string moves and another 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.
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 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 suggested with my colleague Brandenberger.
But it turns out we relate to a 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 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.
In 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 there might be these things.
So I cannot say that this is the reason that string theory is giving you three plus one,
but it could be a model for it.
And 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 Whitten.
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 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.
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 of string theory.
I mean, starting with Venetiano, who wasn't talking about strings, I mean, he wrote down
the beginning of a string so we cannot ignore that for sure.
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 Venetiano and Nambu and
the Soskin and others were pushing it green and shorts were pushing it and so forth.
So this was our shirk and so on.
So these were the initial periods of pioneers, I would say, of string theory.
And then 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 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 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 deeper connections of holography and it continues.
And there are many people within this range which I haven't even mentioned that 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 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 write all of their names and the collaborations that led to this.
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 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 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 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 and 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.
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 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 they're a huge group they should be similar thing and these 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 context of string there we should have very long term
view.
Yes exactly just as a tiny tangent we mentioned Edward Whitten 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.
Yes more than that he was my advisor 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 is not only brilliant but you know he is also multifaceted in terms of the impact he
has had in not only physics but also mathematics you know he's got in the fields medal because
of his work in mathematics and rightly so you know 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.
So 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 the subject he
has had 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 like 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.
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 a 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 like the elegance and the rigor
of mathematics and I like the power of ideas and 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 I was
troubled by that so I was at crossroads when I decided to go to graduate school in physics
because I did not like some of the lack of rigors I was seeing in physics on the other
hand to me mathematics even though it was rigorous I think it sometimes were I didn't
see the point of it in other words when I see when I see you know the math there and
by itself could be beautiful but I really wanted more than that I want to say okay what
does it teach us about something else something more than just math so I wasn't I wasn't that
enamored with just math but physics was a little bit bothersome nevertheless I decided
to go to physics and I decided to go to Princeton and I started working with Edward Whitten
as my thesis advisor and at that time I was trying to put physics in rigorous mathematical
terms I took one of field theory I tried to make rigorous out of it and so on and no matter
how hard I was trying I was not being able to do that and I was falling behind from my
classes I was not learning much physics and I was not making it rigorous and to me it was
this dichotomy between math and physics what am I doing I like math but this is not exact
risk there comes Edward Whitten as my advisor and I see him in action thinking about math
and physics he was amazing in math he knew all about the math it was no problem with
him but he thought about physics in a way which did not find this tension between the
two it was much more harmonious for him he would draw the Feynman diagrams but he wouldn't
view it as a formalism he was viewed oh yeah the particle goes over there and this is what's
going on and so wait you're thinking really is this particle this is really electron
going there oh yeah yeah it's not it's not taking literally perturbation no no you just
feel like the electron you're moving with this guy and do that and so on and you're thinking
invariantly about physics or the way he thought about relativity like you know I was thinking
about this momentum he was thinking invariantly about physics just like the way you think about
invariant concepts in relativity which don't depend on the frame of reference he was thinking
about the physics in invariant ways that the way that doesn't that gives you a bigger perspective
so this gradually helped me appreciate that interconnections between ideas and physics
replaces mathematical rigor that the different facets reinforce each other we say oh I cannot
rigorously define what I mean by this but this thing connects with this other physics I've seen
and this other thing and they together form an elegant story and that's replaced for me what I
believed as a solidness which I found in math as a rigor you know solid I found that replaced the
rigor and solidness in physics so I found okay that's the way you can hang on to it is not wishy
washy it's not like somebody is just not being able to prove it just making up a story it was
more than that and it was no tension with mathematics in fact mathematics was helping it
like friends and so much more harmonious and gives insights to physics so that's I think one
of the main things I learned from interactions with Witten and I think that now perhaps I have
taken that to a far extreme maybe he wouldn't go this far as I have namely I use physics to define
new mathematics in a way which would be far less rigorous than a physics might necessarily believe
because I take the physical intuition perhaps literally in many ways that could teach us about
so now I've gained so much confidence in physical intuition that I make bold statements that sometimes
you know takes math math friends off guard so for an example of it is mirror symmetry so
so we were studying these compactification of string string geometries this is after my phd
now I've by the time I had come to Harvard we're studying these aspects of string compactification
on these complicated manifolds six-dimensional space is called Kalabiyan manifolds very complicated
and I noticed with a couple other colleagues that there was a symmetry in physics suggested
between different kalabias suggested that you couldn't actually compute the Euler characteristic
of a kalabia Euler characteristic is counting the number of points minus the number of edges
plus the number of faces minus so you can count the alternating sequence of properties of the
space which is a topological property of a space so Euler characteristic of the kalabia was a property
of the space and so we noticed that from the physics formulas of string moves in a kalabia
you cannot distinguish we cannot compute the Euler characteristic you can only compute the absolute
value of it now this bothered us because how could you not compute the actual sign
unless the both sides were the same so I conjectured maybe for every kalabia with
the Euler characteristic positive there's one with negative I told this to my colleague yeah
who was whose namesake is kalabia that I'm making this conjecture is it possible
that for every kalabia there's one with the opposite Euler characteristic
sounds not reasonable I said why I said well we know more kalabias with negative Euler
characteristic than positive I said but physics says we cannot distinguish them at least I don't
see how so we conjectured that for every kalabia with one sign there's the other one despite the
mathematical evidence despite the mathematical evidence despite the expert telling us is not
the right idea if a few years later this symmetry mirror symmetry between the sign with the opposite
sign was later confirmed by mathematicians so this is actually the opposite view that is physics
is so sure about it that you're going against the mathematical wisdom telling them they better
look for it so taking the the the physical intuition literally and then having that drive the
the mathematics exactly and by now we have so confident about many such examples that has
affected modern mathematics in ways like this that we are much more confident about our understanding
of what string theories these are another aspects other aspects of why we feel string
theories quite is doing these kind of things I've been hearing you talk quite a bit about
string theory landscape and the swamp land what the heck are those two concepts okay very good
question so let's go back to what I was describing about Feynman yes Feynman was trying to do these
diagrams for graviton and electrons and all that he found that he's getting infinities he cannot
resolve okay the natural conclusion is that field theories and gravity and quantum theory don't go
together and you cannot have it so in other words field theories and gravity are inconsistent with
quantum mechanics period string theory came up with examples but didn't address the question
more broadly that is it true that every field theory can be coupled to gravity in a quantum
mechanical way it turns out that Feynman was essentially right all almost all particle physics
theories no matter what you add to it when you put gravity in it doesn't work only rare exceptions
work so string theory are those rare exceptions so therefore the general principle that Feynman
found was correct quantum field theory and gravity and quantum mechanics don't go together except for
joules exceptional cases there are exceptional cases okay the total vastness of quantum field
theories that are there we call the set of quantum field theories possible things which ones can be
consistently coupled to gravity we call that subspace the landscape the rest of them we call the
swamp land it doesn't mean they are bad quantum field theories they're perfectly fine but when
you couple them to gravity they don't make sense unfortunately and it turns out that the ratio of
them the number of theories which are consistent with gravity to the ones which without the ratio
of the area of the landscape to the swamp land in other words is measure zero and so the swamp
land is infinitely large the swamp lands infinitely large so let me give you one example take a theory
in four dimension with matter with maximum amount of supersymmetry can you get it turns out a theory
in four dimension with maximum amount of supersymmetry is characterized just with one thing a group what
we call the gauge group once you pick a group you have to find the theory okay so does every group
make sense yeah as far as quantum field theory every group makes sense there are infinitely many
groups there are infinitely many quantum field theories but it turns out they're only finite
number of them which are consistent with gravity out of that same list so you can take any group but
only find number of them the ones who's what we call the rank of the group the ones whose rank
is less than 23 anyone bigger than rank 23 belongs to the swamp land they're infinitely many of them
they're beautiful field theories but not when you include gravity so so then this becomes a hopeful
thing so in other words in our universe we have gravity therefore we are part of that dual subset
now is this dual subset small or large yeah it turns out that subset is humongous but we believe
still finite the set of possibilities is infinite but the set of consistent ones i mean the set of
quantum field theories are infinite but the consistent ones are finite but humongous the
fact that the humongous is the problem we are facing in string theory because we do not know
which one of these possibilities the universe we live in if we knew we could make more specific
predictions about our universe we don't know and that is one of the challenges when string theory
which point on the landscape which corner of this landscape do we live in we don't know so what do we
do well there are there are principles that are beginning to emerge so i will give you one example
of it you look at the patterns of what you're getting in terms of these good ones the the ones
which are in the landscape compared to the ones which are not you find certain patterns i'll give
you one pattern you find in the all the ones that you get from string theory gravitational force
is always there but it's always always the weakest force however you could easily imagine field
theories for which gravity is not the weakest force for example take our universe if you take a mass
of the electron if you increase the mass of electron by a huge factor the gravitational
attraction of the electrons will be bigger than the electric repulsion between two electrons
and the gravity will be stronger that's all it happens that it's not the case in our universe
because electron is very tiny in mass compared to that just like our universe gravity is the weakest
force we find in all these other ones which are part of the good ones the gravity is the weakest
force this is called the weak gravity conjecture we conjecture that all the points in the landscape
have this property our universe being just an example of it so there are these qualitative
features that we are beginning to see but how do we argue for this just by looking patterns
just by looking string theory has this no that's not enough we need more more reason more better
reasoning and it turns out there is the reasoning for this turns out to be studying black holes
ideas of black holes turn out to put certain restrictions of what a good quantum filter
should be it turns out using black hole the fact that the black holes evaporate the fact
that the black holes evaporate gives you a way to to check the relation between the mass and
the charge of elementary particle because what you can do you can take a charged particle and
throw it into a charged black hole and wait it to evaporate and by the looking at the properties
of evaporation you find that if it cannot evaporate particles whose mass is less than their charge
then it will never evaporate you'll be stuck and so the possibility of a black hole evaporation
forces you to have particles whose mass is sufficiently small so that the gravity is weaker
so you connect this fact to the other fact so we begin to find different facts that reinforce
each other so different parts of the physics reinforce each other and once they all kind of
come together you believe that you're getting the principle correct so weak gravity conjecture
is one of the principles we believe in as a necessity of these conditions so these are the
predictions string theory are making is that enough well it's qualitative it's a semi-quantity
it's just the mass of the electron should be less than some number but that number is if I call
that number one the mass of the electron turns out to be 10 to the minus 20 actually so it's
much less than one it's not one but on the other hand there's a similar reasoning for a big black
hole in our universe and if that evaporation should take place gives you another restriction
tells you the mass of the electron is bigger than 10 to the is now in this way is bigger than
something it shows bigger than 10 to the minus 30 in the blank unit so you find uh-huh the mass of
the electron should be less than one but bigger than 10 to the minus 30 in our universe the mass
of the electron stands to minus 20 okay now this kind of you could call post fiction but I would say
it follows from principles that we now understand from string theory first principle so we are
making beginning to make these kinds of predictions which are very much uh connected to aspects of
particle physics that we didn't think are related to gravity we thought just take any electron mass
you want what's the problem it has a problem with gravity and so that conjecture has also a happy
consequence that it explains that our universe like why the heck is gravity so weak as a force
and that's not only an accident but almost a necessity if these forces are to coexist effectively
exactly so that's that's that's the reinforcement of of of what we know in our universe but we are
finding that as a general principle so we want to know what aspects of our universe universe is
forced on us like the weak gravity conjecture and other aspects do we understand how much of them do
we understand can we have particles lighter than neutrinos or maybe that's not possible you see the
neutrino mass it turns out to be related to dark energy in a mysterious way naively there's no relation
between dark energy and a mass of a particle we have found arguments from within the swamp
land kind of ideas why it has to be related and so so they're beginning to be these connections
between graph consistency of quantum gravity and aspects of our universe gradually being
sharpened but we are still far from a precise quantitative prediction like
we have to have such and such but that's the hope that we are going in that direction
coming up with the theory of everything that unifies general relativity in quantum field
theories uh this is one of the big dreams of human civilization us descendants of apes wondering
about how this world works so a lot of people dream uh what are your thoughts about sort of other
out there ideas theories of everything or unifying theories so there's a quantum loop gravity
there's also more sort of like a friend of mine Eric Weinstein beginning to propose something
called geometric unity so these kinds of attempts whether it's through mathematical physics or
through other avenues or with Steven Wolfram a more computational view of the universe again
in his case it's these hyper graphs that are very tiny objects as well uh similarly a string theory
in trying to grapple with this world what do you think is there any of these uh theories that are
compelling to you they're interesting that may turn out to be true or at least may turn out to
contain ideas that are useful yes i think the latter i would say that the containing ideas that
are true is my opinion was what these some of these ideas might be for example loop quantum
gravity is to me not a complete theory of gravity in any sense but they have some nuggets of truth
in them and typically what i expect happen and i have seen examples of this within string theory
aspects which we didn't think are part of string theory come to be part of it for example i'll give
you one example string was believed to be 10 dimensional and then there was this 11 dimensional
super gravity and nobody know what the heck is that why are we getting 11 dimensional super
gravity whereas string is saying it should be 10 dimensional 11 was the maximum dimension you can
have a super gravity but string was saying sorry we're 10 dimensional so for for a while we thought
that theory is wrong because how could it be because string theory is definitely theory of
everything we later learned that one of the circles of string theory itself was tiny that we had not
appreciated that fact and we discovered by doing thought experiments of string theory that there's
got to be an extra circle and that circle is connected to an 11 dimensional perspective
and that's what later on got called m theory so so so there are these kind of things that you know
we do not know what exactly string theory is we're still learning so we do not have a final
formulation of string theory it's very well could be the different facets of different ideas come
together like loop quantum gravity or whatnot but i wouldn't put them on par namely loop quantum
gravity is a scatter of ideas about what happens to space when they get very tiny for example
you replace things by discrete data and try to quantize it and so on and you know it sounds
like a natural idea to quantize space you know if you were naively trying to do quantum space you
might think about trying to take points and put them together in some discrete fashion in some way
that is reminiscent of loop quantum gravity string theory is more subtle than that for example i
would just give you an example and this is the kind of thing that we didn't put in by hand we got it
out and so it's more subtle than so what happens if you squeeze the space to be smaller and smaller
well you think that after a certain distance the notion of distance should break down no when
it goes smaller than plank scale should break down what happens in string theory we do not
know the full answer to that but we know the following namely if you take a space and bring
it smaller and smaller if the box gets smaller than the plank scale by a factor of 10 it is
equivalent by the duality transformation to a space which is 10 times bigger
so there's a symmetry called a t-duality which takes l to one over l well l is measured in
plank units or more precisely string units this inversion is a very subtle effect and
i would not have been or any physicist would not have been able to design a theory which has this
property that when you make the space smaller it is as if you're making it bigger that means
there is no there's no experiment you can do to distinguish the size of the space
this is remarkable for example Einstein would have said of course i can measure the size of the space
what do i do well i take a flashlight i i send the light around measure how long it takes for
the light to go around the space and bring back and find the radius or circumference of the the
universe what's the problem i said well suppose you do that and you shrink it said well they get
smaller and smaller so what i said well it turns out in string theory there are two different kinds
of photons one photon measures one over l the other one measures l and so this duality reformulates
and when the space gets smaller it says oh no you better use the bigger perspective because the
smaller one it's harder to deal with so you do this one so so these examples of loop quantum
gravity have none of these features these features that i'm telling you about we have
learned from string theory but they nevertheless have some of these ideas like topological
gravity aspects are emphasized in the context of loop quantum gravity in some form and so these
ideas might be there in some kernel in some corners of string theory in fact we i wrote a paper
about topological string theory and some connections would potentially loop quantum gravity which could
be part of that so they're little facets of connections i wouldn't say they're complete but
i would say most probably what would happen to some of these ideas the good ones at least
they'll be absorbed within to string theory if if they're correct let me ask a crazy out there
question can physics help us understand life so uh we spoke so confidently about the laws of physics
being able to explain reality but and we even said words like theory of everything implying
that the word everything is actually describing everything is it possible that the four laws
we've been talking about are actually missing they are accurate in describing what they're
describing but they're missing the description of a lot of other things like emergence of life
and emergence of perhaps consciousness so is there do you ever think about this kind of stuff
where we would need to understand extra physics to try to explain the emergence of these complex
pockets of interesting weird stuff that we call life and consciousness in this big homogeneous
universe that's mostly boring and nothing is happening so first of all we don't claim that
string theory is the theory of everything in the sense that we know enough what this theory is we
don't know enough about string theory itself we are learning it so i wouldn't say okay give me
whatever i will tell you what it's hard to work now however i would say by definition by definition
to me physics is checking all reality any form of reality i call it physics that's my definition i
mean i may not know a lot of it like maybe the origin of life and so on maybe a piece of that
but i would call that as part of physics to me reality is what we're after i don't claim i know
everything about reality i don't claim string theory necessarily has the tools right now to
describe all the reality either but we are learning what it is so i would say that i would not put a
border to say no you know from this point onwards it's not my territory somebody else's but whether
we need new ideas and string theory to describe other reality reality features for sure i believe
as i mentioned i don't believe anything's any of the laws we know today is final so therefore yes
we will need new ideas this is a very tricky thing for us to understand and be precise about
but just because you understand the physics doesn't necessarily mean that you understand the
emergence of chemistry biology life intelligence consciousness so those are built it's like you
might understand the way bricks work but to understand what it means to have a happy family
right you don't construct you don't get from the bricks so directly you right theory you could
if you ran the universe over again but just understanding the rules of the universe doesn't
necessarily give you a sense of the weird beautiful things that emerge right no so let me let me
describe what you just said so there are two questions one is whether or not the techniques
i use and let's say quantum field theory and so on will describe how the society works yes
okay this is far distance far for different scales of questions that we're asking here
the question is is there a change of is there a new law which takes over that cannot be connected
to the older laws that we know or more fundamental laws that we know do you need new laws to describe
it i don't think that's necessarily the case in many of these phenomena like chemistry or so on
you mentioned so we do expect you know in principle chemistry can be described by quantum mechanics
we don't think there's going to be a magical thing but chemistry is complicated yeah indeed there
are rules of chemistry that you know chemists that put down which has not been explained yet
using quantum mechanics do i believe that they will be at something described by quantum mechanics
yes i do i don't think they are going to be sitting there in the shells forever but maybe
it's too complicated and maybe you know we will wait for very powerful quantum computers or what
not to solve those problems i don't know but i don't think in that context we have no principles
to be added to fix those so by by by i'm perfectly fine in the intermediate situation to have rules
of thumb or you know principles that chemists have found which are you working which are not
founded on the basis of quantum mechanical laws which does the job similarly as biologists
do not found everything in terms of chemistry but they think you know there's no reason why
chemistry cannot they don't think necessarily they're doing something amazingly not possible
with chemistry coming back to your question does consciousness for example bring this new ingredient
if indeed it needs a new ingredient i will call that new ingredient part of physical law we have
to understand it to me that so i wouldn't put a line to say okay from this point onwards you
cannot it's disconnected it's totally disconnected from string theory whatever we have to do something
else it's not a line what i'm referring to is can physics of a few centuries from now that
doesn't understand consciousness be much bigger than the physics of today where the the textbook
grows it definitely will i would say i will grow i would not i don't know if it grows because of
consciousness being part of it or we have different view of consciousness i do not know where the
consciousness will fit i'm not it's going to be hard for me to to to to to guess i mean i can make
random guesses now which probably most right most likely it's wrong but let me just do just
for the sake of discussion you know i could say you know you know brain could be their quantum
computer classical computer their arguments against it's being a quantum thing so it's probably
classical and if it's classical it could be like what we are doing in machine learning slightly
more fancy and so on okay people can go to this argument to no end and to see whether consciousness
exists or not or life does it have any meaning or is there is there a phase transition where you
can say does electron have a life or not at what level does the particle become life maybe there's
no definite definition of life in that same way that you know we cannot say electron if you
you know a good i like this example quite a bit um you know we distinguish between liquid and a gas
phase like water is liquid or or vapor is gas we say they're different you can distinguish them
actually that's not true it's it's not true because we know from physics that you can
change temperatures and pressure to go from liquid to the gas without making any phase
transition so there is no point that you can say this was a liquid and this was a gas you can
continuously change the parameters to go from one to the other so at the end it's very different
looking like you know i know that water is different from vapor but you know there is no
precise point this happens i feel many of these things that we think like consciousness clearly
dead person is not conscious on the other one is so there's a difference like water and vapor
but there's no point you could say that this is conscious there's no sharp transition so it
could very well be that what we call heuristically in daily life consciousness is is similar or
life is similar to that i don't know if it's like that i don't know i'm just hypothesizing as possible
like there's no there's no discrete phases there's no discrete phase transition like that yeah yeah
but it's you might there might be you know concepts of temperature and pressure that we need to
understand to describe what the heck consciousness in life is that that we're totally missing
i think that's not a useless question even those questions that is back to our original
discussion of philosophy i would say consciousness and free will for example are topics that are
very much so in the realm of philosophy currently yes i don't think they will always be i agree with
i agree with you and i think i am i'm fine with some topics being part of a different realm
than physics today because we don't have the right tools just like biology was i mean before we had
dna and all that genetics and all that gradually began to take hold i mean at the when mandolin
when people were beginning with various experiments with biology and chemistry and something gradually
they came together so it wasn't like together so yeah i'd be perfectly understanding of a
situation where we don't have the tools so do the experiments that you think as is defines the
consciousness in different form and gradually we'll build it and connect it and yes we might
discover new principles of nature that we didn't know i don't know but i would say that if they are
they'll be deeply connected with the else we don't we have never we have seen in physics
we don't have things in isolation you cannot you cannot compartmentalize you know this is gravity
this is electricity this is that we have learned they all talk to each other there's no way to
to make them you know in one corner and don't talk so the same thing with anything anything
which is real so consciousness is real so therefore we have to connect it to everything else so to me
once you connect that you cannot say it's not reality and once this reality is physics i call
it physics it may not be the physics i know today for sure it's not but but i wouldn't i would i would
be surprised if there's disconnected realities that you know you cannot you cannot imagine them as
the parts of the same soup so i guess god doesn't have a biology or chemistry textbook and mostly
or maybe uh he or she reads it for fun biology and chemistry but when you're trying to get some
work done it'll be going to the physics textbook okay uh what advice let's put on your wise
visionary hat what advice do you have for young people today you've um you've dedicated your book
actually to your kids to your family what advice would you give to them with what advice would you
give to young people today thinking about their career thinking about life of how to live successful
life how to live a good life yes uh yes i have three sons and in fact to them i have i have tried
not to give too much advice so even though i've tried to kind of not give advice maybe indirectly
that has been some impact my oldest one is doing biophysics for example and the the second one is
doing machine learning and the third one is doing theoretical computer science so there are there are
these facets of interest which which are not too far from my area but i have not tried to to impact
them in in that way but and they have followed their own interests and i think that's the advice i
would give to any young person follow your own interest and let it that take you wherever it
takes you um and this i did in my own case that uh i was planning to study economics and electrical
engineering when i started mit and you know i discovered that i'm more passionate about
math and physics and at that time i didn't feel math and physics would make a good career and so i
was kind of hesitant to go in that direction but i did because i i kind of felt that that's what i'm
driven to do so i didn't i don't regret it and i'm i'm lucky in the sense that you know society
supports people like me we're doing you know these abstract stuff which which may or may not be
experimentally verified even let alone apply to the daily technology in our lifetimes i'm lucky
i'm doing that and i feel that uh if people follow their interests they will find the niche that
they're good at and this coincidence of hopefully their interests and and uh abilities are kind of
aligned at least some extent to be able to drive them to something which is successful
and not to be driven by things like you know this doesn't make a good career or this doesn't do that
and my parents expect that or what about this and i think ultimately you have to live with yourself
and you only have one life and it's short very short i can tell you i'm getting i'm getting there
so i know it's short so you really want not to not to not to do things that you don't want to do
so i think follow your interests my strongest advice to young people yeah it's scary when your
interest doesn't directly map to a career of the past or of the day so you're almost anticipating
future careers that could be created it's scary um but yeah there's something to that especially
when the interest and the ability align that you will pay you will pave a path that will find a way
to make money especially in this society in the in in the capitalistic united states society it feels
like um ability and passion paves away yes at the very least you can sell funny t-shirts yes
you've mentioned uh life is short do you think about um your mortality are you afraid of death
uh i don't think about my mortality um i think that i don't think about my death and i don't think
about death in general too much first of all it's something that i can't too much about and i think
it's something that it doesn't it doesn't drive my everyday action it is natural to expect that it's
somewhat like the time reversal situation so we believe that we have this approximate symmetry
nature time reversal going forward we die going backwards we get born yeah so what was it if we
get born it wasn't such a good or bad feeling i have no feeling of it so you know who knows what
the death will feel like uh the moment of death or whatnot so i don't know it is not known but uh
in what form do we exist before after again it's something that it's uh it's partly philosophical
maybe i like how you draw comfort from symmetry it does seem that there is something asymmetric here
breaking of symmetry because there's there's something to the creative force of the human spirit
that goes only one way right that it seems the finiteness of life is the thing that drives the
creativity and so it does seem that that um at least the contemplation of the finiteness of life
of mortality is the thing that helps you get your stuff together yes i think that's true but actually
i have a different perspective on that a little bit yes namely uh suppose i told you you have your
immortal yes i think your life will be totally boring after that because you will not there's
i think part of the reason we have enjoyment in life is the finiteness of it yes and so i think
immortality might be a blessing and immortality may not so i think that we value things because
we have that finite life we we appreciate things we want to do this we want to do that we have
motivation if i told you you know you have infinite life oh i don't i don't need to do this today i have
another it's a billion or trillion or infinite life so why do i do now there is no motivation
a lot of the things that we do are driven by that finiteness the finiteness of this resources so i
think it is the blessing in disguise i don't regret it that we have more finite life and i think
i think that the the process of being part of this thing that you know the the reality
to me part of what attracts me to science is to connect to that immortality kind of namely the
loss the reality beyond us to me i'm i'm i'm resigned to the fact that not only me everybody's
going to die so this is a little bit of a consolation none of us are going to be around so
therefore okay and none of none of the people before me are around so therefore yeah okay this
is this something everybody goes through so so taking that minuscule version of okay how tiny
we are and how short time it is and so on to connect to the deeper truth beyond us the reality
beyond us is what sense of quote unquote immortality i would get namely i at least i can hang on to
this little piece of truth even though i know i know it's not complete i know it's going to be
imperfect i know it's going to change and it's going to be improved but having a little bit
deeper insight than than just the naïve thing around us little earth here and little galaxy and
so on makes me feel a little bit more uh more pleasure to to live this life so i think that's
the way i view my my role as a scientist yeah this the scarcity of this life helps us appreciate the
beauty of the the immortal the universal truths of that physics present us and maybe maybe one day
physics will will have something to say about that that beauty in itself explaining why the heck
it's so beautiful to appreciate the laws of physics and yet
why it's so tragic that we would die so quickly yes we die so quickly so that can be a bit longer
that's for sure it would be very nice maybe physics will help out well come on it was uh
an incredible conversation thank you so much once again for painting a beautiful picture
of the history of physics and it kind of presents a hopeful um view of the future of physics so i
really really appreciate that it's a huge honor that you talk to me and waste all your valuable
time with me i really appreciate it thanks lex it was a pleasure and i love talking with you
and this is a wonderful set of discussions i really enjoyed my time with this discussion thank you
thanks for listening to this conversation with kamar and wafa and thank you to headspace
jordan harmer just show square space and all form check them out in the description to support
the podcast and now let me leave you with some words from the great richard fineman physics
isn't the most important thing love is thank you for listening and hope to see you next time