Cumrun Vafa is a theoretical physicist at Harvard. Please support this podcast by checking out our sponsors:
- Headspace: https://headspace.com/lex to get free 1 month trial
- The Jordan Harbinger Show: https://www.youtube.com/thejordanharbingershow
- Squarespace: https://lexfridman.com/squarespace and use code LEX to get 10% off
- Allform: https://allform.com/lex to get 20% off

CORRECTIONS:
- I'm currently hiring folks to help me with editing and image overlays so there may be some errors in overlays (as in this episode) as we build up a team. I ask for your patience.
- At 1 hour 27 minute mark, we overlay an image of Brian Greene. We meant to overlay an image of Michael Green, an early pioneer of string theory: https://bit.ly/michael-green-physicist
- The image overlay of the heliocentric model is incorrect.

EPISODE LINKS:
Cumrun's Twitter: https://twitter.com/cumrunv
Cumrun's Website: https://www.cumrunvafa.org
Puzzles to Unravel the Universe (book): https://amzn.to/3BFk5ms

PODCAST INFO:
Podcast website: https://lexfridman.com/podcast
Apple Podcasts: https://apple.co/2lwqZIr
Spotify: https://spoti.fi/2nEwCF8
RSS: https://lexfridman.com/feed/podcast/
Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41

OUTLINE:
0:00 - Introduction
1:51 - Difference between math and physics
4:34 - Evolution of quantum mechanics
7:52 - Can mathematics lead humanity off track
8:51 - Beauty in mathematics
14:10 - Philosophers using symmetry
20:04 - How can ancient geometry be used to understand reality
23:16 - Key ideas in the history of physics
26:09 - Einstein's special relativity
29:46 - Physicists building intuition
37:44 - Best work by Einstein
39:28 - Quantum mechanics
49:30 - Quantum gravity
51:45 - String theory
1:07:54 - 10th Dimension
1:14:32 - Skepticism regarding string theory
1:25:37 - Key figures in string theory
1:29:56 - String Theory's Nobel Prize
1:33:01 - Edward Witten
1:41:39 - String Theory Landscape & Swamplands
1:50:29 - Theories of everything
2:04:55 - Advice for young people
2:07:57 - Death

SOCIAL:
- Twitter: https://twitter.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- Medium: https://medium.com/@lexfridman
- Reddit: https://reddit.com/r/lexfridman
- Support on Patreon: https://www.patreon.com/lexfridman

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 Harmer Deshow, Squarespace, and Allform.

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 1 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.

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.

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.

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 1 idea which is more important and we start with there and go to the next idea, next 1 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 1 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 mathematics sometimes does.

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 this switching back and forth between ideas makes us more fluid about a 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 seeing which 1 is a 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 1 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 1 place and then ending up at like the fourth step and realizing all along that the place you started at was wrong.

So is that happen 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 different starting place altogether?

Perhaps I give an example to see how it goes, and in fact, the historical example is Newton's work on classical mechanics.

So Newton formulated the laws of mechanics, you know, the force F equals to ma and his other laws, and they look very simple, elegant, and so forth.

Later, when we studied more examples of mechanics and other similar things, physicists came up with the idea that the notion of Potential is interesting.

Potential was an abstract idea which kind of came, you could take its gradient and relate it to the force, so you don't really need a 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 wanna 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.

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 1 which minimizes this integral or this action.

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

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 m a gives you the same fact that this path is a minimum 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 1 to the other doesn't take exactly 1 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 and the average correct.

When we say amplitude, do you mean probability?

Yes, the amplitude means if you sum up all these paths with 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 1 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 old 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.

Like say, oh, this is such a beautiful math.

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

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 that math plays, not to be antagonistic towards it and not to over-welcoming it.

What about looking at a particular characteristics of both physical ideas and mathematical ideas, which is beauty?

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 1 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.

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

So therefore, beauty is going to lead us somewhere.

It doesn't mean if you just have beauty, if I just look at something is beautiful, then I'm fine.

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

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

Partly is 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.

Like in both the visual space, like 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, it's kind of interesting.

It makes you wonder like, which 1 is the chicken or the egg?

Is symmetry the chicken in our conception of beauty of 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 this is just because we, 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.

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, 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, you know, 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.

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 new 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.

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, it'll 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.

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 that we had, but none of them are exactly correct and none of them are gonna 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, you know, 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.

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, that 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.

So these Greek philosophers are 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.

So they really want to deeply understand that fact.

And 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.

Aristotle didn't agree with this argument.

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

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 gonna get hungry, you're gonna move towards 1 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.

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

Because I could see a conception of the universe that kind of tends towards perfect symmetry and is stuck there, not stuck there, but achieves that optimal and stays there.

The idea that you would spontaneously break out of symmetry, like have these perturbations, jump out of symmetry and back.

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

And then the idea that you may not be at the center of the universe.

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 would 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.

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.

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

Platonic solids, the 5 solids they had discovered, had these beautiful solids, they thought it must be good for some reality.

They attached 1 to air, 1 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 3 dimensions.

Now, we know now, we kind of laugh at the way they were trying to connect that symmetry to the laws of 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 thoughts, processes in the following way.

In the context of string theory, which is the field life 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.

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 we sometimes we have, we ask the following question.

Suppose I want to get this particular, you know, physical reality.

I want to have this 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 2 spheres touching each other and shrinking to 0 size, that gives you strong forces.

If you have 1 of them, it gives you the weak forces.

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

So these geometrical translation of physics is 1 of my favorite things that we have discovered in modern physics in the context of strength theory.

The sad thing is when you go into multiple dimensions and we'll talk about it is we start to lose our capacity to visually intuit the world we're discussing.

And then we go into the realm of mathematics and we'll lose that.

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

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

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 string theory.

Sure, so I mentioned the classical mechanics and the Euler-Lagrange formulation.

See all Lex Fridman transcripts on Youtube

Cumrun Vafa: String Theory | Lex Fridman Podcast #204