Month: December 2018

Physicists are talking more than ever lately about dualities, but you’ve been studying them for decades. Why does the subject interest you?

People keep finding new facets of dualities. Dualities are interesting because they frequently answer questions that are otherwise out of reach. For example, you might have spent years pondering a quantum theory and you understand what happens when the quantum effects are small, but textbooks don’t tell you what you do if the quantum effects are big; you’re generally in trouble if you want to know that. Frequently dualities answer such questions. They give you another description, and the questions you can answer in one description are different than the questions you can answer in a different description.

What are some of these newfound facets of dualities?

It’s open-ended because there are so many different kinds of dualities. There are dualities between a gauge theory [a theory, such as a quantum field theory, that respects certain symmetries] and another gauge theory, or between a string theory for weak coupling [describing strings that move almost independently from one another] and a string theory for strong coupling. Then there’s AdS/CFT duality, between a gauge theory and a gravitational description. That duality was discovered 20 years ago, and it’s amazing to what extent it’s still fruitful. And that’s largely because around 10 years ago, new ideas were introduced that rejuvenated it. People had new insights about entropy in quantum field theory — the whole story about “it from qubit.”

That’s the idea that space-time and everything in it emerges like a hologram out of information stored in the entangled quantum states of particles.

Yes. Then there are dualities in math, which can sometimes be interpreted physically as consequences of dualities between two quantum field theories. There are so many ways these things are interconnected that any simple statement I try to make on the fly, as soon as I’ve said it I realize it didn’t capture the whole reality. You have to imagine a web of different relationships, where the same physics has different descriptions, revealing different properties. In the simplest case, there are only two important descriptions, and that might be enough. If you ask me about a more complicated example, there might be many, many different ones.

Given this web of relationships and the issue of how hard it is to characterize all duality, do you feel that this reflects a lack of understanding of the structure, or is it that we’re seeing the structure, only it’s very complicated? 

I’m not certain what we should hope for. Traditionally, quantum field theory was constructed by starting with the classical picture [of a smooth field] and then quantizing it. Now we’ve learned that there are a lot of things that happen that that description doesn’t do justice to. And the same quantum theory can come from different classical theories. Now, Nati Seiberg [a theoretical physicist who works down the hall] would possibly tell you that he has faith that there’s a better formulation of quantum field theory that we don’t know about that would make everything clearer. I’m not sure how much you should expect that to exist. That would be a dream, but it might be too much to hope for; I really don’t know.

There’s another curious fact that you might want to consider, which is that quantum field theory is very central to physics, and it’s actually also clearly very important for math. But it’s extremely difficult for mathematicians to study; the way physicists define it is very hard for mathematicians to follow with a rigorous theory. That’s extremely strange, that the world is based so much on a mathematical structure that’s so difficult.

What do you see as the relationship between math and physics?

I prefer not to give you a cosmic answer but to comment on where we are now. Physics in quantum field theory and string theory somehow has a lot of mathematical secrets in it, which we don’t know how to extract in a systematic way. Physicists are able to come up with things that surprise the mathematicians. Because it’s hard to describe mathematically in the known formulation, the things you learn about quantum field theory you have to learn from physics.

I find it hard to believe there’s a new formulation that’s universal. I think it’s too much to hope for. I could point to theories where the standard approach really seems inadequate, so at least for those classes of quantum field theories, you could hope for a new formulation. But I really can’t imagine what it would be.

You can’t imagine it at all? 

No, I can’t. Traditionally it was thought that interacting quantum field theory couldn’t exist above four dimensions, and there was the interesting fact that that’s the dimension we live in. But one of the offshoots of the string dualities of the 1990s was that it was discovered that quantum field theories actually exist in five and six dimensions. And it’s amazing how much is known about their properties. 

I’ve heard about the mysterious (2,0) theory, a quantum field theory describing particles in six dimensions, which is dual to M-theory describing strings and gravity in seven-dimensional AdS space. Does this (2,0) theory play an important role in the web of dualities?

Yes, that’s the pinnacle. In terms of conventional quantum field theory without gravity, there is nothing quite like it above six dimensions. From the (2,0) theory’s existence and main properties, you can deduce an incredible amount about what happens in lower dimensions. An awful lot of important dualities in four and fewer dimensions follow from this six-dimensional theory and its properties. However, whereas what we know about quantum field theory is normally from quantizing a classical field theory, there’s no reasonable classical starting point of the (2,0) theory. The (2,0) theory has properties [such as combinations of symmetries] that sound impossible when you first hear about them. So you can ask why dualities exist, but you can also ask why is there a 6-D theory with such and such properties? This seems to me a more fundamental restatement. 

Dualities sometimes make it hard to maintain a sense of what’s real in the world, given that there are radically different ways you can describe a single system. How would you describe what’s real or fundamental?

What aspect of what’s real are you interested in? What does it mean that we exist? Or how do we fit into our mathematical descriptions?

The latter.

Well, one thing I’ll tell you is that in general, when you have dualities, things that are easy to see in one description can be hard to see in the other description. So you and I, for example, are fairly simple to describe in the usual approach to physics as developed by Newton and his successors. But if there’s a radically different dual description of the real world, maybe some things physicists worry about would be clearer, but the dual description might be one in which everyday life would be hard to describe.

What would you say about the prospect of an even more optimistic idea that there could be one single quantum gravity description that really does help you in every case in the real world?

Well, unfortunately, even if it’s correct I can’t guarantee it would help. Part of what makes it difficult to help is that the description we have now, even though it’s not complete, does explain an awful lot. And so it’s a little hard to say, even if you had a truly better description or a more complete description, whether it would help in practice.

Are you speaking of M-theory?

M-theory is the candidate for the better description.

You proposed M-theory 22 years ago. What are its prospects today?

Personally, I thought it was extremely clear it existed 22 years ago, but the level of confidence has got to be much higher today because AdS/CFT has given us precise definitions, at least in AdS space-time geometries. I think our understanding of what it is, though, is still very hazy. AdS/CFT and whatever’s come from it is the main new perspective compared to 22 years ago, but I think it’s perfectly possible that AdS/CFT is only one side of a multifaceted story. There might be other equally important facets.

What’s an example of something else we might need?

Maybe a bulk description of the quantum properties of space-time itself, rather than a holographic boundary description. There hasn’t been much progress in a long time in getting a better bulk description. And I think that might be because the answer is of a different kind than anything we’re used to. That would be my guess.

Are you willing to speculate about how it would be different?

I really doubt I can say anything useful. I guess I suspect that there’s an extra layer of abstractness compared to what we’re used to. I tend to think that there isn’t a precise quantum description of space-time — except in the types of situations where we know that there is, such as in AdS space. I tend to think, otherwise, things are a little bit murkier than an exact quantum description. But I can’t say anything useful.

The other night I was reading an old essay by the 20th-century Princeton physicist John Wheeler. He was a visionary, certainly. If you take what he says literally, it’s hopelessly vague. And therefore, if I had read this essay when it came out 30 years ago, which I may have done, I would have rejected it as being so vague that you couldn’t work on it, even if he was on the right track.

You’re referring to Information, Physics, Quantum, Wheeler’s 1989 essay propounding the idea that the physical universe arises from information, which he dubbed “it from bit.” Why were you reading it? 

I’m trying to learn about what people are trying to say with the phrase “it from qubit.” Wheeler talked about “it from bit,” but you have to remember that this essay was written probably before the term “qubit” was coined and certainly before it was in wide currency. Reading it, I really think he was talking about qubits, not bits, so “it from qubit” is actually just a modern translation.

Don’t expect me to be able to tell you anything useful about it — about whether he was right. When I was a beginning grad student, they had a series of lectures by faculty members to the new students about theoretical research, and one of the people who gave such a lecture was Wheeler. He drew a picture on the blackboard of the universe visualized as an eye looking at itself. I had no idea what he was talking about. It’s obvious to me in hindsight that he was explaining what it meant to talk about quantum mechanics when the observer is part of the quantum system. I imagine there is something we don’t understand about that.

Observing a quantum system irreversibly changes it, creating a distinction between past and future. So the observer issue seems possibly related to the question of time, which we also don’t understand. With the AdS/CFT duality, we’ve learned that new spatial dimensions can pop up like a hologram from quantum information on the boundary. Do you think time is also emergent — that it arises from a timeless complete description?

I tend to assume that space-time and everything in it are in some sense emergent. By the way, you’ll certainly find that that’s what Wheeler expected in his essay. As you’ll read, he thought the continuum was wrong in both physics and math. He did not think one’s microscopic description of space-time should use a continuum of any kind — neither a continuum of space nor a continuum of time, nor even a continuum of real numbers. On the space and time, I’m sympathetic to that. On the real numbers, I’ve got to plead ignorance or agnosticism. It is something I wonder about, but I’ve tried to imagine what it could mean to not use the continuum of real numbers, and the one logician I tried discussing it with didn’t help me.

Do you consider Wheeler a hero?

I wouldn’t call him a hero, necessarily, no. Really I just became curious what he meant by “it from bit,” and what he was saying. He definitely had visionary ideas, but they were too far ahead of their time. I think I was more patient in reading a vague but inspirational essay than I might have been 20 years ago. He’s also got roughly 100 interesting-sounding references in that essay. If you decided to read them all, you’d have to spend weeks doing it. I might decide to look at a few of them.

Why do you have more patience for such things now?

I think when I was younger I always thought the next thing I did might be the best thing in my life. But at this point in life I’m less persuaded of that. If I waste a little time reading somebody’s essay, it doesn’t seem that bad.

Do you ever take your mind off physics and math?

My favorite pastime is tennis. I am a very average but enthusiastic tennis player.

In contrast to Wheeler, it seems like your working style is to come to the insights through the calculations, rather than chasing a vague vision. 

In my career I’ve only been able to take small jumps. Relatively small jumps. What Wheeler was talking about was an enormous jump. And he does say at the beginning of the essay that he has no idea if this will take 10, 100 or 1,000 years.

And he was talking about explaining how physics arises from information.

Yes. The way he phrases it is broader: He wants to explain the meaning of existence. That was actually why I thought you were asking if I wanted to explain the meaning of existence.

I see. Does he have any hypotheses?

No. He only talks about things you shouldn’t do and things you should do in trying to arrive at a more fundamental description of physics.

Do you have any ideas about the meaning of existence?

No. [Laughs.]

Correction: This article was updated on Nov. 29, 2017, to clarify that M-theory is the leading candidate for a unified theory of everything. Other ideas have been proposed that also claim to unify the fundamental forces.

This article was reprinted on Wired.com.

These dynamical events would be mixed in with the more mundane quantum jitter from those particle pairs that popped up in the inflaton field and engendered so-called “two-point correlations” throughout the sky. A pair of particles might, for instance, have surfaced in some other primordial field, and one member of this pair might then have decayed into two inflaton particles while the other decayed into just a single inflaton particle, yielding a three-point correlation, or triangle, in the sky. Or, two mystery particles might have collided and split into four inflaton particles, producing a four-point correlation. Rarer events would have yielded five-point, six-point and even higher-point correlations, with their numbers, sizes and interior angles encoding the types and relationships of the particles that produced them. The unitarity principle promises that by tallying the shapes ever more precisely, cosmologists will achieve an increasingly detailed account of the primordial universe, just as physicists at the Large Hadron Collider in Europe hone their theory of the known particles and look for evidence of new ones by collecting statistics on how particles morph and scatter during collisions.

Following Maldacena’s calculation of the gravitational floor, other researchers demonstrated that even many simple inflationary models generate much more pronounced non-Gaussianity than the bare minimum. Clocksmiths like Silverstein and Kleban have since been busy working out the distinct set of triangles that their models would produce — predictions that will become increasingly testable in the coming years. Progress accelerated in 2014, when a small experiment based at the South Pole appeared to make a momentous discovery about the universe’s birth. The announcement drummed up interest in cosmological triangles, even though the supposed discovery ultimately proved a grave disappointment.

As news began to spread on March 17, 2014, that the “smoking gun” of cosmic inflation had been detected, Stanford University’s press office posted a celebratory video on YouTube. In the footage, the cosmologist Andrei Linde, one of the decorated pioneers of inflationary cosmology, and his wife, the string and supergravity theorist and cosmologist Renata Kallosh, answer their door to find their Stanford colleague Chao-Lin Kuo on the doorstep, accompanied by a camera crew.

“It’s five sigma, at point two,” Kuo says in the video.

“Discovery?” Kallosh asks, after a beat. She hugs Kuo, almost melting, as Linde exclaims, “What?”

Viewers learn that BICEP2, an experiment co-led by Kuo, has detected a swirl pattern in the cosmic microwave background that would have been imprinted by ripples in space-time known as “primordial gravitational waves.” And these could only have arisen during cosmic inflation, as corkscrew-like particles popped up in the gravitational field and then became stretched and permanently frozen into the shape of the universe.

In the next scene, Linde sips champagne with his wife and their guest. In the early 1980s, Linde, Alexei Starobinsky, Alan Guth and other young cosmologists devised the theory of cosmic inflation as a patch for the broken 1930s-era Big Bang theory, which described the universe as expanding outward from a “singularity” — a nonsensical point of infinite density — and couldn’t explain why the universe hadn’t become mottled and contorted as it grew. Cosmic inflation provided a clever fix for these problems, and BICEP2’s finding suggested that the theory was conclusively proved. “If this is true,” Linde says to the camera, “this is a moment of understanding of nature of such a magnitude that it just overwhelms. Let’s see. Let’s just hope that this is not a trick.”

To many researchers, the most exciting thing about the alleged discovery was the strength of the swirl signal, measured as r = 0.2. The measurement indicated that inflation occurred at an extremely high energy scale and at the earliest moments in time, near the time-energy domain where gravity, as well as the effects of strings, branes or other exotica, would have been strong. The higher the energy scale of inflation, the more cross-wiring there would be between the inflaton and these other primordial ingredients. The result would be pronounced triangles and other non-Gaussianities in the sky.

“After BICEP, we all stopped what we were doing and started thinking about inflation,” Arkani-Hamed said. “Inflation is like having a gigantic particle accelerator at much higher energy scales than you can get to on Earth.” The question became how such an accelerator would operate, he said, “and if there really was exotic stuff up there [near the inflation scale], how you could go about looking for it.”

As these investigations took off, more details of BICEP2’s analysis emerged. It became clear that the discovery was indeed a trick of nature: The team’s telescope at the South Pole had picked up the swirly glow of galactic dust rather than the effect of primordial gravitational waves. A mix of anguish and anger swept through the field. Two years on, primordial gravitational waves still haven’t been detected. In January, BICEP2’s successor, the BICEP/Keck Array, reported that the value of r can be no more than 0.07, which lowers the ceiling on the energy scale of inflation and moves it further below the scale of strings or other exotic physics.

Nonetheless, many researchers were now aware of the potential gold mine of information contained in triangles and other non-Gaussianities. It had become apparent that these fossils from inflation were worth digging for, even if they were buried deeper than BICEP2 had briefly promised. “Yeah, rwent down a little bit,” Maldacena said. But it’s not so bad, in his opinion: A relatively high scale is still possible.

In a paper last spring that drew on previous work by other researchers, Maldacena and Arkani-Hamed used symmetry arguments to show that a key feature of string theory could manifest itself in triangles. String theory predicts an infinite tower of “higher-spin states” — essentially, strings vibrating at an infinitely rising sequence of pitches. So far, no fundamental particles with a “spin” value greater than two have been discovered. Maldacena and Arkani-Hamed showed that the existence of such a higher-spin state would result in alternating peaks and troughs in the strength of the signal produced by triangles in the sky as they grow more elongated. For string theorists, this is exciting. “You can’t build a consistent interacting theory of such a particle except if you have an infinite tower of them” like the tower in string theory, explained Daniel Baumann, a theoretical cosmologist at the University of Amsterdam. Finding the oscillatory pattern in the triangles in the sky would confirm that this tower exists. “Just seeing one particle of spin greater than two would be indicative of string theory being present.”

Other researchers are pursuing similarly general predictions. In February, Kamionkowski and collaborators reported detailed information about primordial particles that is encoded in the geometry of four-point correlations, which “get interesting,” he said, because four points can lie flat or sweep into the third dimension. Observing the signals predicted by Arkani-Hamed, Maldacena and Kamionkowski would be like striking gold, but the gold is buried deep: Their strength is probably near the gravitational floor and will require at least 1,000 times the sensitivity of current equipment to detect. Other researchers prefer to tinker with bespoke string models that predict more pronounced triangles and other shapes. “So far we’ve explored only, I think, a very small fraction of the possibilities for non-Gaussianity,” Kamionkowski said.

Meanwhile, Linde and Kallosh are pushing in a totally different direction. Over the past three years, they’ve become enamored with a class of models called “cosmological alpha-attractors” that do not predict any non-Gaussianities above the gravitational floor at all. According to these models, cosmic inflation was completely pure, driven by a solitary inflaton field. The field is described by a Kähler manifold, which maps onto the geometric disk seen in Escher’s drawing of angels and devils. The Escherian geometry provides a continuum of possible values for the energy scale of inflation, including values so low that the inflaton’s cross-wiring to the gravitational field and other primordial fields would be extremely weak. If such a model does describe the universe, then swirls, triangles and other shapes might never be detected.

Linde isn’t bothered by this. In supporting the alpha-attractor models, he and Kallosh are staking a position in favor of simplicity and theoretical beauty, at the expense of ever knowing for sure whether their cosmological origin story is correct. An alpha-attractor universe, Linde said, is like one of the happy families in the famous opening line of Anna Karenina. As he paraphrased Tolstoy: “Any happy family, well, they look in a sense alike. But all unhappy families — they’re unhappy for different reasons.”

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Will our universe turn out to be “happy” and completely free of distinguishing features? Baumann, who co-authored a book last year on string cosmology, argues that models like Linde’s and Kallosh’s are too simple to be plausible. “They are building these models from the bottom up,” he said. “Introducing a single field, trying to be very minimal — it would have been a beautiful model of the world.” But, he said, when you try to embed inflation into a fundamental theory of nature, it’s very hard to engineer a single field acting by itself, immune to the effects of everything else. “String theory has many of these effects; you can’t ignore them.”

And so the search for triangles and other non-Gaussianities is under way. Between 2009 and 2013, the Planck space telescope mapped the cosmic microwave background at the highest resolution yet, and scientists have since been scouring the map for statistical excesses of triangles and other shapes. As of their most recent analysis, they haven’t found any; given the sensitivity of their instruments and their 2-D searching ground, they only ever had an outside chance of doing so. But the scientists are continuing to parse the data in new ways, with another non-Gaussianity analysis expected this year.

Hiranya Peiris, an astrophysicist at University College London who searches for non-Gaussianities in the Planck data, said that she and her collaborators are taking cues from string cosmologists in determining which signals to look for. Peiris is keen to test a string-inflationary mechanism called axion monodromy, including variants recently developed by Silverstein and collaborators Raphael Flauger, Mehrdad Mirbabayi, and Leonardo Senatore that generate an oscillatory pattern in triangles as a function of their size that can be much more pronounced than the pattern studied by Arkani-Hamed and Maldacena. To find such a signal, Peiris and her team must construct templates of the pattern and match them with the data “in a very numerically intensive and demanding analysis,” she said. “Then we have to do careful statistical tests to make sure we are not being fooled by random fluctuations in the data.”

Some string models have already been ruled out by this data analysis. Regarding the public debate about whether string theory is too divorced from empirical testing to count as science, Silverstein said, “I find it surreal, because we are currently doing some traditional science with string theory.”

Moving forward, cosmologists plan to scour ever larger volumes of the universe’s large-scale structure. Starting in 2020, the proposed SPHEREx mission could measure non-Gaussianity sensitively enough in the distribution of 300 million galaxies to determine whether inflation was driven by one clock or two cross-wired clocks (according to models of the theory known as single- and multi-field inflation, respectively). “Just to reach this level would dramatically reduce the number of possible inflation theories,” said Doré, who is working on the SPHEREx project. A few years further out, the Large Synoptic Survey Telescope will map 20 billion cosmological structures. If the statistical presence of triangles is not detected in the universe’s large-scale structure, there is yet another, perhaps final, approach. By mapping an ultra-faint radio signal called the 21-centimeter line, which is emitted by hydrogen atoms and traces back to the creation of the first stars, cosmologists would be able to measure even more “modes,” or arrangements of structures. “It’s going to have information about the whole volume of the universe,” Maldacena said.

If or when triangles show up, they will, one by one, reveal the nature of the inflaton clock and why it ticked. But will enough clues be gathered before we run out of sky in which to gather them?

The promise of unitarity — that information can be scrambled but never lost — comes with a caveat.

“If we assume we can make perfect measurements and we have an infinite sky and so on,” Maldacena said, “then in principle all the interactions and information about particles during inflation is contained in these correlators” — that is, three-point correlations, four-point correlations and so on. But perfect measurements are impossible. And worse, the sky is finite. There is a cosmic horizon: the farthest distance from which light has had time to reach us, and thus, beyond which we cannot see. During inflation, and over the entire history of the accelerating expansion of the universe since then, swirls, triangles, quadrilaterals and other shapes have been flying past this horizon and out of sight. And with them, the subtlest of signals, associated with the rarest, highest-energy processes during inflation, are lost: Cosmologists will never be able to gather enough statistics in our finite patch of sky to tease them out, precluding a complete accounting of nature’s fundamental constituents.

In his paper with Maldacena, Arkani-Hamed initially included a discussion of this issue, but he removed most of it. He finds the possibility of a limit to knowledge “tremendously disturbing” and sees it as evidence that quantum mechanics must be extended. One possible way to do this is suggested by his work on the amplituhedron, which casts quantum mechanical probabilities (and with them, unitarity) as emergent consequences of an underlying geometry. He plans to discuss this possibility in a forthcoming paper that will relate an analogue of the amplituhedron to non-Gaussianities in the sky.

People vary in the extent to which they are bothered by a limit to knowledge. “I’m more practical,” Zaldarriaga said. “There are, like, tens or many tens or orders of magnitude more modes that in principle we could see, that we have not been able to measure just because of technological or theoretical inability. So, these ‘in principle’ questions are interesting, but we are way before this point.”

Kleban also feels hopeful. “Yeah, it’s a finite amount of information,” he said. “But you could say the same thing about evolution, right? There’s a limited number of fossils, and yet we have a pretty good idea of what happened, and it’s getting better and better.”

If all goes well, enough fossils will turn up in the sky to tell a more complete story. A vast searching ground awaits.

Correction: This article was revised on April 19, 2016, to reflect that the Keck Array is BICEP2’s successor, not its predecessor, and on April 21, 2016, to correct the spelling of Mehrdad Mirbabayi’s surname.

This article was reprinted on Wired.com.