What do extra dimensions have to do with the strength of gravity? What is a tower of gravitons? How can we detect extra dimensions even if we can’t perceive them? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPT (AUTO-GENERATED)

I always say that one of the things that separates real science from pseudoscience is that while in both you're allowed to say whatever crazy idea pops into your head, in real science, you're obligated to take that idea seriously. You can imagine a late evening. You're hanging out with friends, spitballing some crazy and wild ideas. Maybe there are some illicit substances involved. Maybe all you need is a good wine and cheese pairing. And then you get an idea. and you feel bold enough to share it with a group, hey, everyone, listen, let's calm down, hey, hey, hey, what if the universe had more dimensions? Powerful idea. Interesting idea. Probably wrong idea, but that's never stopped us before. Now, in pseudoscience, this is where the line of thinking largely stops, or you just start spitting out loosely connected ideas that branch off of it. But if you said this to a room full of physicists, you would see something magical happen.

you would start to see these very serious, very smart people taking the idea seriously. And what does it mean to take a wild idea seriously? It means we're going to explore if the idea actually works and if there's a way we can test it. So does the universe have extra dimensions? Well, let's take the idea seriously and see where it takes us. To see if a wild and crazy and potentially wonderful idea actually works in the real world that we happen to find ourselves in, we have to do two things. Actually, make that three. One, we have to see if this new idea fixes any problems that we might have. Does it resolve a long-standing tension? Does it offer a new insight? Does it explain an enduring mystery? For this new idea to work, it has to, you know, do work. And so it has to help us in our journey to a greater understanding of the universe. Two, for this idea to work, it has to fit into known physics. Now, that doesn't mean it can't break anything.

If there's anything physicists like doing, it's breaking all their toys. But we have to figure out what breaks and where and why so that we understand the implications of the new idea. Three, we have to use this new idea to make predictions. We're going to test this sucker out, so we need something to point to, something to probe, something to peel apart and see what goes on inside. And lastly, wait, that makes this number four. Okay, so you need four things to take an idea seriously in physics. Okay, four. Number four, we need to design a way to make those tests happen. Do we need a new observatory or a collider? Can we use old archive data? Can we take an existing setup and twist a knob and look at things through a new angle? Nature is the ultimate arbiter of our ideas, and we have to allow nature to put the idea to the test. Now, when it comes to potentially more dimensions in the universe, we've done all three or four. We've done it all.

We still don't know if there are large extra dimensions. Spoiler alert, I guess. But that's because this is a really sticky, tough problem that requires a lot of nuance and care. And rarely in science do you get clear-cut black and white answers. You instead get a series of, oh, that's interesting, followed by, maybe it works, followed by, ah, nah, turns out that was the wrong approach, followed by, well, what if we tried this instead, and then on and on and on. Like I said, we're going to take our ideas, even the wild ones, seriously. So let's see where this goes. The idea of extra dimensions has been floating around the popular imagination since well back into the 1800s. Just look at the monsters of Lovecraftian lore, for example. But physicists didn't really glom onto the idea until 1919 when a guy named Theodore Kaluza said, hey, Albert, you've got a really great general theory of relativity that operates in four dimensions. Three of space and one at a time.

Well, what if we added an extra dimension to it? I think it might solve some longstanding problems in science. See, taking a wild idea seriously. Kaluza's theory solved a problem of unification. He found that if you add in an extra spatial dimension to our universe, then you could write down a single set of equations that included both gravity and electromagnetism in one formula, in one theory. That's neat. That tells us that there might be deeper connections between the two wildly different forces. It tells us that, oh, if we understand gravity through the language of curvature of space and time, maybe we could understand electromagnetism through a similar language of geometry. That would open up so many cool revelations and insights and technological marvels. One problem, where exactly is that extra dimension? If I go out for a walk, I can choose any direction I want. I can go left or right, forward or backward, up or down.

There's no extra freedom of movement that I've somehow been ignoring this all time. There's no readily apparent direction that is perpendicular to all the other directions. So where is this dimension? We're taking this idea seriously. And step one was putting it to work. Okay, extra dimensions can do something useful in our understanding of physics. But this idea also has to connect to everything else we know about the universe. And everything else we know about the universe does not point to the existence of an extra dimension. We even checked behind the couch cushions. Nope, no extra dimension there. So if an extra dimension brings us new insight in physics, then where does this extra dimension exist? Seven years later, in 1926, another physicist, Oscar Klein, proposed an idea of where the extra dimension could be. It's right here. It's right in front of us. It's everywhere, actually, but it's all curled up on itself so tightly that we never notice.

And that when we move through the normal three dimensions, when we go about living our lives, we're actually wrapping around this tiny curled up dimension again and again and again. We're like circumnavigating that dimension over and over and over again as we travel. And in this dimension is curled up so small that it escapes our everyday notice. The best analogy I have for this, and it's a terrible analogy, but it's the best I got, is those rolling table thingies at x-ray scanners at the airport. You know, your bag comes out of the x-ray machine and then it goes from a conveyor belt to these like rolly thingies. And then you can push your bag down to put your belt back on and all that kind of stuff. Think of those rollers as compact dimensions. When you roll your bag down, it only moves in one direction. But in the process, it circumnavigates all those little rollers, which are curled up in a second dimension. The rollers aren't just going left and right.

They're also going up and down in these big circles. And your bag causes motion through that extra dimension, but but it just keeps on rolling down the line. You don't notice that extra movement. You just notice your bag rolling on down. To make this work, The idea of extra dimensions worked. The extra dimension, or dimensions if you're feeling saucy, have to be way, way small, like all the way down to around the Planck scale. So we're talking, I don't know, like 10 to the minus 33 centimeters or so. To put that scale in perspective, just how tiny that is, you, as in your body sitting right there, is closer to the size of the entire observable universe than the Planck scale is to you. That's small. Too small for us to notice in our day-to-day life or even day-to-day high-energy experiments. So the extra dimension that makes Kaluza's idea work is right here, but all curled up and super tiny.

For the aficionados, you already know that Kaluza-Klein theory, as this idea came to be called, would go underground for a couple decades and then re-emerge as the backbone of string theory. which would go on to require not one, not two, but ten, or maybe eleven, depending on what kind of mood Ed Whitten is in today, compact extra dimensions. Once again, all those dimensions are curled up on themselves at nearly the Planck scale, so we have no hope of directly observing or accessing or experiencing or smelling them. But I'm not talking about string theory today. I'm not interested in super tiny, super curled up, all cutesy-wootsy extra dimensions. I'm interested in large extra dimensions. Obviously, these dimensions can't be too big, otherwise we would have noticed them by now. We'd have a new set of words to complement left, right, up, down, forward, backward. But maybe these extra dimensions can be large compared to the Planck scale, which, to be fair, is literally everything.

And maybe these large extra dimensions don't have all that big of an interaction with everything else. Plus, take this idea seriously. If there are extra dimensions that are not curled up at the Planck scale, can they do anything for us? Can they get some work done? And oh yes, large extra dimensions can get a lot of work done, which is why I'm devoting an entire episode just to this topic. The problem that large extra dimensions just might solve is called the hierarchy problem, and it's one of the nastiest outstanding problems in modern physics. Here's the thing. We've got four forces of nature. Three of them, electromagnetism, strong nuclear, and weak nuclear, are all roughly the same strength. Not really. There are actually many orders of magnitude different from each other, but they're kind of sort of close. And then there's gravity.

Gravity is so weak that it could be billions upon billions and then thrown some trillions on top of that strong and it would still be the weakest of the forces. Here's another way to put it. We discovered just how out of whack the forces of nature are compared to each other when we discovered in the mid-20th century that at high energies, we could merge some of them together. At around 246 gigaelectronvolts, which is just a unit of measure of energy, the electromagnetic and weak nuclear forces combine into a single force called appropriately enough the electroweak force. So that's how much energy you need to bring to the table to get these two forces into alignment, to get them to merge together. If you want gravity to join the party, though, then you need to go all the way up to the Planck energy, which is 10,000 trillion times stronger.

As an aside, yes, there's also the Strong Force and the Grand Unification Scale, where three of the forces merge together, which isn't much smaller than the Planck Scale, but we're not talking about that right now. We're really, really interested in the difference between the weak force and gravity, because those are the two weakest forces of nature, and because we know it's responsible for splitting electromagnetism and weak, and that's the Higgs boson. We don't know how or why the strong force got split off, so we'll save that as a homework problem for later generations. All of this is a roundabout way of repeating that gravity is way weaker than it should be. Okay, great. How do large extra dimensions solve this problem? Well, what if gravity wasn't actually so weak? Or put it another way, what if the Planck scale unification energy wasn't really that high? What if they only appeared that way to us from our perspective?

What if there is more to the universe than just, you know, the universe? What if what we called the universe with its stars and galaxies and all sorts of nonsense and its forces of nature to govern and guide all that nonsense existed in our usual three spatial dimensions? What if there was another dimension? Well, normally we wouldn't notice because all this stuff of the universe was stuck to the normal three. Like, imagine we're ants on the floor. We have everything we need in two dimensions. Scent trails, bits of dropped food, a colony to call home. All of our material existence is contained within these two dimensions. If we're an ant on the floor, we would have no awareness and not even a way to access a third dimension. It could exist, but it wouldn't change anything about our experience of the world. And so by analogy, maybe everything that we call physics, everything that we call material existence, everything that we call reality is confined to three dimensions.

But there's a fourth dimension that nothing experiences, nothing interacts with, nothing talks to. And so we wouldn't know it, but maybe gravity is different. Maybe gravity can spill out into the fourth dimension. Maybe for some special reason, the gravitational force gets to spread out through all the dimensions of the universe while everything else is stuck to the floor. Yeah, it's a crazy idea, but so is Patreon. Patreon.com slash PMSutter is how you can keep supporting this show, and I truly do appreciate it. It's a crazy idea and we love crazy ideas in physics, but we're always going to take them seriously. This idea would explain why gravity is so weak. It gets diluted amongst all the extra dimensions. So only some of it stretches out in our normal three. Sorry, dimension of time. You're not going to be a big part of the story. We're just talking about space here. Like, not enough olive oil to dip your bread in?

We're left a little dry and crusty when it comes to the gravitational strength. Most of gravity is getting wasted, blasting out into hidden, inaccessible dimensions. Another way to put this is that maybe the Planck energy scale is much, much more normal than it appears. But it's only that scale across the full universe. It's normal across the full universe with all of its multidimensional glory. And to us, because we only get to see and experience a thin cross-section of the complete cosmos, does the Planck scale appear so big? This solves a problem. It does work for us. By adding this crazy idea of an extra dimension, we can explain the hierarchy problem by saying, no, no, no, this isn't physics that's driving gravity to be so weak. It's our perspective. It's geometry. Why gravity and not the other forces? Well, for one, that's the only way this idea can work.

Because if the other forces also experienced the extra dimension, then we would have literally seen it by now because photons would be slipping into the extra dimension. But, I mean, to be fair, gravity is special. We know that gravity is a response of space-time to the presence of matter and energy. Thanks, Albert. And so maybe it gets some superpowers that set it apart from the other forces of nature. You know, it's not unreasonable to say. Okay, and exactly how many dimensions are we talking about here? Kaluza and Klein set the stage by introducing one extra dimension. Then string theorists had a lot of fun introducing many more. So maybe there's just one extra dimension. Maybe there are a dozen. I don't know. We're going to figure out how to test it either way. And just how large are these large extra dimensions anyway? They can't be big enough that we would have seen them in our experiments already. So they have to be at least small enough to escape current detection.

And to put the size of the extra dimension within range of the next generation of particle colliders, because we've already checked with the current generation, But if they're just a little teensy bit smaller than what we can currently probe with our experiments, then they have to be around a tenth of a millimeter across. A tenth of a millimeter? That's not much smaller than the hair on your head. Not my head, because I'm bald, but your head, presumably. Yeah, that's tiny, but that's way, way, way, way bigger than the Planck scale. And the only reason we haven't noticed this compact, curled-up dimension existing everywhere throughout the universe at the scale of less than a millimeter is that only gravity gets to experience it. You wave your hand around, you don't get to experience that extra dimension, but gravity does. So let's take this wild idea even more seriously. We've seen how it can fix a problem. We've seen how it connects to the rest of our understanding of the world.

Now we need to figure out how to test it. To test it, I want you to imagine rolling up a piece of paper into a tight cylinder. Or if you happen to be near a source of paper, you can do it in real life. The analogy works either way. The long length of the tube is one of our real usual dimensions. The stuff where the cosmos, you know, happens. The rolled upside is one of the large extra dimensions. Maybe as big as a millimeter, which for our purposes, compared to the Planck scale, is absolutely gigantic. Now imagine sending a particle down the length of the paper. Make it something massless, like a photon. If the tube only had one dimension, then that photon would travel down its length at the speed of light, which is what photons do. But if that photon had access to the extra dimension, if it could experience the extra dimension and travel through it, then its path along the rolled up tube would be different. It wouldn't just travel down the length. That's way too boring.

It would also circulate around and around the extra dimension. It would still travel at the speed of light, but its motion would include movement through the extra hidden dimension. Its motion would include the roundy, aroundy bit. But from our perspective, the extra dimensions are so tightly curled up, maybe you're really, really good at rolling up paper, that we can't see the full motion of the photon as it spirals around. We only see the motion down the length. From our perspective, the photon would now travel less than the speed of light because some of its motion is getting tucked away into dimensions that we can't perceive. But any particle that travels slower than light must have mass. So if photons could access extra dimensions, then they would appear to us to be normal, massive particles. Because some of their motion gets tucked away into hidden dimensions, which would make our perspective make it look like they are traveling at a speed less than light.

But the photon appears to be massless as far as we can tell, so we can conclude that it can't access extra dimensions. But what about gravity? We don't have a quantum theory of gravity, but if we did, we strongly suspect that we would view the gravitational force to be carried by a massless particle called the graviton, because that's a cool sounding name. But if the graviton leaked into extra dimensions like this idea says they do, then it would appear to be massive. It would not appear to be massless anymore because some of its movement would be captured by the hidden dimensions. Because of pure geometry of rolling up some of the dimensions and allowing particles to travel through those extra dimensions, It looks like massless particles suddenly have mass. And what's more, we have to include quantum mechanics in the mix, because of course we do when we take our wild ideas seriously. And quantum mechanics says that every particle has a wave associated with it.

In the long dimension of the tube, the length of the tube, which is in our very rough analogy is our usual dimensions of reality. That little graviton with its little wave can have any wavelength that it wants. There's nothing to stop it. But in the compact rolled up dimension, the wavelengths have to fit. You have to have whole wavelengths, a one, three, four, so on, like plucked strings on a guitar. Only certain wavelengths will fit going around. So the action of rolling up one of the dimensions of the universe creates a quantum effect on any particles that can access it. What it does is this really crazy thing where the single massless particle that just wants to live its life and travel freely through all the extra dimensions gets effectively split into a number of different massive particles. One particle for each wavelength that can fit around the rolled up dimensions. Not just a few particles.

An infinite number of particles, each one with a different wavelength and a different mass. Keep in mind, there's still only one single massless particle, but because we have a severely restricted point of view, we don't get to follow the particle in its travels through the extra dimensions. What we see instead appears to be an infinite number of massive particles. This is wild. This is known as the graviton tower or the Kaluza-Klein tower or just the tower if you're in a hurry. What this means is that we now have a tool to peer into the extra dimensions of the universe. Not directly, sorry, we're still little ants crawling on the floor looking for scraps, but those extra gravitons can now exist as real particles. They have mass, they have range, they have speeds, they have lifetimes, they have properties that manifest in the real world that we can then go looking for.

We don't get to see a massless graviton, but because it can access dimensions that we can't, from our perspective, we now have an infinite number of massive gravitons that we can go looking for. And most crucially, these gravitons get to slip away into extra dimensions. Just like you imagine a bad guy doing in a bad sci-fi movie is a cheap plot device. Oh, we're about to get the evil mastermind that, oh, there he goes, slipping into another dimension. A little graviton gets created through some high-energy process. From our perspective, it doesn't just appear as a single massless graviton. It appears as a whole number of massive gravitons, and these gravitons can slip away into extra dimensions that we can't normally perceive. By the way, there's an extra bit of jargon here that I need to get off my chest for various nerdy reasons sponsored by string theory. Our usual universe is sometimes called the brain. Not thinking brain, but membrane.

And the extra dimensions are called the bulk, but I'm not a big fan of this jargon because it leads to a lot of confusion and extra bookkeeping to keep track of the bulky bits and the brainy bits. So that's all I'm going to say about it, just so you know. We don't get to follow the gravitons into the extra dimensions, but if we keep careful accounting, we can see if we're missing anything. If we run a high energy particle collider experiment, and trust me, this is something we absolutely love to do. then some of those reactions will create this tower of gravitons, which sounds like something out of Lord of the Rings, but I digress. These gravitons will have mass and energy and momentum, and then they'll slip away because that's what they do. So when we run our experiments, we'll know there's a certain amount of mass and energy and momentum going in because we designed our experiment to know these sorts of things.

And then at the end, we'll find missing mass and energy and momentum, also because we designed our experiments to know these kinds of things. If the numbers don't math up, then we have evidence that the Tower of Gravitons is stealing away some momentum and taking it into extra dimensions. So we did that. And we found nothing. So far, with all of our experiments around the world, we find no evidence of missing momentum. No signs of towers of gravitons slipping away into hidden dimensions. As usual in physics, like I said at the beginning, this doesn't rule out the idea completely. It only places limits on how big the extra dimensions can be. If the extra dimensions are very small, then that means our current colliders can't reach the energies needed to start making those towers of gravitons. But there are other ways to poke at this too.

Clever physicists have, over the decades, devised a series of experiments that you can fit on a single lab bench to accurately measure the strength of gravity. Since gravity is allowed to escape away into extra dimensions, then the closer you get to where those dimensions exist, then you would expect some deviations from normal Newtonian gravitational interactions. And we can go big. I know we have all these fancy, super expensive particle gliders and all that. But nothing beats nature itself when it comes to the raw ability to make really big explosions. A typical supernova detonation makes even the Large Hadron Collider look like a joke. And it should produce numbers, massive numbers, of massive gravitons. These gravitons then existing would get caught up inside any neutron star that would come out of the business end of a supernova. But these gravitons wouldn't last forever, even in the warm and snug confines of a neutron star.

As they decay, they would provide their own source of heat and radiation, which would show up as a unique signature in the light emitted from the neutron stars. You put all these together and we have some pretty tight constraints on how large the large extra dimensions can possibly be. For low numbers of extra dimensions, like two or three dimensions, we're talking only a hundredth of a nanometer. That's how big they can be. For larger numbers of dimensions, like five or six extra ones, they have to be even smaller. This is all far tinier than the promised largeness of the large extra dimensions. And it puts a big wet blanket on the whole idea. The whole point of this exercise was to get rid of the hierarchy problem. But the only way to bring the Planck unification energy scale down was to have large extra dimensions be large. But now we know they're not so large after all, which doesn't exactly solve the hierarchy problem. So are we done? Not quite.

All of these calculations and assumptions and testing were based on a model developed in 1998 by Nima Arkani Ahmed, Savas Dimopoulos, and Gia Diwali. Their model assumed that the extra dimensions were spatially flat. Well, how can they be both flat and curled up on themselves? Well, that's because cylinders and donuts are geometrically flat. Parallel lines stay parallel. Triangles stay as triangles, but they have different topologies. So it's all good, and donuts are delicious. But what if the extra dimensions aren't flat? I know our usual universe spatial dimensions appear to be flat, but whoever said the extra ones have to obey the same rules? They're extra. They can do whatever they want. In 1999, Lisa Randall and Raman Sundaram made a modification to the old flat space model where they said, well, what if the extra dimensions have a big curvature to them?

This curvature to the extra dimensions changes how the Tower of Gravitons, which is now, by the way, one of my favorite jargon phrases ever, behaves. The whole tower was built on the graviton wavelengths having to fit as they wrap around the extra dimension. This turned a single massless graviton into a whole bunch of massive gravitons starting with very light ones and going on up. But no more. With curvature, the gravitons have a lot more flexibility to do whatever they want. This accomplishes two things. One, we can still solve our hierarchy problem by allowing gravitons to slip away to extra dimensions. And two, the gravitons that appear in our corner of the universe can now have a very high mass so they can escape experimental detection. This is good news and bad news. The good news is that this allows the whole extra dimension shtick to solve the hierarchy problem while still evading current experimental constraints.

The bad news is that this allows the whole extra dimension shtick to solve the hierarchy problem while still evading current experimental constraints. It makes the theory work, but it potentially makes the theory untestable. At present, we don't have any firm constraints on the Randall-Sundrum version of large extra dimensions. There are some proposals out there exploring how we might be able to manufacture some of the lowest mass-predicted gravitons with upcoming experiments, or find some clever way to see evidence for those same gravitons in the various high-energy processes that dot the universe. So the idea... It's not fringe, but it's not exactly favored. It seems unlikely because once you start having to add complications to theories and once you start finding reasons to escape experimental constraints... we don't like the idea as much because we like stuff that can work. We like stuff that we can test with today's technology and tomorrow's technology.

We always like that because then we have an excuse to go ask for more funding. But once things start to get a little bit ridiculous, a little bit far-fetched, we just turn our attention to other things. But we're going to keep taking this idea seriously. But if we see no evidence that extra dimensions exist, or have no way of reasonably accessing that evidence with current and future technologies, then no matter how appealing the idea might be, or how many problems it might resolve, or how cool it might sound to your circle of friends, if we're going to go all the way and take a wild idea as seriously as possible... then we have to be willing to let it go. Seriously. Thanks to Tim C, at Producer Evie, Brad G, and Michael P for the questions that led to today's episode. Thank you to everyone for all of your contributions to Patreon. That's patreon.com slash pmsutter. Thank you for asking questions. Keep this show going. That is by far the most important thing.

Vital thing you can do is askaspaceman at gmail.com or the website askaspaceman.com. Thank you for the lovely reviews that you are dropping on your favorite podcasting platform. They are a delight to read to see how this podcast has affected your life. This podcast has changed my life. I love doing every single episode and sharing the joy of this universe with you. But thank you for just listening and asking questions. I do want to thank my top Patreon contributors this month. They're Justin G, Chris L, Alberto M, Duncan M, Corey D, Michael P, Nyla, Sam R, Joshua, Scott M, Scott M, Lewis M, John W, Alexis, Gilbert M, Rob W, Jessica M, Jules R, Jim L, David S, Scott R, Heather, Mike S, Pete H, Steve S, Lisa R, Kevin B, Eileen G, Stephen W, Deb A, Michael J, Philip L, and Stephen B. That's patreon.com slash pmsutter. And I will see you next time for more complete knowledge of time and space. Thank you.

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