back to indexCumrun Vafa: String Theory | Lex Fridman Podcast #204
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The following is a conversation with Kamran Valfa,
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a theoretical physicist at Harvard
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specializing in string theory.
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He is the winner of the 2017 Breakthrough Prize
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in Fundamental Physics,
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which is the most lucrative academic prize in the world.
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Quick mention of our sponsors,
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Headspace, Jordan Harmer's show,
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Squarespace, and Allform.
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Check them out in the description to support this podcast.
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As a side note, let me say that string theory
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is a theory of quantum gravity
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that unifies quantum mechanics and general relativity.
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It says that quarks, electrons, and all other particles
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are made up of much tinier strings of vibrating energy.
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They vibrate in 10 or more dimensions,
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depending on the flavor of the theory.
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Different vibrating patterns result in different particles.
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From its origins, for a long time,
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string theory was seen as too good not to be true,
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but has recently fallen out of favor
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in the physics community,
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partly because over the past 40 years,
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it has not been able to make any novel predictions
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that could then be validated through experiment.
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Nevertheless, to this day,
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it remains one of our best candidates
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for a theory of everything,
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or a theory that unifies the laws of physics.
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Let me mention that a similar story happened
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with neural networks
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in the field of artificial intelligence,
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where it fell out of favor
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after decades of promise and research,
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but found success again in the past decade
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as part of the deep learning revolution.
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So I think it pays to keep an open mind,
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since we don't know which of the ideas in physics
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may be brought back decades later
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and be found to solve the biggest mysteries
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in theoretical physics.
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String theory still has that promise.
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This is the Lex Friedman podcast,
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and here's my conversation with Kamran Wafa.
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What is the difference between mathematics
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Well, that's a difficult question,
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because in many ways,
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math and physics are unified in many ways.
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So to distinguish them is not an easy task.
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I would say that perhaps the goals
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of math and physics are different.
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Math does not care to describe reality, physics does.
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That's the major difference.
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But a lot of the thoughts, processes, and so on,
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which goes to understanding the nature and reality,
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are the same things that mathematicians do.
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So in many ways, they are similar.
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Mathematicians care about deductive reasoning,
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and physicists or physics in general,
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we care less about that.
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We care more about interconnection of ideas,
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about how ideas support each other,
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or if there's a puzzle, discord between ideas.
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That's more interesting for us.
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And part of the reason is that we have learned in physics
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that the ideas are not sequential.
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And if we think that there's one idea
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which is more important,
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and we start with there and go to the next idea,
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and next one, and deduce things from that,
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like mathematicians do,
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we have learned that the third or fourth thing
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we deduce from that principle
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turns out later on to be the actual principle.
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And from a different perspective,
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starting from there leads to new ideas,
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which the original one didn't lead to,
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and that's the beginning of a new revolution in science.
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So this kind of thing we have seen again and again
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in the history of science,
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we have learned to not like deductive reasoning
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because that gives us a bad starting point,
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to think that we actually have the original thought process
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should be viewed as the primary thought,
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and all these are deductions,
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like the way mathematicians sometimes do.
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So in physics, we have learned to be skeptical
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of that way of thinking.
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We have to be a bit open to the possibility
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that what we thought is a deduction of a hypothesis
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is actually the reason that's true is the opposite.
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And so we reverse the order.
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And so this switching back and forth between ideas
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makes us more fluid about deductive fashion.
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Of course, it sometimes gives a wrong impression
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like physicists don't care about rigor.
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They just say random things.
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They are willing to say things that are not backed
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by the logical reasoning.
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That's not true at all.
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So despite this fluidity
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in saying which one is a primary thought,
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we are very careful about trying to understand
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what we have really understood in terms of relationship
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So that's an important ingredient.
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And in fact, solid math, being behind physics
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is I think one of the attractive features
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of a physical law.
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So we look for beautiful math underpinning it.
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Can we dig into that process of starting from one place
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and then ending up at like the fourth step
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and realizing all along that the place you started at
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So is that happened when there's a discrepancy
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between what the math says
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and what the physical world shows?
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Is that how you then can go back
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and do the revolutionary idea
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for different starting place altogether?
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Perhaps I give an example to see how it goes.
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And in fact, the historical example is Newton's work
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on classical mechanics.
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So Newton formulated the laws of mechanics,
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the force F equals to MA and his other laws,
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and they look very simple, elegant, and so forth.
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Later, when we studied more examples of mechanics
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and other similar things, physicists came up with the idea
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that the notion of potential is interesting.
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Potential was an abstract idea, which kind of came,
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you could take its gradient and relate it to the force.
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So you don't really need it a priori,
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but it solved, helped some thoughts.
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And then later, Euler and Lagrange reformulated
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Newtonian mechanics in a totally different way
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in the following fashion.
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They said, if you take,
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if you wanna know where a particle at this point
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and at this time, how does it get to this point
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at the later time, is the following.
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You take all possible paths connecting this particle
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from going from the initial point to the final point,
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and you compute the action.
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And what is an action?
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Action is the integral over time
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of the kinetic term of the particle minus its potential.
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So you take this integral,
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and each path will give you some quantity.
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And the path it actually takes, the physical path,
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is the one which minimizes this integral or this action.
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Now, this sounded like a backward step from Newton's.
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Newton's formula seemed very simple.
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F equals to ma, and you can write F is minus
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the gradient of the potential.
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So why would anybody start formulating such a simple thing
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in terms of this complicated looking principle?
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You have to study the space of all paths and all things
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and find the minimum, and then you get the same equation.
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So what's the point?
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So Euler and Lagrange's formulation of Newton,
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which was kind of recasting in this language,
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is just a consequence of Newton's law.
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F equals to ma gives you the same fact
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that this path is a minimum action.
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Now, what we learned later, last century,
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was that when we deal with quantum mechanics,
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Newton's law is only an average correct.
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And the particle going from one to the other
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doesn't take exactly one path.
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It takes all the paths with the amplitude,
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which is proportional to the exponential
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of the action times an imaginary number, i.
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And so this fact turned out to be the reformulation
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of quantum mechanics.
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We should start there as the basis of the new law,
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which is quantum mechanics, and Newton is only
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an approximation on the average correct.
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And when you say amplitude, you mean probability?
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Yes, the amplitude means if you sum up all these paths
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with exponential i times the action,
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if you sum this up, you get the number, complex number.
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You square the norm of this complex number,
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gives you a probability to go from one to the other.
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Is there ways in which mathematics can lead us astray
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when we use it as a tool to understand the physical world?
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Yes, I would say that mathematics can lead us astray
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as much as old physical ideas can lead us astray.
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So if you get stuck in something,
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then you can easily fool yourself
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that just like the thought process,
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we have to free ourselves of that.
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Sometimes math does that role, like say,
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oh, this is such a beautiful math.
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I definitely want to use it somewhere.
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And so you just get carried away
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and you just get maybe carried too far away.
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So that is certainly true, but I wouldn't say
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it's more dangerous than old physical ideas.
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To me, new math ideas is as much potential
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to lead us astray as old physical ideas,
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which could be long held principles of physics.
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So I'm just saying that we should keep an open mind
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about the role the math plays,
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not to be antagonistic towards it
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and not to over, over welcoming it.
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We should just be open to possibilities.
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What about looking at a particular characteristics
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of both physical ideas and mathematical ideas,
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You think beauty leads us astray, meaning,
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and you offline showed me a really nice puzzle
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that illustrates this idea a little bit.
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Now, maybe you can speak to that or another example
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where beauty makes it tempting for us to assume
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that the law and the theory we found
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is actually one that perfectly describes reality.
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I think that beauty does not lead us astray
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because I feel that beauty is a requirement
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for principles of physics.
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So beauty is a fundamental in the universe?
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I think beauty is fundamental.
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At least that's the way many of us view it.
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It's not emergent.
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It's not emergent.
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I think Hardy is the mathematician who said
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that there's no permanent place for ugly mathematics.
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And so I think the same is true in physics
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that if we find the principle which looks ugly,
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we are not going to be, that's not the end stage.
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So therefore beauty is going to lead us somewhere.
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Now, it doesn't mean beauty is enough.
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It doesn't mean if you just have beauty,
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if I just look at something is beautiful, then I'm fine.
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No, that's not the case.
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Beauty is certainly a criteria that every good
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physical theory should pass.
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That's at least the view we have.
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Why do we have this view?
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That's a good question.
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It is partly, you could say, based on experience
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of science over centuries, partly is philosophical view
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of what reality is or should be.
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And in principle, it could have been ugly
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and we might have had to deal with it,
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but we have gotten maybe confident through examples
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in the history of science to look for beauty.
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And our sense of beauty seems to incorporate
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a lot of things that are essential for us
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to solve some difficult problems like symmetry.
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We find symmetry beautiful
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and the breaking of symmetry beautiful.
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Somehow symmetry is a fundamental part
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of how we conceive of beauty at all layers of reality,
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which is interesting.
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Like in both the visual space, like the way we look at art,
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we look at each other as human beings,
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the way we look at creatures in the biological space,
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the way we look at chemistry,
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and then into the physics world as the work you do.
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It's kind of interesting.
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It makes you wonder like,
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which one is the chicken or the egg?
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Is symmetry the chicken and our conception of beauty
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the egg or the other way around?
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Or somehow the fact that the symmetry is part of reality,
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it somehow creates a brain that then is able to perceive it.
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Or maybe this is just because we,
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maybe it's so obvious, it's almost trivial,
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that symmetry, of course,
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will be part of every kind of universe that's possible.
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And then any kind of organism that's able to observe
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that universe is going to appreciate symmetry.
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Well, these are good questions.
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We don't have a deep understanding
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of why we get attracted to symmetry.
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Why do laws of nature seem to have symmetries underlying
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them and the reasoning or the examples of whether,
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if there wasn't symmetry,
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we would have understood it or not.
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We could have said that, yeah, if there were, you know,
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things which didn't look that great,
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we could understand them.
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For example, we know that symmetries get broken
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and we have appreciated nature
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in the broken symmetry phase as well.
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The world we live in has many things
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which do not look symmetric,
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but even those have underlying symmetry
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when you look at it more deeply.
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So we have gotten maybe spoiled perhaps
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by the appearance of symmetry all over the place.
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And we look for it.
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And I think this is perhaps related to a sense of aesthetics
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that scientists have.
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And we don't usually talk about it among scientists.
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In fact, it's kind of a philosophical view
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of why do we look for simplicity or beauty or so forth.
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And I think in a sense, scientists are a lot
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like philosophers.
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Sometimes I think, especially modern science
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seems to shun philosophers and philosophical views.
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And I think at their peril, I think in my view,
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science owes a lot to philosophy.
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And in my view, many scientists, in fact,
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probably all good scientists
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are perhaps amateur philosophers.
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They may not state that they are philosophers
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or they may not like to be labeled philosophers,
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but in many ways what they do
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is like what is philosophical takes of things.
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Looking for simplicity or symmetry
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is an example of that in my opinion, or seeing patterns.
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You see, for example, another example of the symmetry
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is like how you come up with new ideas in science.
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You see, for example, an idea A
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is connected with an idea B.
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Okay, so you study this connection very deeply.
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And then you find the cousin of an idea A,
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let me call it A prime.
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And then you immediately look for B prime.
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If A is like B and if there's an A prime,
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then you look for B prime.
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Well, it completes the picture.
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Well, it's philosophically appealing
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to have more balance in terms of that.
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And then you look for B prime and lo and behold,
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you find this other phenomenon,
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which is a physical phenomenon, which you call B prime.
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So this kind of thinking motivates
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asking questions and looking for things.
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And it has guided scientists, I think, through many centuries
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and I think it continues to do so today.
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And I think if you look at the long arc of history,
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I suspect that the things that will be remembered
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is the philosophical flavor of the ideas of physics
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and chemistry and computer science and mathematics.
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Like, I think the actual details
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will be shown to be incomplete or maybe wrong,
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but the philosophical intuitions
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will carry through much longer.
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There's a sense in which, if it's true,
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that we haven't figured out most of how things work,
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currently, that it'll all be shown as wrong and silly.
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It'd almost be a historical artifact.
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But the human spirit, whatever,
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like the longing to understand,
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the way we perceive the world, the way we conceive of it,
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of our place in the world, those ideas will carry on.
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I completely agree.
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In fact, I believe that almost,
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well, I believe that none of the principles
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or laws of physics we know today are exactly correct.
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All of them are approximations to something.
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They are better than the previous versions that we had,
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but none of them are exactly correct,
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and none of them are gonna stand forever.
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So I agree that that's the process we are heading,
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And yes, indeed, the thought process
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and that philosophical take is common.
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So when we look at older scientists,
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or maybe even all the way back to Greek philosophers
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and the things that the way they thought and so on,
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almost everything they said about nature was incorrect.
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But the way they thought about it
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and many things that they were thinking
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is still valid today.
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For example, they thought about symmetry breaking.
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They were trying to explain the following.
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This is a beautiful example, I think.
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They had figured out that the Earth is round,
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and they said, okay, Earth is round.
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They have seen the length of the shadow of a meter stick,
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and they have seen that if you go
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from the equator upwards north,
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they find that depending on how far away you are,
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that the length of the shadow changes.
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And from that, they had even measured
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the radius of the Earth to good accuracy.
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That's brilliant, by the way, the fact that they did that.
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Very brilliant, very brilliant.
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So these Greek philosophers are very smart.
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And so they had taken it to the next step.
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They asked, okay, so the Earth is round,
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why doesn't it move?
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They thought it doesn't move.
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They were looking around, nothing seemed to move.
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So they said, okay, we have to have a good explanation.
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It wasn't enough for them to be there.
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So they really wanna deeply understand that fact.
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And they come up with a symmetry argument.
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And the symmetry argument was,
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oh, if the Earth is a spherical,
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it must be at the center of the universe for sure.
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So they said the Earth is at the center of the universe.
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And they said, if the Earth is going to move,
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which direction does it pick?
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Any direction it picks, it breaks that spherical symmetry
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because you have to pick a direction.
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And that's not good because it's not symmetrical anymore.
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So therefore, the Earth decides to sit put
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because it would break the symmetry.
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So they had the incorrect science.
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They thought Earth doesn't move.
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But they had this beautiful idea
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that symmetry might explain it.
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But they were even smarter than that.
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Aristotle didn't agree with this argument.
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He said, why do you think symmetry prevents it from moving?
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Because the preferred position?
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He gave an example.
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He said, suppose you are a person
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and we put you at the center of a circle
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and we spread food around you on a circle around you,
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loaves of bread, let's say.
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And we say, okay, stay at the center of the circle forever.
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Are you going to do that
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just because it's a symmetric point?
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No, you are going to get hungry.
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You're going to move towards one of those loaves of bread,
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despite the fact that it breaks the symmetry.
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So from this way, he tried to argue
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being at the symmetric point
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may not be the preferred thing to do.
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And this idea of spontaneous symmetry breaking
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is something we just use today
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to describe many physical phenomena.
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So spontaneous symmetry breaking
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is the feature that we now use.
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But this idea was there thousands of years ago,
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but applied incorrectly to the physical world,
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but now we are using it.
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So these ideas are coming back in different forms.
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So I agree very much that the thought process
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is more important and these ideas are more interesting
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than the actual applications that people may find today.
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Did they use the language of symmetry
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and the symmetry breaking and spontaneous symmetry breaking?
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That's really interesting.
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Because I could see a conception of the universe
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that kind of tends towards perfect symmetry
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and is stuck there, not stuck there,
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but achieves that optimal and stays there.
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The idea that you would spontaneously
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break out of symmetry, like have these perturbations,
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like jump out of symmetry and back,
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that's a really difficult idea to load into your head.
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Like where does that come from?
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And then the idea that you may not be
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at the center of the universe.
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That is a really tough idea.
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Right, so symmetry sometimes is an explanation
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of being at the symmetric point.
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It's sometimes a simple explanation of many things.
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Like if you have a bowl, a circular bowl,
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then the bottom of it is the lowest point.
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So if you put a pebble or something,
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it will slide down and go there at the bottom
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and stays there at the symmetric point
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because it's the preferred point, the lowest energy point.
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But if that same symmetric circular bowl that you had
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had a bump on the bottom, the bottom might not be
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at the center, it might be on a circle on the table,
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in which case the pebble would not end up at the center,
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it would be the lower energy point.
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Symmetrical, but it breaks the symmetry
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once it takes a point on that circle.
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So we can have symmetry reasoning for where things end up
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or symmetry breakings, like this example would suggest.
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We talked about beauty.
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I find geometry to be beautiful.
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You have a few examples that are geometric
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in nature in your book.
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How can geometry in ancient times or today
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be used to understand reality?
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And maybe how do you think about geometry
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as a distinct tool in mathematics and physics?
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Yes, geometry is my favorite part of math as well.
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And Greeks were enamored by geometry.
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They tried to describe physical reality using geometry
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and principles of geometry and symmetry.
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Platonic solids, the five solids they had discovered
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had these beautiful solids.
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They thought it must be good for some reality.
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There must be explaining something.
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They attached one to air, one to fire and so forth.
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They tried to give physical reality to symmetric objects.
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These symmetric objects are symmetries of rotation
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and discrete symmetry groups we call today
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of rotation group in three dimensions.
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Now, we know now, we kind of laugh at the way
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they were trying to connect that symmetry
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to the laws of the realities of physics.
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But actually it turns out in modern days,
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we use symmetries in not too far away
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exactly in these kinds of thoughts processes
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in the following way.
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In the context of string theory,
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which is the field light study,
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we have these extra dimensions.
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And these extra dimensions are compact tiny spaces typically
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but they have different shapes and sizes.
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We have learned that if these extra shapes and sizes
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have symmetries, which are related
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to the same rotation symmetries
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that the Greek we're talking about,
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if they enjoy those discrete symmetries
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and if you take that symmetry and caution the space by it,
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in other words, identify points under these symmetries,
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you get properties of that space at the singular points
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which force emanates from them.
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Forces like the ones we have seen in nature today,
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like electric forces, like strong forces, like weak forces.
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So these same principles that were driving them
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to connect geometry and symmetries to nature
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is driving today's physics,
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now much more modern ideas, but nevertheless,
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the symmetries connecting geometry to physics.
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In fact, often sometimes we ask the following question,
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suppose I want to get this particular physical reality,
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I wanna have this particles with these forces and so on,
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It turns out that you can geometrically design
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the space to give you that.
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You say, oh, I put the sphere here, I will do this,
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I will shrink them.
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So if you have two spheres touching each other
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and shrinking to zero size, that gives you strong forces.
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If you have one of them, it gives you the weak forces.
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If you have this, you get that.
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And if you want to unify forces, do the other thing.
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So these geometrical translation of physics
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is one of my favorite things that we have discovered
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in modern physics and the context of string theory.
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The sad thing is when you go into multiple dimensions
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and we'll talk about it is we start to lose our capacity
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to visually intuit the world we're discussing.
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And then we go into the realm of mathematics
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and we'll lose that.
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Unfortunately, our brains are such that we're limited.
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But before we go into that mysterious, beautiful world,
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let's take a small step back.
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And you also in your book have this kind of
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through the space of puzzles, through the space of ideas,
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have a brief history of physics, of physical ideas.
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Now, we talked about Newtonian mechanics leading all
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through different Lagrangian, Hamiltonian mechanics.
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Can you describe some of the key ideas
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in the history of physics?
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Maybe lingering on each from electromagnetism to relativity
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to quantum mechanics and to today,
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as we'll talk about with quantum gravity and string theory.
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Sure, so I mentioned the classical mechanics
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and the Euler Lagrangian formulation.
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One of the next important milestones for physics
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were the discoveries of laws of electricity and magnetism.
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So Maxwell put the discoveries all together
link |
in the context of what we call the Maxwell's equations.
link |
And he noticed that when he put these discoveries
link |
that Faraday's and others had made about electric
link |
and magnetic phenomena in terms of mathematical equations,
link |
it didn't quite work.
link |
There was a mathematical inconsistency.
link |
Now, one could have had two attitudes.
link |
One would say, okay, who cares about math?
link |
I'm doing nature, electric force, magnetic force,
link |
math I don't care about.
link |
But it bothered him.
link |
It was inconsistent.
link |
The equations he were writing, the two equations
link |
he had written down did not agree with each other.
link |
And this bothered him, but he figured out,
link |
if you add this jiggle, this equation
link |
by adding one little term there, it works.
link |
At least it's consistent.
link |
What is the motivation for that term?
link |
He said, I don't know.
link |
Have we seen it in experiments?
link |
Why did you add it?
link |
Well, because of mathematical consistency.
link |
So he said, okay, math forced him to do this term.
link |
He added this term, which we now today call the Maxwell term.
link |
And once he added that term, his equations were nice,
link |
differential equations, mathematically consistent,
link |
beautiful, but he also found the new physical phenomena.
link |
He found that because of that term,
link |
he could now get electric and magnetic waves
link |
moving through space at a speed that he could calculate.
link |
So he calculated the speed of the wave
link |
and lo and behold, he found it's the same
link |
as the speed of light, which puzzled him
link |
because he didn't think light had anything
link |
to do with electricity and magnetism.
link |
But then he was courageous enough to say,
link |
well, maybe light is nothing
link |
but these electric and magnetic fields moving around.
link |
And he wasn't alive to see the verification
link |
of that prediction and indeed it was true.
link |
So this mathematical inconsistency,
link |
which we could say this mathematical beauty drove him
link |
to this physical, very important connection
link |
between light and electric and magnetic phenomena,
link |
which was later confirmed.
link |
So then physics progresses and it comes to Einstein.
link |
Einstein looks at Maxwell's equation,
link |
says, beautiful, these are nice equation,
link |
except we get one speed light.
link |
Who measures this light speed?
link |
And he asked the question, are you moving?
link |
Are you not moving?
link |
If you move, the speed of light changes,
link |
but Maxwell's equation has no hint
link |
of different speeds of light.
link |
It doesn't say, oh, only if you're not moving,
link |
you get the speed, it's just you always get the speed.
link |
So Einstein was very puzzled and he was daring enough
link |
to say, well, you know, maybe everybody gets
link |
the same speed for light.
link |
And that motivated his theory of special relativity.
link |
And this is an interesting example
link |
because the idea was motivated from physics,
link |
from Maxwell's equations, from the fact
link |
that people try to measure the properties of ether,
link |
which was supposed to be the medium
link |
in which the light travels through.
link |
And the idea was that only in that medium,
link |
the speed of, if you're at risk with respect
link |
to the ether, the speed, the speed of light,
link |
then if you're moving, the speed changes
link |
and people did not discover it.
link |
Michelson and Morley's experiment showed there's no ether.
link |
So then Einstein was courageous enough to say,
link |
you know, light is the same speed for everybody,
link |
regardless of whether you're moving or not.
link |
And the interesting thing is about special theory
link |
of relativity is that the math underpinning it
link |
It's a linear algebra, nothing terribly deep.
link |
You can teach it at a high school level, if not earlier.
link |
Okay, does that mean Einstein's special relativity
link |
So this is an example where simple math, you know,
link |
linear algebra leads to deep physics.
link |
Einstein's theory of special relativity.
link |
Motivated by this inconsistency that Maxwell's equation
link |
would suggest for the speed of light,
link |
depending on who observes it.
link |
What's the most daring idea there,
link |
that the speed of light could be the same everywhere?
link |
That's the basic, that's the guts of it.
link |
That's the core of Einstein's theory.
link |
That statement underlies the whole thing.
link |
Speed of light is the same for everybody.
link |
It's hard to swallow and it doesn't sound right.
link |
It sounds completely wrong on the face of it.
link |
And it took Einstein to make this daring statement.
link |
It would be laughing in some sense.
link |
How could anybody make this possibly ridiculous claim?
link |
And it turned out to be true.
link |
How does that make you feel?
link |
Because it still sounds ridiculous.
link |
It sounds ridiculous until you learn
link |
that our intuition is at fault
link |
about the way we conceive of space and time.
link |
The way we think about space and time is wrong
link |
because we think about the nature of time as absolute.
link |
And part of it is because we live in a situation
link |
where we don't go with very high speeds.
link |
There are speeds that are small
link |
compared to the speed of light.
link |
And therefore the phenomena we observe
link |
does not distinguish the relativity of time.
link |
The time also depends on who measures it.
link |
There's no absolute time.
link |
When you say it's noon today and now,
link |
it depends on who's measuring it.
link |
And not everybody would agree with that statement.
link |
And to see that you would have to have fast observer
link |
moving speeds close to the speed of light.
link |
So this shows that our intuition is at fault.
link |
And a lot of the discoveries in physics
link |
precisely is getting rid of the wrong old intuition.
link |
And it is funny because we get rid of it,
link |
but it's always lingers in us in some form.
link |
Like even when I'm describing it,
link |
I feel like a little bit like, isn't it funny?
link |
As you're just feeling the same way.
link |
But we kind of replace it by an intuition.
link |
And actually there's a very beautiful example of this,
link |
how physicists do this, try to replace their intuition.
link |
And I think this is one of my favorite examples
link |
about how physicists develop intuition.
link |
It goes to the work of Galileo.
link |
So, again, let's go back to Greek philosophers
link |
or maybe Aristotle in this case.
link |
Now, again, let's make a criticism.
link |
He thought that the heavier objects fall faster
link |
than the lighter objects.
link |
It kind of makes sense.
link |
And people say about the feather and so on,
link |
but that's because of the air resistance.
link |
But you might think like,
link |
if you have a heavy stone and a light pebble,
link |
the heavy one will fall first.
link |
If you don't do any experiments,
link |
that's the first gut reaction.
link |
I would say everybody would say that's the natural thing.
link |
Galileo did not believe this.
link |
And he kind of did the experiment.
link |
Famously it said he went on the top of Pisa Tower
link |
and he dropped these heavy and light stones
link |
and they fell at the same time
link |
when he dropped it at the same time from the same height.
link |
So he said, I'm done.
link |
I've showed that the heavy and lighter objects
link |
fall at the same time.
link |
I did the experiment.
link |
Scientists at that time did not accept it.
link |
Because at that time, science was not just experimental.
link |
The experiment was not enough.
link |
They didn't think that they have to soil their hands
link |
in doing experiments to get to the reality.
link |
They said, why is it the case?
link |
So Galileo had to come up with an explanation
link |
of why heavier and lighter objects fall at the same rate.
link |
This is the way he convinced them using symmetry.
link |
He said, suppose you have three bricks,
link |
the same shape, the same size, same mass, everything.
link |
And we hold these three bricks at the same height
link |
Which one will fall to the ground first?
link |
Everybody said, of course, we know it's symmetry
link |
tells you they're all the same shape,
link |
same size, same height.
link |
Of course, they fall at the same time.
link |
Yeah, we know that.
link |
He said, okay, what if we move these bricks around
link |
with the same height?
link |
Does it change the time they hit the ground?
link |
They said, if it's the same height,
link |
again, by the symmetry principle,
link |
because the height translation horizontal
link |
translates to the symmetry, no, it doesn't matter.
link |
They all fall at the same rate.
link |
Does it matter how close I bring them together?
link |
Okay, suppose I make the two bricks touch
link |
and then let them go.
link |
Do they fall at the same rate?
link |
But then he said, well, the two bricks that touch
link |
are twice more mass than this other brick.
link |
And you just agreed that they fall at the same rate.
link |
They say, yeah, yeah, we just agreed.
link |
That's right, that's great.
link |
So he deconfused them by the symmetry reasoning.
link |
So this way of repackaging some intuition,
link |
a different type of intuition.
link |
When the intuitions clash,
link |
then you side on the, you replace the intuition.
link |
In some of these more difficult physical ideas,
link |
physics ideas in the 20th century and the 21st century,
link |
it starts becoming more and more difficult
link |
to then replace the intuition.
link |
What does the world look like
link |
for an object traveling close to the speed of light?
link |
You start to think about the edges
link |
of supermassive black holes,
link |
and you start to think like, what's that look like?
link |
Or I've been into gravitational waves recently.
link |
It's like when the fabric of space time
link |
is being morphed by gravity,
link |
like what's that actually feel like?
link |
If I'm riding a gravitational wave, what's that feel like?
link |
I mean, I think some of those are more sort of hippy,
link |
not useful intuitions to have,
link |
but if you're an actual physicist
link |
or whatever the particular discipline is,
link |
I wonder if it's possible to meditate,
link |
to sort of escape through thinking,
link |
prolong thinking and meditation on a world,
link |
like live in a visualized world that's not like our own
link |
in order to understand a phenomenon deeply.
link |
So like replace the intuition,
link |
like through rigorous meditation on the idea
link |
in order to conceive of it.
link |
I mean, if we talk about multiple dimensions,
link |
I wonder if there's a way to escape
link |
with a three dimensional world in our mind
link |
in order to then start to reason about it.
link |
It's, the more I talk to topologists,
link |
the more they seem to not operate at all
link |
in the visual space.
link |
They really trust the mathematics,
link |
like which is really annoying to me because topology
link |
and differential geometry feels like it has a lot
link |
of potential for beautiful pictures.
link |
Yes, I think they do.
link |
Actually, I would not be able to do my research
link |
if I don't have an intuitive feel about geometry.
link |
And we'll get to it as you mentioned before
link |
that how, for example, in strength theory,
link |
you deal with these extra dimensions.
link |
And I'll be very happy to describe how we do it
link |
because without intuition, we will not get anywhere.
link |
And I don't think you can just rely on formalism.
link |
I don't think any physicist just relies on formalism.
link |
That's not physics.
link |
That's not understanding.
link |
So we have to intuit it.
link |
And that's crucial.
link |
And there are steps of doing it.
link |
And we learned it might not be trivial,
link |
but we learn how to do it.
link |
Similar to what this Galileo picture I just told you,
link |
you have to build these gradually.
link |
But you have to connect the bricks.
link |
Exactly, you have to connect the bricks, literally.
link |
So yeah, so then, so going back to your question
link |
about the path of the history of the science.
link |
So I was saying about the electricity and magnetism
link |
and the special relativity where simple idea
link |
led to special relativity.
link |
But then he went further thinking about acceleration
link |
in the context of relativity.
link |
And he came up with general relativity
link |
where he talked about the fabric of space time
link |
being curved and so forth and matter
link |
affecting the curvature of the space and time.
link |
So this gradually became a connection
link |
between geometry and physics.
link |
Namely, he replaced Newton's gravitational force
link |
with a very geometrical, beautiful picture.
link |
It's much more elegant than Newton's,
link |
but much more complicated mathematically.
link |
So when we say it's simpler,
link |
we mean in some form it's simpler,
link |
but not in pragmatic terms of equation solving.
link |
The equations are much harder to solve
link |
in Einstein's theory.
link |
And in fact, so much harder that Einstein himself
link |
couldn't solve many of the cases.
link |
He thought, for example, you couldn't solve the equation
link |
for a spherical symmetric matter,
link |
like if you had a symmetric sun,
link |
he didn't think you can actually solve his equation for that.
link |
And a year after he said that it was solved by Schwarzschild.
link |
So it was that hard
link |
that he didn't think it's gonna be that easy.
link |
So yeah, deformism is hard.
link |
But the contrast between the special relativity
link |
and general relativity is very interesting
link |
because one of them has almost trivial math
link |
and the other one has super complicated math.
link |
Both are physically amazingly important.
link |
And so we have learned that, you know,
link |
the physics may or may not require complicated math.
link |
We should not shy from using complicated math
link |
like Einstein did.
link |
Nobody, Einstein wouldn't say,
link |
I'm not gonna touch this math because it's too much,
link |
you know, tensors or, you know, curvature
link |
and I don't like the four dimensional space time
link |
because I can't see four dimension.
link |
He wasn't doing that.
link |
He was willing to abstract from that
link |
because physics drove him in that direction.
link |
But his motivation was physics.
link |
Physics pushed him.
link |
Just like Newton pushed to develop calculus
link |
because physics pushed him that he didn't have the tools.
link |
So he had to develop the tools
link |
to answer his physics questions.
link |
So his motivation was physics again.
link |
So to me, those are examples which show
link |
that math and physics have this symbiotic relationship
link |
which kind of reinforce each other.
link |
Here I'm using, I'm giving you examples of both of them,
link |
namely Newton's work led to development
link |
of mathematics, calculus.
link |
And in the case of Einstein, he didn't develop
link |
Riemannian geometry, he just used them.
link |
So it goes both ways and in the context of modern physics,
link |
we see that again and again, it goes both ways.
link |
Let me ask a ridiculous question.
link |
You know, you talk about your favorite soccer player,
link |
the bar, I'll ask the same question about Einstein's ideas
link |
which is, which one do you think
link |
is the biggest leap of genius?
link |
Is it the E equals MC squared?
link |
Is it Brownian motion?
link |
Is it special relativity, is it general relativity?
link |
Which of the famous set of papers he's written in 1905
link |
and in general, his work was the biggest leap of genius?
link |
In my opinion, it's special relativity.
link |
The idea that speed of light is the same for everybody
link |
is the beginning of everything he did.
link |
The beginning is the seed.
link |
Once you embrace that weirdness,
link |
all the weirdness, all the rest.
link |
I would say that's, even though he says
link |
the most beautiful moment for him,
link |
he says that is when he realized that if you fall
link |
in an elevator, you don't know if you're falling
link |
or whether you're in the falling elevator
link |
or whether you're next to the earth, gravitational.
link |
That to him was his aha moment,
link |
which inertial mass and gravitational mass
link |
being identical geometrically and so forth
link |
as part of the theory, not because of, you know,
link |
some funny coincidence.
link |
That's for him, but I feel from outside at least,
link |
it feels like the speed of light being the same
link |
is the really aha moment.
link |
The general relativity to you is not
link |
like the conception of space time.
link |
In a sense, the conception of space time
link |
already was part of the special relativity
link |
when you talk about length contraction.
link |
So general relativity takes that to the next step,
link |
but beginning of it was already space,
link |
length contracts, time dilates.
link |
So once you talk about those, then yeah,
link |
you can dilate more or less different places
link |
than its curvature.
link |
So you don't have a choice.
link |
So it kind of started just with that same simple thought.
link |
Speed of light is the same for all.
link |
Where does quantum mechanics come into view?
link |
Exactly, so this is the next step.
link |
So Einstein's, you know, developed general relativity
link |
and he's beginning to develop the foundation
link |
of quantum mechanics at the same time,
link |
the photoelectric effects and others.
link |
And so quantum mechanics overtakes, in fact,
link |
Einstein in many ways because he doesn't like
link |
the probabilistic interpretation of quantum mechanics
link |
and the formulas that's emerging,
link |
but fits his march on and try to, for example,
link |
combine Einstein's theory of relativity
link |
with quantum mechanics.
link |
So Dirac takes special relativity,
link |
tries to see how is it compatible with quantum mechanics.
link |
Can we pause and briefly say what is quantum mechanics?
link |
So quantum mechanics, so I discussed briefly
link |
when I talked about the connection
link |
between Newtonian mechanics
link |
and the Euler Lagrange reformulation
link |
of the Newtonian mechanics and interpretation
link |
of this Euler Lagrange formulas in terms of the paths
link |
that the particle take.
link |
So when we say a particle goes from here to here,
link |
we usually think it classically follows
link |
a specific trajectory, but actually in quantum mechanics,
link |
it follows every trajectory with different probabilities.
link |
And so there's this fuzziness.
link |
Now, most probable, it's the path that you actually see
link |
and deviation from that is very, very unlikely
link |
and probabilistically very minuscule.
link |
So in everyday experiments,
link |
we don't see anything deviated from what we expect,
link |
but quantum mechanics tells us that the things
link |
Things are not as precise as the line you draw.
link |
Things are a bit like cloud.
link |
So if you go to microscopic scales,
link |
like atomic scales and lower,
link |
these phenomena become more pronounced.
link |
You can see it much better.
link |
The electron is not at the point,
link |
but the cloud spread out around the nucleus.
link |
And so this fuzziness, this probabilistic aspect of reality
link |
is what quantum mechanics describes.
link |
Can I briefly pause on that idea?
link |
Do you think quantum mechanics
link |
is just a really damn good approximation,
link |
a tool for predicting reality,
link |
or does it actually describe reality?
link |
Do you think reality is fuzzy at that level?
link |
Well, I think that reality is fuzzy at that level,
link |
but I don't think quantum mechanics
link |
is necessarily the end of the story.
link |
So quantum mechanics is certainly an improvement
link |
over classical physics.
link |
That much we know by experiments and so forth.
link |
Whether I'm happy with quantum mechanics,
link |
whether I view quantum mechanics,
link |
for example, the thought,
link |
the measurement description of quantum mechanics,
link |
am I happy with it?
link |
Am I thinking that's the end stage or not?
link |
I don't think we're at the end of that story.
link |
And many physicists may or may not view this way.
link |
Some do, some don't.
link |
But I think that it's the best we have right now,
link |
It's the best approximation for reality we know today.
link |
And so far, we don't know what it is,
link |
the next thing that improves it or replaces it and so on.
link |
But as I mentioned before,
link |
I don't believe any of the laws of physics we know today
link |
are permanently exactly correct.
link |
That doesn't bother me.
link |
I'm not like dogmatic saying,
link |
I have figured out this is the law of nature.
link |
I know everything.
link |
No, no, that's the beauty about science
link |
is that we are not dogmatic.
link |
And we are willing to, in fact,
link |
we are encouraged to be skeptical of what we ourselves do.
link |
So you were talking about Dirac.
link |
Yes, I was talking about Dirac, right.
link |
So Dirac was trying to now combine
link |
this Schrodinger's equations,
link |
which was described in the context of trying to talk about
link |
how these probabilistic waves of electrons
link |
move for the atom,
link |
which was good for speeds
link |
which were not too close to the speed of light,
link |
to what happens when you get to the near the speed of light.
link |
So then you need relativity.
link |
So then Dirac tried to combine Einstein's relativity
link |
with quantum mechanics.
link |
So he tried to combine them
link |
and he wrote this beautiful equation, the Dirac equation,
link |
which roughly speaking,
link |
take the square root of the Einstein's equation
link |
in order to connect it to Schrodinger's
link |
time evolution operator,
link |
which is first order in time derivative
link |
to get rid of the naive thing
link |
that Einstein's equation would have given,
link |
which is second order.
link |
So you have to take a square root.
link |
Now square root usually has a plus or minus sign
link |
And when he did this,
link |
he originally didn't notice this plus,
link |
didn't pay attention to this plus or minus sign,
link |
but later physicists pointed out to Dirac says,
link |
look, there's also this minus sign.
link |
And if you use this minus sign,
link |
you get negative energy.
link |
In fact, it was very, very annoying that, you know,
link |
somebody else tells you this obvious mistake you make.
link |
Pauli famous physicist told Dirac, this is nonsense.
link |
You're going to get negative energy with your equation,
link |
which negative energy without any bottom,
link |
you can go all the way down to negative.
link |
Infinite energy, so it doesn't make any sense.
link |
Dirac thought about it.
link |
And then he remembered Pauli's exclusion principle
link |
Pauli had said, you know,
link |
there's this principle called the exclusion principle
link |
that, you know, two electrons cannot be on the same orbit.
link |
And so Dirac said, okay, you know what?
link |
All these negative energy states are filled orbits,
link |
So according to you,
link |
Mr. Pauli, there's no place to go.
link |
So therefore they only have to go positive.
link |
Sounded like a big cheat.
link |
And then Pauli said, oh, you know what?
link |
We can change orbits from one orbit to another.
link |
What if I take one of these negative energy orbits
link |
and put it up there?
link |
Then it seems to be a new particle,
link |
which has opposite properties to the electron.
link |
It has positive energy, but it has positive charge.
link |
Dirac was a bit worried.
link |
He said, maybe that's proton
link |
because proton has plus charge.
link |
But then he said, oh, maybe it's proton.
link |
But then they said, no, no, no, no.
link |
It has the same mass as the electron.
link |
It cannot be proton because proton is heavier.
link |
He says, well, then maybe another part we haven't seen.
link |
By that time, Dirac himself was getting a little bit worried
link |
about his own equation and his own crazy interpretation.
link |
Until a few years later, Anderson,
link |
in the photographic place that he had gotten
link |
from these cosmic rays,
link |
he discovered a particle which goes
link |
in the opposite direction that the electron goes
link |
when there's a magnetic field,
link |
and with the same mass,
link |
exactly like what Dirac had predicted.
link |
And this was what we call now positron.
link |
And in fact, beginning with the work of Dirac,
link |
we know that every particle has an antiparticle.
link |
And so this idea that there's an antiparticle
link |
came from this simple math.
link |
There's a plus and a minus
link |
from the Dirac's quote unquote mistake.
link |
So again, trying to combine ideas,
link |
sometimes the math is smarter than the person
link |
who uses it to apply it,
link |
and you try to resist it,
link |
and then you kind of confront it by criticism,
link |
which is the way it should be.
link |
So physicists comes and said, no, no, that's wrong,
link |
and you correct it, and so on.
link |
So that is a development of the idea
link |
there's particle, there's antiparticle, and so on.
link |
So this is the beginning of development
link |
of quantum mechanics and the connection with relativity,
link |
but the thing was more challenging
link |
because we had to also describe
link |
how electric and magnetic fields work with quantum mechanics.
link |
This was much more complicated
link |
because it's not just one point.
link |
Electric and magnetic fields were everywhere.
link |
So you had to talk about fluctuating
link |
and a fuzziness of electrical fields
link |
and magnetic fields everywhere.
link |
And the math for that was very difficult to deal with.
link |
And this led to a subject called quantum field theory.
link |
Fields like electric and magnetic fields had to be quantum,
link |
had to be described also in a wavy way.
link |
Feynman in particular was one of the pioneers
link |
along with Schrodingers and others
link |
to try to come up with a formalism
link |
to deal with fields like electric and magnetic fields,
link |
interacting with electrons in a consistent quantum fashion.
link |
And they developed this beautiful theory,
link |
quantum electrodynamics from that.
link |
And later on that same formalism,
link |
quantum field theory led to the discovery of other forces
link |
and other particles all consistent
link |
with the idea of quantum mechanics.
link |
So that was how physics progressed.
link |
And so basically we learned that all particles
link |
and all the forces are in some sense related
link |
to particle exchanges.
link |
And so for example, electromagnetic forces
link |
are mediated by a particle we call photon and so forth.
link |
And same for other forces that they discovered,
link |
strong forces and the weak forces.
link |
So we got the sense of what quantum field theory is.
link |
Is that a big leap of an idea that particles
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are fluctuations in the field?
link |
Like the idea that everything is a field.
link |
It's the old Einstein, light is a wave,
link |
both a particle and a wave kind of idea.
link |
Is that a huge leap in our understanding
link |
of conceiving the universe as fields?
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I would say that viewing the particles,
link |
this duality that Bohr mentioned
link |
between particles and waves,
link |
that waves can behave sometimes like particles,
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sometimes like waves,
link |
is one of the biggest leaps of imagination
link |
that quantum mechanics made physics do.
link |
So I agree that that is quite remarkable.
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Is duality fundamental to the universe
link |
or is it just because we don't understand it fully?
link |
Like will it eventually collapse
link |
into a clean explanation that doesn't require duality?
link |
Like that a phenomena could be two things at once
link |
and both to be true.
link |
So that seems weird.
link |
So in fact I was going to get to that
link |
when we get to string theory
link |
but maybe I can comment on that now.
link |
Duality turns out to be running the show today
link |
and the whole thing that we are doing is string theory.
link |
Duality is the name of the game.
link |
So it's the most beautiful subject
link |
and I want to talk about it.
link |
Let's talk about it in the context of string theory then.
link |
So we do want to take a next step into,
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because we mentioned general relativity,
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we mentioned quantum mechanics,
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is there something to be said about quantum gravity?
link |
Yes, that's exactly the right point to talk about.
link |
So namely we have talked about quantum fields
link |
and I talked about electric forces,
link |
photon being the particle carrying those forces.
link |
So for gravity, quantizing gravitational field
link |
which is this curvature of space time according to Einstein,
link |
you get another particle called graviton.
link |
So what about gravitons?
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Should be there, no problem.
link |
So then you start computing it.
link |
What do I mean by computing it?
link |
Well, you compute scattering of one graviton
link |
off another graviton, maybe with graviton with an electron
link |
and so on, see what you get.
link |
Feynman had already mastered this quantum electrodynamics.
link |
He said, no problem, let me do it.
link |
Even though these are such weak forces,
link |
the gravity is very weak.
link |
So therefore to see them,
link |
these quantum effects of gravitational waves was impossible.
link |
It's even impossible today.
link |
So Feynman just did it for fun.
link |
He usually had this mindset that I want to do something
link |
which I will see in experiment,
link |
but this one, let's just see what it does.
link |
And he was surprised because the same techniques
link |
he was using for doing the same calculations,
link |
quantum electrodynamics, when applied to gravity failed.
link |
The formulas seem to make sense,
link |
but he had to do some integrals
link |
and he found that when he does those integrals,
link |
he got infinity and it didn't make any sense.
link |
Now there were similar infinities in the other pieces
link |
but he had managed to make sense out of those before.
link |
This was no way he could make sense out of it.
link |
He just didn't know what to do.
link |
He didn't feel it's an urgent issue
link |
because nobody could do the experiment.
link |
So he was kind of said, okay, there's this thing,
link |
but okay, we don't know how to exactly do it,
link |
but that's the way it is.
link |
So in some sense, a natural conclusion
link |
from what Feynman did could have been like,
link |
gravity cannot be consistent with quantum theory,
link |
but that cannot be the case
link |
because gravity is in our universe,
link |
quantum mechanics in our universe,
link |
they both together somehow should work.
link |
So it's not acceptable to say they don't work together.
link |
So that was a puzzle.
link |
How does it possibly work?
link |
And then we get to the string theory.
link |
So this is the puzzle of quantum gravity.
link |
The particle description of quantum gravity failed.
link |
So the infinity shows up.
link |
What do we do with infinity?
link |
Let's get to the fun part.
link |
Let's talk about string theory.
link |
Let's discuss some technical basics of string theory.
link |
What is string theory?
link |
How many dimensions are we talking about?
link |
What are the different states?
link |
How do we represent the elementary particles
link |
and the laws of physics using this new framework?
link |
So string theory is the idea
link |
that the fundamental entities are not particles,
link |
but extended higher dimensional objects
link |
like one dimensional strings, like loops.
link |
These loops could be open like with two ends,
link |
like an interval or a circle without any ends.
link |
And they're vibrating and moving around in space.
link |
So how big they are?
link |
Well, you can of course stretch it and make it big,
link |
or you can just let it be whatever it wants.
link |
It can be as small as a point
link |
because the circle can shrink to a point
link |
and be very light,
link |
or you can stretch it and becomes very massive,
link |
or it could oscillate and become massive that way.
link |
So it depends on which kind of state you have.
link |
In fact, the string can have infinitely many modes,
link |
depending on which kind of oscillation it's doing.
link |
Like a guitar has different harmonics,
link |
string has different harmonics,
link |
but for the string, each harmonic is a particle.
link |
So each particle will give you,
link |
ah, this is a more massive harmonic, this is a less massive.
link |
So the lightest harmonic, so to speak, is no harmonics,
link |
which means like the string shrunk to a point,
link |
and then it becomes like a massless particles
link |
or light particles like photon and graviton and so forth.
link |
So when you look at tiny strings,
link |
which are shrunk to a point, the lightest ones,
link |
they look like the particles that we think,
link |
they're like particles.
link |
In other words, from far away, they look like a point.
link |
But of course, if you zoom in,
link |
there's this tiny little circle that's there
link |
that's shrunk to almost a point.
link |
Should we be imagining, this is to the visual intuition,
link |
should we be imagining literally strings
link |
that are potentially connected as a loop or not?
link |
We knew, and when somebody outside of physics
link |
is imagining a basic element of string theory,
link |
which is a string,
link |
should we literally be thinking about a string?
link |
Yes, you should literally think about string,
link |
but string with zero thickness.
link |
With zero thickness.
link |
So notice, it's a loop of energy, so to speak,
link |
if you can think of it that way.
link |
And so there's a tension like a regular string,
link |
if you pull it, there's, you know, you have to stretch it.
link |
But it's not like a thickness, like you're made of something,
link |
It's not made of atoms or something like that.
link |
But it is very, very tiny.
link |
Much smaller than elementary particles of physics.
link |
So we think if you let the string to be by itself,
link |
the lowest state, there'll be like fuzziness
link |
or a size of that tiny little circle,
link |
which is like a point,
link |
about, could be anything between,
link |
we don't know the exact size,
link |
but in different models have different sizes,
link |
but something of the order of 10 to the minus,
link |
let's say 30 centimeters.
link |
So 10 to the minus 30 centimeters,
link |
just to compare it with the size of the atom,
link |
which is 10 to the minus eight centimeters,
link |
is 22 orders of magnitude smaller.
link |
Unimaginably small, I would say.
link |
So we basically think from far away,
link |
string is like a point particle.
link |
And that's why a lot of the things that we learned
link |
about point particle physics
link |
carries over directly to strings.
link |
So therefore there's not much of a mystery
link |
why particle physics was successful,
link |
because a string is like a particle
link |
when it's not stretched.
link |
But it turns out having this size,
link |
being able to oscillate, get bigger,
link |
turned out to be resolving this puzzles
link |
that Feynman was having in calculating his diagrams,
link |
and it gets rid of those infinities.
link |
So when you're trying to do those infinities,
link |
the regions that give infinities to Feynman,
link |
as soon as you get to those regions,
link |
then this string starts to oscillate,
link |
and these oscillation structure of the strings
link |
resolves those infinities to finite answer at the end.
link |
So the size of the string,
link |
the fact that it's one dimensional,
link |
gives a finite answer at the end.
link |
Resolves this paradox.
link |
Now, perhaps it's also useful to recount
link |
of how string theory came to be.
link |
Because it wasn't like somebody say,
link |
well, let me solve the problem of Einstein's,
link |
solve the problem that Feynman had with unifying
link |
Einstein's theory with quantum mechanics
link |
by replacing the point by a string.
link |
No, that's not the way the thought process,
link |
the thought process was much more random.
link |
Physicist, then it's John on this case,
link |
was trying to describe the interactions
link |
they were seeing in colliders, in accelerators.
link |
And they were seeing that some process,
link |
in some process, when two particles came together
link |
and joined together and when they were separately,
link |
in one way, and the opposite way, they behave the same way.
link |
In some way, there was a symmetry, a duality,
link |
which he didn't understand.
link |
The particles didn't seem to have that symmetry.
link |
He said, I don't know what it is,
link |
what's the reason that these colliders
link |
and experiments we're doing seems to have the symmetry,
link |
but let me write the mathematical formula,
link |
which exhibits that symmetry.
link |
He used gamma functions, beta functions and all that,
link |
you know, complete math, no physics,
link |
other than trying to get symmetry out of his equation.
link |
He just wrote down a formula as the answer for a process,
link |
not a method to compute it.
link |
Just say, wouldn't it be nice if this was the answer?
link |
Physics looked at this one, that's intriguing,
link |
it has the symmetry all right, but what is this?
link |
Where is this coming from?
link |
Which kind of physics gives you this?
link |
A few years later, people saw that,
link |
oh, the equation that you're writing,
link |
the process you're writing in the intermediate channels
link |
that particles come together,
link |
seems to have all the harmonics.
link |
Harmonics sounds like a string.
link |
Let me see if what you're describing
link |
has anything to do with the strings.
link |
And people try to see if what he's doing
link |
has anything to do with the strings.
link |
If I study scattering of two strings,
link |
I get exactly the formula you wrote down.
link |
That was the reinterpretation
link |
of what he had written in the formula as the strings,
link |
but still had nothing to do with gravity.
link |
It had nothing to do with resolving the problems
link |
of gravity with quantum mechanics.
link |
It was just trying to explain a process
link |
that people were seeing in hydronic physics collisions.
link |
So it took a few more years to get to that point.
link |
They did notice that,
link |
physicists noticed that whenever you try to find
link |
the spectrum of strings, you always get a massless particle
link |
which has exactly the properties
link |
that the graviton is supposed to have.
link |
And no particle in hydronic physics that had that property.
link |
You are getting a massless graviton
link |
as part of this scattering without looking for it.
link |
It was forced on you.
link |
People were not trying to solve quantum gravity.
link |
Quantum gravity was pushed on them.
link |
I don't want this graviton.
link |
They couldn't get rid of it.
link |
They gave up trying to get rid of it.
link |
Physicists, Sherk and Schwartz said,
link |
you know what, string theory is theory of quantum gravity.
link |
They've changed their perspective altogether.
link |
We are not describing the hydronic physics.
link |
We are describing this theory of quantum gravity.
link |
And that's when string theory probably got like exciting
link |
that this could be the unifying theory.
link |
Exactly, it got exciting,
link |
but at the same time, not so fast.
link |
Namely, it should have been fast, but it wasn't
link |
because particle physics through quantum field theory
link |
were so successful at that time.
link |
This is mid seventies, standard model of physics,
link |
electromagnetism and unification of electromagnetic forces
link |
with all the other forces were beginning to take place
link |
without the gravity part.
link |
Everything was working beautifully for particle physics.
link |
And so that was the shining golden age
link |
of quantum field theory and all the experiments,
link |
standard model, this and that, unification,
link |
spontaneous symmetry breaking was taking place.
link |
All of them was nice.
link |
This was kind of like a side show
link |
and nobody was paying so much attention.
link |
This exotic string is needed for quantum gravity.
link |
Maybe there's other ways, maybe we should do something else.
link |
So, yeah, it wasn't paid much attention to.
link |
And this took a little bit more effort
link |
to try to actually connect it to reality.
link |
There are a few more steps.
link |
First of all, there was a puzzle
link |
that you were getting extra dimensions.
link |
String was not working well
link |
with three spatial dimension on one time.
link |
It needed extra dimension.
link |
Now, there are different versions of strings,
link |
but the version that ended up being related
link |
to having particles like electron,
link |
what we call fermions, needed 10 dimensions,
link |
what we call super string.
link |
Why the word super?
link |
It turns out this version of the string,
link |
which had fermions, had an extra symmetry,
link |
which we call supersymmetry.
link |
This is a symmetry between a particle and another particle
link |
with exactly the same properties,
link |
same mass, same charge, et cetera.
link |
The only difference is that one of them
link |
has a little different spin than the other one.
link |
And one of them is a boson, one of them is a fermion
link |
because of that shift of spin.
link |
Otherwise, they're identical.
link |
So there was this symmetry.
link |
String theory had this symmetry.
link |
In fact, supersymmetry was discovered
link |
through string theory, theoretically.
link |
So theoretically, the first place that this was observed
link |
when you were describing these fermionic strings.
link |
So that was the beginning of the study of supersymmetry
link |
was via string theory.
link |
And then it had remarkable properties
link |
that the symmetry meant and so forth
link |
that people began studying supersymmetry after that.
link |
And that was a kind of a tangent direction
link |
at the beginning for string theory.
link |
But people in particle physics started also thinking,
link |
oh, supersymmetry is great.
link |
Let's see if we can have supersymmetry
link |
in particle physics and so forth.
link |
Forget about strings.
link |
And they developed on a different track as well.
link |
Supersymmetry in different models
link |
became a subject on its own right,
link |
understanding supersymmetry and what does this mean?
link |
Because it unified bosons and fermion,
link |
unified some ideas together.
link |
So photon is a boson, electron is a fermion.
link |
Could things like that be somehow related?
link |
It was a kind of a natural kind of a question
link |
to try to kind of unify
link |
because in physics, we love unification.
link |
Now, gradually, string theory was beginning
link |
to show signs of unification.
link |
It had graviton, but people found that you also have
link |
things like photons in them,
link |
different excitations of string behave like photons,
link |
another one behaves like electron.
link |
So a single string was unifying all these particles
link |
That's remarkable.
link |
It's in 10 dimensions though.
link |
It is not our universe
link |
because we live in three plus one dimension.
link |
How could that be possibly true?
link |
So this was a conundrum.
link |
It was elegant, it was beautiful,
link |
but it was very specific
link |
about which dimension you're getting,
link |
which structure you're getting.
link |
It wasn't saying, oh, you just put D equals to four,
link |
you'll get your space time dimension that you want.
link |
No, it didn't like that.
link |
It said, I want 10 dimensions and that's the way it is.
link |
So it was very specific.
link |
Now, so people try to reconcile this
link |
by the idea that, you know,
link |
maybe these extra dimensions are tiny.
link |
So if you take three macroscopic spatial dimensions
link |
on one time and six extra tiny spatial dimensions,
link |
like tiny spheres or tiny circles,
link |
then it avoids contradiction with manifest fact
link |
that we haven't seen extra dimensions in experiments today.
link |
So that was a way to avoid conflict.
link |
Now, this was a way to avoid conflict,
link |
but it was not observed in experiments.
link |
A string observed in experiments?
link |
No, because it's so small.
link |
So it's beginning to sound a little bit funny.
link |
Similar feeling to the way perhaps Dirac had felt
link |
about this positron plus or minus, you know,
link |
it was beginning to sound a little bit like,
link |
oh yeah, not only I have to have 10 dimension,
link |
but I have to have this, I have to also this.
link |
And so conservative physicists would say,
link |
hmm, you know, I haven't seen these experiments.
link |
I don't know if they are really there.
link |
Are you pulling my leg?
link |
Do you want me to imagine things that are not there?
link |
So this was an attitude of some physicists
link |
towards string theory, despite the fact
link |
that the puzzle of gravity and quantum mechanics
link |
merging together work, but still was this skepticism.
link |
You're putting all these things that you want me
link |
to imagine there, these extra dimensions
link |
that I cannot see, aha, aha.
link |
And you want me to believe that string
link |
that you have not even seen the experiments are real,
link |
aha, okay, what else do you want me to believe?
link |
So this kind of beginning to sound a little funny.
link |
Now, I will pass forward a little bit further.
link |
A few decades later, when string theory became
link |
the mainstream of efforts to unify the forces
link |
and particles together, we learned
link |
that these extra dimensions actually solved problems.
link |
They weren't a nuisance the way they originally appeared.
link |
First of all, the properties of these extra dimensions
link |
reflected the number of particles we got in four dimensions.
link |
If you took these six dimensions to have like five holes
link |
or four holes, change the number of particles
link |
that you see in four dimensional space time,
link |
you get one electron and one muon if you had this,
link |
but if you did the other J shape, you get something else.
link |
So geometrically, you could get different kinds of physics.
link |
So it was kind of a mirroring of geometry by physics
link |
down in the macroscopic space.
link |
So these extra dimension were becoming useful.
link |
Fine, but we didn't need the extra dimension
link |
to just write an electron in three dimensions,
link |
we did rewrote it, so what?
link |
Was there any other puzzle?
link |
Yes, there were, Hawking.
link |
Hawking had been studying black holes in mid 70s
link |
following the work of Bekenstein,
link |
who had predicted that black holes have entropy.
link |
So Bekenstein had tried to attach the entropy
link |
to the black hole.
link |
If you throw something into the black hole,
link |
the entropy seems to go down
link |
because you had something entropy outside the black hole
link |
and you throw it, black hole was unique,
link |
so the entropy did not have any, black hole had no entropy.
link |
So the entropy seemed to go down.
link |
And so that's against the laws of thermodynamics.
link |
So Bekenstein was trying to say, no, no,
link |
therefore black hole must have an entropy.
link |
So he was trying to understand that he found that
link |
if you assign entropy to be proportional
link |
to the area of the black hole, it seems to work.
link |
And then Hawking found not only that's correct,
link |
he found the correct proportionality factor
link |
of a one quarter of the area and Planck units
link |
is the correct amount of entropy.
link |
And he gave an argument using
link |
quantum semi classical arguments,
link |
which means basically using a little bit
link |
of a quantum mechanics,
link |
because he didn't have the full quantum mechanics
link |
of string theory, he could do some aspects
link |
of approximate quantum arguments.
link |
So he heuristic quantum arguments led
link |
to this entropy formula.
link |
But then he didn't answer the following question.
link |
He was getting a big entropy for the black hole,
link |
the black hole with the size of the horizon
link |
of a black hole is huge, has a huge amount of entropy.
link |
What are the microstates of this entropy?
link |
When you say, for example, the gas is entropy,
link |
you count where the atoms are,
link |
you count this bucket or that bucket,
link |
there's an information about there and so on, you count them.
link |
For the black hole, the way Hawking was thinking,
link |
there was no degree of freedom, you throw them in,
link |
and there was just one solution.
link |
So where are these entropy?
link |
What are these microscopic states?
link |
They were hidden somewhere.
link |
So later in string theory,
link |
the work that we did with my colleague Strominger,
link |
in particular showed that these ingredients
link |
in string theory of black hole arise
link |
from the extra dimensions.
link |
So the degrees of freedom are hidden
link |
in terms of things like strings,
link |
wrapping these extra circles in these hidden dimensions.
link |
And then we started counting how many ways
link |
like the strings can wrap around this circle
link |
and the extra dimension or that circle
link |
and counted the microscopic degrees of freedom.
link |
And lo and behold, we got the microscopic degrees
link |
of freedom that Hawking was predicting four dimensions.
link |
So the extra dimensions became useful
link |
for resolving a puzzle in four dimensions.
link |
The puzzle was where are the degrees of freedom
link |
of the black hole hidden?
link |
The answer, hidden in the extra dimensions.
link |
The tiny extra dimensions.
link |
So then by this time, it was beginning to,
link |
we see aspects that extra dimensions
link |
are useful for many things.
link |
It's not a nuisance.
link |
It wasn't to be kind of, you know, be ashamed of.
link |
It was actually in the welcome features.
link |
New feature, nevertheless.
link |
How do you intuit the 10 dimensional world?
link |
So yes, it's a feature for describing certain phenomena
link |
like the entropy in black holes,
link |
but what you said that to you a theory becomes real
link |
or becomes powerful when you can connect it
link |
to some deep intuition.
link |
So how do we intuit 10 dimensions?
link |
Yes, so I will explain how some of the analogies work.
link |
First of all, we do a lot of analogies.
link |
And by analogies, we build intuition.
link |
So I will start with this example.
link |
I will try to explain that if we are in 10 dimensional space,
link |
if we have a seven dimensional plane
link |
and eight dimensional plane,
link |
we ask typically in what space do they intersect each other
link |
in what dimension?
link |
That might sound like,
link |
how do you possibly give an answer to this?
link |
So we start with lower dimensions.
link |
We start with two dimensions.
link |
We say, if you have one dimension and a point,
link |
do they intersect typically on a plane?
link |
So a line one dimensional, a point zero dimension
link |
on a two dimensional plane, they don't typically meet.
link |
But if you have a one dimensional line and another line,
link |
which is one plus one on a plane,
link |
they typically intersect at a point.
link |
Typically means if you're not parallel,
link |
typically they intersect at a point.
link |
So one plus one is two and in two dimension,
link |
they intersect at the zero dimensional point.
link |
So you see two dimension, one and one, two,
link |
two minus two is zero.
link |
So you get point out of intersection.
link |
Let's go to three dimension.
link |
You have a plane, two dimensional plane and a point.
link |
Do they intersect?
link |
How about the plane and a line?
link |
A plane is two dimensional and a line is one.
link |
Two plus one is three.
link |
In three dimension, a plane and a line meet at points,
link |
which is zero dimensional.
link |
Three minus three is zero.
link |
Okay, so plane and a line intersect
link |
at a point in three dimension.
link |
How about the plane and a plane in 3D?
link |
Well, plane is two and this is two.
link |
Two plus two is four.
link |
In 3D, four minus three is one.
link |
They intersect on a one dimensional line.
link |
Okay, we're beginning to see the pattern.
link |
Okay, now come to the question.
link |
We're in 10 dimension.
link |
Now we have the intuition.
link |
We have a seven dimensional plane
link |
and eight dimensional plane in 10 dimension.
link |
They intersect on a plane.
link |
What's the dimension?
link |
Well, seven plus eight is 15 minus 10 is five.
link |
We draw the same picture as two planes
link |
and we write seven dimension, eight dimension,
link |
but we have gotten the intuition
link |
from the lower dimensional one.
link |
It doesn't scare us anymore.
link |
So we draw this picture.
link |
We cannot see all the seven dimensions
link |
by looking at this two dimensional visualization of it,
link |
but it has all the features we want.
link |
It has, so we draw this picture.
link |
It says seven, seven,
link |
and they meet at the five dimensional plane.
link |
So we have built this intuition.
link |
Now, this is an example of how we come up with intuition.
link |
Let me give you more examples of it
link |
because I think this will show you
link |
that people have to come up with intuitions to visualize it.
link |
Otherwise, we will be a little bit lost.
link |
So what you just described is kind of
link |
in these high dimensional spaces,
link |
focus on the meeting place of two planes
link |
in high dimensional spaces.
link |
Exactly, how the planes meet, for example,
link |
what's the dimension of their intersection and so on.
link |
So how do we come up with intuition?
link |
We borrow examples from lower dimensions,
link |
build up intuition and draw the same pictures
link |
as if we are talking about 10 dimensions,
link |
but we are drawing the same as a two dimensional plane
link |
because we cannot do any better.
link |
But our words change, but not our pictures.
link |
So your sense is we can have a deep understanding
link |
of reality by looking at its slices,
link |
at lower dimensional slices.
link |
And this brings me to the next example I wanna mention,
link |
Let's think about how do we think about the sphere?
link |
Well, the sphere is a sphere, the round nice thing,
link |
but sphere has a circular symmetry.
link |
Now, I can describe the sphere in the following way.
link |
I can describe it by an interval,
link |
which is thinking about this going from the north
link |
of the sphere to the south.
link |
And at each point, I have a circle attached to it.
link |
So you can think about the sphere as a line
link |
with a circle attached with each point,
link |
the circle shrinks to a point at end points
link |
So I can say, oh, one way to think about the sphere
link |
is an interval where at each point on that interval,
link |
there's another circle I'm not drawing.
link |
But if you like, you can just draw it.
link |
Say, okay, I won't draw it.
link |
So from now on, there's this mnemonic.
link |
I draw an interval when I wanna talk about the sphere
link |
and you remember that the end points of the interval
link |
mean a strong circle, that's all.
link |
And they say, yeah, I see, that's a sphere, good.
link |
Now, we wanna talk about the product of two spheres.
link |
That's four dimensional, how can I visualize it?
link |
Easy, you just take an interval and another interval,
link |
that's just gonna be a square.
link |
A square is a four dimensional space, yeah, why is that?
link |
Well, at each point on the square, there's two circles,
link |
one for each of those directions you drew.
link |
And when you get to the boundaries of each direction,
link |
one of the circles shrink on each edge of that square.
link |
And when you get to the corners of the square,
link |
all both circles shrink.
link |
This is a sphere times a sphere, I have defined interval.
link |
I just described for you a four dimensional space.
link |
Do you want a six dimensional space?
link |
No problem, take a corner of a room.
link |
In fact, if you want to have a sphere times a sphere
link |
times a sphere times a sphere, take a cube.
link |
A cube is a rendition of this six dimensional space,
link |
two sphere times another sphere times another sphere,
link |
where three of the circles I'm not drawing for you.
link |
For each one of those directions, there's another circle.
link |
But each time you get to the boundary of the cube,
link |
one circle shrinks.
link |
When the boundaries meet, two circles shrinks.
link |
When three boundaries meet, all the three circles shrink.
link |
So I just give you a picture.
link |
Now, mathematicians come up with amazing things.
link |
Like, you know what, I want to take a point in space
link |
You know, these concepts like topology and geometry,
link |
complicated, how do you do?
link |
In this picture, it's very easy.
link |
Blow it up in this picture means the following.
link |
You think about this cube, you go to the corner
link |
and you chop off a corner.
link |
Chopping off the corner replaces the point.
link |
Replace the point by a triangle.
link |
So you're blowing up a point and then this triangle
link |
is what they call P2, projective two space.
link |
But these pictures are very physical and you feel it.
link |
There's nothing amazing.
link |
I'm not talking about six dimension.
link |
Four plus six is 10, the dimension of string theory.
link |
So we can visualize it, no problem.
link |
Okay, so that's building the intuition
link |
to a complicated world of string theory.
link |
Nevertheless, these objects are really small.
link |
And just like you said, experimental validation
link |
is very difficult because the objects are way smaller
link |
than anything that we currently have the tools
link |
and accelerators and so on to reveal through experiment.
link |
So there's a kind of skepticism
link |
that's not just about the nature of the theory
link |
because of the 10 dimensions, as you've explained,
link |
but in that we can't experimentally validate it
link |
and it doesn't necessarily, to date,
link |
maybe you can correct me,
link |
predict something fundamentally new.
link |
So it's beautiful as an explaining theory,
link |
which means that it's very possible
link |
that it is a fundamental theory
link |
that describes reality and unifies the laws,
link |
but there's still a kind of skepticism.
link |
And me, from sort of an outside observer perspective,
link |
have been observing a little bit of a growing cynicism
link |
about string theory in the recent few years.
link |
Can you describe the cynicism about,
link |
sort of by cynicism I mean a cynicism
link |
about the hope for this theory
link |
of pushing theoretical physics forward?
link |
Can you do describe why this is cynicism
link |
and how do we reverse that trend?
link |
Yes, first of all, the criticism for string theory
link |
is healthy in a sense that in science
link |
we have to have different viewpoints and that's good.
link |
So I welcome criticism and the reason for criticism
link |
and I think that is a valid reason
link |
is that there has been zero experimental evidence
link |
for string theory.
link |
That is no experiment has been done
link |
to show that there's this loop of energy moving around.
link |
And so that's a valid objection and valid worry.
link |
And if I were to say, you know what,
link |
string theory can never be verified
link |
or experimentally checked, that's the way it is,
link |
they would have every right to say
link |
what you're talking about is not science.
link |
Because in science we will have to have
link |
experimental consequences and checks.
link |
The difference between string theory
link |
and something which is not scientific
link |
is that string theory has predictions.
link |
The problem is that the predictions we have today
link |
of string theory is hard to access by experiments
link |
available with the energies we can achieve
link |
with the colliders today.
link |
It doesn't mean there's a problem with string theory,
link |
it just means technologically we're not that far ahead.
link |
Now, we can have two attitudes.
link |
You say, well, if that's the case, why are you studying
link |
Because you can't do experiment today.
link |
Now, this is becoming a little bit more like mathematics
link |
You say, well, I want to learn,
link |
I want to know how the nature works
link |
even though I cannot prove it today
link |
that this is it because of experiments.
link |
That should not prevent my mind not to think about it.
link |
So that's the attitude many string theorists follow,
link |
that it should be like this.
link |
Now, so that's an answer to the criticism,
link |
but there's actually a better answer to the criticism,
link |
We don't have experimental evidence for string theory,
link |
but we have theoretical evidence for string theory.
link |
And what do I mean by theoretical evidence
link |
for string theory?
link |
String theory has connected different parts
link |
of physics together.
link |
It didn't have to.
link |
It has brought connections between part of physics,
link |
although suppose you're just interested
link |
in particle physics.
link |
Suppose you're not even interested in gravity at all.
link |
It turns out there are properties
link |
of certain particle physics models
link |
that string theory has been able to solve using gravity,
link |
using ideas from string theory,
link |
ideas known as holography,
link |
which is relating something which has to do with particles
link |
to something having to do with gravity.
link |
Why did it have to be this rich?
link |
The subject is very rich.
link |
It's not something we were smart enough to develop.
link |
As I explained to you,
link |
the development of string theory
link |
came from accidental discovery.
link |
It wasn't because we were smart enough
link |
to come up with the idea,
link |
oh yeah, string of course has gravity in it.
link |
No, it was accidental discovery.
link |
So some people say it's not fair to say
link |
we have no evidence for string theory.
link |
Graviton, gravity is an evidence for string theory.
link |
It's predicted by string theory.
link |
We didn't put it by hand, we got it.
link |
So there's a qualitative check.
link |
Okay, gravity is a prediction of string theory.
link |
It's a postdiction because we know gravity existed.
link |
But still, logically it is a prediction
link |
because really we didn't know it had the graviton
link |
that we later learned that, oh, that's the same as gravity.
link |
So literally that's the way it was discovered.
link |
It wasn't put in by hand.
link |
So there are many things like that,
link |
that there are different facets of physics,
link |
like questions in condensed matter physics,
link |
questions of particle physics,
link |
questions about this and that have come together
link |
to find beautiful answers by using ideas
link |
from string theory at the same time
link |
as a lot of new math has emerged.
link |
That's an aspect which I wouldn't emphasize
link |
as evidence to physicists necessarily,
link |
because they would say, okay, great, you got some math,
link |
but what's it do with reality?
link |
But as I explained, many of the physical principles
link |
we know of have beautiful math underpinning them.
link |
So it certainly leads further confidence
link |
that we may not be going astray,
link |
even though that's not the full proof as we know.
link |
So there are these aspects that give further evidence
link |
for string theory, connections between each other,
link |
connection with the real world,
link |
but then there are other things that come about
link |
and I can try to give examples of that.
link |
So these are further evidences
link |
and these are certain predictions of string theory.
link |
They are not as detailed as we want,
link |
but there are still predictions.
link |
Why is the dimension of space and time three plus one?
link |
Say, I don't know, just deal with it, three plus one.
link |
But in physics, we want to know why.
link |
Well, take a random dimension from one to infinity.
link |
What's your random dimension?
link |
A random dimension from one to infinity would not be four.
link |
Eight would most likely be a humongous number,
link |
I mean, there's no, if you choose any reasonable distribution
link |
which goes from one to infinity,
link |
three or four would not be your pick.
link |
The fact that we are in three or four dimension
link |
is already strange.
link |
The fact that strings are sorry,
link |
I cannot go beyond 10 or maybe 11 or something.
link |
The fact that there's this upper bound,
link |
the range is not from one to infinity,
link |
it's from one to 10 or 11 or whatnot,
link |
it already brings a natural prior.
link |
Oh yeah, three or four is just on the average.
link |
If you pick some of the compactification,
link |
then it could easily be that.
link |
So in other words, it makes it much more possible
link |
that it could be three of our universe.
link |
So the fact that the dimension already is so small,
link |
it should be surprising.
link |
We don't ask that question.
link |
We should be surprised because we could have conceived
link |
of universes with our pre dimension.
link |
Why is it that we have such a small dimension?
link |
That's number one.
link |
So good theory of the universe should give you
link |
an intuition of the why it's four or three plus one.
link |
And it's not obvious that it should be.
link |
That should be explained.
link |
We take that as an assumption,
link |
but that's a thing that should be explained.
link |
Yeah, so we haven't explained that in string theory.
link |
Actually, I did write a model within string theory
link |
to try to describe why we end up
link |
with three plus one space time dimensions,
link |
which are big compared to the rest of them.
link |
And even though this has not been,
link |
the technical difficulties to prove it is still not there,
link |
but I will explain the idea because the idea connects
link |
to some other piece of elegant math,
link |
which is the following.
link |
Consider a universe made of a box, three dimensional box.
link |
Or in fact, if we start in string theory,
link |
nine dimensional box,
link |
because we have nine spatial dimension on one time.
link |
So imagine a nine dimensional box.
link |
So we should imagine the box of a typical size of the string,
link |
So the universe would naturally start
link |
with a very tiny nine dimensional box.
link |
What do strings do?
link |
Well, strings go around the box
link |
and move around and vibrate and all that,
link |
but also they can wrap around one side of the box
link |
to the other because I'm imagining a box
link |
with periodic boundary conditions.
link |
So what we call the torus.
link |
So the string can go from one side to the other.
link |
This is what we call a winding string.
link |
The string can wind around the box.
link |
Now, suppose you have, you've now evolved the universe.
link |
Because there's energy, the universe starts to expand.
link |
But it doesn't expand too far.
link |
Well, because there are these strings
link |
which are wrapped around
link |
from one side of the wall to the other.
link |
When the universe, the walls of the universe are growing,
link |
it is stretching the string
link |
and the strings are becoming very, very massive.
link |
So it becomes difficult to expand.
link |
It kind of puts a halt on it.
link |
In order to not put a halt,
link |
a string which is going this way
link |
and a string which is going that way
link |
should intersect each other
link |
and disconnect each other and unwind.
link |
So a string which winds this way
link |
and the string which finds the opposite way
link |
should find each other to reconnect
link |
and this way disappear.
link |
So if they find each other and they disappear.
link |
But how can strings find each other?
link |
Well, the string moves and another string moves.
link |
A string is one dimensional, one plus one is two
link |
and one plus one is two and two plus two is four.
link |
In four dimensional space time, they will find each other.
link |
In a higher dimensional space time,
link |
they typically miss each other.
link |
So if the dimension were too big,
link |
they would miss each other,
link |
they wouldn't be able to expand.
link |
So in order to expand, they have to find each other
link |
and three of them can find each other
link |
and those can expand and the other one will be stuck.
link |
So that explains why within string theory,
link |
these particular dimensions are really big
link |
and full of exciting stuff.
link |
That could be an explanation.
link |
That's a model we suggested with my colleague Brandenberger.
link |
But it turns out to be related to a deep piece of math.
link |
You see, for mathematicians,
link |
manifolds of dimension bigger than four are simple.
link |
Four dimension is the hardest dimension for math,
link |
And it turns out the reason it's difficult is the following.
link |
It turns out that in higher dimension,
link |
you use what's called surgery in mathematical terminology,
link |
where you use these two dimensional tubes
link |
to maneuver them off of each other.
link |
So you have two plus two becoming four.
link |
In higher than four dimension,
link |
you can pass them through each other
link |
without them intersecting.
link |
In four dimension, two plus two
link |
doesn't allow you to pass them through each other.
link |
So the same techniques that work in higher dimension
link |
don't work in four dimension because two plus two is four.
link |
The same reasoning I was just telling you
link |
about strings finding each other in four
link |
ends up to be the reason why four is much more complicated
link |
to classify for mathematicians as well.
link |
So there might be these things.
link |
So I cannot say that this is the reason
link |
that string theory is giving you three plus one,
link |
but it could be a model for it.
link |
And so there are these kinds of ideas
link |
that could underlie why we have three extra dimensions
link |
which are large and the rest of them are small.
link |
But absolutely, we have to have a good reason.
link |
We cannot leave it like that.
link |
Can I ask a tricky human question?
link |
So you are one of the seminal figures in string theory.
link |
You got the Breakthrough Prize.
link |
You've worked with Edward Witten.
link |
There's no Nobel Prize that has been given on string theory.
link |
Credit assignment is tricky in science.
link |
It makes you quite sad, especially big, like LIGO,
link |
big experimental projects when so many incredible people
link |
have been involved and yet the Nobel Prize is annoying
link |
in that it's only given to three people.
link |
Who do you think gets the Nobel Prize
link |
for string theory at first?
link |
If it turns out that it, if not in full, then in part,
link |
is a good model of the way the physics of the universe works.
link |
Who are the key figures?
link |
Maybe let's put Nobel Prize aside.
link |
Who are the key figures?
link |
Okay, I like the second version of the question.
link |
Because I think to try to give a prize to one person
link |
in string theory doesn't do justice to the diversity
link |
So there was quite a lot of incredible people
link |
in the history of string theory.
link |
Quite a lot of people.
link |
I mean, starting with Veneziano,
link |
who wasn't talking about strings.
link |
I mean, he wrote down the beginning of the strings.
link |
We cannot ignore that for sure.
link |
And so you start with that and you go on
link |
with various other figures and so on.
link |
So there are different epochs in string theory
link |
and different people have been pushing it.
link |
And so for example, the early epoch,
link |
we just told you people like Veneziano,
link |
and Nambu, and the Susskind, and others were pushing it.
link |
Green and Schwarz were pushing it and so forth.
link |
So this was, or Scherck and so on.
link |
So these were the initial periods of pioneers,
link |
I would say, of string theory.
link |
And then there were the mid 80s that Edward Witten
link |
was the major proponent of string theory.
link |
And he really changed the landscape of string theory
link |
in terms of what people do and how we view it.
link |
And I think his efforts brought a lot of attention
link |
to the community of string theory.
link |
To the community about high energy community
link |
to focus on this effort as the correct theory
link |
of unification of forces.
link |
So he brought a lot of research as well as, of course,
link |
the first rate work he himself did to this area.
link |
So that's in mid 80s and onwards,
link |
and also in mid 90s where he was one of the proponents
link |
of the duality revolution in string theory.
link |
And with that came a lot of these other ideas
link |
that led to breakthroughs involving, for example,
link |
the example I told you about black holes and holography,
link |
and the work that was later done by Maldacena
link |
about the properties of duality between particle physics
link |
and quantum gravity and the deeper connections
link |
of holography, and it continues.
link |
And there are many people within this range,
link |
which I haven't even mentioned.
link |
They have done fantastic important things.
link |
How it gets recognized, I think, is secondary,
link |
in my opinion, than the appreciation
link |
that the effort is collective.
link |
That, in fact, that to me is the more important part
link |
of science that gets forgotten.
link |
For some reason, humanity likes heroes,
link |
and science is no exception.
link |
We like heroes, but I personally try to avoid that trap.
link |
I feel, in my work, most of my work is with colleagues.
link |
I have much more collaborations than sole author papers,
link |
and I enjoy it, and I think that that's, to me,
link |
one of the most satisfying aspects of science
link |
is to interact and learn and debate ideas with colleagues
link |
because that influx of ideas enriches it,
link |
and that's why I find it interesting.
link |
To me, science, if I was on an island,
link |
and if I was developing string theory by myself
link |
and had nothing to do with anybody,
link |
it would be much less satisfying, in my opinion.
link |
Even if I could take credit I did it,
link |
it won't be as satisfying.
link |
Sitting alone with a big metal drinking champagne, no.
link |
I think, to me, the collective work is more exciting,
link |
and you mentioned my getting the breakthrough.
link |
When I was getting it, I made sure to mention
link |
that it is because of the joint work
link |
that I've done with colleagues.
link |
At that time, it was around 180 or so collaborators,
link |
and I acknowledged them in the webpage for them.
link |
I write all of their names
link |
and the collaborations that led to this.
link |
So, to me, science is fun when it's collaboration,
link |
and yes, there are more important
link |
and less important figures, as in any field,
link |
and that's true, that's true in string theory as well,
link |
but I think that I would like to view this
link |
as a collective effort.
link |
So, setting the heroes aside,
link |
the Nobel Prize is a celebration of,
link |
what's the right way to put it,
link |
that this idea turned out to be right.
link |
So, like, you look at Einstein
link |
didn't believe in black holes,
link |
and then black holes got their Nobel Prize.
link |
Do you think string theory will get its Nobel Prize,
link |
Nobel Prizes, if you were to bet money?
link |
If this was an investment meeting
link |
and we had to bet all our money,
link |
do you think he gets the Nobel Prizes?
link |
I think it's possible that none of the living physicists
link |
will get the Nobel Prize in string theory,
link |
but somebody will.
link |
Because, unfortunately, the technology available today
link |
is not very encouraging
link |
in terms of seeing directly evidence for string theory.
link |
Do you think it ultimately boils down to
link |
the Nobel Prize will be given
link |
when there is some direct or indirect evidence?
link |
There would be, but I think that part of this
link |
breakthrough prize was precisely the appreciation
link |
that when we have sufficient evidence,
link |
theoretical as it is, not experiment,
link |
because of this technology lag,
link |
you appreciate what you think is the correct path.
link |
So, there are many people who have been recognized precisely
link |
because they may not be around
link |
when it actually gets experimented,
link |
even though they discovered it.
link |
So, there are many things like that
link |
that's going on in science.
link |
So, I think that I would want to attach less significance
link |
to the recognitions of people.
link |
And I have a second review on this,
link |
which is there are people who look at these works
link |
that people have done and put them together
link |
and make the next big breakthrough.
link |
And they get identified with, perhaps rightly,
link |
with many of these new visions.
link |
But they are on the shoulders of these little scientists.
link |
Which don't get any recognition.
link |
You know, yeah, you did this little work.
link |
Oh yeah, you did this little work.
link |
Oh yeah, yeah, five of you.
link |
Oh yeah, these showed this pattern.
link |
And then somebody else, it's not fair.
link |
To me, those little guys, which kind of like,
link |
like seem to do the little calculation here,
link |
a little thing there, which doesn't rise to the occasion
link |
of this grandiose kind of thing,
link |
doesn't make it to the New York Times headlines and so on,
link |
deserve a lot of recognition.
link |
And I think they don't get enough.
link |
I would say that there should be this Nobel prize
link |
for, you know, they have these Doctors Without Borders,
link |
they're a huge group.
link |
They should do a similar thing.
link |
And these String Theors Without Borders kind of,
link |
everybody is doing a lot of work.
link |
And I think that I would like to see that effort recognized.
link |
I think in the long arc of history,
link |
we're all little guys and girls
link |
standing on the shoulders of each other.
link |
I mean, it's all going to look tiny in retrospect.
link |
If we celebrate, the New York Times,
link |
you know, as a newspaper,
link |
or the idea of a newspaper in a few centuries from now
link |
will be long forgotten.
link |
Yes, I agree with that.
link |
Especially in the context of String Theory,
link |
we should have a very long term view.
link |
Just as a tiny tangent, we mentioned Edward Witten.
link |
And he, in a bunch of walks of life for me as an outsider,
link |
comes up as a person who is widely considered as like
link |
one of the most brilliant people in the history of physics,
link |
just as a powerhouse of a human,
link |
like the exceptional places that a human mind can rise to.
link |
You've gotten the chance to work with him.
link |
Yes, more than that.
link |
He was my advisor, PhD advisor.
link |
So I got to know him very well
link |
and I benefited from his insights.
link |
In fact, what you said about him is accurate.
link |
He is not only brilliant,
link |
but he is also multifaceted in terms of the impact
link |
he has had in not only physics, but also mathematics.
link |
He has gotten the Fields Medal
link |
because of his work in mathematics.
link |
And rightly so, he has used his knowledge of physics
link |
in a way which impacted deep ideas in modern mathematics.
link |
And that's an example of the power of these ideas
link |
in modern high energy physics and string theory,
link |
the applicability of it to modern mathematics.
link |
So he's quite an exceptional individual.
link |
We don't come across such people a lot in history.
link |
So I think, yes, indeed,
link |
he's one of the rare figures in this history of subject.
link |
He has had great impact on a lot of aspects
link |
of not just string theory,
link |
a lot of different areas in physics,
link |
and also, yes, in mathematics as well.
link |
So I think what you said about him is accurate.
link |
I had the pleasure of interacting with him as a student
link |
and later on as colleagues writing papers together
link |
What impact did he have on your life?
link |
Like what have you learned from him?
link |
If you were to look at the trajectory of your mind
link |
of the way you approach science and physics and mathematics,
link |
how did he perturb that trajectory in a way?
link |
Yes, he did actually.
link |
So I can explain because when I was a student,
link |
I had the biggest impact by him,
link |
clearly as a grad student at Princeton.
link |
So I think that was a time where I was a little bit confused
link |
about the relation between math and physics.
link |
I got a double major in mathematics and physics
link |
at MIT because I really enjoyed both.
link |
And I liked the elegance and the rigor of mathematics.
link |
And I liked the power of ideas in physics
link |
and its applicability to reality
link |
and what it teaches about the real world around us.
link |
But I saw this tension between rigorous thinking
link |
in mathematics and lack thereof in physics.
link |
And this troubled me to no end.
link |
I was troubled by that.
link |
So I was at crossroads when I decided
link |
to go to graduate school in physics
link |
because I did not like some of the lack of rigors
link |
I was seeing in physics.
link |
On the other hand, to me, mathematics,
link |
even though it was rigorous,
link |
I didn't see the point of it.
link |
In other words, the math theorem by itself could be beautiful
link |
but I really wanted more than that.
link |
I wanted to say, okay, what does it teach us
link |
about something else, something more than just math?
link |
So I wasn't that enamored with just math
link |
but physics was a little bit bothersome.
link |
Nevertheless, I decided to go to physics
link |
and I decided to go to Princeton
link |
and I started working with Edward Witten
link |
as my thesis advisor.
link |
And at that time I was trying to put physics
link |
in rigorous mathematical terms.
link |
I took quantum field theory.
link |
I tried to make rigorous out of it and so on.
link |
And no matter how hard I was trying,
link |
I was not being able to do that.
link |
And I was falling behind from my classes.
link |
I was not learning much physics
link |
and I was not making it rigorous.
link |
And to me, it was this dichotomy between math and physics.
link |
I like math but this is not exactly this.
link |
There comes Edward Witten as my advisor
link |
and I see him in action thinking about math and physics.
link |
He was amazing in math.
link |
He knew all about the math.
link |
It was no problem with him.
link |
But he thought about physics in a way
link |
which did not find this tension between the two.
link |
It was much more harmonious.
link |
For him, he would draw the Feynman diagrams
link |
but he wouldn't view it as a formalism.
link |
He was viewed, oh yeah, the particle goes over there
link |
and this is what's going on.
link |
And so wait, you're thinking really,
link |
is this particle, this is really electron going there?
link |
It's not the form or the result perturbation.
link |
You just feel like the electron.
link |
You're moving with this guy and do that and so on.
link |
And you're thinking invariantly about physics
link |
or the way he thought about relativity.
link |
Like I was thinking about this momentum system.
link |
He was thinking invariantly about physics,
link |
just like the way you think about invariant concepts
link |
and relativity, which don't depend on the frame of reference.
link |
He was thinking about the physics in invariant ways,
link |
the way that doesn't, that gives you a bigger perspective.
link |
So this gradually helped me appreciate
link |
that interconnections between ideas and physics
link |
replaces mathematical rigor.
link |
That the different facets reinforce each other.
link |
They say, oh, I cannot rigorously define
link |
what I mean by this,
link |
but this thing connects with this other physics I've seen
link |
and this other thing.
link |
And they together form an elegant story.
link |
And that replaced for me what I believed as a solidness,
link |
which I found in math as a rigor, solid.
link |
I found that replaced the rigor and solidness in physics.
link |
So I found, okay, that's the way you can hang onto.
link |
It is not wishy washy.
link |
It's not like somebody is just not being able to prove it,
link |
just making up a story.
link |
It was more than that.
link |
And it was no tension with mathematics.
link |
In fact, mathematics was helping it, like friends.
link |
And so much more harmonious and gives insights to physics.
link |
So that's, I think, one of the main things I learned
link |
from interactions with Witten.
link |
And I think that now perhaps I have taken that
link |
Maybe he wouldn't go this far as I have.
link |
Namely, I use physics to define new mathematics
link |
in a way which would be far less rigorous
link |
than a physicist might necessarily believe,
link |
because I take the physical intuition,
link |
perhaps literally in many ways that could teach us about.
link |
So now I've gained so much confidence
link |
in physical intuition that I make bold statements
link |
that sometimes takes math friends off guard.
link |
So an example of it is mirror symmetry.
link |
So we were studying these compactification
link |
of string geometries.
link |
This is after my PhD now.
link |
I've, by the time I come to Harvard,
link |
we're studying these aspects of string compactification
link |
on these complicated manifolds,
link |
six dimensional spaces called Kalabial manifolds,
link |
And I noticed with a couple other colleagues
link |
that there was a symmetry in physics suggested
link |
between different Kalabials.
link |
It suggested that you couldn't actually compute
link |
the Euler characteristic of a Kalabia.
link |
Euler characteristic is counting the number of points
link |
minus the number of edges plus the number of faces minus.
link |
So you can count the alternating sequence
link |
of properties of a space,
link |
which is a topological property of a space.
link |
So Euler characteristics of the Kalabia
link |
was a property of the space.
link |
And so we noticed that from the physics formalism,
link |
if string moves in a Kalabia,
link |
you cannot distinguish,
link |
we cannot compute the Euler characteristic.
link |
You can only compute the absolute value of it.
link |
Now this bothered us
link |
because how could you not compute the actual sign
link |
unless the both sides were the same?
link |
So I conjectured maybe for every Kalabia
link |
with Euler characteristics positive,
link |
there's one with negative.
link |
I told this to my colleague Yao
link |
who's namesake is Kalabia,
link |
that I'm making this conjecture.
link |
Is it possible that for every Kalabia,
link |
there's one with the opposite Euler characteristic?
link |
Sounds not reasonable.
link |
He said, well, we know more Kalabias
link |
with negative Euler characteristics than positive.
link |
I said, but physics says we cannot distinguish them.
link |
At least I don't see how.
link |
So we conjectured that for every Kalabia
link |
with one sign, there's the other one,
link |
despite the mathematical evidence,
link |
despite the mathematical evidence,
link |
despite the expert telling us it's not the right idea.
link |
If a few years later, this symmetry, mirror symmetry
link |
between the sign with the opposite sign
link |
was later confirmed by mathematicians.
link |
So this is actually the opposite view.
link |
That is physics is so sure about it
link |
that you're going against the mathematical wisdom,
link |
telling them they better look for it.
link |
So taking the physical intuition literally
link |
and then having that drive the mathematics.
link |
And now we are so confident about many such examples
link |
that has affected modern mathematics in ways like this,
link |
that we are much more confident
link |
about our understanding of what string theory is.
link |
These are another aspects,
link |
other aspects of why we feel string theory is correct.
link |
It's doing these kinds of things.
link |
I've been hearing your talk quite a bit
link |
about string theory, landscape and the swamp land.
link |
What the heck are those two concepts?
link |
Okay, very good question.
link |
So let's go back to what I was describing about Feynman.
link |
Feynman was trying to do these diagrams for graviton
link |
and electrons and all that.
link |
He found that he's getting infinities he cannot resolve.
link |
Okay, the natural conclusion is that field theories
link |
and gravity and quantum theory don't go together
link |
and you cannot have it.
link |
So in other words, field theories and gravity
link |
are inconsistent with quantum mechanics, period.
link |
String theory came up with examples
link |
but didn't address the question more broadly
link |
that is it true that every field theory
link |
can be coupled to gravity in a quantum mechanical way?
link |
It turns out that Feynman was essentially right.
link |
Almost all particle physics theories,
link |
no matter what you add to it,
link |
when you put gravity in it, doesn't work.
link |
Only rare exceptions work.
link |
So string theory are those rare exceptions.
link |
So therefore the general principle
link |
that Feynman found was correct.
link |
Quantum field theory and gravity and quantum mechanics
link |
don't go together except for Joule's exceptional cases.
link |
There are exceptional cases.
link |
Okay, the total vastness of quantum field theories
link |
that are there we call the set of quantum field theories,
link |
Which ones can be consistently coupled to gravity?
link |
We call that subspace the landscape.
link |
The rest of them we call the swampland.
link |
It doesn't mean they are bad quantum field theories,
link |
they are perfectly fine.
link |
But when you couple them to gravity,
link |
they don't make sense, unfortunately.
link |
And it turns out that the ratio of them,
link |
the number of theories which are consistent with gravity
link |
to the ones without,
link |
the ratio of the area of the landscape
link |
to the swampland, in other words, is measure zero.
link |
So the swampland's infinitely large?
link |
The swampland's infinitely large.
link |
So let me give you one example.
link |
Take a theory in four dimension with matter
link |
with maximum amount of supersymmetry.
link |
Can you get, it turns out a theory in four dimension
link |
with maximum amount of supersymmetry
link |
is characterized just with one thing, a group.
link |
What we call the gauge group.
link |
Once you pick a group, you have to find the theory.
link |
Okay, so does every group make sense?
link |
As far as quantum field theory, every group makes sense.
link |
There are infinitely many groups,
link |
there are infinitely many quantum field theories.
link |
But it turns out there are only finite number of them
link |
which are consistent with gravity out of that same list.
link |
So you can take any group but only finite number of them,
link |
the ones who's, what we call the rank of the group,
link |
the ones whose rank is less than 23.
link |
Any one bigger than rank 23 belongs to the swampland.
link |
There are infinitely many of them.
link |
They're beautiful field theories,
link |
but not when you include gravity.
link |
So then this becomes a hopeful thing.
link |
So in other words, in our universe, we have gravity.
link |
Therefore, we are part of that jewel subset.
link |
Now, is this jewel subset small or large?
link |
It turns out that subset is humongous,
link |
but we believe still finite.
link |
The set of possibilities is infinite,
link |
but the set of consistent ones,
link |
I mean, the set of quantum field theories are infinite,
link |
but the consistent ones are finite, but humongous.
link |
The fact that they're humongous
link |
is the problem we are facing in string theory,
link |
because we do not know which one of these possibilities
link |
the universe we live in.
link |
If we knew, we could make more specific predictions
link |
about our universe.
link |
And that is one of the challenges when string theory,
link |
which point on the landscape,
link |
which corner of this landscape do we live in?
link |
Well, there are principles that are beginning to emerge.
link |
So I will give you one example of it.
link |
You look at the patterns of what you're getting
link |
in terms of these good ones,
link |
the ones which are in the landscape
link |
compared to the ones which are not.
link |
You find certain patterns.
link |
I'll give you one pattern.
link |
You find in all the ones that you get from string theory,
link |
gravitational force is always there,
link |
but it's always, always the weakest force.
link |
However, you could easily imagine field theories
link |
for which gravity is not the weakest force.
link |
For example, take our universe.
link |
If you take mass of the electron,
link |
if you increase the mass of electron by a huge factor,
link |
the gravitational attraction of the electrons
link |
will be bigger than the electric repulsion
link |
between two electrons.
link |
And the gravity will be stronger.
link |
It happens that it's not the case in our universe
link |
because electron is very tiny in mass compared to that.
link |
Just like our universe, gravity is the weakest force.
link |
We find in all these other ones,
link |
which are part of the good ones,
link |
the gravity is the weakest force.
link |
This is called the weak gravity conjecture.
link |
We conjecture that all the points in the landscape
link |
have this property.
link |
Our universe being just an example of it.
link |
So there are these qualitative features
link |
that we are beginning to see.
link |
But how do we argue for this?
link |
Just by looking patterns?
link |
Just by looking string theory as this?
link |
No, that's not enough.
link |
We need more reason, more better reasoning.
link |
And it turns out there is.
link |
The reasoning for this turns out to be studying black holes.
link |
Ideas of black holes turn out to put certain restrictions
link |
of what a good quantum filter should be.
link |
It turns out using black hole,
link |
the fact that the black holes evaporate,
link |
the fact that the black holes evaporate
link |
gives you a way to check the relation
link |
between the mass and the charge of elementary particle.
link |
Because what you can do, you can take a charged particle
link |
and throw it into a charged black hole
link |
and wait it to evaporate.
link |
And by looking at the properties of evaporation,
link |
you find that if it cannot evaporate particles
link |
whose mass is less than their charge,
link |
then it will never evaporate.
link |
You will be stuck.
link |
And so the possibility of a black hole evaporation
link |
forces you to have particles whose mass
link |
is sufficiently small so that the gravity is weaker.
link |
So you connect this fact to the other fact.
link |
So we begin to find different facts
link |
that reinforce each other.
link |
So different parts of the physics reinforce each other.
link |
And once they all kind of come together,
link |
you believe that you're getting the principle correct.
link |
So weak gravity conjecture
link |
is one of the principles we believe in
link |
as a necessity of these conditions.
link |
So these are the predictions string theory are making.
link |
Well, it's qualitative.
link |
It's a semi quantity.
link |
It's just the mass of the electron
link |
should be less than some number.
link |
But that number is, if I call that number one,
link |
the mass of the electron
link |
turns out to be 10 to the minus 20 actually.
link |
So it's much less than one.
link |
But on the other hand,
link |
there's a similar reasoning for a big black hole
link |
And if that evaporation should take place,
link |
gives you another restriction,
link |
tells you the mass of the electron
link |
is bigger than 10 to the,
link |
now in this case, bigger than something.
link |
It shows bigger than 10 to the minus 30 in the Planck unit.
link |
the mass of the electron should be less than one,
link |
but bigger than 10 to the minus 30.
link |
the mass of the electron is 10 to the minus 20.
link |
Okay, now this kind of you could call postiction,
link |
but I would say it follows from principles
link |
that we now understand from string theory, first principle.
link |
So we are making, beginning to make
link |
these kinds of predictions,
link |
which are very much connected to aspects of particle physics
link |
that we didn't think are related to gravity.
link |
We thought, just take any electron mass you want.
link |
What's the problem?
link |
It has a problem with gravity.
link |
And so that conjecture
link |
has also a happy consequence
link |
that it explains that our universe,
link |
like why the heck is gravity so weak as a force
link |
and that's not only an accident, but almost a necessity
link |
if these forces are to coexist effectively?
link |
Exactly, so that's the reinforcement
link |
of what we know in our universe,
link |
but we are finding that as a general principle.
link |
So we want to know what aspects of our universe
link |
like the weak gravity conjecture and other aspects.
link |
How much of them do we understand?
link |
Can we have particles lighter than neutrinos?
link |
Or maybe that's not possible.
link |
You see the neutrino mass,
link |
it turns out to be related to dark energy
link |
in a mysterious way.
link |
Naively, there's no relation between dark energy
link |
and the mass of a particle.
link |
We have found arguments
link |
from within the swampland kind of ideas,
link |
why it has to be related.
link |
And so there are beginning to be these connections
link |
between graph consistency of quantum gravity
link |
and aspects of our universe gradually being sharpened.
link |
But we are still far from a precise quantitative prediction
link |
like we have to have such and such, but that's the hope,
link |
that we are going in that direction.
link |
Coming up with the theory of everything
link |
that unifies general relativity and quantum field theory
link |
is one of the big dreams of human civilization.
link |
Us descendants of apes wondering about how this world works.
link |
So a lot of people dream.
link |
What are your thoughts about sort of other out there ideas,
link |
theories of everything or unifying theories?
link |
So there's a quantum loop gravity.
link |
There's also more sort of like a friend of mine,
link |
Eric Weinstein beginning to propose
link |
something called geometric unity.
link |
So these kinds of attempts,
link |
whether it's through mathematical physics
link |
or through other avenues,
link |
or with Stephen Wolfram,
link |
a more computational view of the universe.
link |
Again, in his case, it's these hyper graphs
link |
that are very tiny objects as well.
link |
Similarly, a string theory
link |
and trying to grapple with this world.
link |
What do you think?
link |
Is there any of these theories that are compelling to you,
link |
that are interesting that may turn out to be true
link |
or at least may turn out to contain ideas that are useful?
link |
Yes, I think the latter.
link |
I would say that the containing ideas that are true
link |
is my opinion was what some of these ideas might be.
link |
For example, loop quantum gravity
link |
is to me not a complete theory of gravity in any sense,
link |
but they have some nuggets of truth in them.
link |
And typically what I expect to happen,
link |
and I have seen examples of this within string theory,
link |
aspects which we didn't think are part of string theory
link |
come to be part of it.
link |
For example, I'll give you one example.
link |
String was believed to be 10 dimensional.
link |
And then there was this 11 dimensional super gravity.
link |
Nobody know what the heck is that?
link |
Why are we getting 11 dimensional super gravity
link |
whereas string is saying it should be 10 dimensional?
link |
11 was the maximum dimension you can have a super gravity,
link |
but string was saying, sorry, we're 10 dimensional.
link |
So for a while we thought that theory is wrong
link |
because how could it be?
link |
Because string theory is definitely a theory of everything.
link |
We later learned that one of the circles
link |
of string theory itself was tiny,
link |
that we had not appreciated that fact.
link |
And we discovered by doing thought experiments
link |
of string theory that there's gotta be an extra circle
link |
and that circle is connected
link |
to an 11 dimensional perspective.
link |
And that's what later on got called M theory.
link |
So there are these kinds of things
link |
that we do not know what exactly string theory is.
link |
We're still learning.
link |
So we do not have a final formulation of string theory.
link |
It's very well could be the different facets
link |
of different ideas come together
link |
like loop quantum gravity or whatnot,
link |
but I wouldn't put them on par.
link |
Namely, loop quantum gravity is a scatter of ideas
link |
about what happens to space when they get very tiny.
link |
For example, you replace things by discrete data
link |
and try to quantize it and so on.
link |
And it sounds like a natural idea to quantize space.
link |
If you were naively trying to do quantum space,
link |
you might think about trying to take points
link |
and put them together in some discrete fashion
link |
in some way that is reminiscent of loop quantum gravity.
link |
String theory is more subtle than that.
link |
For example, I will just give you an example.
link |
And this is the kind of thing that we didn't put in by hand,
link |
And so it's more subtle than,
link |
so what happens if you squeeze the space
link |
to be smaller and smaller?
link |
Well, you think that after a certain distance,
link |
the notion of distance should break down.
link |
You know, when you go smaller than Planck scale,
link |
should break down.
link |
What happens in string theory?
link |
We do not know the full answer to that,
link |
but we know the following.
link |
Namely, if you take a space
link |
and bring it smaller and smaller,
link |
if the box gets smaller than the Planck scale
link |
by a factor of 10,
link |
it is equivalent by the duality transformation
link |
to a space which is 10 times bigger.
link |
So there's a symmetry called T duality,
link |
which takes L to one over L.
link |
Well, L is measured in Planck units,
link |
or more precisely string units.
link |
This inversion is a very subtle effect.
link |
And I would not have been,
link |
or any physicist would not have been able to design a theory
link |
which has this property,
link |
that when you make the space smaller,
link |
it is as if you're making it bigger.
link |
That means there is no experiment you can do
link |
to distinguish the size of the space.
link |
This is remarkable.
link |
For example, Einstein would have said,
link |
of course I can't measure the size of the space.
link |
Well, I take a flashlight,
link |
I send the light around,
link |
measure how long it takes for the light
link |
to go around the space,
link |
and bring back and find the radius
link |
or circumference of the universe.
link |
What's the problem?
link |
I said, well, suppose you do that,
link |
and you shrink it.
link |
He said, well, it gets smaller and smaller.
link |
I said, well, it turns out in string theory,
link |
there are two different kinds of photons.
link |
One photon measures one over L,
link |
the other one measures L.
link |
And so this duality reformulates.
link |
And when the space gets smaller,
link |
it says, oh no, you better use the bigger perspective
link |
because the smaller one is harder to deal with.
link |
So you do this one.
link |
So these examples of loop quantum gravity
link |
have none of these features.
link |
These features that I'm telling you about,
link |
we have learned from string theory.
link |
But they nevertheless have some of these ideas
link |
like topological gravity aspects
link |
are emphasized in the context of loop quantum gravity
link |
And so these ideas might be there in some kernel,
link |
in some corners of string theory.
link |
In fact, I wrote a paper about topological string theory
link |
and some connections with potentially loop quantum gravity,
link |
which could be part of that.
link |
So there are little facets of connections.
link |
I wouldn't say they're complete,
link |
but I would say most probably what will happen
link |
to some of these ideas, the good ones at least,
link |
they will be absorbed to string theory,
link |
if they are correct.
link |
Let me ask a crazy out there question.
link |
Can physics help us understand life?
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So we spoke so confidently about the laws of physics
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being able to explain reality.
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But, and we even said words like theory of everything,
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implying that the word everything
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is actually describing everything.
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Is it possible that the four laws we've been talking about
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are actually missing,
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they are accurate in describing what they're describing,
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but they're missing the description
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of a lot of other things,
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like emergence of life
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and emergence of perhaps consciousness.
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So is there, do you ever think about this kind of stuff
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where we would need to understand extra physics
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to try to explain the emergence of these complex pockets
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of interesting weird stuff that we call life
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and consciousness in this big homogeneous universe
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that's mostly boring and nothing is happening yet?
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So first of all, we don't claim that string theory
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is the theory of everything in the sense that
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we know enough what this theory is.
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We don't know enough about string theory itself,
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we are learning it.
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So I wouldn't say, okay, give me whatever,
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I will tell you how it works, no.
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However, I would say by definition,
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by definition to me physics is checking all reality.
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Any form of reality, I call it physics,
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that's my definition.
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I mean, I may not know a lot of it,
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like maybe the origin of life and so on,
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maybe a piece of that,
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but I would call that as part of physics.
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To me, reality is what we're after.
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I don't claim I know everything about reality.
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I don't claim string theory necessarily has the tools
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right now to describe all the reality either,
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but we are learning what it is.
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So I would say that I would not put a border to say,
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no, from this point onwards, it's not my territory,
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it's somebody else's.
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But whether we need new ideas in string theory
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to describe other reality features, for sure I believe,
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as I mentioned, I don't believe any of the laws
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we know today is final.
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So therefore, yes, we will need new ideas.
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This is a very tricky thing for us to understand
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and be precise about.
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But just because you understand the physics
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doesn't necessarily mean that you understand
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the emergence of chemistry, biology, life,
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intelligence, consciousness.
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So those are built, it's like you might understand
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the way bricks work, but to understand what it means
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to have a happy family, you don't get from the bricks.
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So directly, in theory you could,
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if you ran the universe over again,
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but just understanding the rules of the universe
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doesn't necessarily give you a sense
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of the weird, beautiful things that emerge.
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Right, no, so let me describe what you just said.
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So there are two questions.
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One is whether or not the techniques I use
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in let's say quantum field theory and so on
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will describe how the society works.
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Okay, that's far different scales of questions
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that we're asking here.
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The question is, is there a change of,
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is there a new law which takes over
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that cannot be connected to the older laws
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that we know, or more fundamental laws that we know?
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Do you need new laws to describe it?
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I don't think that's necessarily the case
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in many of these phenomena like chemistry
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or so on you mentioned.
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So we do expect in principle chemistry
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can be described by quantum mechanics.
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We don't think there's gonna be a magical thing,
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but chemistry is complicated.
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Yeah, indeed, there are rules of chemistry
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that chemists have put down which has not been explained yet
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using quantum mechanics.
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Do I believe that they will be something
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described by quantum mechanics?
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I don't think they are going to be sitting there
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in this just forever, but maybe it's too complicated
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and maybe we'll wait for very powerful quantum computers
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or whatnot to solve those problems.
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But I don't think in that context
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we have new principles to be added to fix those.
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So I'm perfectly fine in the intermediate situation
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to have rules of thumb or principles that chemists have found
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which are working, which are not founded
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on the basis of quantum mechanical laws, which does the job.
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Similarly, as biologists do not found everything
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in terms of chemistry, but they think,
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there's no reason why chemistry cannot.
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They don't think necessarily they're doing something
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amazingly not possible with chemistry.
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Coming back to your question,
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does consciousness, for example, bring this new ingredient?
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If indeed it needs a new ingredient,
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I will call that new ingredient part of physical law.
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We have to understand it.
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To me that, so I wouldn't put a line to say,
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okay, from this point onwards, it's disconnected.
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It's fully disconnected from string theory or whatever.
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We have to do something else.
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What I'm referring to is can physics of a few centuries
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from now that doesn't understand consciousness
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be much bigger than the physics of today,
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where the textbook grows?
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It definitely will.
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I would say, it will grow.
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I don't know if it grows because of consciousness
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being part of it or we have different view of consciousness.
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I do not know where the consciousness will fit.
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It's gonna be hard for me to guess.
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I mean, I can make random guesses now
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which probably most likely is wrong,
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but let me just do just for the sake of discussion.
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I could say, brain could be their quantum computer,
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classical computer.
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Their arguments against this being a quantum thing,
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so it's probably classical, and if it's classical,
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it could be like what we are doing in machine learning,
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slightly more fancy and so on.
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Okay, people can go to this argument to no end
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and to some whether consciousness exists or not,
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or life, does it have any meaning?
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Or is there a phase transition where you can say,
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does electron have a life or not?
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At what level does a particle become life?
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Maybe there's no definite definition of life
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in that same way that, we cannot say electron,
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if you, I like this example quite a bit.
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We distinguish between liquid and a gas phase,
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like water is liquid or vapor is gas,
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and we say they're different.
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You can distinguish them.
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Actually, that's not true.
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It's not true because we know from physics
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that you can change temperatures and pressure
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to go from liquid to the gas
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without making any phase transition.
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So there is no point that you can say this was a liquid
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and this was a gas.
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You can continuously change the parameters
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to go from one to the other.
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So at the end, it's very different looking.
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Like, I know that water is different from vapor,
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but there's no precise point this happens.
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I feel many of these things that we think,
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like consciousness, clearly dead person
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is not conscious and the other one is.
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So there's a difference like water and vapor,
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but there's no point you could say that this is conscious.
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There's no sharp transition.
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So it could very well be that what we call heuristically
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in daily life, consciousness is similar,
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or life is similar to that.
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I don't know if it's like that or not.
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I'm just hypothesizing it's possible.
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There's no discrete phases.
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There's no discrete phase transition like that.
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Yeah, yeah, but there might be concepts of temperature
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and pressure that we need to understand
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to describe what the head consciousness in life is
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that we're totally missing.
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I think that's not a useless question.
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Even those questions,
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they is back to our original discussion of philosophy.
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I would say consciousness and free will, for example,
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are topics that are very much so
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in the realm of philosophy currently.
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But I don't think they will always be.
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And I think I'm fine with some topics
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being part of a different realm than physics today
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because we don't have the right tools,
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just like biology was.
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I mean, before we had DNA and all that genetics
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and all that gradually began to take hold.
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I mean, when people were beginning phase experiments
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with biology and chemistry and so on,
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gradually they came together.
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So it wasn't like together.
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So yeah, I'd be perfectly understanding of a situation
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where we don't have the tools.
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So do these experiments that you think
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as defines a conscious in different form
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and gradually we'll build it and connect it.
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And yes, we might discover new principles of nature
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that we didn't know.
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I don't know, but I would say that if they are,
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they will be deeply connected with the else.
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We have seen in physics,
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we don't have things in isolation.
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You cannot compartmentalize,
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this is gravity, this is electricity, this is that.
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We have learned they all talk to each other.
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There's no way to make them in one corner and don't talk.
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So the same thing with anything, anything which is real.
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So consciousness is real.
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So therefore we have to connect it to everything else.
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So to me, once you connect it,
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you cannot say it's not reality.
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And once it's reality, it's physics.
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I call it physics.
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It may not be the physics I know today, for sure it's not,
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but I would be surprised if there's disconnected realities
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that you cannot imagine them as part of the same soup.
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So I guess God doesn't have a biology or chemistry textbook
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and mostly, or maybe he or she reads it for fun,
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biology and chemistry,
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but when you're trying to get some work done,
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it'll be going to the physics textbook.
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Okay, what advice, let's put on your wise visionary hat.
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What advice do you have for young people today?
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You've dedicated your book actually to your kids,
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What advice would you give to them?
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What advice would you give to young people today
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thinking about their career, thinking about life,
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of how to live successful life, how to live a good life?
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Yes, yes, I have three sons.
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And in fact, to them, I have tried not to give
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So even though I've tried to kind of not give advice,
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maybe indirectly it has been some impact.
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My oldest one is doing biophysics, for example,
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and the second one is doing machine learning
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and the third one is doing theoretical computer science.
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So there are these facets of interest
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which are not too far from my area,
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but I have not tried to impact them in that way,
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but they have followed their own interests.
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And I think that's the advice I would give
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to any young person, follow your own interests
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and let that take you wherever it takes you.
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And this I did in my own case that I was planning
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to study economics and electrical engineering
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when I started at MIT.
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And I discovered that I'm more passionate
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about math and physics.
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And at that time I didn't feel math and physics
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would make a good career.
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And so I was kind of hesitant to go in that direction,
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but I did because I kind of felt that
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that's what I'm driven to do.
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So I don't regret it, I'm lucky in the sense
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that society supports people like me
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who are doing these abstract stuff,
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which may or may not be experimentally verified
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even let alone applied to the technology in our lifetimes.
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I'm lucky I'm doing that.
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And I feel that if people follow their interests,
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they will find the niche that they're good at.
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And this coincidence of hopefully their interests
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and abilities are kind of aligned,
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at least some extent to be able to drive them
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to something which is successful.
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And not to be driven by things like,
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this doesn't make a good career,
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or this doesn't do that, and my parents expect that,
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or what about this?
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And I think ultimately you have to live with yourself
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and you only have one life and it's short, very short.
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I can tell you I'm getting there.
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So I know it's short.
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So you really want not to do things
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that you don't want to do.
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So I think following an interest
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is my strongest advice to young people.
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Yeah, it's scary when your interest
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doesn't directly map to a career of the past or of today.
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So you're almost anticipating future careers
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that could be created.
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But yeah, there's something to that,
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especially when the interest and the ability align,
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that you will pave a path,
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that will find a way to make money,
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especially in this society,
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in a capitalistic United States society.
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It feels like ability and passion paves the way.
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At the very least, you can sell funny T shirts.
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You've mentioned life is short.
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Do you think about your mortality?
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Are you afraid of death?
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I don't think about my mortality.
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I think that I don't think about my death.
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I don't think about death in general too much.
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First of all, it's something that I can't do much about,
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and I think it's something
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that it doesn't drive my everyday action.
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It is natural to expect
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that it's somewhat like the time reversal situation.
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So we believe that we have this approximate symmetry
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in nature, time reversal.
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Going forward, we die.
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Going backwards, we get born.
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So what was it to get born?
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It wasn't such a good or bad feeling.
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I have no feeling of it.
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So who knows what the death will feel like,
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the moment of death or whatnot.
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but in what form do we exist before or after?
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Again, it's something that it's partly philosophical maybe.
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I like how you draw comfort from symmetry.
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It does seem that there is something asymmetric here,
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a breaking of symmetry,
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because there's something to the creative force
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of the human spirit that goes only one way.
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That it seems the finiteness of life
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is the thing that drives the creativity.
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And so it does seem that at least the contemplation
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of the finiteness of life, of mortality,
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is the thing that helps you get your stuff together.
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Yes, I think that's true,
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but actually I have a different perspective
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on that a little bit.
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Namely, suppose I told you you're immortal.
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I think your life will be totally boring after that,
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because you will not,
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I think part of the reason we have enjoyment in life
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is the finiteness of it.
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And so I think mortality might be a blessing,
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and immortality may not.
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So I think that we value things
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because we have that finite life.
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We appreciate things.
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We want to do this.
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We want to do that.
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We have motivation.
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If I told you, you know, you have infinite life.
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Oh, I don't, I don't need to do this today.
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I have another billion or trillion or infinite life.
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So why do I do now?
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There is no motivation.
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A lot of the things that we do
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are driven by that finiteness of these resources.
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So I think it is a blessing in disguise.
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I don't regret it that we have more finite life.
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And I think that the process of being part of this thing,
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that, you know, the reality,
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to me, part of what attracts me to science
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is to connect to that immortality kind of,
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namely the laws, the reality beyond us.
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To me, I'm resigned to the fact that not only me,
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everybody's going to die.
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So this is a little bit of a consolation.
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None of us are going to be around.
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So therefore, okay,
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and none of the people before me are around.
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So therefore, yeah, okay,
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this is something everybody goes through.
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So taking that minuscule version of,
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okay, how tiny we are and how short time it is and so on,
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to connect to the deeper truth beyond us,
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the reality beyond us,
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is what sense of, quote unquote, immortality I would get.
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Namely, at least I can hang on
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to this little piece of truth,
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even though I know, I know it's not complete.
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I know it's going to be imperfect.
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I know it's going to change and it's going to be improved.
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But having a little bit deeper insight
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than just the naive thing around us,
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little earth here and little galaxy and so on,
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makes me feel a little bit more pleasure to live this life.
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So I think that's the way I view my role as a scientist.
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Yeah, the scarcity of this life helps us appreciate
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the beauty of the immortal,
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the universal truths of that physics present us.
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And maybe one day physics will have something to say
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about that beauty in itself,
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explaining why the heck it's so beautiful
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to appreciate the laws of physics,
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and yet why it's so tragic that we would die so quickly.
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Yes, we die so quickly.
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So that can be a bit longer, that's for sure.
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It would be very nice.
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Maybe physics will help out.
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Well, Kamran, it was an incredible conversation.
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Thank you so much once again
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for painting a beautiful picture of the history of physics.
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And it kind of presents a hopeful view
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of the future of physics.
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So I really, really appreciate that.
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It's a huge honor that you would talk to me
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and waste all your valuable time with me.
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I really appreciate it.
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It was a pleasure, and I loved talking with you.
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And this is wonderful set of discussions.
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I really enjoyed my time with this discussion.
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Thanks for listening to this conversation
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And thank you to Headspace, Jordan Harmerjee Show,
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Squarespace, and Allform.
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Check them out in the description to support this podcast.
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And now, let me leave you with some words
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from the great Richard Feynman.
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"'Physics isn't the most important thing.
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Thank you for listening, and hope to see you next time.