# What’s in a Conjecture? An ER=EPR Example

A few weeks back, Caltech’s Institute of Quantum Information and Matter released a short film titled Quantum is Calling. It’s the second in what looks like will become a series of pieces featuring Hollywood actors popularizing ideas in physics. The first used the game of Quantum Chess to talk about superposition and entanglement. This one, featuring Zoe Saldana, is about a conjecture by Juan Maldacena and Leonard Susskind called ER=EPR. The conjecture speculates that pairs of entangled particles (as investigated by Einstein, Podolsky, and Rosen) are in some sense secretly connected by wormholes (or Einstein-Rosen bridges).

The film is fun, but I’m not sure ER=EPR is established well enough to deserve this kind of treatment.

At this point, some of you are nodding your heads for the wrong reason. You’re thinking I’m saying this because ER=EPR is a conjecture.

I’m not saying that.

The fact of the matter is, conjectures play a very important role in theoretical physics, and “conjecture” covers a wide range. Some conjectures are supported by incredibly strong evidence, just short of mathematical proof. Others are wild speculations, “wouldn’t it be convenient if…” ER=EPR is, well…somewhere in the middle.

Most popularizers don’t spend much effort distinguishing things in this middle ground. I’d like to talk a bit about the different sorts of evidence conjectures can have, using ER=EPR as an example.

Our friendly neighborhood space octopus

The first level of evidence is motivation.

At its weakest, motivation is the “wouldn’t it be convenient if…” line of reasoning. Some conjectures never get past this point. Hawking’s chronology protection conjecture, for instance, points out that physics (and to some extent logic) has a hard time dealing with time travel, and wouldn’t it be convenient if time travel was impossible?

For ER=EPR, this kind of motivation comes from the black hole firewall paradox. Without going into it in detail, arguments suggested that the event horizons of older black holes would resemble walls of fire, incinerating anything that fell in, in contrast with Einstein’s picture in which passing the horizon has no obvious effect at the time. ER=EPR provides one way to avoid this argument, making event horizons subtle and smooth once more.

Motivation isn’t just “wouldn’t it be convenient if…” though. It can also include stronger arguments: suggestive comparisons that, while they could be coincidental, when put together draw a stronger picture.

In ER=EPR, this comes from certain similarities between the type of wormhole Maldacena and Susskind were considering, and pairs of entangled particles. Both connect two different places, but both do so in an unusually limited way. The wormholes of ER=EPR are non-traversable: you cannot travel through them. Entangled particles can’t be traveled through (as you would expect), but more generally can’t be communicated through: there are theorems to prove it. This is the kind of suggestive similarity that can begin to motivate a conjecture.

(Amusingly, the plot of the film breaks this in both directions. Keanu Reeves can neither steal your cat through a wormhole, nor send you coded messages with entangled particles.)

Nor live forever as the portrait in his attic withers away

Motivation is a good reason to investigate something, but a bad reason to believe it. Luckily, conjectures can have stronger forms of evidence. Many of the strongest conjectures are correspondences, supported by a wealth of non-trivial examples.

In science, the gold standard has always been experimental evidence. There’s a reason for that: when you do an experiment, you’re taking a risk. Doing an experiment gives reality a chance to prove you wrong. In a good experiment (a non-trivial one) the result isn’t obvious from the beginning, so that success or failure tells you something new about the universe.

In theoretical physics, there are things we can’t test with experiments, either because they’re far beyond our capabilities or because the claims are mathematical. Despite this, the overall philosophy of experiments is still relevant, especially when we’re studying a correspondence.

“Correspondence” is a word we use to refer to situations where two different theories are unexpectedly computing the same thing. Often, these are very different theories, living in different dimensions with different sorts of particles. With the right “dictionary”, though, you can translate between them, doing a calculation in one theory that matches a calculation in the other one.

Even when we can’t do non-trivial experiments, then, we can still have non-trivial examples. When the result of a calculation isn’t obvious from the beginning, showing that it matches on both sides of a correspondence takes the same sort of risk as doing an experiment, and gives the same sort of evidence.

Some of the best-supported conjectures in theoretical physics have this form. AdS/CFT is technically a conjecture: a correspondence between string theory in a hyperbola-shaped space and my favorite theory, N=4 super Yang-Mills. Despite being a conjecture, the wealth of nontrivial examples is so strong that it would be extremely surprising if it turned out to be false.

ER=EPR is also a correspondence, between entangled particles on the one hand and wormholes on the other. Does it have nontrivial examples?

Some, but not enough. Originally, it was based on one core example, an entangled state that could be cleanly matched to the simplest wormhole. Now, new examples have been added, covering wormholes with electric fields and higher spins. The full “dictionary” is still unclear, with some pairs of entangled particles being harder to describe in terms of wormholes. So while this kind of evidence is being built, it isn’t as solid as our best conjectures yet.

I’m fine with people popularizing this kind of conjecture. It deserves blog posts and press articles, and it’s a fine idea to have fun with. I wouldn’t be uncomfortable with the Bohemian Gravity guy doing a piece on it, for example. But for the second installment of a star-studded series like the one Caltech is doing…it’s not really there yet, and putting it there gives people the wrong idea.

I hope I’ve given you a better idea of the different types of conjectures, from the most fuzzy to those just shy of certain. I’d like to do this kind of piece more often, though in future I’ll probably stick with topics in my sub-field (where I actually know what I’m talking about 😉 ). If there’s a particular conjecture you’re curious about, ask in the comments!

# The Parable of the Entanglers and the Bootstrappers

There’s been some buzz around a recent Quanta article by K. C. Cole, The Strange Second Life of String Theory. I found it a bit simplistic of a take on the topic, so I thought I’d offer a different one.

String theory has been called the particle physicist’s approach to quantum gravity. Other approaches use the discovery of general relativity as a model: they’re looking for a big conceptual break from older theories. String theory, in contrast, starts out with a technical problem (naive quantum gravity calculations that give infinity) proposes physical objects that could solve the problem (strings, branes), and figures out which theories of these objects are consistent with existing data (originally the five superstring theories, now all understood as parts of M theory).

That approach worked. It didn’t work all the way, because regardless of whether there are indirect tests that can shed light on quantum gravity, particle physics-style tests are far beyond our capabilities. But in some sense, it went as far as it can: we’ve got a potential solution to the problem, and (apart from some controversy about the cosmological constant) it looks consistent with observations. Until actual evidence surfaces, that’s the end of that particular story.

When people talk about the failure of string theory, they’re usually talking about its aspirations as a “theory of everything”. String theory requires the world to have eleven dimensions, with seven curled up small enough that we can’t observe them. Different arrangements of those dimensions lead to different four-dimensional particles. For a time, it was thought that there would be only a few possible arrangements: few enough that people could find the one that describes the world and use it to predict undiscovered particles.

That particular dream didn’t work out. Instead, it became apparent that there were a truly vast number of different arrangements of dimensions, with no unique prediction likely to surface.

By the time I took my first string theory course in grad school, all of this was well established. I was entering a field shaped by these two facts: string theory’s success as a particle-physics style solution to quantum gravity, and its failure as a uniquely predictive theory of everything.

The quirky thing about science: sociologically, success and failure look pretty similar. Either way, it’s time to find a new project.

A colleague of mine recently said that we’re all either entanglers or bootstrappers. It was a joke, based on two massive grants from the Simons Foundation. But it’s also a good way to summarize two different ways string theory has moved on, from its success and from its failure.

The entanglers start from string theory’s success and say, what’s next?

As it turns out, a particle-physics style understanding of quantum gravity doesn’t tell you everything you need to know. Some of the big conceptual questions the more general relativity-esque approaches were interested in are still worth asking. Luckily, string theory provides tools to answer them.

Many of those answers come from AdS/CFT, the discovery that string theory in a particular warped space-time is dual (secretly the same theory) to a more particle-physics style theory on the edge of that space-time. With that discovery, people could start understanding properties of gravity in terms of properties of particle-physics style theories. They could use concepts like information, complexity, and quantum entanglement (hence “entanglers”) to ask deeper questions about the structure of space-time and the nature of black holes.

The bootstrappers, meanwhile, start from string theory’s failure and ask, what can we do with it?

Twisting up the dimensions of string theory yields a vast number of different arrangements of particles. Rather than viewing this as a problem, why not draw on it as a resource?

“Bootstrappers” explore this space of particle-physics style theories, using ones with interesting properties to find powerful calculation tricks. The name comes from the conformal bootstrap, a technique that finds conformal theories (roughly: theories that are the same at every scale) by “pulling itself by its own boostraps”, using nothing but a kind of self-consistency.

Many accounts, including Cole’s, attribute people like the boostrappers to AdS/CFT as well, crediting it with inspiring string theorists to take a closer look at particle physics-style theories. That may be true in some cases, but I don’t think it’s the whole story: my subfield is bootstrappy, and while it has drawn on AdS/CFT that wasn’t what got it started. Overall, I think it’s more the case that the tools of string theory’s “particle physics-esque approach”, like conformal theories and supersymmetry, ended up (perhaps unsurprisingly) useful for understanding particle physics-style theories.

Not everyone is a “boostrapper” or an “entangler”, even in the broad sense I’m using the words. The two groups also sometimes overlap. Nevertheless, it’s a good way to think about what string theorists are doing these days. Both of these groups start out learning string theory: it’s the only way to learn about AdS/CFT, and it introduces the bootstrappers to a bunch of powerful particle physics tools all in one course. Where they go from there varies, and can be more or less “stringy”. But it’s research that wouldn’t have existed without string theory to get it started.

# So You Want to Prove String Theory (Or: Nima Did Something Cool Again)

Nima Arkani-Hamed, of Amplituhedron fame, has been making noises recently about proving string theory.

Now, I can already hear the smartarses in the comments correcting me here. You can’t prove a scientific theory, you can only provide evidence for it.

Well, in this case I don’t mean “provide evidence”. (Direct evidence for string theory is quite unlikely at the moment given the high energies at which it becomes relevant and large number of consistent solutions, but an indirect approach might yet work.) I actually mean “prove”.

See, there are two ways to think about the problem of quantum gravity. One is as an experimental problem: at high enough energies for quantum gravity to be relevant, what actually happens? Since it’s going to be a very long time before we can probe those energies, though, in practice we instead have a technical problem: can we write down a theory that looks like gravity in familiar situations, while avoiding the pesky infinities that come with naive attempts at quantum gravity?

If you can prove that string theory is the only theory that does that, then you’ve proven string theory. If you can prove that string theory is the only theory that does that [with certain conditions] then you’ve proven string theory [with certain conditions].

That, in broad terms, is what Nima has been edging towards. At this year’s Strings conference, he unveiled some progress towards that goal. And since I just recently got around to watching his talk, you get to hear my take on it.

Nima has been working with Yu-tin Huang, an amplitudeologist who tends to show up everywhere, and one of his students. Working in parallel, an all-star cast has been doing a similar calculation for Yang-Mills theory. The Yang-Mills story is cool, and probably worth a post in its own right, but I think you guys are more interested in the quantum gravity one.

What is Nima doing here?

Nima is looking at scattering amplitudes, probabilities for particles to scatter off of each other. In this case, the particles are gravitons, the particle form of gravitational waves.

Normally, the problems with quantum gravity show up when your scattering amplitudes have loops. Here, Nima is looking at amplitudes without loops, the most important contributions when the force in question is weak (the “weakly coupled” in Nima’s title).

Even for these amplitudes you can gain insight into quantum gravity by seeing what happens at high energies (the “UV” in the title). String amplitudes have nice behavior at high energies, naive gravity amplitudes do not. The question then becomes, are there other amplitudes that preserve this nice behavior, while still obeying the rules of physics? Or is string theory truly unique, the only theory that can do this?

The team that asked a similar question about Yang-Mills theory found that string theory was unique, that every theory that obeyed their conditions was in some sense “stringy”. That makes it even more surprising that, for quantum gravity, the answer was no: the string theory amplitude is not unique. In fact, Nima and his collaborators found an infinite set of amplitudes that met their conditions, related by a parameter they could vary freely.

What are these other amplitudes, then?

Nima thinks they can’t be part of a consistent theory, and he’s probably right. They have a number of tests they haven’t done: in particular, they’ve only been looking at amplitudes involving two gravitons scattering off each other, but a real theory should have consistent answers for any number of gravitons interacting, and it’s doesn’t look like these “alternate” amplitudes can be generalized to work for that.

That said, at this point it’s still possible that these other amplitudes are part of some sort of sensible theory. And that would be incredibly interesting, because we’ve never seen anything like that before.

There are approaches to quantum gravity besides string theory, sure. But common to all of them is an inability to actually calculate scattering amplitudes. If there really were a theory that generated these “alternate” amplitudes, it wouldn’t correspond to any existing quantum gravity proposal.

(Incidentally, this is also why this sort of “proof” of string theory might not convince everyone. Non-string quantum gravity approaches tend to talk about things fairly far removed from scattering amplitudes, so some would see this kind of thing as apples and oranges.)

I’d be fascinated to see where this goes. Either we have a new set of gravity scattering amplitudes to work with, or string theory turns out to be unique in a more rigorous and specific way than we’ve previously known. No matter what, something interesting is going to happen.

After the talk David Gross drew on his experience of the origin of string theory to question whether this work is just retreading the path to an old dead end. String theory arose from an attempt to find a scattering amplitude with nice properties, but it was only by understanding this amplitude physically in terms of vibrating strings that it was able to make real progress.

I generally agree with Nima’s answer, but to re-frame it in my own words: in the amplitudes sub-field, there’s something of a cycle. We try to impose general rules, until by using those rules we have a new calculation technique. We then do a bunch of calculations with the new technique. Finally, we look at the results of those calculations, try to find new general rules, and start the cycle again.

String theory is the result of people applying general rules to scattering amplitudes and learning enough to discover not just a new calculation technique, but a new physical theory. Now, we’ve done quite a lot of string theory calculations, and quite a lot more quantum field theory calculations as well. We have a lot of “data”.

And when you have a lot of data, it becomes much more productive to look for patterns. Now, if we start trying to apply general rules, we have a much better idea of what we’re looking for. This lets us get a lot further than people did the first time through the cycle. It’s what let Nima find the Amplituhedron, and it’s something Yu-tin has a pretty good track record of as well.

So in general, I’m optimistic. As a community, we’re poised to find out some very interesting things about what gravity scattering amplitudes can look like. Maybe, we’ll even prove string theory. [With certain conditions, of course. 😉 ]

# Most of String Theory Is Not String Pheno

Last week, Sabine Hossenfelder wrote a post entitled “Why not string theory?” In it, she argued that string theory has a much more dominant position in physics than it ought to: that it’s crowding out alternative theories like Loop Quantum Gravity and hogging much more funding than it actually merits.

If you follow the string wars at all, you’ve heard these sorts of arguments before. There’s not really anything new here.

That said, there were a few sentences in Hossenfelder’s post that got my attention, and inspired me to write this post.

So far, string theory has scored in two areas. First, it has proved interesting for mathematicians. But I’m not one to easily get floored by pretty theorems – I care about math only to the extent that it’s useful to explain the world. Second, string theory has shown to be useful to push ahead with the lesser understood aspects of quantum field theories. This seems a fruitful avenue and is certainly something to continue. However, this has nothing to do with string theory as a theory of quantum gravity and a unification of the fundamental interactions.

(Bolding mine)

Here, Hossenfelder explicitly leaves out string theorists who work on “lesser understood aspects of quantum field theories” from her critique. They’re not the big, dominant program she’s worried about.

What Hossenfelder doesn’t seem to realize is that right now, it is precisely the “aspects of quantum field theories” crowd that is big and dominant. The communities of string theorists working on something else, and especially those making bold pronouncements about the nature of the real world, are much, much smaller.

Let’s define some terms:

Phenomenology (or pheno for short) is the part of theoretical physics that attempts to make predictions that can be tested in experiments. String pheno, then, covers attempts to use string theory to make predictions. In practice, though, it’s broader than that: while some people do attempt to predict the results of experiments, more work on figuring out how models constructed by other phenomenologists can make sense in string theory. This still attempts to test string theory in some sense: if a phenomenologist’s model turns out to be true but it can’t be replicated in string theory then string theory would be falsified. That said, it’s more indirect. In parallel to string phenomenology, there is also the related field of string cosmology, which has a similar relationship with cosmology.

If other string theorists aren’t trying to make predictions, what exactly are they doing? Well, a large number of them are studying quantum field theories. Quantum field theories are currently our most powerful theories of nature, but there are many aspects of them that we don’t yet understand. For a large proportion of string theorists, string theory is useful because it provides a new way to understand these theories in terms of different configurations of string theory, which often uncovers novel and unexpected properties. This is still physics, not mathematics: the goal, in the end, is to understand theories that govern the real world. But it doesn’t involve the same sort of direct statements about the world as string phenomenology or string cosmology: crucially, it doesn’t depend on whether string theory is true.

Last week, I said that before replying to Hossenfelder’s post I’d have to gather some numbers. I was hoping to find some statistics on how many people work on each of these fields, or on their funding. Unfortunately, nobody seems to collect statistics broken down by sub-field like this.

As a proxy, though, we can look at conferences. Strings is the premier conference in string theory. If something has high status in the string community, it will probably get a talk at Strings. So to investigate, I took a look at the talks given last year, at Strings 2015, and broke them down by sub-field.

Here I’ve left out the historical overview talks, since they don’t say much about current research.

“QFT” is for talks about lesser understood aspects of quantum field theories. Amplitudes, my own sub-field, should be part of this: I’ve separated it out to show what a typical sub-field of the QFT block might look like.

“Formal Strings” refers to research into the fundamentals of how to do calculations in string theory: in principle, both the QFT folks and the string pheno folks find it useful.

“Holography” is a sub-topic of string theory in which string theory in some space is equivalent to a quantum field theory on the boundary of that space. Some people study this because they want to learn about quantum field theory from string theory, others because they want to learn about quantum gravity from quantum field theory. Since the field can’t be cleanly divided into quantum gravity and quantum field theory research, I’ve given it its own category.

While all string theory research is in principle about quantum gravity, the “Quantum Gravity” section refers to people focused on the sorts of topics that interest non-string quantum gravity theorists, like black hole entropy.

Finally, we have String Cosmology and String Phenomenology, which I’ve already defined.

Don’t take the exact numbers here too seriously: not every talk fit cleanly into a category, so there were some judgement calls on my part. Nonetheless, this should give you a decent idea of the makeup of the string theory community.

The biggest wedge in the diagram by far, taking up a majority of the talks, is QFT. Throwing in Amplitudes (part of QFT) and Formal Strings (useful to both), and you’ve got two thirds of the conference. Even if you believe Hossenfelder’s tale of the failures of string theory, then, that only matters to a third of this diagram. And once you take into account that many of the Holography and Quantum Gravity people are interested in aspects of QFT as well, you’re looking at an even smaller group. Really, Hossenfelder’s criticism is aimed at two small slices on the chart: String Pheno, and String Cosmo.

Of course, string phenomenologists also have their own conference. It’s called String Pheno, and last year it had 130 participants. In contrast, LOOPS’ 2015, the conference for string theory’s most famous “rival”, had…190 participants. The fields are really pretty comparable.

Now, I have a lot more sympathy for the string phenomenologists and string cosmologists than I do for loop quantum gravity. If other string theorists felt the same way, then maybe that would cause the sort of sociological effect that Hossenfelder is worried about.

But in practice, I don’t think this happens. I’ve met string theorists who didn’t even know that people still did string phenomenology. The two communities are almost entirely disjoint: string phenomenologists and string cosmologists interact much more with other phenomenologists and cosmologists than they do with other string theorists.

You want to talk about sociology? Sociologically, people choose careers and fund research because they expect something to happen soon. People don’t want to be left high and dry by a dearth of experiments, don’t feel comfortable working on something that may only be vindicated long after they’re dead. Most people choose the safe option, the one that, even if it’s still aimed at a distant goal, is also producing interesting results now (aspects of quantum field theories, for example).

The people that don’t? Tend to form small, tight-knit, passionate communities. They carve out a few havens of like-minded people, and they think big thoughts while the world around them seems to only care about their careers.

If you’re a loop quantum gravity theorist, or a quantum gravity phenomenologist like Hossenfelder, and you see some of your struggles in that paragraph, please realize that string phenomenology is like that too.

I feel like Hossenfelder imagines a world in which string theory is struck from its high place, and alternative theories of quantum gravity are of comparable size and power. But from where I’m sitting, it doesn’t look like it would work out that way. Instead, you’d have alternatives grow to the same size as similarly risky parts of string theory, like string phenomenology. And surprise, surprise: they’re already that size.

In certain corners of the internet, people like to argue about “punching up” and “punching down”. Hossenfelder seems to think she’s “punching up”, giving the big dominant group a taste of its own medicine. But by leaving out string theorists who study QFTs, she’s really “punching down”, or at least sideways, and calling out a sub-group that doesn’t have much more power than her own.

# The “Lies to Children” Model of Science Communication, and The “Amplitudes Are Weird” Model of Amplitudes

Let me tell you a secret.

Scattering amplitudes in N=4 super Yang-Mills don’t actually make sense.

Scattering amplitudes calculate the probability that particles “scatter”: coming in from far away, interacting in some fashion, and producing new particles that travel far away in turn. N=4 super Yang-Mills is my favorite theory to work with: a highly symmetric version of the theory that describes the strong nuclear force. In particular, N=4 super Yang-Mills has conformal symmetry: if you re-scale everything larger or smaller, you should end up with the same predictions.

You might already see the contradiction here: scattering amplitudes talk about particles coming in from very far away…but due to conformal symmetry, “far away” doesn’t mean anything, since we can always re-scale it until it’s not far away anymore!

So when I say that I study scattering amplitudes in N=4 super Yang-Mills, am I lying?

Well…yes. But it’s a useful type of lie.

There’s a concept in science writing called “lies to children”, first popularized in a fantasy novel.

This one.

When you explain science to the public, it’s almost always impossible to explain everything accurately. So much background is needed to really understand most of modern science that conveying even a fraction of it would bore the average audience to tears. Instead, you need to simplify, to skip steps, and even (to be honest) to lie.

The important thing to realize here is that “lies to children” aren’t meant to mislead. Rather, they’re chosen in such a way that they give roughly the right impression, even as they leave important details out. When they told you in school that energy is always conserved, that was a lie: energy is a consequence of symmetry in time, and when that symmetry is broken energy doesn’t have to be conserved. But “energy is conserved” is a useful enough rule that lets you understand most of everyday life.

In this case, the “lie” that we’re calculating scattering amplitudes is fairly close to the truth. We’re using the same methods that people use to calculate scattering amplitudes in theories where they do make sense, like QCD. For a while, people thought these scattering amplitudes would have to be zero, since anything else “wouldn’t make sense”…but in practice, we found they were remarkably similar to scattering amplitudes in other theories. Now, we have more rigorous definitions for what we’re calculating that avoid this problem, involving objects called polygonal Wilson loops.

This illustrates another principle, one that hasn’t (yet) been popularized by a fantasy novel. I’d like to call it the “amplitudes are weird” principle. Time and again we amplitudes-folks will do a calculation that doesn’t really make sense, find unexpected structure, and go back to figure out what that structure actually means. It’s been one of the defining traits of the field, and we’ve got a pretty good track record with it.

A couple of weeks back, Lance Dixon gave an interview for the SLAC website, talking about his work on quantum gravity. This was immediately jumped on by Peter Woit and Lubos Motl as ammo for the long-simmering string wars. To one extent or another, both tried to read scientific arguments into the piece. This is in general a mistake: it is in the nature of a popularization piece to contain some volume of lies-to-children, and reading a piece aimed at a lower audience can be just as confusing as reading one aimed at a higher audience.

In the remainder of this post, I’ll try to explain what Lance was talking about in a slightly higher-level way. There will still be lies-t0-children involved, this is a popularization blog after all. But I should be able to clear up a few misunderstandings. Lubos probably still won’t agree with the resulting argument, but it isn’t the self-evidently wrong one he seems to think it is.

Lance Dixon has done a lot of work on quantum gravity. Those of you who’ve read my old posts might remember that quantum gravity is not so difficult in principle: general relativity naturally leads you to particles called gravitons, which can be treated just like other particles. The catch is that the theory that you get by doing this fails to be predictive: one reason why is that you get an infinite number of erroneous infinite results, which have to be papered over with an infinite number of arbitrary constants.

Working with these non-predictive theories, however, can still yield interesting results. In the article, Lance mentions the work of Bern, Carrasco, and Johansson. BCJ (as they are abbreviated) have found that calculating a gravity amplitude often just amounts to calculating a (much easier to find) Yang-Mills amplitude, and then squaring the right parts. This was originally found in the context of string theory by another three-letter group, Kawai, Lewellen, and Tye (or KLT). In string theory, it’s particularly easy to see how this works, as it’s a basic feature of how string theory represents gravity. However, the string theory relations don’t tell the whole story: in particular, they only show that this squaring procedure makes sense on a classical level. Once quantum corrections come in, there’s no known reason why this squaring trick should continue to work in non-string theories, and yet so far it has. It would be great if we had a good argument why this trick should continue to work, a proof based on string theory or otherwise: for one, it would allow us to be much more confident that our hard work trying to apply this trick will pay off! But at the moment, this falls solidly under the “amplitudes are weird” principle.

Using this trick, BCJ and collaborators (frequently including Lance Dixon) have been calculating amplitudes in N=8 supergravity, a highly symmetric version of those naive, non-predictive gravity theories. For this particular, theory, the theory you “square” for the above trick is N=4 super Yang-Mills. N=4 super Yang-Mills is special for a number of reasons, but one is that the sorts of infinite results that lose you predictive power in most other quantum field theories never come up. Remarkably, the same appears to be true of N=8 supergravity. We’re still not sure, the relevant calculation is still a bit beyond what we’re capable of. But in example after example, N=8 supergravity seems to be behaving similarly to N=4 super Yang-Mills, and not like people would have predicted from its gravitational nature. Once again, amplitudes are weird, in a way that string theory helped us discover but by no means conclusively predicted.

If N=8 supergravity doesn’t lose predictive power in this way, does that mean it could describe our world?

In a word, no. I’m not claiming that, and Lance isn’t claiming that. N=8 supergravity simply doesn’t have the right sorts of freedom to give you something like the real world, no matter how you twist it. You need a broader toolset (string theory generally) to get something realistic. The reason why we’re interested in N=8 supergravity is not because it’s a candidate for a real-world theory of quantum gravity. Rather, it’s because it tells us something about where the sorts of dangerous infinities that appear in quantum gravity theories really come from.

That’s what’s going on in the more recent paper that Lance mentioned. There, they’re not working with a supersymmetric theory, but with the naive theory you’d get from just trying to do quantum gravity based on Einstein’s equations. What they found was that the infinity you get is in a certain sense arbitrary. You can’t get rid of it, but you can shift it around (infinity times some adjustable constant 😉 ) by changing the theory in ways that aren’t physically meaningful. What this suggests is that, in a sense that hadn’t been previously appreciated, the infinite results naive gravity theories give you are arbitrary.

The inevitable question, though, is why would anyone muck around with this sort of thing when they could just use string theory? String theory never has any of these extra infinities, that’s one of its most important selling points. If we already have a perfectly good theory of quantum gravity, why mess with wrong ones?

Here, Lance’s answer dips into lies-to-children territory. In particular, Lance brings up the landscape problem: the fact that there are 10^500 configurations of string theory that might loosely resemble our world, and no clear way to sift through them to make predictions about the one we actually live in.

This is a real problem, but I wouldn’t think of it as the primary motivation here. Rather, it gets at a story people have heard before while giving the feeling of a broader issue: that string theory feels excessive.

Why does this have a Wikipedia article?

Think of string theory like an enormous piece of fabric, and quantum gravity like a dress. You can definitely wrap that fabric around, pin it in the right places, and get a dress. You can in fact get any number of dresses, elaborate trains and frilly togas and all sorts of things. You have to do something with the extra material, though, find some tricky but not impossible stitching that keeps it out of the way, and you have a fair number of choices of how to do this.

From this perspective, naive quantum gravity theories are things that don’t qualify as dresses at all, scarves and socks and so forth. You can try stretching them, but it’s going to be pretty obvious you’re not really wearing a dress.

What we amplitudes-folks are looking for is more like a pencil skirt. We’re trying to figure out the minimal theory that covers the divergences, the minimal dress that preserves modesty. It would be a dress that fits the form underneath it, so we need to understand that form: the infinities that quantum gravity “wants” to give rise to, and what it takes to cancel them out. A pencil skirt is still inconvenient, it’s hard to sit down for example, something that can be solved by adding extra material that allows it to bend more. Similarly, fixing these infinities is unlikely to be the full story, there are things called non-perturbative effects that probably won’t be cured. But finding the minimal pencil skirt is still going to tell us something that just pinning a vast stretch of fabric wouldn’t.

This is where “amplitudes are weird” comes in in full force. We’ve observed, repeatedly, that amplitudes in gravity theories have unexpected properties, traits that still aren’t straightforwardly explicable from the perspective of string theory. In our line of work, that’s usually a sign that we’re on the right track. If you’re a fan of the amplituhedron, the project here is along very similar lines: both are taking the results of plodding, not especially deep loop-by-loop calculations, observing novel simplifications, and asking the inevitable question: what does this mean?

That far-term perspective, looking off into the distance at possible insights about space and time, isn’t my style. (It isn’t usually Lance’s either.) But for the times that you want to tell that kind of story…well, this isn’t that outlandish of a story to tell. And unless your primary concern is whether a piece gives succor to the Woits of the world, it shouldn’t be an objectionable one.

# When to Look under the Bed

Last week, 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.

# Don’t Watch the Star, Watch the Crowd

I didn’t comment last week on Hawking’s proposed solution of the black hole firewall problem. The media buzz around it was a bit less rabid than the last time he weighed in on this topic, but there was still a lot more heat than light.

The impression I get from the experts is that Hawking’s proposal (this time made in collaboration with Andrew Strominger and Malcom Perry, the former of whom is famous for, among other things, figuring out how string theory can explain the entropy of black holes) resembles some earlier suggestions, with enough new elements to make it potentially interesting but potentially just confusing. It’s a development worth paying attention to for specialists, but it’s probably not the sort of long-awaited answer the media seems to be presenting it as.

This raises a question: how, as a non-specialist, are you supposed to tell the difference? Sure, you can just read blogs like mine, but I can’t report on everything.

I may have a pretty solid grounding in physics, but I know almost nothing about music. I definitely can’t tell what makes a song good. About the best I can do is see if I can dance to it, but that doesn’t seem to be a reliable indicator of quality music. Instead, my best bet is usually to watch the crowd.

Lasers may make this difficult.

Ask the star of a show if they’re doing good work, and they’re unlikely to be modest. Ask the average music fan, though, and you get a better idea. Watch music fans as a group, and you get even more information.

When a song starts playing everywhere you go, when people start pulling it out at parties and making their own imitations of it, then maybe it’s important. That might not mean it’s good, but it does mean it’s worth knowing about.

When Hawking or Strominger or Witten or anyone whose name you’ve heard of says they’ve solved the puzzle of the century, be cautious. If it really is worth your attention, chances are it won’t be the last you’ll hear about it. Other physicists will build off of it, discuss it, even spin off a new sub-field around it. If it’s worth it, you won’t have to trust what the stars of the physics world say: you’ll be able to listen to the crowd.

# Romeo and Juliet, through a Wormhole

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 “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.

# Sorry Science Fiction, Quantum Gravity Doesn’t Do What You Think It Does

I saw Interstellar this week. There’s been a lot of buzz among physicists about it, owing in part to the involvement of black hole expert Kip Thorne in the film’s development. I’d just like to comment on one aspect of the film that bugged me, a problem that shows up pretty frequently in science fiction.

In the film, Michael Caine plays a theoretical physicist working for NASA. His dream is to save humanity from an Earth plagued by a blight that is killing off the world’s food supply. To do this, he plans to build giant anti-gravity spaceships capable of taking as many people as possible away from the dying Earth to find a new planet capable of supporting human life. And in order to do that, apparently, he needs a theory of quantum gravity.

The thing is, quantum gravity has nothing to do with making giant anti-gravity spaceships.

Michael Caine lied to us?

This mistake isn’t unique to Interstellar. Lots of science fiction works assume that once we understand quantum gravity then everything else will follow: faster than light travel, wormholes, anti-gravity…pretty much every sci-fi staple.

It’s not just present in science fiction, either. Plenty of science popularizers like to mention all of the marvelous technology that’s going to come out of quantum gravity, including people who really should know better. A good example comes from a recent piece by quantum gravity researcher Sabine Hossenfelder:

But especially in high energy physics and quantum gravity, progress has basically stalled since the development of the standard model in the mid 70s. […] it is a frustrating situation and this makes you wonder if not there are other reasons for lack of progress, reasons that we can do something about. Especially in a time when we really need a game changer, some breakthrough technology, clean energy, that warp drive, a transporter!

None of these are things we’re likely to get from quantum gravity, and the reason is rather basic. It boils down to one central issue: if we can’t control the classical physics, we can’t control the quantum physics.

When science fiction authors speculate about the benefits of quantum gravity, they’re thinking about the benefits of quantum mechanics. Understanding the quantum world has allowed some of the greatest breakthroughs of the 20th century, from miniaturizing circuits to developing novel materials.

The assumption writers make is that the same will be true for quantum gravity: understand it, and gravity technology will flow. But this assumption forgets that quantum mechanics was so successful because it let us understand things we were already working with.

In order to miniaturize circuits, you have to know how to build a circuit in the first place. Only then, when you try to make the circuit smaller and don’t understand why it stops working, does quantum mechanics step in to tell you what you’re missing. Quantum mechanics helps us develop new materials because it helps us understand how existing materials work.

We don’t have any gravity circuits to shrink down, or gravity materials to understand. When gravity limits our current technology, it does so on a macro level (such as the effect of the Earth’s gravity on GPS satellites) not on a quantum level. If there isn’t a way to build anti-gravity technology using classical physics, there probably isn’t a way using quantum physics.

Scientists and popularizers generally argue that we can’t know what the future will bring. This is true, up to a point. When Maxwell wrote down equations to unify electricity and magnetism he could not have imagined the wealth of technology we have today. And often, technologies come from unexpected places. The spinoff technologies of the space race are the most popular example, another is that CERN (the facility that houses the Large Hadron Collider) was instrumental in developing the world wide web.

While it’s great to emphasize the open-ended promise of scientific advances (especially on grant applications!), in this context it’s misleading because it erases the very real progress people are making on these issues without quantum gravity.

Want to invest in clean energy? There are a huge number of scientists working on it, with projects ranging from creating materials that can split water using solar energy to nuclear fusion. Quantum gravity is just about the last science likely to give us clean energy, and I’m including the social sciences in that assessment.

That’s not obviously related to quantum gravity either. There has actually been some research into warp drives, but they’re based on a solution to Einstein’s equations without quantum mechanics. It’s not clear whether quantum gravity has something meaningful to say about them…while there are points to be made, from what I’ve been able to gather they’re more related to talking about how other quantum systems interact with gravity than the quantum properties of gravity itself. The same seems to apply to the difficulties involved in wormholes, another sci-fi concept that comes straight out of Einstein’s theory.

As for teleportation, that’s an entirely different field, and it probably doesn’t work how you think it does.

So what is quantum gravity actually good for?

Quantum gravity becomes relevant when gravity becomes very strong, places where Einstein’s theory would predict infinitely dense singularities. That means the inside of black holes, and the Big Bang. Quantum gravity smooths out these singularities, which means it can tell you about the universe’s beginnings (by smoothing out the big bang and showing what could cause it), or its long-term future (for example, problems with the long-term evolution of black holes).

These are important questions! They tell us about where we come from and where we’re going: in short, about our ultimate place in the universe. Almost every religion in history has tried to answer these questions. They’re very important to us as a species, even if they don’t directly impact our daily lives.

What they are not, however, is a source of technology.

So please, science fiction, use some other field for your plot-technology. There are plenty of scientific advances to choose from, people who are really working on cutting-edge futuristic stuff. They don’t need to wait on a theory of quantum gravity to get their work done. Neither do you.

# The Three Things Everyone Gets Wrong about the Big Bang

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.

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?