Does Spacetime Emerge From Quantum Information?

Quantizing gravity is an important goal of contemporary physics, but after decades of effort it’s proven to be an extremely tough nut to crack. So it’s worth considering a very slight shift of emphasis. What if the right strategy is not “finding the right theory of gravity and quantizing it,” but “finding a quantum theory out of which gravity emerges”?

That’s one way of thinking about a new and exciting approach to the problem known as “tensor networks” or the “AdS/MERA correspondence.” If you want to have the background and basic ideas presented in a digestible way, the talented Jennifer Ouellette has just published an article at Quanta that lays it all out. If you want to dive right into some of the nitty-gritty, my young and energetic collaborators and I have a new paper out:

Consistency Conditions for an AdS/MERA Correspondence
Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen

The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an AdS spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.

(And we’re not the only Caltech-flavored group to be thinking about this stuff.)

Between the Quanta article and our paper you should basically be covered, but let me give the basic idea. It started when quantum-information theorists interested in condensed-matter physics, in particular Giufre Vidal and Glen Evenbly, were looking for ways to find the quantum ground state (the wave function with lowest possible energy) of toy-model systems of spins (qubits) arranged on a line. A simple problem, but one that is very hard to solve, even on a computer — Hilbert space is just too big to efficiently search through it. So they turned to the idea of a “tensor network.”

A tensor network is a way of building up a complicated, highly-entangled state of many particles, by starting with a simple initial state. The particular kind of network that Vidal and Evenbly became interested in is called the MERA, for Multiscale Entanglement Renormalization Ansatz (see for example). Details can be found in the links above; what matters here is that the MERA takes the form of a lattice that looks a bit like this.

tensor banner - circle_0

Our initial simple starting point is actually at the center of this diagram. The various links represent tensors acting on that initial state to make something increasingly more complicated, culminating in the many-body state at the circular boundary of the picture.

Here’s the thing: none of this had anything to do with gravity. It was a just a cute calculational trick to find quantum states of interacting electron spins. But this kind of picture can’t help but remind certain theoretical physicists of a very famous kind of spacetime: Anti-de Sitter space (AdS), the maximally symmetric solution to Einstein’s equation in the presence of a negative cosmological constant. (Or at least the “spatial” part thereof, which is simply a hyperbolic plane.)

cft-correspondence

Of course, someone has to be the first to actually do the noticing, and in this case it was a young physicist named Brian Swingle. Brian is a condensed-matter physicist himself, but he was intellectually curious enough to take courses on string theory as a grad student. There he learned that string theorists love AdS — it’s the natural home of Maldacena’s celebrated gauge/gravity duality, with a gauge theory living on the flat-space “boundary” and gravity lurking in the AdS “bulk.” Swingle wondered whether the superficial similarity between the MERA tensor network and AdS geometry wasn’t actually a sign of something deeper — an AdS/MERA correspondence?

And the answer is — maybe! Some of the features of AdS gravity are certainly captured by the MERA, so the whole thing kind of smells right. But, as we say in the paper above with the expansive list of authors, it doesn’t all just fall together right away. Some things you would like to be true in AdS don’t happen automatically in the MERA interpretation. Which isn’t a deal-killer — it’s just a sign that we have to, at the very least, work a bit harder. Perhaps there’s a generalization of the simple MERA that must be considered, or a slightly more subtle version of the purported correspondence.

The possibility is well worth pursuing. As amazing (and thoroughly checked) as the traditional AdS/CFT correspondence is, there are still questions about it that we haven’t satisfactorily answered. The tensor networks, on the other hand, are extremely concrete, well-defined objects, for which you should in principle be able to answer any question you might have. Perhaps more intriguingly, the idea of “string theory” never really enters the game. The “bulk” where gravity lives emerges directly from a set of interacting spins, in a context where the original investigators weren’t thinking about gravity at all. The starting point doesn’t even necessarily have anything to do with “spacetime,” and certainly not with the dynamics of spacetime geometry. So I certainly hope that people remain excited and keep thinking in this direction — it would be revolutionary if you could build a complete theory of quantum gravity directly from some interacting qubits.

Posted in arxiv, Science | 36 Comments

How to Build a Cloud Chamber to Detect Cosmic Rays

Sorry, I have no idea how to build a cloud chamber, I’m just a theorist. But Samatha here can help you out (and be much more charming than I would be in the process).

Posted in Science | 8 Comments

Quantum Field Theory and the Limits of Knowledge

Last week I had the pleasure of giving a seminar to the philosophy department at the University of North Carolina. Ordinarily I would have talked about the only really philosophical work I’ve done recently (or arguably ever), deriving the Born Rule in the Everett approach to quantum mechanics. But in this case I had just talked about that stuff the day before, at a gathering of local philosophers of science.

So instead I decided to use the opportunity to get some feedback on another idea I had been thinking about — our old friend, the claim that The Laws of Physics Underlying Everyday Life Are Completely Understood (also here, here). In particular, given that I was looking for feedback from a group of people that had expertise in philosophical matters, I homed in on the idea that quantum field theory has a unique property among physical theories: any successful QFT tells us very specifically what its domain of applicability is, allowing us to distinguish the regime where it should be accurate from the regime where we can’t make predictions.

The talk wasn’t recorded, but here are the slides. I recycled a couple of ones from previous talks, but mostly these were constructed from scratch.

The punchline of the talk was summarized in this diagram, showing different regimes of phenomena and the arrows indicating what they depend on:

layers

There are really two arguments going on here, indicated by the red arrows with crosses through them. These two arrows, I claim, don’t exist. The physics of everyday life is not affected by dark matter or any new particles or forces, and its only dependence on the deeper level of fundamental physics (whether it be string theory or whatever) is through the intermediary of what Frank Wilczek has dubbed “The Core Theory” — the Standard Model plus general relativity. The first argument (no new important particles or forces) relies on basic features of quantum field theory, like crossing symmetry and the small number of species that go into making up ordinary matter. The second argument is more subtle, relying on the idea of effective field theory.

So how did it go over? I think people were properly skeptical and challenging, but for the most part they got the point, and thought it was interesting. (Anyone who was in the audience is welcome to chime in and correct me if that’s a misimpression.) Mostly, since this was a talk to philosophers rather than physicists, I spent my time doing a pedagogical introduction to quantum field theory, rather than diving directly into any contentious claims about it — and learning something new is always a good thing.

Posted in Philosophy, Science | 59 Comments

A Personal Narrative

I was very pleased to learn that I’m among this year’s recipients of a Guggenheim Fellowship. The Fellowships are mid-career awards, meant “to further the development of scholars and artists by assisting them to engage in research in any field of knowledge and creation in any of the arts, under the freest possible conditions and irrespective of race, color, or creed.” This year 173 Fellowships were awarded, chosen from 3,100 applications. About half of the winners are in the creative arts, and the majority of those remaining are in the humanities and social sciences, leaving eighteen slots for natural scientists. Only two physicists were chosen, so it’s up to Philip Phillips and me to uphold the honor of our discipline.

The Guggenheim application includes a “Career Narrative” as well as a separate research proposal. I don’t like to share my research proposals around, mostly because I’m a theoretical physicist and what I actually end up doing rarely bears much resemblance to what I had previously planned to do. But I thought I could post my career narrative, if only on the chance that it might be useful to future fellowship applicants (or young students embarking on their own research careers). Be warned that it’s more personal than most things I write on the blog here, not to mention that it’s beastly long. Also, keep in mind that the purpose of the document was to convince people to give me money — as such, it falls pretty heavily on the side of grandiosity and self-justification. Be assured that in real life I remain meek and humble.

Continue reading

Posted in Academia, Personal | 42 Comments

Against Aioli

Now that we’ve figured out the existence of God and the reality of time, let’s get down to the important issues: please stop putting aioli on hot dogs.

Recently, a casual restaurant called the Dog Haus opened right on the street I drive down on my way to and from work. It’s a pretty simple concept: fancy hot dogs and sausages. As restaurant concepts go, this is right in my wheelhouse, combining two things I love very much: (1) fanciness, and (2) hot dogs. I am precisely the target audience for this establishment. I would not be surprised if some marketer had shown a picture of me in his PowerPoint presentation to the Dog Haus board meeting at one point.

However, upon actually eating at the Dog Haus a couple of times, my overall impression was one of grave disappointment. I had sampled a couple of their suggested special items — things like “Das Brat,” which comes with bratwurst, whole grain mustard aioli, white american cheese, caramelized onions, and sauerkraut. In each case, the offering came across as too bland and goopy to really qualify as anything special. I have had hot dogs at baseball stadiums that brought me greater pleasure.

But I persevered, out of a conviction that I should like this kind of place. Finally I decided to forgo the suggested menu offerings and just get a plain dog and put on the condiments myself.

It was heavenly. Spicy, crisp, lively, and served on an amazing Hawaiian bread bun. The hot dog I had been waiting for all my life.

It took me a while, but I eventually sussed out why I could take the Dog Haus raw ingredients and create something special, but was turned off by all of their pre-suggested menu items. Namely: the suggestions they put forward were far too likely to feature an innocent sausage drowned in “aioli.”

Photo of a Dog Haus dog (with aioli). From A Moveable Feast, whose author is far too forgiving of this abomination.

Photo of a Dog Haus dog (with aioli). From A Moveable Feast, whose author is far too forgiving of this abomination.

It’s not just the Dog Haus. I’ve been to a disturbing number of upscale burger joints that seem to think that aioli is what one puts on cheeseburgers. (Not to mention “brioche buns” — don’t get me started.)

It is not. Traditionally, on burgers one puts ketchup, and on hot dogs and sausages one puts mustard, in addition to whatever other creative accoutrements one is inspired to add. But not aioli, a garlicky kind of mayonnaise meant for eggs or fish or something else light and delicate.

I am here to inform the gourmet chefs of the world that hot dogs and hamburgers are not light and delicate foodstuffs. They are robust, coarse, energetic foods, and they require condiments that can stand up to the challenge. Something with a kick, with some life in it — not a greasy white emulsion of oil globules.

It’s not hard to see why such an obvious mistake is being made. You want to brand your dogs and burgers — traditionally classified as simple peasant fare — as something upscale and sophisticated. Mustard and ketchup are the antithesis of upscale sophistication, so you peer into your list of French condiments and see what comes up. (Whatever appears first in alphabetical order, apparently.)

The solution is equally obvious: better-quality mustard and ketchup. The Dog Haus even has such things, which explains why it’s not hard to build a memorable dog all by yourself, if you don’t make the mistake of letting them do it for you.

I will close with a picture of Joël Robuchon, one of the greatest chefs of our age, eating at In-And-Out Burger. I bet he was sad that “animal-style” burgers involve Thousand Island dressing.

20100224_robuchon_560x375

Posted in Food and Drink | 41 Comments

The Reality of Time

The idea that time isn’t “real” is an ancient one — if we’re allowed to refer to things as “ancient” under the supposition that time isn’t real. You will recall the humorous debate we had at our Setting Time Aright conference a few years ago, in which Julian Barbour (the world’s most famous living exponent of the view that time isn’t real) and Tim Maudlin (who believes strongly that time is real, and central) were game enough to argue each other’s position, rather than their own. Confusingly, they were both quite convincing.

smithsonian-mag The subject has come up once again with two new books by Lee Smolin: Time Reborn, all by himself, and The Singular Universe and the Reality of Time, with philosopher Roberto Mangabeira Unger. This new attention prompted me to write a short essay for Smithsonian magazine, laying out the different possibilities.

Personally I think that the whole issue is being framed in a slightly misleading way. (Indeed, this mistaken framing caused me to believe at first that Lee and I were in agreement, until his book actually came out.) The stance of Maudlin and Smolin and others isn’t merely that time is “real,” in the sense that it exists and plays a useful role in how we talk about the world. They want to say something more: that the passage of time is real. That is, that time is more than simply a label on different moments in the history of the universe, all of which are independently pretty much equal. They want to attribute “reality” to the idea of the universe coming into being, moment by moment.

3metaphysics

Such a picture — corresponding roughly to the “possibilism” option in the picture above, although I won’t vouch that any of these people would describe their own views that way — is to be contrasted with the “eternalist” picture of the universe that has been growing in popularity ever since Laplace introduced his Demon. This is the view, in the eyes of many, that is straightforwardly suggested by our best understanding of the laws of physics, which don’t seem to play favorites among different moments of time.

According to eternalism, the apparent “flow” of time from past to future is indeed an illusion, even if the time coordinate in our equations is perfectly real. There is an apparent asymmetry between the past and future (many such asymmetries, really), but that can be traced to the simple fact that the entropy of the universe was very low near the Big Bang — the Past Hypothesis. That’s an empirical feature of the configuration of stuff in the universe, not a defining property of the nature of time itself.

Personally, I find the eternalist block-universe view to be perfectly acceptable, so I think that these folks are working hard to tackle a problem that has already been solved. There are more than enough problems that haven’t been solved to occupy my life for the rest of its natural span of time (as it were), so I’m going to concentrate on those. But who knows? If someone could follow this trail and be led to a truly revolutionary and successful picture of how the universe works, that would be pretty awesome.

Posted in Philosophy, Science, Time | 79 Comments

Guest Post: Don Page on God and Cosmology

Don Page is one of the world’s leading experts on theoretical gravitational physics and cosmology, as well as a previous guest-blogger around these parts. (There are more world experts in theoretical physics than there are people who have guest-blogged for me, so the latter category is arguably a greater honor.) He is also, somewhat unusually among cosmologists, an Evangelical Christian, and interested in the relationship between cosmology and religious belief.

Longtime readers may have noticed that I’m not very religious myself. But I’m always willing to engage with people with whom I disagree, if the conversation is substantive and proceeds in good faith. I may disagree with Don, but I’m always interested in what he has to say.

Recently Don watched the debate I had with William Lane Craig on “God and Cosmology.” I think these remarks from a devoted Christian who understands the cosmology very well will be of interest to people on either side of the debate.


Open letter to Sean Carroll and William Lane Craig:

I just ran across your debate at the 2014 Greer-Heard Forum, and greatly enjoyed listening to it. Since my own views are often a combination of one or the others of yours (though they also often differ from both of yours), I thought I would give some comments.

I tend to be skeptical of philosophical arguments for the existence of God, since I do not believe there are any that start with assumptions universally accepted. My own attempt at what I call the Optimal Argument for God (one, two, three, four), certainly makes assumptions that only a small fraction of people, and perhaps even only a small fraction of theists, believe in, such as my assumption that the world is the best possible. You know that well, Sean, from my provocative seminar at Caltech in November on “Cosmological Ontology and Epistemology” that included this argument at the end.

I mainly think philosophical arguments might be useful for motivating someone to think about theism in a new way and perhaps raise the prior probability someone might assign to theism. I do think that if one assigns theism not too low a prior probability, the historical evidence for the life, teachings, death, and resurrection of Jesus can lead to a posterior probability for theism (and for Jesus being the Son of God) being quite high. But if one thinks a priori that theism is extremely improbable, then the historical evidence for the Resurrection would be discounted and not lead to a high posterior probability for theism.

I tend to favor a Bayesian approach in which one assigns prior probabilities based on simplicity and then weights these by the likelihoods (the probabilities that different theories assign to our observations) to get, when the product is normalized by dividing by the sum of the products for all theories, the posterior probabilities for the theories. Of course, this is an idealized approach, since we don’t yet have _any_ plausible complete theory for the universe to calculate the conditional probability, given the theory, of any realistic observation.

For me, when I consider evidence from cosmology and physics, I find it remarkable that it seems consistent with all we know that the ultimate theory might be extremely simple and yet lead to sentient experiences such as ours. A Bayesian analysis with Occam’s razor to assign simpler theories higher prior probabilities would favor simpler theories, but the observations we do make preclude the simplest possible theories (such as the theory that nothing concrete exists, or the theory that all logically possible sentient experiences occur with equal probability, which would presumably make ours have zero probability in this theory if there are indeed an infinite number of logically possible sentient experiences). So it seems mysterious why the best theory of the universe (which we don’t have yet) may be extremely simple but yet not maximally simple. I don’t see that naturalism would explain this, though it could well accept it as a brute fact.

One might think that adding the hypothesis that the world (all that exists) includes God would make the theory for the entire world more complex, but it is not obvious that is the case, since it might be that God is even simpler than the universe, so that one would get a simpler explanation starting with God than starting with just the universe. But I agree with your point, Sean, that theism is not very well defined, since for a complete theory of a world that includes God, one would need to specify the nature of God.

For example, I have postulated that God loves mathematical elegance, as well as loving to create sentient beings, so something like this might explain both why the laws of physics, and the quantum state of the universe, and the rules for getting from those to the probabilities of observations, seem much simpler than they might have been, and why there are sentient experiences with a rather high degree of order. However, I admit there is a lot of logically possible variation on what God’s nature could be, so that it seems to me that at least we humans have to take that nature as a brute fact, analogous to the way naturalists would have to take the laws of physics and other aspects of the natural universe as brute facts. I don’t think either theism or naturalism solves this problem, so it seems to me rather a matter of faith which makes more progress toward solving it. That is, theism per se cannot deduce from purely a priori reasoning the full nature of God (e.g., when would He prefer to maintain elegant laws of physics, and when would He prefer to cure someone from cancer in a truly miraculous way that changes the laws of physics), and naturalism per se cannot deduce from purely a priori reasoning the full nature of the universe (e.g., what are the dynamical laws of physics, what are the boundary conditions, what are the rules for getting probabilities, etc.).

In view of these beliefs of mine, I am not convinced that most philosophical arguments for the existence of God are very persuasive. In particular, I am highly skeptical of the Kalam Cosmological Argument, which I shall quote here from one of your slides, Bill:

  1. If the universe began to exist, then there is a transcendent cause
    which brought the universe into existence.
  2. The universe began to exist.
  3. Therefore, there is a transcendent cause which brought the
    universe into existence.

I do not believe that the first premise is metaphysically necessary, and I am also not at all sure that our universe had a beginning. Continue reading

Posted in Guest Post, Religion | 813 Comments

Auction: Multiply-Signed Copy of Why Evolution Is True

Here is a belated but very welcome spinoff of our Moving Naturalism Forward workshop from 2012: Jerry Coyne was clever enough to bring along a copy of his book, Why Evolution Is True, and have all the participants sign it. He subsequently gathered a few more distinguished autographs, and to make it just a bit more beautiful, artist Kelly Houle added some original illustrations. Jerry is now auctioning off the book to benefit Doctors Without Borders. Check it out:

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Here is the list of signatories:

  • Dan Barker
  • Sean Carroll
  • Jerry Coyne
  • Richard Dawkins
  • Terrence Deacon
  • Simon DeDeo
  • Daniel Dennett
  • Owen Flanagan
  • Anna Laurie Gaylor
  • Rebecca Goldstein
  • Ben Goren
  • Kelly Houle
  • Lawrence Krauss
  • Janna Levin
  • Jennifer Ouellette
  • Massimo Pigliucci
  • Steven Pinker
  • Carolyn Porco
  • Nicholas Pritzker
  • Alex Rosenberg
  • Don Ross
  • Steven Weinberg

Jerry is hoping it will fetch a good price to benefit the charity, so we’re spreading the word. I notice that a baseball signed by Mickey Mantle goes for about $2000. In my opinion a book signed by Steven Weinberg alone should go for even more, so just imagine what this is worth. You have ten days to get your bids in — and if it’s a bit pricey for you personally, I’m sure there’s someone who loves you enough to buy it for you.

Posted in Miscellany | 38 Comments

What Happens Inside the Quantum Wave Function?

Many things can “happen” inside a quantum wave function, of course, including everything that actually does happen — formation of galaxies, origin of life, Lady Gaga concerts, you name it. But given a certain quantum wave function, what actual is happening inside it?

A surprisingly hard problem! Basically because, unlike in classical mechanics, in quantum mechanics the wave function describes superpositions of different possible measurement outcomes. And you can easily cook up situations where a single wave function can be written in many different ways as superpositions of different things. Indeed, it’s inevitable; a humble quantum spin can be written as a superposition of “spinning clockwise” or “spinning counterclockwise” with respect to the z-axis, but it can equally well be written as a superposition of similar behavior with respect to the z-axis, or indeed any axis at all. Which one is “really happening”?

Answer: none of them is “really happening” as opposed to any of the others. The possible measurement outcomes (in this case, spinning clockwise or counterclockwise with respect to some chosen axis) only become “real” when you actually measure the thing. Put more objectively: when the quantum system interacts with a large number of degrees of freedom, becomes entangled with them, and decoherence occurs. But the perfectly general and rigorous picture of all that process is still not completely developed.

So to get some intuition, let’s start with the simplest possible version of the problem: what happens inside a wave function (describing “system” but also “measurement device” and really, the whole universe) that is completely stationary? I.e., what dynamically processes are occurring while the wave function isn’t changing at all?

You’re first guess here — nothing at all “happens” inside a wave function that doesn’t evolve with time — is completely correct. That’s what I explain in the video above, of a talk I gave at the Philosophy of Cosmology workshop in Tenerife. The talk is based on my recent paper with Kim Boddy and Jason Pollack.

Surprisingly, this claim — “nothing is happening if the quantum state isn’t changing with time” — manages to be controversial! People have this idea that a time-independent quantum state has a rich inner life, with civilizations rising and falling within even though the state is literally exactly the same at every moment in time. I’m not precisely sure why. It would be more understandable if that belief got you something good, like an answer to some pressing cosmological problem. But it’s the opposite — believing that all sorts of things are happening inside a time-independent state creates cosmological problems, in particular the Boltzmann Brain problem, where conscious observers keep popping into existence in empty space. So we’re in the funny situation where believing the correct thing — that nothing is happening when the quantum state isn’t changing — solves a problem, and yet some people prefer to believe the incorrect thing, even though that creates problems for them.

Quantum mechanics is a funny thing.

Posted in Science | 60 Comments

From Child Preacher to Adult Humanist

One of the best experiences I had at last year’s Freedom From Religion Foundation convention was listening to this wonderful talk by Anthony Pinn. (Talk begins at 5:40.)

Pinn, growing up outside Buffalo NY, became a preacher in his local church at the ripe young age of 12. Now, there’s nothing an audience of atheists likes better than a story of someone who was devoutly religious and later does an about-face to embrace atheism. (Not an uncommon path, with many possible twists, as you can read in Daniel Dennett and Linda LaScola’s Caught in the Pulpit.) And Pinn gives it to us, hitting all the best notes: being in love with Jesus but also with thinking critically, being surprised to meet theologians who read the Bible as literature rather than as The Word, and ultimately losing his faith entirely while studying at Harvard Divinity School.

But there’s a lot more to his message than a congratulatory triumph of rationality over superstition. Through his life, Pinn has been concerned with the effect that ideas and actions have on real people, especially the African-American community. His mother always reminded him to “move through the world knowing your footsteps matter,” valuable advice no matter what your ontological orientation might be.

This comes out in the Q&A period — often not worth listening to, but in this case it’s the highlight of the presentation. The audience of atheists are looking for yet more self-affirmation, demanding to know why more Blacks haven’t accepted the truth of a secular worldview. Pinn is very frank: naturalism hasn’t yet offered African-Americans a “soft landing.” Too many atheists, he points out, spend a lot of time critiquing religious traditions, and a lot of time patting themselves on the back for being rational and fair-minded, and not nearly enough time constructing something positive, a system of networks and support structures free of the spiritual trappings. It’s a good message for us to hear.

It would have been fantastic to have Anthony at Moving Naturalism Forward. Next time! (Not that there are currently any plans for a next time.)

Posted in Humanity, Religion | 40 Comments