The Hidden Dimension All Around You — Physics Explains Why You Can’t See It _ Susskind Explains

Añadido: 2026-05-18

[00:00:00]Your eyes are the problem. Not bad eyes, human eyes.

[00:00:05]Every sense you have was built by evolution to navigate roughly 3 m of space at roughly human speeds. That's all it needed to do. The universe, however, was not designed with your convenience in mind. Think about what your sensors actually are. They're instruments. And like every instrument ever built, they have a range. A thermometer measures temperatures between certain numbers and then it stops. A radio receiver picks up frequencies inside a window and ignores everything outside that window. Your eyes respond to a sliver of the electromagnetic spectrum, a band of wavelengths so narrow that if you laid out the full spectrum from a radio wave to a gamma ray, the part you can see would be thinner than a human hair drawn across a football field. That's your window onto reality. that sliver and you've spent your entire life convinced that what you see through that sliver is the whole picture. It isn't. And the place where it breaks down most completely, most beautifully, and most violently is right here in the question of dimensions. How many dimensions does space have? You think you know, you've lived in space your whole life. You feel like an expert. But expertise built on three meters of human experience at human speeds at human energies that is not expertise in the structure of the universe. That's expertise in survival.

[00:01:32]Those are different things. I want to build this argument carefully because it's too easy to wave your hands at extra dimensions and make it sound like science fiction. I've seen it done. I've done it myself in early lectures when I was still figuring out how to talk about this stuff without either boring people or misleading them. The boring version is all mathematics and nobody follows it. The misleading version is all metaphor and nobody learns anything real. I'm going to try for the third option, the version where I actually tell you what's going on. So, let's start at the beginning. What is a dimension? A dimension is not a place.

[00:02:11]It's not a direction in the way you point your finger. It's a degree of freedom. It's an independent way that something can change its position. If you're a bug on a wire, you have one degree of freedom. You can move forward or backward along the wire, and that's it. You are a one-dimensional creature.

[00:02:28]Not because the wire is in some special location, but because only one number is needed to tell someone where you are.

[00:02:35]Give me one number, I can find you. Take that bug and put it on a tabletop. Now you need two numbers. The table topper is two-dimensional. Put a bird in the air. Latitude, longitude, uh, altitude.

[00:02:48]Three numbers, three dimensions. That's the key idea. Dimensions are the number of independent coordinates you need to specify a location. No more, no less.

[00:03:00]Now, you've been told your whole life that space has three dimensions. And in a room like this one, at these speeds, at these energies, for any practical purpose you will ever encounter as a human being, that's true. Walk forward, backward, walk left, right, go up, down, three axes, three numbers, you're done.

[00:03:21]The statement is so obvious, it barely feels like physics. It feels like just looking around. And that's exactly where the danger is. The history of physics is littered with things that seemed obvious until someone looked more carefully and found that obvious was a story the universe was telling us because we hadn't asked hard enough. The earth felt flat. The sun appeared to go around us.

[00:03:43]Time seemed absolute the same for everyone, ticking at the same rate regardless of how fast you moved. Every single one of those intuitions was wrong. Every single one was corrected not by philosophy, not by pure thought, but by people who pushed physics into territory where the ordinary human intuition could not follow and then came back and reported what they found. The question of dimensions is the same kind of question. And the people who first started pushing on it were not science fiction writers. They were mathematicians and physicists working on something else entirely who kept running into the same strange hint that the universe had more directions in it than they could see. Let me tell you about one of them. His name was Theodore Kuza.

[00:04:31]He was a mathematician in Germany. And in 1919, right in the middle of the revolution that Einstein had just uh ignited with general relativity, he sat down and did something beautiful and slightly insane. He took Einstein's field equations, the equations that describe how gravity curves spacetime.

[00:04:51]And he asked, "What happens if I write these equations not in four dimensions, three of space plus one of time, but in five? What if there was one more spatial dimension that nobody has noticed?" And here is where it gets strange. When Kuza wrote out the five-dimensional version of Einstein's equations and then looked at what extra terms appeared, he found sitting right there inside the mathematics uninvited, unrequested Maxwell's equations, the equations that govern electricity and magnetism, they just fell out. Gravity and electromagnetism, two completely separate forces, by every account anyone had ever given, turned out to be unified inside a five-dimensional version of Einstein's theory. They weren't two things. They were two faces of one thing. And the reason they looked separate was that the extra dimension was hidden. Kuza mailed this to Einstein. Einstein sat on it for 2 years. He sat on it because he couldn't find anything wrong with it. And that made him nervous because the result was so extraordinary that finding nothing wrong with it was not good enough. You needed to find something right with it.

[00:05:56]You needed a reason to believe the fifth dimension was actually there and not just a mathematical coincidence. That reason came from a Swedish physicist named Oscar Klene. And it came in the form of a question. Why can't we see this extra dimension? If it's there, why doesn't everything move around in it?

[00:06:14]Why don't we have five-dimensional physics in our everyday experience?

[00:06:18]Klein's answer was this. The extra dimension is there, but it is curled up.

[00:06:24]It is compact. It is rolled into a circle so small that nothing in our experience, no particle, no instrument, no experiment at human scales can detect the curvature, think of it this way. A garden hose seen from far away looks like a line. It's one-dimensional to anyone standing far enough back. But walk up to it, look closely, and you see it has a circumference. It has a circular cross-section. That cross-section is real. It's a second dimension. But if you're the kind of observer who can only see things at coarse resolution, the cross-section is invisible to you and the hose looks like a line. Klein calculated the size of this rolledup dimension. The number he got is called the plank length, roughly 10 theus 35 m. That is not a small number. That is a number so small that no instrument built by human hands has ever probed it or is likely to probe it in our lifetimes. The Large Hadron Collider at CERN, the most powerful particle accelerator ever constructed, operates at length scales about 20 orders of magnitude larger than the plank length. 20 orders of magnitude.

[00:07:38]That's the difference between a single atom in the observable universe. The Kuza Klein dimension, if it exists, is hiding at a depth that makes our most powerful tools look like blunt wooden sticks. So that's the Kuza Klein story.

[00:07:54]And for a while, a long while, it was considered a curiosity, a beautiful piece of mathematics that might or might not correspond to anything real. The physics community moved on to quantum mechanics, then to quantum field theory, then to the standard model of particle physics. The extra dimension idea sat in the corner, occasionally dusted off, mostly ignored, and then string theory happened. I was there when uh string theory happened. Um, not at the very beginning. The very beginning was in the late 1960s when people were trying to understand the strong nuclear force and Gabrieli Vanessiano wrote down a formula that described particle scattering in a way nobody expected and Yoichiro Nambu and others [snorts] realized that this formula was describing something that looked like a vibrating string. I was around for the early part of that working on related ideas and I remember the mood. There was excitement and there was confusion in roughly equal parts.

[00:08:59]What matters for this discussion is what string theory requires because string theory unlike every other framework in physics I've ever encountered does not leave the number of dimensions as a free parameter. It doesn't say hey how many dimensions do you want? Pick a number.

[00:09:16]It says there is one and only one number of dimensions in which the mathematics is consistent. And that number is not four. It's not five. It's 10. Or in an extension of the theory called M theory, 11. When people hear this for the first time, the reaction is usually somewhere between skepticism and laughter. 10 dimensions. Where are they? Why can't we see them? And the answer is the same answer Klene gave in 1926, just dressed up in vastly more sophisticated mathematics. The extra dimensions are compact. They're curled up. They're small. And uh not just small, they're curled up into elaborate geometric shapes called calabi manifolds, which are six-dimensional mathematical objects of staggering complexity and beauty. Each one encoding a different possible physics for the low energy world we actually observe. Let me try a different way of thinking about this because I find the garden hose analogy useful, but uh but limited.

[00:10:19]Here's another one. Imagine you are an ant living on the surface of a very large sphere. You don't know you're on a sphere. From your perspective, you're walking on a flat surface and the geometry you experience is flat parallel lines stay parallel. Angles in a triangle add up to 180°.

[00:10:40]All the usual uklidian rules. Now imagine that sphere starts to shrink. It gets smaller and smaller. Eventually, it gets so small that the sphere itself is not much bigger than you are. And now you can feel the curvature. The geometry changes. Parallel lines start to converge. Triangle angles no longer add up. Right. But now imagine the sphere shrinks further to the size of a cell, to the size of a molecule, to the size of an atom. At that scale, you can't experience the curvature at all. You're too big to fit inside the geometry of the compact space. All you feel is the flat featureless projection, the shadow that the compact space casts into your large dimensions. That's what we are.

[00:11:28]We're too big. Not intellectually. Our minds can reach to the plank scale and beyond. But our bodies, our instruments, our energies, these are all too coarse to excite the modes that live in the compact dimensions. We live in the projection. We see the shadow and we've mistaken the shadow for the whole thing.

[00:11:49]Now I want to go somewhere more radical because what I've told you so far, Kuza Klein, string theory, extra dimensions, that's the polite version. That's the version where extra dimensions are just more of what we already know, just curled up small. There's a more disturbing version and it's connected to something I spent a large part of my career working on and fighting about and eventually I believe getting right. It's called the holographic principle and it says something that even after all these years I find genuinely unsettling.

[00:12:23]Here's where it gets strange. Not just strange in the way physics is always strange at the edges. Strange in the way that makes you question what you mean by real. In the late 1980s and early 1990s, Jacob Beckinstein and Stephven Hawking working from completely different starting points discovered something about black holes that should have been impossible. They found that a black hole has entropy.

[00:12:48]That doesn't sound crazy uh until you ask [snorts] where does the entropy live. Entropy is a measure of information. The number of ways a physical system can be arranged internally while looking the same from the outside. For a box of gas, the entropy lives in the volume of the box.

[00:13:06]For a glass of water, it lives in the volume of the water. Volume is the natural home of entropy for any system in three spatial dimensions. But for a black hole, Beckenstein and Hawking found that the entropy is not proportional to the volume. It's proportional to the surface area. The area of the event horizon, the two-dimensional boundary of the black hole, not its three-dimensional interior. The information content of a black hole is not stored in three dimensions. It's stored in two. When I first encountered this, I thought that's a coincidence or an approximation or an artifact of the particular way Hawking was counting things. I spent years, years trying to make it go away because if it didn't go away, it meant something I was not ready to accept. It didn't go away. What it meant, what I eventually had to accept along with Gerard Hof, who came to the same conclusion from his own direction, is that the fundamental storage of information in the universe appears to be two-dimensional. The three-dimensional world you experience is in a precise and calculable sense encoded on a two-dimensional surface.

[00:14:20]The inside is written on the outside.

[00:14:23]The volume is a projection of the area.

[00:14:25]I want to be very careful here because this is the point where people start reaching for words like illusion and simulation. And I want to stop that before it starts. The three-dimensional world is not an illusion. Illusion means something false, something that deceives you, something that isn't there. When you stub your toe, the pain is real. The toe is real. The three dimensions of the room you're standing in are real. What the holographic principle is saying is something more subtle and more interesting than it's all fake. It's saying that the information needed to describe everything happening in a volume of space can be completely captured by the information on the boundary of that space. The description in three dimensions and the description in two dimensions are equally valid.

[00:15:15]They're dual to each other. They encode the same physics. The question of which one is really real may be the wrong question. That last sentence is the one that keeps me up at night. I spent years fighting Stephven Hawking over a related issue, the black hole information paradox. The question of whether information that falls into a black hole is destroyed. Hawking said it was. He said it loudly, confidently, with the full force of his enormous reputation and his considerable intellect. And for a long time, most of the physics community believed him. I thought he was wrong. Huft thought he was wrong. We argued about it uh publicly for decades.

[00:15:56]It became known as the black hole war, which is a dramatic name for what was at its core a very technical argument about the unitarity of quantum mechanics and the nature of information in the presence of strong gravitational fields.

[00:16:12]In the end, Hawking conceded he changed his mind publicly at a conference in Dublin in 2004. He acknowledged that information was not destroyed, that it was preserved and uh in some form encoded on the surface of the black hole and eventually returned to the world when the black hole evaporated. It was one of the most satisfying moments of my scientific life. And I'm not going to pretend otherwise. When you've been on the losing side of the establishment for 20 years and you turn out to be right, you are allowed to feel good about that.

[00:16:45]But here's what I need you to understand. Hawkings concession was not just a victory in an academic argument.

[00:16:53]It was a confirmation of something much deeper. It was a confirmation that information is real, that it is conserved, and that the laws that govern it are not three-dimensional laws, but something more fundamental, something that lives on boundaries, on surfaces, on the two-dimensional membranes that enclose three-dimensional regions of space. The holographic principle wasn't just a cute fact about black holes. It was a hint about the architecture of reality itself. Let me come at the dimension problem from one more direction because I think the full picture requires it. I want to talk about what physicists mean when they say a dimension is large versus small and why the distinction matters more than it might seem. When we say the extra dimensions in string theory are small, plank scale small, we mean that quantum fluctuations at that scale effectively freeze out those dimensions. Nothing at low energies, meaning nothing at the energies available to us in our laboratories, in our particle accelerators, in the observable universe can excite oscillations in those dimensions. They're inert, dead, invisible, not because they aren't there, but because we don't have the energy to poke them. But there's another possibility uh first proposed seriously in 1998 and 1999 by Nema Arani Hamemed Savos Demopoulos and Gia Dvali the add model and by Lisa Randall and Ramen Sundrum. The extra dimensions don't have to be plank scale small. They could be much larger maybe even large enough in principle to be detected at accelerator scales. The reason we haven't seen them is not just their size, but the fact that the particles of the standard model, quarks, electrons, photons, all the constituents of normal matter are confined to a three-dimensional membrane. They can't move in the extra dimensions. They're stuck on the brain like water molecules stuck on the surface of a soap film, unable to leave the film and travel through the air around it. Gravity, however, is different. Gravity in these models leaks into the extra dimensions. And this is testable. It means that at short enough distances, gravity should deviate from the inverse square law that Newton wrote down three and a half centuries ago.

[00:19:13]Below some critical scale, gravity should get stronger faster than expected because it's spreading into extra dimensions that are normally hidden.

[00:19:21]Experiments have been done to test this.

[00:19:24]You take two masses, bring them very close together, measure the gravitational force, and see whether it falls off as one over the distance squared or more steeply. So far, down to about 50 micrometers, about the width of a human hair, gravity behaves exactly as Newton predicted. But below that scale, we haven't tested. There's room for extra dimensions as large as a fraction of a millimeter, and we would not yet know. I find that remarkable. A dimension larger than a human hair could in principle be sitting right next to you. And every experiment done so far is consistent with its existence. That's not a prediction that it's there, but it's an honest accounting of what we don't know. And what we don't know is more interesting than what we do. Now, I want to say something about mathematics that uh I think is important and often misunderstood.

[00:20:21]Um, people sometimes ask, "Aren't extra dimensions just a mathematical trick?

[00:20:26]Aren't you just playing with numbers?

[00:20:28]Doesn't the fact that the math works in 10 dimensions just mean the math is flexible, not that reality has 10 dimensions?" That's a fair question. And the answer is yes. Mathematics can be flexible, but some mathematics is not flexible in the way you're imagining.

[00:20:46]The consistency of string theory in 10 dimensions is not the same as saying we chose to work in 10 dimensions because it's convenient. It's more like saying we tried to build a consistent quantum theory of gravity and every time we tried it in fewer than 10 dimensions, we ran into contradictions, negative probabilities, infinities we couldn't remove, symmetries that broke in ways they weren't supposed to. 10 dimensions is not a choice. It's a demand. The mathematics requires it the way the mathematics of special relativity requires the speed of light to be the same in every reference frame. You don't get to vote on these things. Whether that mathematical demand corresponds to physical reality is a separate question and it's the hard question and I won't pretend it's settled. String theory remains unconfirmed by experiment. The extra dimensions have not been directly observed. I believe the theory contains deep truths about the universe. The holographic principle emerged from it and the holographic principle has been confirmed in specific models called ads CFT where it is exact but belief is not the same as proof. And I've spent enough of my life arguing against people who confuse those two things that I'm not about to do it myself. What I can tell you is that the structure of the arguments, the way that electromagnetism falls out of Kuza's five-dimensional gravity, the way that black hole entropy comes out proportional to area rather than volume, the way that the quantum gravity in a box turns out to be equivalent to a quantum field theory on the walls of that box with one fewer dimension. These are not coincidences.

[00:22:27]They are not flukes. They have the smell of something real. And in physics, when something has that smell, when the same structure keeps appearing from different directions, when you approach the problem from five different angles and they all point to the same place, you take it seriously, even if you can't yet prove it. I've been doing physics for over 50 years. I've seen a lot of ideas come and go. I've had ideas come and go.

[00:22:52]The extra dimension story has not gone.

[00:22:55]It has gotten richer, more constrained, more connected to things we actually understand. That's what good physics does. It gets harder to dismiss over time, not easier. Let me talk about one more thing and then I'll leave you with the question that I think is the right question to be asking. There's a recent development, recent meaning the last 15 years or so, in which extra dimensions have become not just a theoretical speculation, but a working tool in condensed matter physics. Physicists studying systems like high temperature superconductors, materials that conduct electricity without resistance, at temperatures that have no business conducting without resistance, have found that the mathematics of string theory extra dimensions gives them better answers than any other tool. have the ads CFT correspondence which says that a gravitational theory in a space with one extra dimension is equivalent to a quantum field theory on the boundary of that space turns out to describe the behavior of strongly coupled electrons in materials on earth.

[00:23:58]Now does that mean the materials actually have extra dimensions? No. What it means is that the mathematical structure of extra dimensions captures something true about how certain quantum systems behave. That the geometry of a higher dimensional space is encoding information about a lower dimensional physical system in a way that is precise, calculable and experimentally useful. The extra dimension in this context is not a place where particles live. It is a description of an emergent property of the system. The renormalization group flow, which is the way physics changes as you zoom in and out on different scales, is geometrized as motion in an extra dimension. That's not metaphor. That's mathematics being used to do real physics on real materials. And what it tells me is that the concept of dimensionality is richer, more flexible, and more physically deep than the intuition you walked in here with tonight. Dimension is not a fixed property of the universe that was handed down from on high. It is something that uh emerges that depends on scale that can be different at different energies and distances and that encodes information about physical systems in ways we are only beginning to understand. The three dimensions of your room are real at the scale of your room.

[00:25:18]But zoom in by 35 orders of magnitude and the geometry changes. Zoom out the cosmological scales and the geometry changes again. Spacetime is curved by matter and energy and the simple uklitian picture breaks down entirely.

[00:25:34]Dimension is not a given. It's a feature. And here is where I land after 50 years of thinking about this. We don't know how many dimensions there are. That's not a failure of physics.

[00:25:46]That's physics working. We know what we'd expect if there are compact extra dimensions of different sizes. We know what signatures to look for at the LHC, what deviations from Newton's law to search for at short distances, what imprints on the cosmic microwave background might hint at higher dimensional topology. We have a program, we're working it, but there is a question underneath all of this that I think is more fundamental than how many dimensions are there? And it's the question I want to leave you with. What is a dimension? Not in the textbook sense. I already gave you that. degrees of freedom, independent coordinates. I know, I know. But what is it physically?

[00:26:27]What determines whether the universe has three large dimensions and seven small ones versus four large dimensions and six small ones versus some entirely different configuration that string theory permits and that we can write down on paper but have never been able to select from first principles. Why this geometry? Why these dimensions? Why does our universe sit in the particular corner of the vast landscape of possible string vacua that it sits in? I don't know. Nobody knows. And the people who tell you they know are either confused or lying. What I do know is this. You walked in here tonight with a picture of space in your head. Three dimensions, flat, uklitian, simple, obvious. That picture is not wrong. It is a projection. It is the view from inside the shadow from creatures built at human scale seeing the sliver that evolution needed us to see. The full structure, the curled dimensions, the holographic encoding, the emergent geometry, the higher dimensional landscape of possibility. That structure is not visible to your eyes. It probably never will be. Not directly, not through any sense organ you possess. But it is legible to physics. It leaves fingerprints. It changes the way gravity falls off at short distances. It encodes itself in the entropy of black holes. It appears inside the mathematics of materials on your laboratory bench. It shows up in the consistency conditions of the only theory we have that unifies gravity with quantum mechanics. Your eyes are the problem. They were never built for this. But your mind, the part that can follow an argument, that can demand consistency, that can refuse to accept an easy answer when the hard answer is more true. That part of you reaches further than your eyes ever could. That's what physics is. Not better eyes, a longer reach. And the question of how many dimensions the universe has, that question is still open, still alive, still sitting there, unresolved in the foundations of the best theories we've ever written down.

[00:28:40]Not because we haven't thought hard enough, because it is genuinely hard.

[00:28:44]Because the universe does not owe us an easy geometry. Figure that out. I mean it. Go figure it out.