Some see string theory as the one great hope for a theory of everything that will unify quantum mechanics and gravity and so unify all of physics into one great, glorious theory of everything. Others see string theory as a catastrophic dead end, one that has consumed a generation of geniuses with nothing to show for it. So why are some of the most brilliant physicists of the past 30-plus years so sure that string theory is right? [MUSIC PLAYING] Why has string theory been the obsession of a generation of theoretical physicists? What exactly is so compelling about tiny vibrating strings? In our last string-theory episode, I talked about what these things really are and covered some history. In short, the strings of string theory are literal strands and loops that vibrate with standing waves simply by changing the vibrational mode and you get different particles analogous to how different vibrational modes on guitar strings give different notes. And, by the way, these strings exist in six compact spatial dimensions on top of the familiar three. In this episode, I'm going tell you why string theory is right, at least why so many of those geniuses think it is. Maybe I can summarize. It's pretty, or at least it started out that way. Its mathematics seem to come together so neatly towards a unified description of all forces and particles, and most importantly that unification includes gravity. I want to try to give you a glimpse into this mathematical elegance. I also want to give you a teaser on why string theory is actually wrong. Don't worry, that topic will get its own whole episode. The greatest criticism of string theory is that it's never made a testable prediction. The space of possible versions of string theory is so vast that nothing can be calculated with certainty, so string theory can neither be verified nor ruled out. It's unfalsifiable. But string theorists might disagree. They might say, maybe half jokingly, that string theory does make one great prediction. It predicts the existence of gravity, which is stupid, of course. Everyone knows that Isaac Newton discovered gravity when he fell out of an apple tree, or something like that. There was definitely an apple tree involved. But the fact is when you start to work out the math of string theory, gravity appears like magic. You don't need to try to fight gravity into string theory. In fact, it will be difficult to remove it, and the quantum gravity of string theory is immune to the main difficulty in uniting general relativity with quantum mechanics. It doesn't give you tiny black holes when you try to describe gravity on the smaller scales. We did talk about this and other problems with developing a quantum theory of gravity in a recent episode, but before we get to the nuts and bolts of how string theory predicts gravity, it's worth taking a moment to see how stringy gravity avoids the problem of black holes. Let's actually start with the regular old point particles of the standard model. When a point particle is moving through space and time it traces a line. On a spacetime diagram, time versus one dimension of space, this is called its world line. In quantum theories of gravity, the gravitational force is communicated by the graviton particle. When the graviton acts on another particle, it exerts its effect at an intersection in their world lines over some distance. But in very strong gravitational interactions, that intersection itself becomes more and more point like. The energy density at that point becomes infinite. More technically, you start to get runaway self-interactions, infinite feedback effects between the graviton and its own field. If you even try to describe very strong gravitational interactions, you get nonsense black holes in the math. OK, let's switch to string theory where particles are not points. They're loops or open-ended strands. The graviton in particular is a loop. When strings move on a spacetime diagram, they trace out sheets or columns. In fact, you can think of a string not as a 1D surface but as a 2D sheet called a world sheet. Now let's look at the interaction of two strings. The vertex is no longer point like. It can't be point like. Even the most energetic interactions are smeared out over the string, so you avoid the danger of black hole creating infinities. OK, put a pin in these world sheets. We're going to need them later. They illustrate why quantum gravity isn't hopelessly broken in string theory, and that's a huge point in favor of string theory, but these world sheets will also help us see why string theory predicts gravity in the first place. And this is the second point in string theory's favor. You see, it turns out that tiny vibrating quantum strings automatically reproduce the theory of general relativity and, in the same mechanism, seem to promise to reproduce all of quantum theory too. This is part of the elegance I spoke of earlier. This stuff appears a little too naturally in the math of string theory to be a coincidence, or so a string theorist might tell you. For some reason, vibrating strings are bizarrely well suited to quantization. By quantization I mean taking a classical large-scale description of something like a ball flying through the air or a vibrating rubber band and turning it into a quantum description. To do this, you basically take the classical equations of motion and follow a standard recipe to turn them into wave equations with various quantum weirdness added in like the uncertainty relation between certain variables. I say basically. This is a tricky process, and it only works if your equations of motion are especially friendly. Schrodinger's equation is the first and easiest example. It quantizes the equations of motion of slow-moving, point-like particles. A while ago, we talked about Paul Dirac developed a wave equation for the electron that took into account Einstein's special theory of relativity. It was a mathematical mess until Dirac added some nonsense terms to the electron-wave function that caused a lot of the mess to cancel out. Those nonsense terms turned out to correspond to antimatter. The resulting Dirac equation is incredibly elegant, and in the pursuit of that elegance Dirac predicted the existence of antimatter. This is a powerful example of how following mathematical prettiness could bring us closer to the truth. Quantizing the motion of strings also starts out ugly, but there are also some math tricks to make it work. A big part of it is making use of symmetries. If the physics of a system doesn't care about how you define particular coordinates or quantities, we say that that parameter is a symmetry of the system or that the system is invariant to transformations in that parameter. Finding symmetries can massively reduce the complexity of the math. A really important type of symmetry in quantum mechanics is gauge symmetry. It's when you can redefine some variable in different ways everywhere in space and still get the same physics. I want to remind you of one particularly crazy result of gauge symmetries. It's a reminder because we covered it, but it's so relevant that it's worth the review. So, we expect the phase of the quantum wave function to be a gauge symmetry of any quantum theory. That means you should be able to shift the location of the peaks and valleys in different ways at different points in space without screwing up the physics. And guess what? In the raw Schrodinger equation, you can't. It breaks various laws of physics. But it turns out that you can add a very special corrective term to the Schrodinger equation that fixes these phase differences preserving local phase invariance. That term looks like what you would get if you added the electromagnetic field to the Schrodinger equation. So in a way, electromagnetism was discovered in its quantum form by studying the symmetries of quantum mechanics. It turns out that exploring a very different symmetry of string theory both makes it possible to quantize the theory and gives us a very different field, the gravitational field. So, like I was saying, when we try to quantize string theory, of course it's a huge mess. Applying the usual old symmetries got physicists some of the way, but to succeed, they needed an extra weird type of symmetry. That symmetry is Weyl symmetry or Weyl invariance. This is a weird one. It says that changing the scale of space itself shouldn't affect the physics of strings. Hermann Weyl actually came up with this symmetry right after Einstein proposed his general theory of relativity. He tried to use it to unify general relativity with electromagnetism. Fun story-- Weyl invented the name gauge symmetry to describe this scale invariance inspired by the gauge of railroad tracks which measures the separation of the tracks. Anyway, Weyl symmetry doesn't work. Turns out that in 4D spacetime it does matter whether you change the scale of space and the separation of its tracks. But it turns out that there's a very particular geometric situation that does have Weyl invariance. That's on the 2D dimensional world sheet of a quantum string. Remember that? Mysteriously, the 2D sheet traced out in spacetime by a vibrating 1D string has this symmetry that lets us redefine the scale on its surface however we like. That means we can smooth out that surface mathematically and write a nice, simple quantum wave equation from the equations of motion, but only for 1D strings making a 2D world sheet, not for any other dimensional object. This is part of what makes strings so compelling. They are quantizable in a way that other structures aren't. But there's a cost to using this symmetry. Just as local phase invariance required us to add the electromagnetic field to the Schrodinger equation, adding Weyl invariance means we need to add a new field. That field looks like a 2D gravity on the world sheet. It's a projection of the 3D gravitational field. So, with our quantized equations of motion in hand, you can predict the quantum oscillations of our string. These are particles, and the first mode looks like the graviton, a quantum particle in the aforementioned gravitational field. If you use string theory to write down the gravitational field in what we call the low-energy limit, which just means not in places like the center of a black hole, then it looks just like the gravitational field in Einstein's theory. OK, a caveat-- you can only get the right particles, including the graviton and the photon, out of string theory for a very specific number of spatial dimensions, nine to be precise. In fact, if string theory makes any predictions, it's the existence of exactly this number of extra dimensions. And this is where string theory starts to look less attractive. Our universe has three spatial dimensions. String theorists hypothesize that the extra dimensions are coiled on themselves so they can't be seen, but that seems like a hell of an extra thing to add in order to make your theory work. There's also no experimental evidence of the existence of these dimensions. And that's just the first of many problems of string theory. But like I said, we're going to need a whole episode for that. Physicists were lead to string theory by the elegance of the math and the fact that it appeared, at least in the beginning, to converge on the right answers. That convergence is also seen in the union of different string theories by M theory and in the discovery of AdS/CFT correspondence-- again, for future episodes. But can such an elegant and rich mathematical structure really have nothing to do with reality? There's plenty of historical precedent for mathematical beauty leading to truth, but there's no fundamental principle that says it has to. Perhaps we're now overly distracted by the elegance of string theory. Philosophical points to consider as we continue to follow the mathematical beauty hopefully towards an increasingly true representation of spacetime. Thanks to the Great Courses Plus for supporting PBS Digital Studios. The Great Courses Plus is a digital learning service that allows you to learn about a range of topics from educators and professors from around the world. You can go to thegreatcoursesp lus.com/spacetime to get access to a library of different video lectures about science, math, history, literature, or even how to cook, play chess, or become a photographer. New subjects, lectures, and professors are added every month. For more information, visit thegreatcoursesp lus.com/spacetime. Last week we talked about one of the most misunderstood concepts in quantum mechanics, the idea of virtual particles and their tenuous connection to reality. You guys asked pretty much every question that I avoided. Uri Nation asks about the photons that mediate the magnetic field or the contact force between two bodies. Aren't they virtual? Well, they are, but they don't exist. These fundamental forces are mediated by fluctuations in the quantum fields of the relevant forces. Those fluctuations can be approximated as the sum of many virtual particles, but the particles themselves are just convenient mathematical building blocks to describe a messy disturbance in the field. Eddie Mitch asked whether the virtual particles are required to explain the Casimir force. So the Casimir effect is sometimes explained as resulting from the exclusion of virtual particles between two very closely separated conducting plates which results in the plates being drawn together. So, if the Casimir effect really is due to a change in the zero-point energy-- and there are those who say it isn't-- but if it is, then it's still misleading to attribute it to virtual particles. More accurately, the conducting plates create a horizon in what would otherwise be a perfect infinite vacuum. In fact, you create two horizons between the plates and one horizon on the outside. Those horizons perturb the vacuum which can lead to the creation of very real particles, as in Hawking radiation. But in the Casimir effect, the double horizon between the plates restricts what real particles can be produced there whereas there's less restriction on the outside of the plates with their single horizon. That leads to a net pressure pushing the plates together. David Ratliff asks if a quantum tree falls in a vacuum and nobody is around to measure it, does it still have energy? Well, believe it or not, it's a serious question as to whether the universe has counter-factual definiteness, whether or not we can make a meaningful statement about the state of the universe without conducting an experiment. To address this seriously, I want you to imagine this gedankenexperiment. You have a box containing a vial of poison connected to a radioactive isotope that could either decay or not, releasing the poison. You put a mime in the box.
