Changing Our Understanding of Multiple Dimensions

Description: What are they, where do they come from, and where�the proof?

Transcript:

So you’re jumping to multiple dimensions, which is also something I work on. And I kind of work on it in connection with trying to answer some of those questions that we just mentioned. But the idea of multiple dimensions has been around for ages in terms of just mathematical concepts. But in terms of physics it was more recent – after Einstein developed his theory of general relativity. And it was observed that his theory works for any number of dimensions. It doesn’t have to be three. But people also think about extra dimensions because of string theory, which is a candidate theory for unifying quantum mechanics and gravity, which seems to require extra dimensions of space. But the other reason we think about extra dimensions is because they might actually have implications for our world and explain properties of matter that we’ve observed, and how they . . . why masses are what they are for example.

Well there’s a number of ways to think about what dimensions are. I hope we all know where three dimensions are, which you can say are left, right; forward, backward; up, down. And if you think about it, three . . . we say there are three dimensions of space. And sometimes we need three coordinates to locate some objects in space. So you can say longitude, latitude and altitude. So if there were more dimensions, you would need more coordinates. Now of course for whatever reason we are not physiologically designed to observe those dimensions, but that doesn’t mean they don’t exist. One way of thinking about it is . . . Maybe the best way of thinking about it is the way that someone named ____________ did it in the late 19th century in a book called “Flatland”. And he said suppose there were two dimensional creatures living in a two dimensional universe? They would have the same trouble conceptualizing three dimensions that we have when we try to conceptualize more than three, such as four. And so he asked questions like, “What would observers in this two dimensional universe see, say, if a three dimensional object like a sphere passed through the universe?” And what this flatland universe would see would be a series of disks that grow in size and then decreased in size. In the same way that we can certainly think about a two dimensional world inside a three dimensional world, it could be that we observe three dimensions but really there are more. And if a hyper sphere – say a four dimensional sphere – passed through our universe, we would see a series of spheres that grew in size and then decreased in size. The fact that we don’t observe those extra dimensions doesn’t mean they don’t exist. And they are hard to conceptualize. They certainly are hard to visualize. But we can think about them mathematically and conceptually without too much trouble.

You want evidence, do you? Well we don’t know if there’s evidence yet. So one reason we think about it is to decide what would be the evidence. So how do we know if these dimensions exist? And of course you can’t answer that question until you’ve really thought it through and thought how are they hidden; what would be the implications? And we haven’t seen them yet. I mean the reasons that we think about it, like I said, are string theory and the fact that they might have implications for our universe. But how can we test whether it has these implications? Well what we’re going to do . . . not me but ________ will do is look for evidence of particles associated with travel in the extra dimensions. That is to say if particles traveled in the extra dimensions, there would be partner particles called “Kaluza-Kline particles” that are like the particles we know about. They have properties that interact similarly, but they have mass. And their mass reflects the extra dimensional geometry. That’s because they have momentum in those extra dimensions. And so what we’ll do is look for evidence of these extra Kaluza-Kline particles. And if we see them, and if they have the properties that we predict, it would be evidence for extra dimensions.

 

 

Recorded On: 11/2/07

Description: Randall explains where it falls short, and a little thing called a brane.

Transcript:

Well the standard model of particle physics, it basically . . . it’s a list of particles and how they interact in some sense. So there’s . . . It turns out there are particles called “quirks” which experience the strong nuclear interactions; weak nuclear interactions; and electro magnetism; and gravity, which is negligible, so we’ll ignore it for now. As a force ________ fundamental particles. And there are particles called “leptons” which don’t experience a strong force. And we know about up and down type quirks which sit inside all matter – inside the proton and neutron. But it turns out there are heavier particles – heavier particles that have the same charge as those particles. In fact there’s what we call three generations of particles where they have the same charges . . . set of charges, but they’re heavy enough. And they interact under the forces I just mentioned – electromagnetism, weak nuclear force, strong nuclear force and gravity. And basically that’s the standard model.

Where it falls short is in explaining masses. In fact there’s some aspect of the standard model that we expect to be completed very soon. And there’s another more subtle aspects, and let me explain those. First of all it’s important to know that if all the symmetries were . . . that are part of the standard model were there forever, every particle wouldn’t have mass. The fundamental particles wouldn’t have mass. Now we know fundamental particles have mass. The question is how does that happen. And it’s because there’s a small breaking of these symmetries – a small breaking of the symmetries. And it’s associated with the mass scale, so there’s some mass scales in which the nature of the theory changes in some sense. And there’s a particle called the “Higgs particle” associated with that. The Higgs particle is associated with the mechanism through which fundamental particles acquire mass. I know it’s a mouthful. But that’s what happens. And so the . . . One of the things that we wanna understand is is there this Higgs particle? We haven’t found it yet. I mean the theory seems to only make sense if something like a Higgs particle is there, but no one has observed it yet. So one thing is to find the Higgs particle, study its properties. But another thing is to understand where does this mass scale come from? Why is this mass scale so small when compared to other scales that exist in the problem? And also, why are forces of such different strength? Gravity is much, much weaker than the other fundamental forces when acting on elementary particles. And the question is why is that? Why is this force so much weaker? So we know that if we just assume these masses are what they are – if we assume this force is much bigger – the theory works beautifully. Its predictions work. But right now there’s no explanation for the scales in the problem. And furthermore it seems almost inconsistent. If you just follow the rules of quantum mechanics and special relativity, you would expect that all the forces should have comparable strength. And the fact that there’s this enormous discrepancy between gravity and other forces means we have to make a fudge in the theory – what we call fine tuning. And so no one believes that’s what’s there, and so we believe there’s something that completes this theory. And that thing that completes the theory might well be something as exotic as extra dimensions of space.

The hierarchy problem is this question of why gravity is so weak compared to the other fundamental forces. That is to say even though gravity seems strong, it’s because you have big, massive objects that act with gravity. If you had two fundamental particles – say you have two electrons separated by some distance – the force of gravity is something like 42, 43 _________ of magnitude smaller than the force of electro magnetism. It’s really, really weak. So the question is why is that? And you can turn that question into a question about mass scales. You can ask the question, “Why is the mass of the Higgs particle that we talked about earlier so much lighter than the energy scale of which gravity would be strong?” After all, although I said gravity is weak when it acts in elementary particles, we know that the strength of gravity becomes bigger as we go to higher and higher masses, bigger and bigger masses. So in principle you could go to a mass scale where gravity was comparable to the other forces. But that mass scale is 16 orders of magnitude bigger than the mass of where this . . . the Higgs particle, for example. And the question is why are these masses as different as we know them to be?

So first of all I wanna say that we didn’t just jump and say, “Let’s solve the problem with extra dimensions.” A lot of very smart theorists have been working on this problem since the standard model of physics . . . particle physics was established around the 1970s. And there are some proposed solutions that work if there are only three dimensions of space. One of the most popular among theoretical particle physicists is called “supersymmetry”, for example, in which the particle spectrum is doubled. And we can come back to that if you’re interested. But supersymmetry works fine in some respects, but it actually . . . there’s no really compelling theory once you include all the (15:15) things you have to include to make the theory work. So it really seemed worth asking, “Is this the only possibility?” And since there are theories like string theories and extra dimensions of space, it was natural to ask could there be solutions with extra dimensions. And one of the ways it might be solved if there was an extra dimension of space is that space time can be very curved – or “warped” is the technical term. Einstein taught us that space time can be curved or warped. It doesn’t have to be flat. It doesn’t have to be the same everywhere. There can be gravitational forces which exist through the geometry of space time. And the consequence of that warping could be that essentially gravity is concentrated elsewhere. It’s much stronger in other regions of space than it is where we are. In fact what we found . . . What my collaborator _________ and I found is that you could have gravity really concentrated in one particular location and exponentially decreasing in strength as you go away. So it’s quite natural to have hierarchies in this scenario. It’s natural for gravity to be weak. It’s natural for masses to be different, because space time itself determines the masses, and those can be different.

What are branes? So branes are . . . is perhaps the place where this gravity is concentrated. So the word “brane” is . . . First of all it’s B-R-A-N-E for the listening public. And branes are membrane-like objects in higher . . . in extra dimensions of space, for example. So even when there’s an extra dimension, it doesn’t mean that we travel throughout. After all, I just said gravity is weak if we live apart from where gravity is concentrated. So it could be that there are lower dimensional surfaces in higher dimensions. So even if there is a fourth dimension of space, it could be that we and the stuff we’re made of in galaxies only travel in three dimensions. Say electro magnetism maybe only is experienced in our three dimensions. That is to say charged particles can only exist on the brane where we live. But there still could be another dimension where gravity travels. So this idea of a brane is that there’s lower dimensional surfaces in higher dimensional space, and we can actually live on those.

 

 

Recorded On: 11/2/07

Description: Exponential warping, Randall says, has large implications.

Transcript:

Well I think the fact that there can be this exponential warping and it has these really dramatic implications is pretty important. It’s important for the reason that I just said, which is that it might explain why mass scales are different. It could be relevant for other places where you’d want different mass scales, such as inflationary cosmology. But we also found something else that was very interesting – that you could actually have an infinite dimension of space; that’s an extra dimension, a fourth dimension of space that you don’t see. And this is really radical in the sense that since basically physicists always thought that if you had extra dimensions, they had to be tiny because we don’t see them. It’s pretty intuitive. If something’s really small, you don’t see it. And so the idea that you had very curled up or finite-sized extra dimensions. And that was basically what people thought was essential – for us not to see them. It turns out that this strong warping that we discovered could also mean that gravity is so concentrated that you don’t see it in an extra dimension of space. So that could have radical implications obviously for our universe.

 

 

Recorded On: 11/2/07

Description: String theory is trying to reconcile quantum mechanics and gravity, Randall says.

Transcript:

Well okay, so first of all what problem is string theory trying to solve? String theory is trying to reconcile quantum mechanics and gravity. And let’s take a step back and see what we mean by that, because in fact we do understand gravity. Einstein’s theory of general relativity describes gravity, and it’s been tested. We’ve seen evidence of general relativity. Quantum mechanics we know very well has been tested on atomic skills. The point is that there exists scales that we can’t test. They’re much too small for experiments to be done – in distance, or much too high energy – where we wouldn’t know how to make predictions. It would look inconsistent. In other words, in the regime of large things where cosmology or general relativity applies, we do fine. It’s just quantum mechanics is negligible on those scales. On small scales, atomic scales we can ignore gravity because gravity is so weak. But there exists tiny distances or very high energies where both forces (22:24) would, in principle, be important. Those aren’t ones where we can experimentally test; but even theoretically we believe we should have a theory which could work at all distance scales. It’s just the fact that we haven’t been able to make experiments to test those yet doesn’t mean there shouldn’t be a theory that describes it. So people have been looking for a candidate theory of what’s called “quantum gravity” for some time. So string theory is a theory of quantum gravity. Or it’s a candidate theory of quantum gravity. And it’s based on the idea that fundamentally we don’t have elementary particles, but we have fundamental oscillating strings. And particles are the oscillation of those strings. And if you . . . You can say how could we not notice those strings in the particles. But if you think about it, if the strings are really tiny, they look like particles. We can’t see it. To see that it’s actually a string, you’d have to see the additional oscillations that a strong can have. And to do that you’d have to be able to test the energies that it would take to make a string oscillate. And it turns out we need to start having __________ approach anywhere near those energies at this point.

So essentially what we’re doing is we’re taking . . . It’s sort of an interaction in the sense that we take some ideas from string theory, such as extra dimensions and branes, and see what could be the implications for particle physics. And if, for example, it was found that we were right, string theorists would have to find ways to predict the kind of geometry we propose. And if that . . . After we did our work . . . At first when we did it, everyone said, “Oh this never happens in string theory.” But after we did it, people found ways that this could happen in string theory. But also some of the more theoretical work such as the infinite work dimension of space, maybe that goes back to string theory. There are possibilities that people haven’t thought about yet. So . . . and it goes back and forth.

 

 

 

Recorded On: 11/2/07