Here is the full transcript of Indian theoretical physicist Dr. Spenta Wadia’s TEDx Talk: String Theory and the Hidden Structure of Space-Time at TEDxStXaviersMumbai conference.
Dr. Spenta Wadia – Physicist
I am going to tell you a story. It’s about our bigger home, the Universe. It’s about the force of gravity that shapes our Universe more than any other force that we know. And yet, it is the least understood of all the forces of nature and presents the greatest challenge for those of us who are in search of the fundamental laws of nature.
So very briefly and very quickly, I will take you from the time of Galileo to Newton, to Maxwell, Einstein, and to the present-day work in string theory. Let me just mention to you that we are all celebrating in the scientific world 100 years of Einstein’s Theory of General Relativity this year.
Galileo discovered a new law of nature which still holds. You all know about this experiment from the Leaning Tower of Pisa, where he took two objects, one very heavy one and one light one, and let it go, and both of them actually under good conditions of weather, basically hit the ground at the same time. So they fall in the same way, independent of their mass. That’s a great law of nature. It’s still valid. To one part in 10^10 actually. Experimentally verified.
So the next big step, actually, in the formulation of theory in science is of course Isaac Newton; and this is his famous law of gravitation that how two masses, actually, two objects, interact with each other. The force goes as the product of the masses divided by the square of the distance by which they are separated; and you notice that this force is actually very weak because I am not really attracted to anyone of you. I am not falling towards you, right? It’s very weak, but when the distance between the two objects becomes very, very small, you see this force is huge and uncontrolled. And in fact, in a sense, defines the rest of our story.
But it is also very large when the masses are very huge, you see? And the important thing is that this force cannot be screened like the force of electromagnetism, because charges come in different signs. I put plus charge, minus charge together; it’s neutral, no force outside.
But here, gravity cannot be screened, and this is the reason why it is really the dominant force of nature that shapes the large-scaled structure of our Universe. The force between objects actually acts instantaneously.
So what this means is the following: that if I have two objects, if I shift this, it just happens together. It’s not that I’ll do something here and then this response. That’s the way it should be as we will see.
But Newton’s law of gravitation has one fundamental defect: that it is instantaneous. It means if some object moves, instantaneously something else moves, which means that the interaction is actually transmitted almost at infinite speed.
Two hundred years later, approximately, Maxwell completed the theory of electromagnetism, and he unified it with what used to be called optics. He showed that light is actually a form of an electromagnetic wave, which travels at a fixed but very high speed. The important thing is that its speed is not infinite. It is finite, but it’s very large. That is why in most of our daily lives, we feel that things happen instantaneously.
This great discovery of Maxwell in the 19th century had a profound impact about 50 years later in the postulation of the special theory of relativity in 1905, by Albert Einstein. And leaving aside all the details, I’ll just tell you in a sentence what the main impact of the theory of special relativity is. That it actually overthrew the idea of simultaneity.
What does it mean? It means that if I have, for example, some rod here with two light bulbs, and I switch them – they’re connected, so the bulbs will go on together, right? This is a simultaneous event for me. However, if you are actually moving with respect to me, at a very high speed, nearly – let’s say – the speed of light or half the speed of light, it won’t be simultaneous for you. So, simultaneity is not universal.
That means what is simultaneous for me or instantaneous is not instantaneous for somebody who’s moving with respect to me, and you will detect it experimentally only if your speed, move or speed is very, very high. So, simultaneity overthrown.
Then, Einstein thought there must be a problem with Newton’s law of gravitation as I mentioned to you, because it is instantaneous. This led to this incredible search by Einstein to develop a law of gravity actually which reduces to Newton’s Law; when for earthly things like the ones we observe, or even our planets. But which actually is the true theory? That is the general theory of relativity that was put forward by him in 1915, 100 years ago.
I want to explain to you actually, what this theory is. It is really one of the great creations of the human mind, and here it goes. So Einstein actually thought of gravity as no gravity. There is no gravity, actually! What is there is that a big lump of matter basically distorts the fabric of space-time.
Just imagine this trampoline over here. There’s a fabric that makes it, you put a big ball on it, it distorts the fabric of the trampoline, distorts the fabric of space-time. And that small, little thing responds to that distortion.
Just like in a trampoline. Take a ping pong ball and just leave it, and it’ll just go towards down. Or if you hit it, it’ll take a circular motion; that’s exactly what it is. So in fact, this cartoon actually is a real representation of what the solution of the equations of general relativity is.
Even coming closer to what we understand, let me make an analogy for you, which is every, it is more to what I am saying now than meets the eye, but that’s too technical for me to go into.
So, imagine that you are actually in a nice place with a very beautiful lake which is very calm, and you throw a stone in it. You throw a stone, and it disturbs the water. There are ripples that move out, and these ripples travel at a fixed speed; that is the speed of sound in water. After a while, they sort of jiggle something else which is on their way.
So suppose you had a piece of wood, little distance away, the wood will feel the water passing by. The key point here is that there is a cause and an effect, and the cause and effect is communicated by a wave which is traveling at a fixed speed. The speed is not infinite, so nothing is instantaneous. Everything has a cause and effect and it’s communicated, actually, alright.
So, now you see, if I go back, you understand what I was saying very easily, because you can relate to this simple experiment.
So now that I have given you this analogy with water, you all know water is the daily experience, water is a smooth object. You don’t really feel that there are molecules that make it up; I mean, you don’t really experience the molecules. They can be seen in terms of very, very powerful microscopes which can resolve distances to distances of the order of an angstrom, of 10 to the minus eight centimeters or something, but 100 years ago, nobody knew this actually.
But yet, now we know that water has a structure, it has a molecular structure, it has phases, all types of things. So, if the analogy with space-time and the fabric of space-time is right – it is right – there’s an obvious question: what is the hidden structure underlying the geometry of space-time which was smooth? What is the hidden structure? Is there something below it that we are not seeing, not experiencing, but which actually holds the whole thing together? Because if you look at just the equations of ordinary fluids or of water, those equations fail when you go to very short distances.
Just like Newton’s laws and this theory of general relativity really fails if you go to very, very small distances. So this granularity we are after, of space-time. So the question is very well-posed. I think it’s one of the great achievements of the subject of string theory, which is going on for the last three decades now, almost, that it has succeeded in at least, in theory, telling you about what are the atoms of space-time, what is the granular structure below this very smooth space-time that we all actually experience. The clue lies in the study of black holes in string theory.
So now, what is a black hole? A black hole is, it is a solution of Einstein’s equations, so it’s consistent to Einstein’s equations. It is also known now today that they exist in nature, so the theory of general relativity had the prediction and can explain objects in the sky, so what better a laboratory than to understand the granular structure of space-time in terms of black holes?
I will tell you what a black hole is. There you see Schwarzschild who actually first found a solution and you see Subrahmanyan Chandrasekhar who predicted the existence of such objects in the physics of collapsing stars. So a black hole is a space-time object. You just imagine the Sun.
Take the Sun, the huge object, it has a mass of 10^33 grams or something. It’s a huge number, and shrink it to three kilometers. That’s a very compact object. That is a black hole. The Sun would become a black hole if you compress all its mass into a radius of approximately three kilometers.
A black hole has a very peculiar feature that it has a surface called the horizon. It’s a one-way gate. If you fall in, you can’t get out. If light falls in, it cannot get out. That’s why it’s called black and falls into the singularity.
We don’t worry about the singularity, that’s some different issue, actually. All right, so this is the black hole, this is our laboratory.
Now, let’s pause. Something very, very important happened in the early part of the 20th century. A new mechanics was discovered. It’s called quantum mechanics. While it is true that the general theory of relativity has very few practical applications except setting your GPS very accurately. That’s the only application I can tell you about.
Quantum mechanics has applications which are totally ubiquitous, I mean everything that is working in this room, all the electronics, all the computers, everything, works on quantum mechanics. The laws of nature are different actually when you approach the system to be very, very small like atoms, electrons, molecules.
But when lots of them come together, then you can apply classical mechanics of Newton. One of the great discoveries of general relativity in the second half of the 20th century is the discovery by Hawking of the fact that black holes are actually hot. They are hot, and they are not really black. I will explain in the next slide.
They are hot, and I have just listed a few temperatures; we know that hot bodies have energy in the form of heat which is measured by a quantity called entropy. They calculated a very famous formula, which is the Bekenstein-Hawking formula, which says that the entropy of a black hole is simply proportional to the area of the horizon of that surface I mentioned to you. So, that’s one result that comes from general relativity, from the smooth description of space-time.
There’s another problem with black holes. That they are not really black because they radiate. As I told you, if you have a black hole of approximately 10^18 grams, it’s very, very hot. It’s like 7,000 degrees Kelvin which means it’s like a white hole, really.
So these properties of black holes, quantum mechanics, and relativity create a paradox actually, a contradiction; and that contradiction is called information loss. The idea is very simple: that a black hole forms by whatever you throw into it: chairs, Shakespeare, Milton, a Bible, whatever. But it always evaporates in the same way, by Hawking radiation. So there is an information loss.
What I think physicists have figured out in the last 100 years is there is a way of dealing with information loss, which is by statistical methods. There’s always some information loss when you average a system of many degrees of freedom and this was, basically, understood by Boltzmann and others. You get what is called a Boltzmann formula for the entropy.
If this formula for the entropy in terms of counting the atoms of space-time agrees with the formula of Hawking and Bekenstein, I think we have made a great progress. Because we have shown that what comes out of the smooth structure can be explained in terms of the underlying granular structure of space-time. The answer is yes, there are atoms of space-time, they are called branes, they are the analogues of the molecules of water. I cannot explain to you what these objects are. That’s another discussion.
But believe me that these are mathematically precisely understood atoms of space-time which are called branes. You use this microscopic understanding of black holes and model the system. There are lots and lots of people who have worked on this, and there are a lot of people from India actually who have made good contributions to this subject. So if you compute the temperature and entropy of a class of black holes then it agrees on the dot with the formula of Hawking and Bekenstein. That’s a great achievement, and that was done by Strominger and Vafa, which set forth an entire development in this subject, about 15-20 years ago.
Then you can calculate Hawking radiation. That also agrees with Hawking’s calculation. Then you can make more precise this fluid dynamics analogy I gave you. That has to do with something called — the fact that gravity is holographic.
Basically, what happens in space-time is coded on the surface of that space-time, like a hologram. What is the most important thing is that with these structures that we know, we can make finite calculations in quantum gravity and really put forth the theory of gravitation which was not really available to Einstein. I think — let me just tell you one last thing. It’s that this type of idea of searching for an indirect way of understanding the granular nature of matter, was actually employed by Einstein and [Vera]. Much before, we actually knew really of the existence of atoms.
The epilogue is that smooth space-time of our experience is an approximate description of the underlying structure that is needed for a complete theory of gravity. This is the subject of intense research today, and a lot of us at the Tata Institute in Mumbai and Bangalore and other places in India are really very much involved in this.
Thank you for your attention.