Physicists are not known for finesse. “Even if it cost us our funding,” I’ve heard a physicist declare, “we’d tell you what we think.” Little wonder I irked the porter who directed me toward central Cambridge.

The University of Cambridge consists of colleges as the US consists of states. Each college has a porter’s lodge, where visitors check in and students beg for help after locking their keys in their rooms. And where physicists ask for directions.

Last March, I ducked inside a porter’s lodge that bustled with deliveries. The woman behind the high wooden desk volunteered to help me, but I asked too many questions. By my fifth, her pointing at a map had devolved to jabbing.

Read the subtext, I told myself. Leave.

Or so I would have told myself, if not for that afternoon.

That afternoon, I’d visited Cambridge’s CMS, which merits every letter in “Centre for Mathematical Sciences.” Home to Isaac Newton’s intellectual offspring, the CMS consists of eight soaring, glass-walled, blue-topped pavilions. Their majesty walloped me as I turned off the road toward the gatehouse. So did the congratulatory letter from Queen Elizabeth II that decorated the route to the restroom.

I visited Nilanjana Datta, an affiliated lecturer of Cambridge’s Faculty of Mathematics, and her student, Felix Leditzky. Nilanjana and Felix specialize in entropies and one-shot information theory. Entropies quantify uncertainties and efficiencies. Imagine compressing many copies of a message into the smallest possible number of bits (units of memory). How few bits can you use per copy? That number, we call the optimal compression rate. It shrinks as the number of copies compressed grows. As the number of copies approaches infinity, that compression rate drops toward a number called the message’s Shannon entropy. If the message is quantum, the compression rate approaches the von Neumann entropy.

Good luck squeezing infinitely many copies of a message onto a hard drive. How efficiently can we compress fewer copies? According to one-shot information theory, the answer involves entropies other than Shannon’s and von Neumann’s. In addition to describing data compression, entropies describe the charging of batteriesthe concentration of entanglementthe encrypting of messages, and other information-processing tasks.

Speaking of compressing messages: Suppose one-shot information theory posted status updates on Facebook. Suppose that that panel on your Facebook page’s right-hand side showed news weightier than celebrity marriages. The news feed might read, “TRENDING: One-shot information theory: Second-order asymptotics.”

Second-order asymptotics, I learned at the CMS, concerns how the optimal compression rate decays as the number of copies compressed grows. Imagine compressing a billion copies of a quantum message ρ. The number of bits needed about equals a billion times the von Neumann entropy HvN(ρ). Since a billion is less than infinity, 1,000,000,000 HvN(ρ) bits won’t suffice. Can we estimate the compression rate more precisely?

The question reminds me of gas stations’ hidden pennies. The last time I passed a station’s billboard, some number like $3.65 caught my eye. Each gallon cost about$3.65, just as each copy of ρ costs about HvN(ρ) bits. But a 9/10, writ small, followed the $3.65. If I’d budgeted$3.65 per gallon, I couldn’t have filled my tank. If you budget HvN(ρ) bits per copy of ρ, you can’t compress all your copies.

Suppose some station’s owner hatches a plan to promote business. If you buy one gallon, you pay $3.654. The more you purchase, the more the final digit drops from four. By cataloguing receipts, you calculate how a tank’s cost varies with the number of gallons, n. The cost equals$3.65 × n to a first approximation. To a second approximation, the cost might equal $3.65 × n + an, wherein a represents some number of cents. Compute a, and you’ll have computed the gas’s second-order asymptotics. Nilanjana and Felix computed a’s associated with data compression and other quantum tasks. Second-order asymptotics met information theory when Strassen combined them in nonquantum problems. These problems developed under attention from Hayashi, Han, Polyanski, Poor, Verdu, and others. Tomamichel and Hayashi, as well as Li, introduced quantumness. In the total-cost expression,$3.65 × n depends on n directly, or “linearly.” The second term depends on √n. As the number of gallons grows, so does √n, but √n grows more slowly than n. The second term is called “sublinear.”

Which is the word that rose to mind in the porter’s lodge. I told myself, Read the sublinear text.

Little wonder I irked the porter. At least—thanks to quantum information, my mistake, and facial expressions’ contagiousness—she smiled.

With thanks to Nilanjana Datta and Felix Leditzky for explanations and references; to Nilanjana, Felix, and Cambridge’s Centre for Mathematical Sciences for their hospitality; and to porters everywhere for providing directions.

BICEP2 and soccer

I’m a Caltech physics graduate student who has been working on BICEP2/Keck Array since 2009. BICEP2 reported the first detection of B-mode polarization on degree angular scales, which John Preskill lists as one of his 10 biggest thrills. In my first post here on Quantum Frontiers, I will allegorically describe the current state of affairs of cosmic microwave background (CMB) cosmology. In a future post, I may share with you some of the insider history of how we arrived at this result and how it has felt to be a graduate student through it all.

BICEP2 is an experimental victory. The interpretation of the result is a work in progress. Emphasizing this distinction, I’ll present a soccer analogy in the spirit of the times. It’s as if there are goals on the board at halftime in a soccer game where neither team is expected to score any goals whatsoever. Although there’s no guarantee, the most likely interpretation of having goals on the board at halftime is that one of the two teams, namely inflationary gravitational waves, will win the game.

FIFA represents particle physics. It has been an international powerhouse for about a century. Fans around the globe are tuned into the World Cup. The discovery of the Higgs boson was the champion last time. Who will win this year?

Major League Soccer (MLS), on the other hand, represents CMB cosmology. It is a young league, only around since the 1990s. Its roots go back to the 1960s via the North American Soccer League, best remembered for the New York Cosmos, (or perhaps their New Jersey neighbors) who won an amazing championship in 1978. If you’re not from North America, you probably don’t pay much attention to MLS. You’ve heard of the LA Galaxy thanks to European superstar “David Planckham,” but you couldn’t name any other team. You may even be annoyed that they call it “soccer” instead of “football.” MLS is divided into Western and Eastern Conferences just as CMB cosmologists are concerned with large and small angular scales. Our story concerns an exhibition game between two Western Conference teams. The San Jose Earthquakes represent the ground-shaking possibility of inflationary gravitational waves. The LA Galaxy represent astronomical foregrounds. (Pick your favorite teams and adjust the analogy to taste.)

Let’s pretend that every time the Earthquakes and the Galaxy have ever played against each other over the years, the result has always been 0-0. Not just a draw. Scoreless. The matches become so boring year after year that they become a comedic punchline. Both sides’ defenses are too strong. To bring the fans back to the stands, the two teams agree to a publicity stunt. They’ll play a game at the South Pole! Crazy, right? The event is sponsored by BICEP, a brand of energy drink.*

Bookmakers take bets on the final score. Since neither team has ever scored against the other, the rules are simplified. You don’t have to bet on who will win or by how many goals. You only have to bet on the total score (detection significance in “sigma”). The odds for zero total score are high, so it’s the safe choice. Payoffs increase a little bit if you’re willing to bet against odds on a positive score, maybe one or two goals. You’ll win a small fortune if you correctly bet that three goals (“evidence”) are on the board by the end. A game ending with five goals or above (“discovery”) earns you a jackpot. Dizzle Mapo**, owner of the BICEP brand and an Earthquakes fan, decides to make it more interesting by putting a sizable chunk of her own money down on the long shot bet that at least five goals will be scored by the end. She doesn’t expect to get her money back. But why not go for it? She has the potential to win the largest sum in the history of sports gambling.

They play the game. It’s a slow one with lots of stoppage time. When the game is over, the final score is still a disappointing nil. Oh well, at least we all had a laugh watching the players stuff hand warmers in their shinguards.

One year later, Dizzle organizes for the two teams to return to South Pole in the BICEP2 friendly. She doesn’t want another stalemate, so as organizer decides to modify the net. Since she’s an Earthquakes fan, she widens only the Galaxy’s net. (The noise-equivalent temperature or NET is a measure of a CMB telescope’s sensitivity. BICEP2 looked only at the 150 GHz band in a field where the CMB was predicted to be brighter than the foregrounds.)

Dizzle discloses the widening of the net to the bookmakers. They will allow her to repeat her wager on the condition that they modify the scoreboard to display only the total score and not the individual team scores. She agrees. If there are any goals on the board, she’ll be pretty sure that they are goals for the Earthquakes. She won’t need to keep close track of which team scores which goals. After all, the Galaxy are the ones with the handicap. Few other bets come in. Most of the world is distracted by the World Cup. Besides, the common wisdom is that the game will end with zero goals, same as always. OK, maybe it’ll end with one or two goals. A week from now hardly anyone will remember the score anyway. Big whoop.

The BICEP2 players themselves are more excited about the game than the fans are. They’re playing to win. They kick in some goals. By minute twenty, the total score climbs to 5.

Wow! (It’s a discovery!) Dizzle screams so loudly that people can hear her through the thin walls of her luxury box. Word spreads across social media that something exciting is happening at some obscure soccer game at South Pole although it’s unclear what. Most of the mainstream media weren’t following it too closely until the rumors. Even the sports journalists were focused on the FIFA World Cup instead. It’s about ten minutes before halftime, and they’re all catching up. By the time they make any sense of the situation, that giant 5 is still on display.

In the next few minutes of playtime, events external to the game start to get weirder. First, an earthquake strikes the city of LA. For real. Second, reporters prepare the news item with a misleading headline, “Earthquakes score big win in BICEP2 soccer match at South Pole.” A more descriptive headline could have read, “Earthquakes likely, Galaxy possibly, scored big gambling win for Dizzle Mapo in BICEP2 soccer match at South Pole.” When asked for comment, Dizzle says, “I just won the biggest sports bet ever! Go Earthquakes!” What she means, of course, is, “I just won a bet that this game would have more than 5 goals scored in total. I won that bet, and my favorite team is likely winning by a strong margin. I’ll keep cheering for them through the second half. I may be able to figure out the exact score for each team if I ask what other spectators around the stadium saw. Next year, I’ll widen both nets and display both teams’ scores.” What the interviewers think she means, however, is, “I just won a bet that the Earthquakes would win big time. They did.” Journalists want to be accurate, but the story is unfamiliar and complicated. They are racing against the clock to break the story.

Soccer fans around the world pause a moment from the World Cup to read the piece. “Earthquakes did well in that BICEP2 game? Oh cool.” Even people who aren’t sports fans at all see the headline. “A soccer match at South Pole? Sounds fascinating!” Only people who read the entire news article learn about the wider net and the simplified scoreboard, and only the dedicated fans actively watching the game know that it’s still ongoing.

A TV camera is set up to broadcast the remainder of the game live. With one minute left in the first half, the referee blows the whistle. A player for the Galaxy is down. It’s unclear from the replay whether it was a foul or a flop. In any case the Galaxy are awarded a penalty kick. The shot goes in.

Now it’s halftime. In an impromptu ceremony, the bookmaker P. R. Letters presents Dizzle with an oversized check. Asked what she plans to do next, she exclaims, “I’m going to watch Spice World!”*** Expert sports commentators at the scene give an accurate halftime report. Five goals were scored, the majority of which were likely scored by the Earthquakes. At least one goal was scored by the Galaxy. Meanwhile, in the rest of the media, a new headline appears, even more misleading than the last one, “What the Dizzle? BICEP stock price drops as Earthquakes proven not to have shut out Galaxy.”

A few hooligans jeer from the sidelines that Dizzle was irresponsible for speaking to media before halftime, nay, before consulting everyone in the stadium for a detailed reconstruction of every play from start to finish. Ignore them. It’s a soccer game at the freakin’ South Pole. It’s the biggest win in sports gambling history. It’s news.  The public deserves to hear it. The confused media wouldn’t even be here in time for the jumbo check and halftime report if it weren’t for all the advance buzz. Is it so wrong that they take a breather from FIFA to learn about MSL and stick around for part two?

I can’t predict what will happen in the second half. Based on the balance of information about the unusual rules and the total score, the Earthquakes are likely in the lead and favored to win. Conceivably, the Galaxy can make a comeback. In fact – again conceivably – the Galaxy could already be in the lead. Maybe they trained much harder than anyone expected to offset their disadvantageously wide net. No matter the outcome, both teams will be good sports about it. Fans on both sides will demand a rematch. Dizzle has announced her plans to host BICEP3 because South Pole soccer is simply fun. There are many other brands of energy drink hoping to sponsor their own exhibition matches. It’s a competitive industry. You can also follow the Eastern Conference, where there’s an entirely different game being played. I’d pay to watch a game in outer space.

* BICEP = CAPITAL MUSCLE!!
** “Dizzle Mapo” refers to the Dark Sector Laboratory (DSL), which has housed the BICEP series of telescopes, and the Martin A. Pomerantz Observatory (MAPO), which currently houses Keck Array.
*** The five Keck Array receivers are named after the Spice Girls.

“Feveral kinds of hairy mouldy fpots”

The book had a sheepskin cover, and mold was growing on the sheepskin. Robert Hooke, a pioneering microbiologist, slid the cover under one of the world’s first microscopes. Mold, he discovered, consists of “nothing elfe but feveral kinds of fmall and varioufly figur’d Mufhroms.” He described the Mufhroms in his treatise Micrographia, a 1665 copy of which I found in “Beautiful Science.” An exhibition at San Marino’s Huntington Library, “Beautiful Science” showcases the physics of rainbows, the stars that enthralled Galileo, and the world visible through microscopes.

Beautiful science of yesterday: An illustration, from Hooke’s Micrographia, of the mold.

“[T]hrough a good Microfcope,” Hooke wrote, the sheepskin’s spots appeared “to be a very pretty fhap’d Vegetative body.”

How like a scientist, to think mold pretty. How like quantum noise, I thought, Hooke’s mold sounds.

Quantum noise hampers systems that transmit and detect light. To phone a friend or send an email—“Happy birthday, Sarah!” or “Quantum Frontiers has released an article”—we encode our message in light. The light traverses a fiber, buried in the ground, then hits a detector. The detector channels the light’s energy into a current, a stream of electrons that flows down a wire. The variations in the current’s strength is translated into Sarah’s birthday wish.

If noise doesn’t corrupt the signal. From encoding “Happy birthday,” the light and electrons might come to encode “Hsappi birthdeay.” Quantum noise arises because light consists of packets of energy, called “photons.” The sender can’t control how many photons hit the detector.

To send the letter H, we send about 108 photons.* Imagine sending fifty H’s. When we send the first, our signal might contain 108- 153 photons; when we send the second, 108 + 2,083; when we send the third, 108 – 6; and so on. Receiving different numbers of photons, the detector generates different amounts of current. Different amounts of current can translate into different symbols. From H, our message can morph into G.

This spring, I studied quantum noise under the guidance of IQIM faculty member Kerry Vahala. I learned to model quantum noise, to quantify it, when to worry about it, and when not. From quantum noise, we branched into Johnson noise (caused by interactions between the wire and its hot environment); amplified-spontaneous-emission, or ASE, noise (caused by photons belched by ions in the fiber); beat noise (ASE noise breeds with the light we sent, spawning new noise); and excess noise (the “miscellaneous” folder in the filing cabinet of noise types).

Beautiful science of today: A microreso-nator—a tiny pendulum-like device— studied by the Vahala group.

Noise, I learned, has structure. It exhibits patterns. It has personalities. I relished studying those patterns as I relish sending birthday greetings while battling noise. Noise types, I see as a string of pearls unearthed in a junkyard. I see them as “pretty fhap[es]” in Hooke’s treatise. I see them—to pay a greater compliment—as “hairy mouldy fpots.”

*Optical-communications ballpark estimates:

• Optical power: 1 mW = 10-3 J/s
• Photon frequency: 200 THz = 2 × 1014 Hz
• Photon energy: h𝜈 = (6.626 × 10-34 J . s)(2 × 1014 Hz) = 10-19 J
• Bit rate: 1 GB = 109 bits/s
• Number of bits per H: 10
• Number of photons per H: (1 photon / 10-19 J) (10-3 J/s)(1 s / 109 bits)(10 bits / 1 H) = 108

An excerpt from this post was published today on Verso, the blog of the Huntington Library, Art Collection, and Botanical Gardens.

With thanks to Bassam Helou, Dan Lewis, Matt Stevens, and Kerry Vahala for feedback. With thanks to the Huntington Library (including Catherine Wehrey) and the Vahala group for the Micrographia image and the microresonator image, respectively.

The theory of everything: Help wanted

When Scientific American writes that physicists are working on a theory of everything, does it sound ambitious enough to you? Do you lie awake at night thinking that a theory of everything should be able to explain, well, everything? What if that theory is founded on quantum mechanics and finds a way to explain gravitation through the microscopic laws of the quantum realm? Would that be a grand unified theory of everything?

The answer is no, for two different, but equally important reasons. First, there is the inherent assumption that quantum systems change in time according to Schrodinger’s evolution: $i \hbar \partial_t \psi(t) = H \psi(t)$. Why? Where does that equation come from? Is it a fundamental law of nature, or is it an emergent relationship between different states of the universe? What if the parameter $t$, which we call time, as well as the linear, self-adjoint operator $H$, which we call the Hamiltonian, are both emergent from a more fundamental, and highly typical phenomenon: the large amount of entanglement that is generically found when one decomposes the state space of a single, static quantum wavefunction, into two (different in size) subsystems: a clock and a space of configurations (on which our degrees of freedom live)? So many questions, so few answers.

The static multiverse

The perceptive reader may have noticed that I italicized the word ‘static’ above, when referring to the quantum wavefunction of the multiverse. The emphasis on static is on purpose. I want to make clear from the beginning that a theory of everything can only be based on axioms that are truly fundamental, in the sense that they cannot be derived from more general principles as special cases. How would you know that your fundamental principles are irreducible? You start with set theory and go from there. If that assumes too much already, then you work on your set theory axioms. On the other hand, if you can exhibit a more general principle from which your original concept derives, then you are on the right path towards more fundamentalness.

In that sense, time and space as we understand them, are not fundamental concepts. We can imagine an object that can only be in one state, like a switch that is stuck at the OFF position, never changing or evolving in any way, and we can certainly consider a complete graph of interactions between subsystems (the equivalent of a black hole in what we think of as space) with no local geometry in our space of configurations. So what would be more fundamental than time and space? Let’s start with time: The notion of an unordered set of numbers, such as $\{4,2,5,1,3,6,8,7,12,9,11,10\}$, is a generalization of a clock, since we are only keeping the labels, but not their ordering. If we can show that a particular ordering emerges from a more fundamental assumption about the very existence of a theory of everything, then we have an understanding of time as a set of ordered labels, where each label corresponds to a particular configuration in the mathematical space containing our degrees of freedom. In that sense, the existence of the labels in the first place corresponds to a fundamental notion of potential for change, which is a prerequisite for the concept of time, which itself corresponds to constrained (ordered in some way) change from one label to the next. Our task is first to figure out where the labels of the clock come from, then where the illusion of evolution comes from in a static universe (Heisenberg evolution), and finally, where the arrow of time comes from in a macroscopic world (the illusion of irreversible evolution).

The axioms we ultimately choose must satisfy the following conditions simultaneously: 1. the implications stemming from these assumptions are not contradicted by observations, 2. replacing any one of these assumptions by its negation would lead to observable contradictions, and 3. the assumptions contain enough power to specify non-trivial structures in our theory. In short, as Immanuel Kant put it in his accessible bedtime story The critique of Pure Reason, we are looking for synthetic a priori knowledge that can explain space and time, which ironically were Kant’s answer to that same question.

The fundamental ingredients of the ultimate theory

Before someone decides to delve into the math behind the emergence of unitarity (Heisenberg evolution) and the nature of time, there is another reason why the grand unified theory of everything has to do more than just give a complete theory of how the most elementary subsystems in our universe interact and evolve. What is missing is the fact that quantity has a quality all its own. In other words, patterns emerge from seemingly complex data when we zoom out enough. This “zooming out” procedure manifests itself in two ways in physics: as coarse-graining of the data and as truncation and renormalization. These simple ideas allow us to reduce the computational complexity of evaluating the next state of a complex system: If most of the complexity of the system is hidden at a level you cannot even observe (think pre retina-display era), then all you have to keep track of is information at the macroscopic, coarse-grained level. On top of that, you can use truncation and renormalization to zero in on the most likely/ highest weight configurations your coarse-grained data can be in – you can safely throw away a billion configurations, if their combined weight is less than 0.1% of the total, because your super-compressed data will still give you the right answer with a fidelity of 99.9%. This is how you get to reduce a 9 GB raw video file down to a 300 MB Youtube video that streams over your WiFi connection without losing too much of the video quality.

I will not focus on the second requirement for the “theory of everything”, the dynamics of apparent complexity. I think that this fundamental task is the purview of other sciences, such as chemistry, biology, anthropology and sociology, which look at the “laws” of physics from higher and higher vantage points (increasingly coarse-graining the topology of the space of possible configurations). Here, I would like to argue that the foundation on which a theory of everything rests, at the basement level if such a thing exists, consists of four ingredients: Math, Hilbert spaces with tensor decompositions into subsystems, stability and compressibility. Now, you know about math (though maybe not of Zermelo-Fraenkel set theory), you may have heard of Hilbert spaces if you majored in math and/or physics, but you don’t know what stability, or compressibility mean in this context. So let me motivate the last two with a question and then explain in more detail below: What are the most fundamental assumptions that we sweep under the rug whenever we set out to create a theory of anything that can fit in a book – or ten thousand books – and still have predictive power? Stability and compressibility.

Math and Hilbert spaces are fundamental in the following sense: A theory needs a Language in order to encode the data one can extract from that theory through synthesis and analysis. The data will be statistical in the most general case (with every configuration/state we attach a probability/weight of that state conditional on an ambient configuration space, which will often be a subset of the total configuration space), since any observer creating a theory of the universe around them only has access to a subset of the total degrees of freedom. The remaining degrees of freedom, what quantum physicists group as the Environment, affect our own observations through entanglement with our own degrees of freedom. To capture this richness of correlations between seemingly uncorrelated degrees of freedom, the mathematical space encoding our data requires more than just a metric (i.e. an ability to measure distances between objects in that space) – it requires an inner-product: a way to measure angles between different objects, or equivalently, the ability to measure the amount of overlap between an input configuration and an output configuration, thus quantifying the notion of incremental change. Such mathematical spaces are precisely the Hilbert spaces mentioned above and contain states (with wavefunctions being a special case of such states) and operators acting on the states (with measurements, rotations and general observables being special cases of such operators). But, let’s get back to stability and compressibility, since these two concepts are not standard in physics.

Stability

Stability is that quality that says that if the theory makes a prediction about something observable, then we can test our theory by making observations on the state of the world and, more importantly, new observations do not contradict our theory. How can a theory fall apart if it is unstable? One simple way is to make predictions that are untestable, since they are metaphysical in nature (think of religious tenets). Another way is to make predictions that work for one level of coarse-grained observations and fail for a lower level of finer coarse-graining (think of Newtonian Mechanics). A more extreme case involves quantum mechanics assumed to be the true underlying theory of physics, which could still fail to produce a stable theory of how the world works from our point of view. For example, say that your measurement apparatus here on earth is strongly entangled with the current state of a star that happens to go supernova 100 light-years from Earth during the time of your experiment. If there is no bound on the propagation speed of the information between these two subsystems, then your apparatus is engulfed in flames for no apparent reason and you get random data, where you expected to get the same “reproducible” statistics as last week. With no bound on the speed with which information can travel between subsystems of the universe, our ability to explain and/or predict certain observations goes out the window, since our data on these subsystems will look like white noise, an illusion of randomness stemming from the influence of inaccessible degrees of freedom acting on our measurement device. But stability has another dimension; that of continuity. We take for granted our ability to extrapolate the curve that fits 1000 data points on a plot. If we don’t assume continuity (and maybe even a certain level of smoothness) of the data, then all bets are off until we make more measurements and gather additional data points. But even then, we can never gather an infinite (let alone, uncountable) number of data points – we must extrapolate from what we have and assume that the full distribution of the data is close in norm to our current dataset (a norm is a measure of distance between states in the Hilbert space).

The emergence of the speed of light

The assumption of stability may seem trivial, but it holds within it an anthropic-style explanation for the bound on the speed of light. If there is no finite speed of propagation for the information between subsystems that are “far apart”, from our point of view, then we will most likely see randomness where there is order. A theory needs order. So, what does it mean to be “far apart” if we have made no assumption for the existence of an underlying geometry, or spacetime for that matter? There is a very important concept in mathematical physics that generalizes the concept of the speed of light for non-relativistic quantum systems whose subsystems live on a graph (i.e. where there may be no spatial locality or apparent geometry): the Lieb-Robinson velocity. Those of us working at the intersection of mathematical physics and quantum many-body physics, have seen first-hand the powerful results one can get from the existence of such an effective and emergent finite speed of propagation of information between quantum subsystems that, in principle, can signal to each other instantaneously through the action of a non-local unitary operator (rotation of the full system under Heisenberg evolution). It turns out that under certain natural assumptions on the graph of interactions between the different subsystems of a many-body quantum system, such a finite speed of light emerges naturally. The main requirement on the graph comes from the following intuitive picture: If each node in your graph is connected to only a few other nodes and the number of paths between any two nodes is bounded above in some nice way (say, polynomially in the distance between the nodes), then communication between two distant nodes will take time proportional to the distance between the nodes (in graph distance units, the smallest number of nodes among all paths connecting the two nodes). Why? Because at each time step you can only communicate with your neighbors and in the next time step they will communicate with theirs and so on, until one (and then another, and another) of these communication cascades reaches the other node. Since you have a bound on how many of these cascades will eventually reach the target node, the intensity of the communication wave is bounded by the effective action of a single messenger traveling along a typical path with a bounded speed towards the destination. There should be generalizations to weighted graphs, but this area of mathematical physics is still really active and new results on bounds on the Lieb-Robinson velocity gather attention very quickly.

Escaping black holes

If this idea holds any water, then black holes are indeed nearly complete graphs, where the notion of space and time breaks down, since there is no effective bound on the speed with which information propagates from one node to another. The only way to escape is to find yourself at the boundary of the complete graph, where the nodes of the black hole’s apparent horizon are connected to low-degree nodes outside. Once you get to a low-degree node, you need to keep moving towards other low-degree nodes in order to escape the “gravitational pull” of the black hole’s super-connectivity. In other words, gravitation in this picture is an entropic force: we gravitate towards massive objects for the same reason that we “gravitate” towards the direction of the arrow of time: we tend towards higher entropy configurations – the probability of reaching the neighborhood of a set of highly connected nodes is much, much higher than hanging out for long near a set of low-degree nodes in the same connected component of the graph. If a graph has disconnected components, then their is no way to communicate between the corresponding spacetimes – their states are in a tensor product with each other. One has to carefully define entanglement between components of a graph, before giving a unified picture of how spatial geometry arises from entanglement. Somebody get to it.

Erik Verlinde has introduced the idea of gravity as an entropic force and Fotini Markopoulou, et al. have introduced the notion of quantum graphity (gravity emerging from graph models). I think these approaches must be taken seriously, if only because they work with more fundamental principles than the ones found in Quantum Field Theory and General Relativity. After all, this type of blue sky thinking has led to other beautiful connections, such as ER=EPR (the idea that whenever two systems are entangled, they are connected by a wormhole). Even if we were to disagree with these ideas for some technical reason, we must admit that they are at least trying to figure out the fundamental principles that guide the things we take for granted. Of course, one may disagree with certain attempts at identifying unifying principles simply because the attempts lack the technical gravitas that allows for testing and calculations. Which is why a technical blog post on the emergence of time from entanglement is in the works.

Compressibility

So, what about that last assumption we seem to take for granted? How can you have a theory you can fit in a book about a sequence of events, or snapshots of the state of the observable universe, if these snapshots look like the static noise on a TV screen with no transmission signal? Well, you can’t! The fundamental concept here is Kolmogorov complexity and its connection to randomness/predictability. A sequence of data bits like:

10011010101101001110100001011010011101010111010100011010110111011110

has higher complexity (and hence looks more random/less predictable) than the sequence:

10101010101010101010101010101010101010101010101010101010101010101010

because there is a small computer program that can output each successive bit of the latter sequence (even if it had a million bits), but (most likely) not of the former. In particular, to get the second sequence with one million bits one can write the following short program:

string s = ’10′;
for n=1 to $499,999$:
s.append(’10’);
n++;
end
print s;

As the number of bits grows, one may wonder if the number of iterations (given above by $499,999$), can be further compressed to make the program even smaller. The answer is yes: The number $499,999$ in binary requires $\log_2 499,999$ bits, but that binary number is a string of 0s and 1s, so it has its own Kolmogorov complexity, which may be smaller than $\log_2 499,999$. So, compressibility has a strong element of recursion, something that in physics we associate with scale invariance and fractals.

You may be wondering whether there are truly complex sequences of 0,1 bits, or if one can always find a really clever computer program to compress any N bit string down to, say, N/100 bits. The answer is interesting: There is no computer program that can compute the Kolmogorov complexity of an arbitrary string (the argument has roots in Berry’s Paradox), but there are strings of arbitrarily large Kolmogorov complexity (that is, no matter what program we use and what language we write it in, the smallest program (in bits) that outputs the N-bit string will be at least N bits long). In other words, there really are streams of data (in the form of bits) that are completely incompressible. In fact, a typical string of 0s and 1s will be almost completely incompressible!

Stability, compressibility and the arrow of time

So, what does compressibility have to do with the theory of everything? It has everything to do with it. Because, if we ever succeed in writing down such a theory in a physics textbook, we will have effectively produced a computer program that, given enough time, should be able to compute the next bit in the string that represents the data encoding the coarse-grained information we hope to extract from the state of the universe. In other words, the only reason the universe makes sense to us is because the data we gather about its state is highly compressible. This seems to imply that this universe is really, really special and completely atypical. Or is it the other way around? What if the laws of physics were non-existent? Would there be any consistent gravitational pull between matter to form galaxies and stars and planets? Would there be any predictability in the motion of the planets around suns? Forget about life, let alone intelligent life and the anthropic principle. Would the Earth, or Jupiter even know where to go next if it had no sense that it was part of a non-random plot in the movie that is spacetime? Would there be any notion of spacetime to begin with? Or an arrow of time? When you are given one thousand frames from one thousand different movies, there is no way to make a single coherent plot. Even the frames of a single movie would make little sense upon reshuffling.

What if the arrow of time emerged from the notions of stability and compressibility, through coarse-graining that acts as a compression algorithm for data that is inherently highly-complex and, hence, highly typical as the next move to make? If two strings of data look equally complex upon coarse-graining, but one of them has a billion more ways of appearing from the underlying raw data, then which one will be more likely to appear in the theory-of-everything book of our coarse-grained universe? Note that we need both high compressibility after coarse-graining in order to write down the theory, as well as large entropy before coarse-graining (from a large number of raw strings that all map to one string after coarse-graining), in order to have an arrow of time. It seems that we need highly-typical, highly complex strings that become easy to write down once we coarse grain the data in some clever way. Doesn’t that seem like a contradiction? How can a bunch of incompressible data become easily compressible upon coarse-graining? Here is one way: Take an N-bit string and define its 1-bit coarse-graining as the boolean AND of its digits. All but one strings will default to 0. The all 1s string will default to 1. Equally compressible, but the probability of seeing the 1 after coarse-graining is $2^{-N}$. With only 300 bits, finding the coarse-grained 1 is harder than looking for a specific atom in the observable universe. In other words, if the coarse-graining rule at time t is the one given above, then you can be pretty sure you will be seeing a 0 come up next in your data. Notice that before coarse-graining, all $2^N$ strings are equally likely, so there is no arrow of time, since there is no preferred string from a probabilistic point of view.

Conclusion, for now

When we think about the world around us, we go to our intuitions first as a starting point for any theory describing the multitude of possible experiences (observable states of the world). If we are to really get to the bottom of this process, it seems fruitful to ask “why do I assume this?” and “is that truly fundamental or can I derive it from something else that I already assumed was an independent axiom?” One of the postulates of quantum mechanics is the axiom corresponding to the evolution of states under Schrodinger’s equation. We will attempt to derive that equation from the other postulates in an upcoming post. Until then, your help is wanted with the march towards more fundamental principles that explain our seemingly self-evident truths. Question everything, especially when you think you really figured things out. Start with this post. After all, a theory of everything should be able to explain itself.

UP NEXT: Entanglement, Schmidt decomposition, concentration measure bounds and the emergence of discrete time and unitary evolution.

Everyone in grad school has taken on the task of picking the perfect research group at some point.  Then some among us had the dubious distinction of choosing the perfect research group twice.  Luckily for me, a year of grad research taught me a lot and I found myself asking group members and PIs (primary investigators) very different questions.  And luckily for you, I wrote these questions down to share with future generations.  My background as an experimental applied physicist showed through initially, so I got Shaun Maguire and Spiros Michalakis to help make it applicable for theorists too, and most of them should be useful outside physics as well.

Questions to break that silence when your potential advisor asks “So, do you have any questions for me?”

1. Are you taking new students?
– 2a. if yes: How many are you looking to take?
– 2b. if no: Ask them about the department or other professors.  They’ve been there long enough to have opinions.  Alternatively, ask what kinds of questions they would suggest you ask other PIs
3. What is the procedure for joining the group?
4. (experimental) Would you have me TA?  (This is the nicest way I thought of to ask if a PI can fund you with a research assistance-ship (RA), though sometimes they just like you to TA their class.)
4. (theory) Funding routes will often be covered by question 3 since TAs are the dominant funding method for theory students, unlike for experimentalists. If relevant, you can follow up with: How does funding for your students normally work? Do you have funding for me?
5. Do new students work for/report to other grad students, post docs, or you directly?
6. How do you like students to arrange time to meet with you?
7. How often do you have group meetings?
8. How much would you like students to prepare for them?
9. Would you suggest I take any specific classes?
10. What makes someone a good fit for this group?

And then for the high bandwidth information transfer.  Grill the group members themselves, and try to ask more than one group member if you can.

1. How much do you prepare for meetings with PI?
2. How long until people lead their own project? – Equivalently, who’s working on what projects.
3. How much do people on different projects communicate? (only group meeting or every day)
4. Is the PI hands on (how often PI wants to meet with you)?
5. Is the PI accessible (how easily can you meet with the PI if you want to)?
6. What is the average time to graduation? (if it’s important to you personally)
7. Does the group/subgroup have any bonding activities?
8. Do you think I should join this group?
9. What are people’s backgrounds?
10. What makes someone a good fit for this group?

Hope that helps.  If you have any other suggested questions, be sure to leave them in the comments.

John Preskill and the dawn of the entanglement frontier

Editor’s Note: John Preskill’s recent election to the National Academy of Sciences generated a lot of enthusiasm among his colleagues and students. In an earlier post today, famed Stanford theoretical physicist, Leonard Susskind, paid tribute to John’s early contributions to physics ranging from magnetic monopoles to the quantum mechanics of black holes. In this post, Daniel Gottesman, a faculty member at the Perimeter Institute, takes us back to the formative years of the Institute for Quantum Information at Caltech, the precursor to IQIM and a world-renowned incubator for quantum information and quantum computation research. Though John shies away from the spotlight, we, at IQIM, believe that the integrity of his character and his role as a mentor and catalyst for science are worthy of attention and set a good example for current and future generations of theoretical physicists.

Preskill’s legacy may well be the incredible number of preeminent research scientists in quantum physics he has mentored throughout his extraordinary career.

When someone wins a big award, it has become traditional on this blog for John Preskill to write something about them. The system breaks down, though, when John is the one winning the award. Therefore I’ve been brought in as a pinch hitter (or should it be pinch lionizer?).

The award in this case is that John has been elected to the National Academy of Sciences, along with Charlie Kane and a number of other people that don’t work on quantum information. Lenny Susskind has already written about John’s work on other topics; I will focus on quantum information.

On the research side of quantum information, John is probably best known for his work on fault-tolerant quantum computation, particularly topological fault tolerance. John jumped into the field of quantum computation in 1994 in the wake of Shor’s algorithm, and brought me and some of his other grad students with him. It was obvious from the start that error correction was an important theoretical challenge (emphasized, for instance, by Unruh), so that was one of the things we looked at. We couldn’t figure out how to do it, but some other people did. John and I embarked on a long drawn-out project to get good bounds on the threshold error rate. If you can build a quantum computer with an error rate below the threshold value, you can do arbitrarily large quantum computations. If not, then errors will eventually overwhelm you. Early versions of my project with John suggested that the threshold should be about $10^{-4}$, and the number began floating around (somewhat embarrassingly) as the definitive word on the threshold value. Our attempts to bound the higher-order terms in the computation became rather grotesque, and the project proceeded very slowly until a new approach and the recruitment of Panos Aliferis finally let us finish a paper with a rigorous proof of a slightly lower threshold value.

Meanwhile, John had also been working on topological quantum computation. John has already written about his excitement when Kitaev visited Caltech and talked about the toric code. The two of them, plus Eric Dennis and Andrew Landahl, studied the application of this code for fault tolerance. If you look at the citations of this paper over time, it looks rather … exponential. For a while, topological things were too exotic for most quantum computer people, but over time, the virtues of surface codes have become obvious (apparently high threshold, convenient for two-dimensional architectures). It’s become one of the hot topics in recent years and there are no signs of flagging interest in the community.

John has also made some important contributions to security proofs for quantum key distribution, known to the cognoscenti just by its initials. QKD allows two people (almost invariably named Alice and Bob) to establish a secret key by sending qubits over an insecure channel. If the eavesdropper Eve tries to live up to her name, her measurements of the qubits being transmitted will cause errors revealing her presence. If Alice and Bob don’t detect the presence of Eve, they conclude that she is not listening in (or at any rate hasn’t learned much about the secret key) and therefore they can be confident of security when they later use the secret key to encrypt a secret message. With Peter Shor, John gave a security proof of the best-known QKD protocol, known as the “Shor-Preskill” proof. Sometimes we scientists lack originality in naming. It was not the first proof of security, but earlier ones were rather complicated. The Shor-Preskill proof was conceptually much clearer and made a beautiful connection between the properties of quantum error-correcting codes and QKD. The techniques introduced in their paper got adopted into much later work on quantum cryptography.

Collaborating with John is always an interesting experience. Sometimes we’ll discuss some idea or some topic and it will be clear that John does not understand the idea clearly or knows little about the topic. Then, a few days later we discuss the same subject again and John is an expert, or at least he knows a lot more than me. I guess this ability to master
topics quickly is why he was always able to answer Steve Flammia’s random questions after lunch. And then when it comes time to write the paper … John will do it. It’s not just that he will volunteer to write the first draft — he keeps control of the whole paper and generally won’t let you edit the source, although of course he will incorporate your comments. I think this habit started because of incompatibilities between the TeX editor he was using and any other program, but he maintains it (I believe) to make sure that the paper meets his high standards of presentation quality.

This also explains why John has been so successful as an expositor. His
lecture notes for the quantum computation class at Caltech are well-known. Despite being incomplete and not available on Amazon, they are probably almost as widely read as the standard textbook by Nielsen and Chuang.

Before IQIM, there was IQI, and before that was QUIC.

He apparently is also good at writing grants. Under his leadership and Jeff Kimble’s, Caltech has become one of the top places for quantum computation. In my last year of graduate school, John and Jeff, along with Steve Koonin, secured the QUIC grant, and all of a sudden Caltech had money for quantum computation. I got a research assistantship and could write my thesis without having to worry about TAing. Postdocs started to come — first Chris Fuchs, then a long stream of illustrious others. The QUIC grant grew into IQI, and that eventually sprouted an M and drew in even more people. When I was a student, John’s group was located in Lauritsen with the particle theory group. We had maybe three grad student offices (and not all the students were working on quantum information), plus John’s office. As the Caltech quantum effort grew, IQI acquired territory in another building, then another, and then moved into a good chunk of the new Annenberg building. Without John’s efforts, the quantum computing program at Caltech would certainly be much smaller and maybe completely lacking a theory side. It’s also unlikely this blog would exist.

The National Academy has now elected John a member, probably more for his research than his twitter account (@preskill), though I suppose you never know. Anyway, congratulations, John!

-D. Gottesman

Of magnetic monopoles and fast-scrambling black holes

Editor’s Note: On April 29th, 2014, the National Academy of Sciences announced the new electees to the prestigious organization. This was an especially happy occasion for everyone here at IQIM, since the new members included our very own John Preskill, Richard P. Feynman Professor of Theoretical Physics and regular blogger on this site. A request was sent to Leonard Susskind, a close friend and collaborator of John’s, to take a trip down memory lane and give the rest of us a glimpse of some of John’s early contributions to Physics. John, congratulations from all of us here at IQIM.

John Preskill was elected to the National Academy of Sciences, an event long overdue. Perhaps it took longer than it should have because there is no way to pigeon-hole him; he is a theoretical physicist, and that’s all there is to it.

John has long been one of my heroes in theoretical physics. There is something very special about his work. It has exceptional clarity, it has vision, it has integrity—you can count on it. And sometimes it has another property: it can surprise. The first time I heard his name come up, sometime around 1979, I was not only surprised; I was dismayed. A student whose name I had never heard of, had uncovered a serious clash between two things, both of which I deeply wanted to believe in. One was the Big-Bang theory and the other was the discovery of grand unified particle theories. Unification led to the extraordinary prediction that Dirac’s magnetic monopoles must exist, at least in principle. The Big-Bang theory said they must exist in fact. The extreme conditions at the beginning of the universe were exactly what was needed to create loads of monopoles; so many that they would flood the universe with too much mass. John, the unknown graduate student, did a masterful analysis. It left no doubt that something had to give. Cosmology gave. About a year later, inflationary cosmology was discovered by Guth who was in part motivated by Preskill’s monopole puzzle.

John’s subsequent career as a particle physicist was marked by a number of important insights which often had that surprising quality. The cosmology of the invisible axion was one. Others had to do with very subtle and counterintuitive features of quantum field theory, like the existence of “Alice strings”. In the very distant past, Roger Penrose and I had a peculiar conversation about possible generalizations of the Aharonov-Bohm effect. We speculated on all sorts of things that might happen when something is transported around a string. I think it was Roger who got excited about the possibilities that might result if a topological defect could change gender. Alice strings were not quite that exotic, only electric charge flips, but nevertheless it was very surprising.

John of course had a long standing interest in the quantum mechanics of black holes: I will quote a passage from a visionary 1992 review paper, “Do Black Holes Destroy Information?

“I conclude that the information loss paradox may well presage a revolution in fundamental physics.”

At that time no one knew the answer to the paradox, although a few of us, including John, thought the answer was that information could not be lost. But almost no one saw the future as clearly as John did. Our paths crossed in 1993 in a very exciting discussion about black holes and information. We were both thinking about the same thing, now called black hole complementarity. We were concerned about quantum cloning if information is carried by Hawking radiation. We thought we knew the answer: it takes too long to retrieve the information to then be able to jump into the black hole and discover the clone. This is probably true, but at that time we had no idea how close a call this might be.

It took until 2007 to properly formulate the problem. Patrick Hayden and John Preskill utterly surprised me, and probably everyone else who had been thinking about black holes, with their now-famous paper “Black Holes as Mirrors.” In a sense, this paper started a revolution in applying the powerful methods of quantum information theory to black holes.

We live in the age of entanglement. From quantum computing to condensed matter theory, to quantum gravity, entanglement is the new watchword. Preskill was in the vanguard of this revolution, but he was also the teacher who made the new concepts available to physicists like myself. We can now speak about entanglement, error correction, fault tolerance, tensor networks and more. The Preskill lectures were the indispensable source of knowledge and insight for us.

Congratulations John. And congratulations NAS.

-L. S.

Clocking in at a Cambridge conference

On Facebook last fall, I posted about statistical mechanics. Statistical mechanics is the physics of hordes of particles. Hordes of molecules, for example, form the stench seeping from a clogged toilet. Hordes change in certain ways but not in the reverse ways, suggesting time points in a direction. Once a stink diffuses into the hall, it won’t regroup in the bathroom. The molecules’ locations distinguish past from future.

The post attracted a comment by Ian Durham, associate professor of physics at St. Anselm College. Minutes later, we were instant-messaging about infinitely long evolutions.*

The next day, I sent Ian a paper draft. His reply made me jump more than a whiff of a toilet would. Would I discuss the paper at a conference he was co-organizing?

I almost replied, Are you sure?

Then I almost replied, Yes, please!

The conference, “Eddington and Wheeler: Information and Interaction,” unfolded this March at the University of Cambridge. Cambridge employed Sir Arthur Eddington, the astronomer whose 1919 observation of starlight during an eclipse catapulted Einstein’s general relativity to fame. Decades later, John Wheeler laid groundwork for quantum information.

Though aware of Eddington’s observation, I hadn’t known he’d researched stat mech. I hadn’t known his opinions about time. Time owns a high-rise in my heart; see the fussiness with which I catalogue “last fall,” “minutes later,” and “the next day.” Conference-goers shared news about time in the Old Combination Room at Cambridge’s Trinity College. Against the room’s wig-filled portraits, our projector resembled a souvenir misplaced by a time traveler.

Trinity College, Cambridge.

Presenter one, Huw Price, argued that time has no arrow. It appears to in our universe: We remember the past and anticipate the future. Once a stench diffuses, it doesn’t regroup. The stench illustrates the Second Law of Thermodynamics, the assumption that entropy increases.

If “entropy” doesn’t ring a bell, never mind; we’ll dissect it in future articles. Suffice it to say that (1) thermodynamics is a branch of physics related to stat mech; (2) according to the Second Law of Thermodynamics, something called “entropy” increases; (3) entropy’s rise distinguishes the past from the future by associating the former with a low entropy and the latter with a large entropy; and (4) a stench’s diffusion illustrates the Second Law and time’s flow.

In as many universes in which entropy increases (time flows in one direction), in so many universe does entropy decrease (does time flow oppositely). So, said Huw Price, postulated the 19th-century stat-mech founder Ludwig Boltzmann. Why would universes pair up? For the reason why, driving across a pothole, you not only fall, but also rise. Each fluctuation from equilibrium—from a flat road—involves an upward path and a downward. The upward path resembles a universe in which entropy increases; the downward, a universe in which entropy decreases. Every down pairs with an up. Averaged over universes, time has no arrow.

Freidel Weinert, presenter five, argued the opposite. Time has an arrow, he said, and not because of entropy.

Ariel Caticha discussed an impersonator of time. Using a cousin of MaxEnt, he derived an equation identical to Schrödinger’s. MaxEnt, short for “the Maximum Entropy Principle,” is a tool used in stat mech. Schrödinger’s Equation describes how quantum systems evolve. To draw from Schrödinger’s Equation predictions about electrons and atoms, physicists assume that features of reality resemble certain bits of math. We assume, for example, that the t in Schrödinger’s Equation represents time.

A t appeared in Ariel’s twin of Schrödinger’s Equation. But Ariel didn’t assume what physicists usually assume. MaxEnt motivated his assumptions. Interpreting Ariel’s equation poses a challenge. If a variable acts like time and smells like time, does it represent time?**

A presenter uses the anachronistic projector. The head between screen and camera belongs to David Finkelstein, who helped develop the theory of general relativity checked by Eddington.

Like Ariel, Bill Wootters questioned time’s role in arguments. The co-creator of quantum teleportation wondered why one tenet of quantum physics has the form it has. Using quantum mechanics, we can’t predict certain experiments’ outcomes. We can predict probabilities—the chance that some experiment will yield Possible Outcome 1, the chance that the experiment will yield Possible Outcome 2, and so on. To calculate these probabilities, we square numbers. Why square? Why don’t the probabilities depend on cubes?

To explore this question, Bill told a story. Suppose some experimenter runs these experiments on Monday and those on Tuesday. When evaluating his story, Bill pointed out a hole: Replacing “Monday” and “Tuesday” with “eight o’clock” and “nine” wouldn’t change his conclusion. Which replacements wouldn’t change it, and which would? To what can we generalize those days?

Little of presentation twelve concerned time. Rüdiger Schack introduced QBism, an interpretation of quantum mechanics that sounds like “cubism.” Casting quantum physics in terms of experimenters’ actions, Rüdiger mentioned time. By the time of the mention, I couldn’t tell what anyone meant by “time.” Raising a hand, I asked for clarification.

“You are young,” Rüdiger said. “But you will grow old and die.”

The comment clanged like the slam of a door. It echoed when I followed Ian into Ascension Parish Burial Ground. On Cambridge’s outskirts, conference-goers visited Eddington’s headstone. We found Wittgenstein’s near an uneven footpath; near tangles of undergrowth, Nobel laureates’. After debating about time, we marked its footprints. Paths of glory lead but to the grave.

Here lies one whose name was writ in a conference title: Sir Arthur Eddington’s grave.

Paths touched by little glory, I learned, have perks. As Rüdiger noted, I was the greenest participant. As he had the manners not to note, I was the least distinguished and the most ignorant. Studenthood freed me to raise my hand, to request clarification, to lack opinions about time. Perhaps I’ll evolve opinions at some t, some Monday down the road. That Monday feels infinitely far off. These days, I’ll stick to evolving science—using that other boon of youth, Facebook.

* You know you’re a theoretical physicist (or a physicist-in-training) when you debate about processes that last till kingdom come.

** As long as the variable doesn’t smell like a clogged toilet.

For videos of the presentations—including the public lecture by best-selling author Neal Stephenson—stay tuned to http://informationandinteraction.wordpress.com.

With gratitude to Ian Durham and Dean Rickles for organizing “Information and Interaction” and for the opportunity to participate. With thanks to the other participants for sharing their ideas and time.

A TED experience

Around one year ago, I unexpectedly received an e-mail asking if I would speak at a local TEDx Youth event themed “Daring Discoveries”.  I hadn’t attended a TEDx conference before (sadly I couldn’t make either of the previous ones held at Caltech).  But I was familiar with the high-profile brand and so enthusiastically accepted the invitation.  A few weeks ago, following a lot of preparation by the speakers and no doubt vastly more by the organizers, the event finally took place.  On many levels it proved to be an unforgettable experience.

One thing that really struck me was that the conference was organized entirely by a team of local high school students.   I find this truly remarkable, especially given the amount of work involved in putting together this sort of thing.  (Finding speakers, fundraising, obtaining a venue, arranging innumerable technical logistics, putting together a webpage, sifting through applications, etc.  I couldn’t imagine keeping track of all those details, much less at that stage!)  The audience was also noteworthy: mostly other high school students from the area, their families, and other community members.  In total there were about 100 participants.  The vast majority reflected underrepresented groups in the sciences, which made it a particularly appealing outreach opportunity.

The organizers secured a venue at Puente Hills Mall in City of Industry.  To get the mental juices flowing numerous classic brain teaser decorated the walls near the entrance.  This one was my favorite:

This is an unusual paragraph. I’m curious how quickly you can find out what is so unusual about it.  It looks so plain you would think nothing was wrong with it! In fact, nothing is wrong with it! It is unusual though. Study it, and think about it, but you still may not find anything odd. But if you work at it a bit, you might find out. Try to do so without any coaching.

Other interesting activities also awaited the participants, including a scavenger hunt and a “big ideas wall” where anyone could jot down ideas they viewed as worth spreading.  It was fun reading what everyone had to say.

The list of speakers was eclectic and, among others, included a college student/entrepreneur, mathematicians, engineers, and educators.  I found everyone’s talks absolutely riveting and felt really honored to be part of such an accomplished group.  For my part I decided to tell a story about quantum computing—in particular the topological approach (what else?).  Preparing was no easy task.  I had to figure out a way to explain what quantum computers are, what they can do for us, why building one is hard, how “non-Abelian anyons” might one day prove to be the salvation, and why this direction is now looking increasingly promising.  Of course without assuming any prior knowledge of quantum mechanics.  And in about 15 minutes or so.

Given where we are in the quest for a quantum computer I had no choice but to conclude on a tentative yet optimistic note.  I made sure though to convey what I think is an extremely important message.  Namely, that the journey towards realizing quantum computing technology is as exciting—if not more so—than the finish line.  That journey will undoubtedly be paved with groundbreaking discoveries that reveal spectacular new insights about how the universe works, forcing us to develop new physics paradigms along the way.  It’s the prospect of such discoveries that energizes me to think about how we might achieve mastery over materials on large scales to hopefully overcome one of our generation’s greatest technological challenges.  The Saturday Morning Breakfast Cereal comic below—which I very recently learned about from one of our colloquium speakers— perfectly encapsulates my view on the problem, both as a science advocate and a physicist working in the trenches.  I thought showing this (censorship mine!) was a good message to leave the audience with.

Tsar Nikita and His Scientists

Once upon a time, a Russian tsar named Nikita had forty daughters:

Every one from top to toe
Was a captivating creature,
Perfect—but for one lost feature.

So wrote Alexander Pushkin, the 19th-century Shakespeare who revolutionized Russian literature. In a rhyme, Pushkin imagined forty princesses born without “that bit” “[b]etween their legs.” A courier scours the countryside for a witch who can help. By summoning the devil in the woods, she conjures what the princesses lack into a casket. The tsar parcels out the casket’s contents, and everyone rejoices.

“[N]onsense,” Pushkin calls the tale in its penultimate line. A “joke.”

The joke has, nearly two centuries later, become reality. Researchers have grown vaginas in a lab and implanted them into teenage girls. Thanks to a genetic defect, the girls suffered from Mayer-Rokitansky-Küster-Hauser (MRKH) syndrome: Their vaginas and uteruses had failed to grow to maturity or at all. A team at Wake Forest and in Mexico City took samples of the girls’ cells, grew more cells, and combined their harvest with vagina-shaped scaffolds. Early in the 2000s, surgeons implanted the artificial organs into the girls. The patients, the researchers reported in the journal The Lancet last week, function normally.

I don’t usually write about reproductive machinery. But the implants’ resonance with “Tsar Nikita” floored me. Scientists have implanted much of Pushkin’s plot into labs. The sexually deficient girls, the craftsperson, the replacement organs—all appear in “Tsar Nikita” as in The Lancet. In poetry as in science fiction, we read the future.

Though threads of Pushkin’s plot survive, society’s view of the specialist has progressed. “Deep [in] the dark woods” lives Pushkin’s witch. Upon summoning the devil, she locks her cure in a casket. Today’s vagina-implanters star in headlines. The Wall Street Journal highlighted the implants in its front section. Unless the patients’ health degrades, the researchers will likely list last week’s paper high on their CVs and websites.

Much as Dr. Atlántida Raya-Rivera, the paper’s lead author, differs from Pushkin’s witch, the visage of Pushkin’s magic wears the nose and eyebrows of science. When tsars or millenials need medical help, they seek knowledge-keepers: specialists, a fringe of society. Before summoning the devil, the witch “[l]ocked her door . . . Three days passed.” I hide away to calculate and study (though days alone might render me more like the protagonist in another Russian story, Chekhov’s “The Bet”). Just as the witch “stocked up coal,” some students stockpile Red Bull before hitting the library. Some habits, like the archetype of the wise woman, refuse to die.

From a Russian rhyme, the bones of “Tsar Nikita” have evolved into cutting-edge science. Pushkin and the implants highlight how attitudes toward knowledge have changed, offering a lens onto science in culture and onto science culture. No wonder readers call Pushkin “timeless.”

But what would he have rhymed with “Mayer-Rokitansky-Küster-Hauser”?

“Tsar Nikita” has many nuances—messages about censorship, for example—that I didn’t discuss. To the intrigued, I recommend The Queen of Spades: And selected works, translated by Anthony Briggs and published by Pushkin Press.