Tag Archives: gravity

When to Look under the Bed

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Last week, Sabine Hossenfelder blogged about a rather interesting experiment, designed to test the quantum properties of gravity. Normally, quantum gravity is essentially unobservable: quantum effects are typically only relevant for very small systems, where gravity is extremely weak. However, there has been a lot of progress in putting larger and larger systems into interesting quantum states, and a team of experimentalists has recently proposed a setup. The experiment wouldn’t have enough detail to, for example, distinguish between rival models of quantum gravity, but it would provide evidence as to whether or not gravity is quantum at all.

Lubos Motl, meanwhile, argues that such an experiment is utterly pointless, because there is no possible way that gravity could not be quantum. I won’t blame you if you don’t read his argument since it’s written in his trademark…aggressive…style, but the gist is that it’s really hard to make sense of the idea that there are non-quantum things in an otherwise quantum world. It causes all sorts of issues with pretty much every interpretation of quantum mechanics, and throws the differences between those interpretations into particularly harsh and obvious light. From this perspective, checking to see if gravity might not actually be quantum (an idea called semi-classical gravity) is a bit like checking for a monster under the bed.

You might find semi-classical gravity!

In general, I share Motl’s reservations about semi-classical gravity. As I mentioned back when journalists were touting the BICEP2 results as evidence of quantum gravity, the idea that gravity could not be quantum doesn’t really make much sense. (Incidentally, Hossenfelder makes a similar point in her post.)

All that said, sometimes in science it’s absolutely worth looking under the bed.

Take another unlikely possibility, that of cell phone radiation causing cancer. Things that cause cancer do it by messing with the molecular bonds in DNA. In order to mess with molecular bonds, you need high-frequency light. That’s how UV light from the sun can cause skin cancer. Cell phones emit microwaves, which are very low-frequency light. It’s what allows them to be useful inside of buildings, where normal light wouldn’t reach. It also means it’s impossible for them to cause cancer.

Nevertheless, if nobody had ever studied whether cell phones cause cancer, it would probably be worth at least one study. If that study came back positive, it would say something interesting, either about the study’s design or about other possible causes of cancer. If negative, the topic could be put to bed more convincingly. As it happens, those studies have been done, and overall confirm the expectations we have from basic science.

Another important point here is that experimentalists and theorists have different priorities, due to their different specializations. Theorists are interested in confirmation for particular theories: they want not just an unknown particle, but a gluino, and not just a gluino, but the gluino predicted by their particular model of supersymmetry. By contrast, experimentalists typically aren’t very interested in proving or disproving one theory or another. Rather, they look for general signals that indicate broad classes of new physics. For example, experimentalists might use the LHC to look for a leptoquark, a particle that allows quarks and leptons to interact, without caring what theory might produce them. Experimentalists are also very interested in improving their techniques. Much like theorists, a lot of interesting work in the field involves pushing the current state-of-the-art as far as it will go.

So, when should we look under the bed?

Well, if nobody has ever looked under this particular bed before, and if seeing something strange under this bed would at least be informative, and if looking under the bed serves as a proving ground for the latest in bed-spelunking technology, then yes, we should absolutely look under this bed.

Just don’t expect to see any monsters.

Romeo and Juliet, through a Wormhole

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Perimeter is hosting this year’s Mathematica Summer School on Theoretical Physics. The school is a mix of lectures on a topic in physics (this year, the phenomenon of quantum entanglement) and tips and tricks for using the symbolic calculation program Mathematica.

Juan Maldacena is one of the lecturers, which gave me a chance to hear his Romeo and Juliet-based explanation of the properties of wormholes. While I’ve criticized some of Maldacena’s science popularization work in the past, this one is pretty solid, so I thought I’d share it with you guys.

You probably think of wormholes as “shortcuts” to travel between two widely separated places. As it turns out, this isn’t really accurate: while “normal” wormholes do connect distant locations, they don’t do it in a way that allows astronauts to travel between them, Interstellar-style. This can be illustrated with something called a Penrose diagram:

Static

Static “Greyish Black” Diagram

In the traditional Penrose diagram, time goes upward, while space goes from side to side. In order to measure both in the same units, we use the speed of light, so one year on the time axis corresponds to one light-year on the space axis. This means that if you’re traveling at a 45 degree line on the diagram, you’re going at the speed of light. Any lower angle is impossible, while any higher angle means you’re going slower.

If we start in “our universe” in the diagram, can we get to the “other universe”?

Pretty clearly, the answer is no. As long as we go slower than the speed of light, when we pass the event horizon of the wormhole we will end up, not in the “other universe”, but at the part of the diagram labeled Future Singularity, the singularity at the center of the black hole. Even going at the speed of light only keeps us orbiting the event horizon for all eternity, at best.

What use could such a wormhole be? Well, imagine you’re Romeo or Juliet.

Romeo has been banished from Verona, but he took one end of a wormhole with him, while the other end was left with Juliet. He can’t go through and visit her, she can’t go through and visit him. But if they’re already considering taking poison, there’s an easier way. If they both jump in to the wormhole, they’ll fall in to the singularity. Crucially, though, it’s the same singularity, so once they’re past the event horizon they can meet inside the black hole, spending some time together before the end.

Depicted here for more typical quantum protagonists, Alice and Bob.

This explains what wormholes really are: two black holes that share a center.

Why was Maldacena talking about this at a school on entanglement? Maldacena has recently conjectured that quantum entanglement and wormholes are two sides of the same phenomenon, that pairs of entangled particles are actually connected by wormholes. Crucially, these wormholes need to have the properties described above: you can’t use a pair of entangled particles to communicate information faster than light, and you can’t use a wormhole to travel faster than light. However, it is the “shared” singularity that ends up particularly useful, as it suggests a solution to the problem of black hole firewalls.

Firewalls were originally proposed as a way of getting around a particular paradox relating three states connected by quantum entanglement: a particle inside a black hole, radiation just outside the black hole, and radiation far away from the black hole. The way the paradox is set up, it appears that these three states must all be connected. As it turns out, though, this is prohibited by quantum mechanics, which only allows two states to be entangled at a time. The original solution proposed for this was a “firewall”, a situation in which anyone trying to observe all three states would “burn up” when crossing the event horizon, thus avoiding any observed contradiction. Maldacena’s conjecture suggests another way: if someone interacts with the far-away radiation, they have an effect on the black hole’s interior, because the two are connected by a wormhole! This ends up getting rid of the contradiction, allowing the observer to view the black hole and distant radiation as two different descriptions of the same state, and it depends crucially on the fact that a wormhole involves a shared singularity.

There’s still a lot of detail to be worked out, part of the reason why Maldacena presented this research here was to inspire more investigation from students. But it does seem encouraging that Romeo and Juliet might not have to face a wall of fire before being reunited.

Got Branes on the Brain?

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You’ve probably heard it said that string theory contains two types of strings: open, and closed. Closed strings are closed loops, like rubber bands. They give rise to gravity, and in superstring theories to supergravity. Open strings have loose ends, like a rubber band cut in half. They give us Yang-Mills forces, and super Yang-Mills for superstrings.

String theory has more than just strings, though. It also has branes.

Branes, short for membranes, are objects like strings but in other dimensions. The simplest to imagine is a two-dimensional membrane, like a sheet of paper. A three-dimensional membrane would fill all of 3D space, like an infinite cube of jello. Higher dimensional membranes also exist, up to string theory’s limit of nine spatial dimensions.

But you can keep imagining them as sheets of paper if you’d like.

So where did these branes come from? Why doesn’t string theory just have strings?

You might think we’re just trying to be as general as possible, including every possible dimension of object. Strangely enough, this isn’t actually what’s going on! As it turns out, branes can be in lower dimensions too: there are zero-dimensional branes that behave like particles, and one-dimensional branes that are similar to, but crucially not the same thing as, the strings we started out with! If we were just trying to get an object for every dimension we wouldn’t need one-dimensional branes, we’d already have strings!

(By the way, there are also “-1” dimensional branes, but that’s a somewhat more advanced topic.)

Instead, branes come from some strange properties of open strings.

I told you that the ends of open strings are “loose”, but that’s just loose language on my part. Mathematically, there are two options: the ends can be free to wander, or they can be fixed in place. If they’re free, they can move wherever they like with no resistance. If they’re fixed, any attempt to move them will just set them vibrating.

The thing is, you choose between these two options not just once, but once per dimension. You could have the end of the string free to move in two dimensions, but fixed in another, like a magnet was sticking it to some sort of 2D surface…like a brane.

Brane-worlds are dangerous places to live.

In mathematics, the fixed dimensions of end of the string are said to have Dirichlet boundary conditions, which is why this type of branes are called Dirichlet branes, or D-branes. In general, D-branes are things strings can end on. That’s why you can have D1-branes, that despite their string-like shape are different from actual strings: rather, they’re things strings can end on.

You might wonder whether we really need these things. Sure, they’re allowed mathematically, but is that really a good enough reason?

As it turns out, D-branes are not merely allowed in string theory, they are required, due to something called T-duality. I’ve talked about dualities before: they’re relationships between different theories that secretly compute the same thing. T-duality was one of the first-discovered dualities in string theory, and it involves relationships between strings wrapped around circular dimensions.

If a dimension is circular, then closed strings can either move around the circle, or wrap around it instead. As it turns out, a string moving around a small circle has the same energy as a string wrapped around a big circle, where here “small” and “big” are comparisons to the length of the string. It’s not just the energy, though: for every physical quantity, the two descriptions (big circle with strings traveling along it, small circle with strings wrapped around it) give the same answer: the two theories are dual.

If it works with closed strings, what about open strings?

Here something weird happens: if you perform the T-duality operation (switch between the small circle and the big one), then the ends of open strings switch from being free to being fixed! This means that even if we start out with no D-branes at all, our theory was equivalent to one with D-branes all along! No matter what we do, we can’t write down a theory that doesn’t have D-branes!

As it turns out, we could have seen this coming even without string theory, just by looking at (super)gravity.

Long before people saw astrophysical evidence for black holes, before they even figured out that stars could collapse, they worked out the black hole solution in general relativity. Without knowing anything about the sort of matter that could form a black hole, they could nevertheless calculate what space-time would look like around one.

In ten dimensional supergravity, you can do these same sorts of calculations. Instead of getting black holes, though, you get black branes. Rather than showing what space-time looks like around a high-mass point, they showed what it would look like around a higher dimensional, membrane-shaped object. And miraculously, they corresponded exactly to the D-branes that are supposed to be part of string theory!

So if we want string theory, or even supergravity, we’re stuck with D-branes. It’s a good thing we are, too, because D-branes are very useful. In the past, I’ve talked about how most of the fundamental forces of nature have multiple types of charge. One way for string theory to reproduce these multiple types of charge is with D-branes. If each open string is connected to two D-branes, it can behave like gluons, carrying a pair of charges. Since each end of the string is stuck to its respective brane, the charge corresponding to each brane must be conserved, just like charges in the real world.

D-branes aren’t one of the original assumptions of string theory, but they’re a large part of what makes string theory tick. M theory, string theory’s big brother, doesn’t have strings at all: just two- and five-dimensional branes. So be grateful for branes: they make the world a much more interesting place.

What Counts as a Fundamental Force?

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I’m giving a presentation next Wednesday for Learning Unlimited, an organization that presents educational talks to seniors in Woodstock, Ontario. The talk introduces the fundamental forces and talks about Yang and Mills before moving on to introduce my work.

While practicing the talk today, someone from Perimeter’s outreach department pointed out a rather surprising missing element: I never mention gravity!

Most people know that there are four fundamental forces of nature. There’s Electromagnetism, there’s Gravity, there’s the Weak Nuclear Force, and there’s the Strong Nuclear Force.

Listed here by their most significant uses.

What ties these things together, though? What makes them all “fundamental forces”?

Mathematically, gravity is the odd one out here. Electromagnetism, the Weak Force, and the Strong Force all share a common description: they’re Yang-Mills forces. Gravity isn’t. While you can sort of think of it as a Yang-Mills force “squared”, it’s quite a bit more complicated than the Yang-Mills forces.

You might be objecting that the common trait of the fundamental forces is obvious: they’re forces! And indeed, you can write down a force law for gravity, and a force law for E&M, and umm…

[Mumble Mumble]

Ok, it’s not quite as bad as xkcd would have us believe. You can actually write down a force law for the weak force, if you really want to, and it’s at least sort of possible to talk about the force exerted by the strong interaction.

All that said, though, why are we thinking about this in terms of forces? Forces are a concept from classical mechanics. For a beginning physics student, they come up again and again, in free-body diagram after free-body diagram. But by the time a student learns quantum mechanics, and quantum field theory, they’ve already learned other ways of framing things where forces aren’t mentioned at all. So while forces are kind of familiar to people starting out, they don’t really match onto anything that most quantum field theorists work with, and it’s a bit weird to classify things that only really appear in quantum field theory (the Weak Nuclear Force, the Strong Nuclear Force) based on whether or not they’re forces.

Isn’t there some connection, though? After all, gravity, electromagnetism, the strong force, and the weak force may be different mathematically, but at least they all involve bosons.

Well, yes. And so does the Higgs.

The Higgs is usually left out of listings of the fundamental forces, because it’s not really a “force”. It doesn’t have a direction, instead it works equally at every point in space. But if you include spin 2 gravity and spin 1 Yang-Mills forces, why not also include the spin 0 Higgs?

Well, if you’re doing that, why not include fermions as well? People often think of fermions as “matter” and bosons as “energy”, but in fact both have energy, and neither is made of it. Electrons and quarks are just as fundamental as photons and gluons and gravitons, just as central a part of how the universe works.

I’m still trying to decide whether my presentation about Yang-Mills forces should also include gravity. On the one hand, it would make everything more familiar. On the other…pretty much this entire post.

Merry Newtonmas!

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Yesterday, people around the globe celebrated the birth of someone whose new perspective and radical ideas changed history, perhaps more than any other.

I’m referring, of course, to Isaac Newton.

Ho ho ho!

Born on December 25, 1642, Newton is justly famed as one of history’s greatest scientists. By relating gravity on Earth to the force that holds the planets in orbit, Newton arguably created physics as we know it.

However, like many prominent scientists, Newton’s greatness was not so much in what he discovered as how he discovered it. Others had already had similar ideas about gravity. Robert Hooke in particular had written to Newton mentioning a law much like the one Newton eventually wrote down, leading Hooke to accuse Newton of plagiarism.

Newton’s great accomplishment was not merely proposing his law of gravitation, but justifying it, in a way that no-one had ever done before. When others (Hooke for example) had proposed similar laws, they were looking for a law that perfectly described the motion of the planets. Kepler had already proposed ellipse-shaped orbits, but it was clear by Newton and Hooke’s time that such orbits did not fully describe the motion of the planets. Hooke and others hoped that if some sufficiently skilled mathematician started with the correct laws, they could predict the planets’ motions with complete accuracy.

The genius of Newton was in attacking this problem from a different direction. In particular, Newton showed that his laws of gravitation do result in (incorrect) ellipses…provided that there was only one planet.

With multiple planets, things become much more complicated. Even just two planets orbiting a single star is so difficult a problem that it’s impossible to write down an exact solution.

Sensibly, Newton didn’t try to write down an exact solution. Instead, he figured out an approximation: since the Sun is much bigger than the planets, he could simplify the problem and arrive at a partial solution. While he couldn’t perfectly predict the motions of the planets, he knew more than that they were just “approximately” ellipses: he had a prediction for how different from ellipses they should be.

That step was Newton’s great contribution. That insight, that science was able not just to provide exact answers to simpler problems but to guess how far those answers might be off, was something no-one else had really thought about before. It led to error analysis in experiments, and perturbation methods in theory. More generally, it led to the idea that scientists have to be responsible, not just for getting things “almost right”, but for explaining how their results are still wrong.

So this holiday season, let’s give thanks to the man whose ideas created science as we know it. Merry Newtonmas everyone!

The Three Things Everyone Gets Wrong about the Big Bang

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Ah, the Big Bang, our most science-y of creation myths. Everyone knows the story of how the universe and all its physical laws emerged from nothing in a massive explosion, growing from a singularity to the size of a breadbox until, over billions of years, it became the size it is today.

bigbang

A hot dense state, if you know what I mean.

…actually, almost nothing in that paragraph is true. There are a lot of myths about the Big Bang, born from physicists giving sloppy explanations. Here are three things most people get wrong about the Big Bang:

1. A Massive Explosion:

When you picture the big bang, don’t you imagine that something went, well, bang?

In movies and TV shows, a time traveler visiting the big bang sees only an empty void. Suddenly, an explosion lights up the darkness, shooting out stars and galaxies until it has created the entire universe.

Astute readers might find this suspicious: if the entire universe was created by the big bang, then where does the “darkness” come from? What does the universe explode into?

The problem here is that, despite the name, the big bang was not actually an explosion.

In picturing the universe as an explosion, you’re imagining the universe as having finite size. But it’s quite likely that the universe is infinite. Even if it is finite, it’s finite like the surface of the Earth: as Columbus (and others) experienced, you can’t get to the “edge” of the Earth no matter how far you go: eventually, you’ll just end up where you started. If the universe is truly finite, the same is true of it.

Rather than an explosion in one place, the big bang was an explosion everywhere at once. Every point in space was “exploding” at the same time. Each point was moving farther apart from every other point, and the whole universe was, as the song goes, hot and dense.

So what do physicists mean when they say that the universe at some specific time was the size of a breadbox, or a grapefruit?

It’s just sloppy language. When these physicists say “the universe”, what they mean is just the part of the universe we can see today, the Hubble Volume. It is that (enormously vast) space that, once upon a time, was merely the size of a grapefruit. But it was still adjacent to infinitely many other grapefruits of space, each one also experiencing the big bang.

2. It began with a Singularity:

This one isn’t so much definitely wrong as probably wrong.

If the universe obeys Einstein’s Theory of General Relativity perfectly, then we can make an educated guess about how it began. By tracking back the expansion of the universe to its earliest stages, we can infer that the universe was once as small as it can get: a single, zero-dimensional point, or a singularity. The laws of general relativity work the same backwards and forwards in time, so just as we could see a star collapsing and know that it is destined to form a black hole, we can see the universe’s expansion and know that if we traced it back it must have come from a single point.

This is all well and good, but there’s a problem with how it begins: “If the universe obeys Einstein’s Theory of General Relativity perfectly”.

In this situation, general relativity predicts an infinitely small, infinitely dense point. As I’ve talked about before, in physics an infinite result is almost never correct. When we encounter infinity, almost always it means we’re ignoring something about the nature of the universe.

In this case, we’re ignoring Quantum Mechanics. Quantum Mechanics naturally makes physics somewhat “fuzzy”: the Uncertainty Principle means that a quantum state can never be exactly in one specific place.

Combining quantum mechanics and general relativity is famously tricky, and the difficulty boils down to getting rid of pesky infinite results. However, several approaches exist to solving this problem, the most prominent of them being String Theory.

If you ask someone to list string theory’s successes, one thing you’ll always hear mentioned is string theory’s ability to understand black holes. In general relativity, black holes are singularities: infinitely small, and infinitely dense. In string theory, black holes are made up of combinations of fundamental objects: strings and membranes, curled up tight, but crucially not infinitely small. String theory smooths out singularities and tamps down infinities, and the same story applies to the infinity of the big bang.

String theory isn’t alone in this, though. Less popular approaches to quantum gravity, like Loop Quantum Gravity, also tend to “fuzz” out singularities. Whichever approach you favor, it’s pretty clear at this point that the big bang didn’t really begin with a true singularity, just a very compressed universe.

3. It created the laws of physics:

Physicists will occasionally say that the big bang determined the laws of physics. Fans of Anthropic Reasoning in particular will talk about different big bangs in different places in a vast multi-verse, each producing different physical laws.

I’ve met several people who were very confused by this. If the big bang created the laws of physics, then what laws governed the big bang? Don’t you need physics to get a big bang in the first place?

The problem here is that “laws of physics” doesn’t have a precise definition. Physicists use it to mean different things.

In one (important) sense, each fundamental particle is its own law of physics. Each one represents something that is true across all of space and time, a fact about the universe that we can test and confirm.

However, these aren’t the most fundamental laws possible. In string theory, the particles that exist in our four dimensions (three space dimensions, and one of time) change depending on how six “extra” dimensions are curled up. Even in ordinary particle physics, the value of the Higgs field determines the mass of the particles in our universe, including things that might feel “fundamental” like the difference between electromagnetism and the weak nuclear force. If the Higgs field had a different value (as it may have early in the life of the universe), these laws of physics would have been different. These sorts of laws can be truly said to have been created by the big bang.

The real fundamental laws, though, don’t change. Relativity is here to stay, no matter what particles exist in the universe. So is quantum mechanics. The big bang didn’t create those laws, it was a natural consequence of them. Rather than springing physics into existence from nothing, the big bang came out of the most fundamental laws of physics, then proceeded to fix the more contingent ones.

In fact, the big bang might not have even been the beginning of time! As I mentioned earlier in this article, most approaches to quantum gravity make singularities “fuzzy”. One thing these “fuzzy” singularities can do is “bounce”, going from a collapsing universe to an expanding universe. In Cyclic Models of the universe, the big bang was just the latest in a cycle of collapses and expansions, extending back into the distant past. Other approaches, like Eternal Inflation, instead think of the big bang as just a local event: our part of the universe happened to be dense enough to form a big bang, while other regions were expanding even more rapidly.

So if you picture the big bang, don’t just imagine an explosion. Imagine the entire universe expanding at once, changing and settling and cooling until it became the universe as we know it today, starting from a world of tangled strings or possibly an entirely different previous universe.

Sounds a bit more interesting to visit in your TARDIS, no?

What Can Replace Space-Time?

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Nima Arkani-Hamed is famous for believing that space-time is doomed, that as physicists we will have to abandon the concepts of space and time if we want to find the ultimate theory of the universe. He’s joked that this is what motivates him to get up in the morning. He tends to bring it up often in talks, both for physicists and for the general public.

The latter especially tend to be baffled by this idea. I’ve heard a lot of questions like “if space-time is doomed, what could replace it?”

In the past, Nima and I both tended to answer this question with a shrug. (Though a more elaborate shrug in his case.) This is the honest answer: we don’t know what replaces space-time, we’re still looking for a good solution. Nima’s Amplituhedron may eventually provide an answer, but it’s still not clear what that answer will look like. I’ve recently realized, though, that this way of responding to the question misses its real thrust.

When people ask me “what could replace space-time?” they’re not asking “what will replace space-time?” Rather, they’re asking “what could possibly replace space-time?” It’s not that they want to know the answer before we’ve found it, it’s that they don’t understand how any reasonable answer could possibly exist.

I don’t think this concern has been addressed much by physicists, and it’s a pity, because it’s not very hard to answer. You don’t even need advanced physics. All you need is some fairly old philosophy. Specifically we’ll use concepts from metaphysics, the branch of philosophy that deals with categories of being.

Think about your day yesterday. Maybe you had breakfast at home, drove to work, had a meeting, then went home and watched TV.

Each of those steps can be thought of as an event. Each event is something that happened that we want to pay attention to. You having breakfast was an event, as was you arriving at work.

These events are connected by relations. Here, each relation specifies the connection between two events. There might be a relation of cause-and-effect, for example, between you arriving at work late and meeting with your boss later in the day.

Space and time, then, can be seen as additional types of relations. Your breakfast is related to you arriving at work: it is before it in time, and some distance from it in space. Before and after, distant in one direction or another, these are all relations between the two events.

Using these relations, we can infer other relations between the events. For example, if we know the distance relating your breakfast and arriving at work, we can make a decent guess at another relation, the difference in amount of gas in your car.

This way of viewing the world, events connected by relations, is already quite common in physics. With Einstein’s theory of relativity, it’s hard to say exactly when or where an event happened, but the overall relationship between two events (distance in space and time taken together) can be thought of much more precisely. As I’ve mentioned before, the curved space-time necessary for Einstein’s theory of gravity can be thought of equally well as a change in the way you measure distances between two points.

So if space and time are relations between events, what would it mean for space-time to be doomed?

The key thing to realize here is that space and time are very specific relations between events, with very specific properties. Some of those properties are what cause problems for quantum gravity, problems which prompt people to suggest that space-time is doomed.

One of those properties is the fact that, when you multiply two distances together, it doesn’t matter which order you do it in. This probably sounds obvious, because you’re used to multiplying normal numbers, for which this is always true anyway. But even slightly more complicated mathematical objects, like matrices, don’t always obey this rule. If distances were this sort of mathematical object, then multiplying them in different orders could give slightly different results. If the difference were small enough, we wouldn’t be able to tell that it was happening in everyday life: distance would have given way to some more complicated concept, but it would still act like distance for us.

That specific idea isn’t generally suggested as a solution to the problems of space and time, but it’s a useful toy model that physicists have used to solve other problems.

It’s the general principle I want to get across: if you want to replace space and time, you need a relation between events. That relation should behave like space and time on the scales we’re used to, but it can be different on very small scales (Big Bang, inside of Black Holes) and on very large scales (long-term fate of the universe).

Space-time is doomed, and we don’t know yet what’s going to replace it. But whatever it is, whatever form it takes, we do know one thing: it’s going to be a relation between events.

N=8: That’s a Whole Lot of Symmetry

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In two weeks, I’m planning an extensive overhaul of the blog. I’ll be switching from 4gravitons.wordpress.com to just 4gravitons.wordpress.com, since I’m no longer a grad student. Don’t worry, I’ll be forwarding traffic from the old address, so if you miss the changeover you’ll have plenty of time to readjust. I’ll also be changing the blog’s look a bit, and adding some new tools and sections, including my current project, a series on the theory N=8 supergravity. This is post will be the last in the N=8 supergravity series.

I’ve told you about how gravity can be thought of as interactions with spin 2 particles, called gravitons. I’ve talked about how adding supersymmetry gives you a whole new type of particle, a gravitino, one different from all of the other particles we’ve seen in nature. Add supersymmetry to gravity, and you get a type of theory called supergravity.

In this post I want to discuss a particularly interesting form of supergravity. It’s called N=8 supergravity, and it’s closely related to N=4 super Yang-Mills.

In my articles about N=4 super Yang-Mills, I talked about supersymmetry. Supersymmetry is a relationship between particles of spin X and particles of spin X-½, but it gets more complicated when N (the number of “directions” of supersymmetry) is greater than one.

I’d encourage you to read at least the two links in the above paragraph. The gist is that just like a symmetrical object can be turned in different directions and still remain the same, a supersymmetrical theory can be “turned” so that a particle with spin X becomes a particle of spin X-½ (a different type of particle), and the theory will remain the same. The higher the number N, the more different directions the theory can be “turned”.

N=4 was something I could depict in a picture. We started with a particle of spin 1, then could “turn” it in four different directions, each resulting in a different particle of spin ½. By combining two different “turns” we ended up with six distinct particles of spin 0. Miraculously, I could fit this all into one image.

N=8 is tougher. This time, we start with 1 particle of spin 2: the graviton, the particle that corresponds to the force of gravity. From there we can “turn” the theory in eight different directions, leading to 8 different gravitino particles with spin 3/2.

After that, things get more complicated. You can “turn” the theory twice to reach spin 1. Spin 1 particles correspond to Yang-Mills forces, the fundamental forces of nature (besides gravity). Photons are the spin 1 particles that correspond to Electromagnetism. The spin 1 particles here, connected as they are to gravity by supersymmetry, are typically called graviphotons. There are 28 distinct graviphotons in N=8 supergravity.

From the graviphotons, we can keep turning, getting to spin ½, where we find 56 new particles of the same “type” as electrons and quarks. On our fourth turn, we get to spin 0, the scalars, with 70 new particles. Turning further takes us back: from spin 0 to spin ½, spin ½ to spin 1, spin 1 to spin 3/2, and spin 3/2 to spin 2, back where we started after eight “turns”.

I’ve tried to depict this in the same way as N=4 super Yang-Mills, but there’s just no way to fit everything in. The best I can do is to take a slice through the space, letting certain particles overlap to give at best a general impression of what’s going on.

Graviton in black, gravitinos in grey, graviphotons in yellow, fermions in orange, scalars in red, and comprehensibility omitted entirely.

Graviton in black, gravitinos in grey, graviphotons in yellow, fermions in orange, scalars in red, making a firework of incomprehensible graphics. Incidentally, happy 4th of July to my American readers.

That picture doesn’t give you any intuition about the numbers. It doesn’t show you why there are 28 graviphotons, or 70 scalars. To explain that, it’s best to turn to another, hopefully more familiar picture, Pascal’s triangle.

Getting math class flashbacks yet?

Pascal’s triangle is a way of writing down how many distinct combinations you can make out of a list, and that’s really all that’s going on here. If you have four directions to “turn” and you pick one, you have four options, while picking two gives you six distinct choices. That’s just the 1-4-6-4-1 line on the triangle. If you go down to the eighth, you’ll spot the numbers from N=8 supergravity: 1 graviton, 8 gravitinos, 28 graviphotons, 56 fermions, and 70 scalars.

That’s a lot of particles. With that many particles, you might wonder if you could somehow fit the real world in there.

Actually, that isn’t such a naive thought. When N=8 supergravity was first discovered, people tried to fit the existing particles of nature inside it, hoping that it could explain them. Over the years though, it was realized that N=8 supergravity simply doesn’t provide enough tools to fully capture the particles of the standard model. Something more diverse, like string theory, would be needed.

That means that N=8 supergravity, like many of the things theorists call theories, does not describe the real world. Instead, it’s interesting for a different reason.

You’ve probably heard that gravity and quantum mechanics are incompatible. That’s not exactly true: you can write down a quantum theory of gravity about as easily as you can write down a quantum theory of anything else. The problem is that most such theories have divergences, infinite results that shouldn’t be infinite. Dealing with those results involves a process called renormalization, which papers over the infinities but reduces our ability to make predictions. For gravity theories, this process has to be performed an infinite number of times, resulting in an infinite loss of predictability. So while you can certainly write down a theory of quantum gravity, you can’t predict anything with it.

String theory is different. It doesn’t have the same sorts of infinite results, doesn’t require renormalization. That, really, is it’s purpose, it’s biggest virtue: everything else is a side benefit.

N=4 super Yang-Mills isn’t a theory of gravity at all, but it does have that same neat trait: you never get this sort of infinite results, so you never need to give up predictive power.

What’s so cool about N=8 supergravity is that it just might be in the same category. By all rights, it shouldn’t be…but loop after loop its divergences seem to be behaving much like N=4 super Yang-Mills. (For those new to this blog, loops are a measure of how complex a calculation is in particle physics. Most practical calculations only involve one or two loops, while four loops represents possibly the most precise test ever performed by science.)

Now, two predictions are at the fore. One suggests that this magic behavior will be broken at the terrifyingly complex level of seven loops. The other proposes that the magic will continue, and N=8 supergravity will never see a divergence. The only way for certain is to do the calculation, look at four gravitons at seven loops and see what happens.

If N=8 supergravity really doesn’t diverge, then the biggest “point” of string theory isn’t unique anymore. If you don’t need all the bells and whistles of string theory to get an acceptable quantum theory of gravity, then maybe there’s a better way to think about the problem of quantum gravity in general. Even if N=8 supergravity doesn’t describe the real world, there may be other ways forward, other ways to handle the problem of divergences. If someone can manage that calculation (not as impossible as it sounds nowadays, but still very very hard) then we might see something really truly new.

(Super)gravity: Meet the Gravitino

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I’m putting together a series of posts about N=8 supergravity, with the goal of creating a guide much like I have for N=4 super Yang-Mills and the (2,0) theory.

N=8 supergravity is what happens when you add the maximum amount of supersymmetry to a theory of gravity. I’m going to strongly recommend that you read both of those posts before reading this one, as there are a number of important concepts there: the idea that different types of particles are categorized by a number called spin, the idea that supersymmetry is a relationship between particles with spin X and particles with spin X-½, and the idea that gravity can be thought of equally as a bending of space and time or as a particle with spin 2, called a graviton.

Knowing all that, if you add supersymmetry to gravity, you’d relate a spin 2 particle (the graviton) to a spin 3/2 particle (for 2-½).

What is a spin 3/2 particle?

Spin 0 particles correspond to a single number, like a temperature, that can vary over space. The Higgs boson is the one example of a spin 0 particle that we know of in the real world. Spin ½ covers electrons, protons, and almost all of the particles that make up ordinary matter, while spin 1 covers Yang-Mills forces. That covers the entire Standard Model, all of the particles scientists have seen in the real world. So what could a spin 3/2 particle possibly be?

We can at least guess at what it would be called. Whatever this spin 3/2 particle is, it’s the supersymmetric partner of the graviton. For somewhat stupid reasons, that means its name is determined by taking “graviton” and adding “-ino” to the end, to get gravitino.

But that still doesn’t answer the question: What is a gravitino?

Here’s the quick answer: A gravitino is a spin 1 particle combined with a spin ½ particle.

What sort of combination am I talking about? Not the one you might think. A gravitino is a fundamental particle, it is not made up of other particles.

 

NOT like this.

So in what sense is it a combination?

A handy way for physicists to think about particles is as manifestations of an underlying field. The field is stronger or weaker in different places, and when the field is “on”, a particle is present. For example, the electron field covers all of space, but only where that electron field is greater than zero do actual electrons show up.

I’ve said that a scalar field is simple to understand because it’s just a number, like a temperature, that takes different values in different places. The other types of fields are like this too, but instead of one number there’s generally a more complicated set of numbers needed to define them. Yang-Mills fields, with spin 1, are forces, with a direction and a strength. This is why they’re often called vector fields. Spin ½ particles have a set of numbers that characterizes them as well. It’s called a spinor, and unfortunately it’s not something I can give you an intuitive definition for. Just be aware that, like vectors, it involves a series of numbers that specify how the field behaves at each point.

It’s a bit like a computer game. The world is full of objects, and different objects have different stats. A weapon might have damage and speed, while a quest-giver would have information about what quests they give. Since everything is just code, though, you can combine the two, and all you have to do is put both types of stats on the same object.

Like this.

For quantum fields, the “stats” are the numbers I mentioned earlier: a single number for scalars, direction and strength for vectors, and the spinor information for spinors. So if you want to combine two of them, say spin 1 and spin ½, you just need a field that has both sets of “stats”.

That’s the gravitino. The gravitino has vector “stats” from the spin 1 part, and spinor “stats” from the spin ½ part. It’s a combination of two types of fundamental particles, to create one that nobody has seen before.

That doesn’t mean nobody will ever see one, though. Gravitinos could well exist in our world, they’re actually a potential (if problematic) candidate for dark matter.

But much like supersymmetry in general, while gravitinos may exist, N=8 of them certainly don’t. N=8 is a whole lot of supersymmetry…but that’s a topic for another post. Stay tuned for the next post in the series!

Gravity is Yang-Mills Squared

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There’s a concept that I’ve wanted to present for quite some time. It’s one of the coolest accomplishments in my subfield, but I thought that explaining it would involve too much technical detail. However, the recent BICEP2 results have brought one aspect of it to the public eye, so I’ve decided that people are ready.

If you’ve been following the recent announcements by the BICEP2 telescope of their indirect observation of primordial gravitational waves, you’ve probably seen the phrases “E-mode polarization” and “B-mode polarization” thrown around. You may even have seen pictures, showing that light in the cosmic microwave background is polarized differently by quantum fluctuations in the inflaton field and by quantum fluctuations in gravity.

But why is there a difference? What’s unique about gravitational waves that makes them different from the other waves in nature?

As it turns out, the difference all boils down to one statement:

Gravity is Yang-Mills squared.

This is both a very simple claim and a very subtle one, and it comes up in many many places in physics.

Yang-Mills, for those who haven’t read my older posts, is a general category that contains most of the fundamental forces. Electromagnetism, the strong nuclear force, and the weak nuclear force are all variants of Yang-Mills forces.

Yang-Mills forces have “spin 1”. Another way to say this is that Yang-Mills forces are vector forces. If you remember vectors from math class, you might remember that a vector has a direction and a strength. This hopefully makes sense: forces point in a direction, and have a strength. You may also remember that vectors can also be described in terms of components. A vector in four space-time dimensions has four components: x, y, z, and time, like so:

\left( \begin{array}{c} x \\ y \\ z \\ t \end{array} \right)

Gravity has “spin 2”.

As I’ve talked about before, gravity bends space and time, which means that it modifies the way you calculate distances. In practice, that means it needs to be something that can couple two vectors together: a matrix, or more precisely, a tensor, like so:

\left( \begin{array}{cccc} xx & xy & xz & xt\\ yx & yy & yz & yt\\ zx & zy & zz & zt\\ tx & ty & tz & tt\end{array} \right)

So while a Yang-Mills force has four components, gravity has sixteen. Gravity is Yang-Mills squared.

(Technical note: gravity actually doesn’t use all sixteen components, because it’s traceless and symmetric. However, often when studying gravity’s quantum properties theorists often add on extra fields to “complete the square” and fill in the remaining components.)

There’s much more to the connection than that, though. For one, it appears in the kinds of waves the two types of forces can create.

In order to create an electromagnetic wave you need a dipole, a negative charge and a positive charge at opposite ends of a line, and you need that dipole to change over time.

Change over time, of course, is a property of Gifs.

Gravity doesn’t have negative and positive charges, it just has one type of charge. Thus, to create gravitational waves you need not a dipole, but a quadrupole: instead of a line between two opposite charges, you have four gravitational charges (masses) arranged in a square. This creates a “breathing” sort of motion, instead of the back-and-forth motion of electromagnetic waves.

This is your brain on gravitational waves.

This is why gravitational waves have a different shape than electromagnetic waves, and why they have a unique effect on the cosmic microwave background, allowing them to be spotted by BICEP2. Gravity, once again, is Yang-Mills squared.

But wait there’s more!

So far, I’ve shown you that gravity is the square of Yang-Mills, but not in a very literal way. Yes, there are lots of similarities, but it’s not like you can just square a calculation in Yang-Mills and get a calculation in gravity, right?

Well actually…

In quantum field theory, calculations are traditionally done using tools called Feynman diagrams, organized by how many loops the diagram contains. The simplest diagrams have no loops, and are called tree diagrams.

Fascinatingly, for tree diagrams the message of this post is as literal as it can be. Using something called the Kawai-Lewellen-Tye relations, the result of a tree diagram calculation in gravity can be found just by taking a similar calculation in Yang-Mills and squaring it.

(Interestingly enough, these relations were originally discovered using string theory, but they don’t require string theory to work. It’s yet another example of how string theory functions as a laboratory to make discoveries about quantum field theory.)

Does this hold beyond tree diagrams? As it turns out, the answer is again yes!
The calculation involved is a little more complicated, but as discovered by Zvi Bern, John Joseph Carrasco, and Henrik Johansson, if you can get your calculation in Yang-Mills into the right format then all you need to do is square the right thing at the right step to get gravity, even for diagrams with loops!

zvi-bern-350

carrasco

This trick, called BCJ duality after its discoverers, has allowed calculations in quantum gravity that far outpace what would be possible without it. In N=8 supergravity, the gravity analogue of N=4 super Yang-Mills, calculations have progressed up to four loops, and have revealed tantalizing hints that the uncontrolled infinities that usually plague gravity theories are absent in N=8 supergravity, even without adding in string theory. Results like these are why BCJ duality is viewed as one of the “foundational miracles” of the field for those of us who study scattering amplitudes.

Gravity is Yang-Mills squared, in more ways than one. And because gravity is Yang-Mills squared, gravity may just be tame-able after all.