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 batteries, the concentration of entanglement, the 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 *H*_{vN}(ρ). Since a billion is less than infinity, 1,000,000,000 *H*_{vN}(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 *H*_{vN}(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 *H*_{vN}(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* + *a*√*n*, 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.*

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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.

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After four or five hours of maxing out my brain, it starts to throb. For the past couple of weeks, after breaking my brain with firewalls each day, I’ve been switching gears and reading about black hole astronomy (real-life honest-to-goodness science with data!) Beyond wanting to know the experimental state-of-the-art related to the fancy math I’ve been thinking about, I also had the selfish motivation that I wanted to do some PR maintenance after Nature’s headline: “Stephen Hawking: ‘There are no black holes’.” I found this headline infuriating when Nature posted it back in January. When taken out of context, this quote makes it seem like Stephen Hawking was saying “hey guys, my bad, we’ve been completely wrong all this time. Turn off the telescopes.” When in reality what he was saying was more like: “hey guys, I think this really hard modern firewall paradox is telling us that we’ve misunderstood an extremely subtle detail and we need to make corrections on the order of a few Planck lengths, but it matters!” When you combine this sensationalism with Nature’s lofty credibility, the result is that even a few of my intelligent scientist peers have interpreted this as the non-existence of astrophysical black holes. Not to mention that it opens a crack for the news media to say things like: ‘if even Stephen Hawking has been wrong all this time, then how can we possibly trust the rest of this scientist lot, especially related to climate change?’ So brain throbbing + sensationalism => learning black hole astronomy + PR maintenance.

Before presenting the evidence, I should wave my hands about what we’re looking for. You have all heard about black holes. They are objects where so much mass gets concentrated in such a small volume that Einstein’s general theory of relativity predicts that once an object passes beyond a certain distance (called the event horizon), then said object will never be able to escape, and must proceed to the center of the black hole. Even photons cannot escape once they pass beyond the event horizon (except when you start taking quantum mechanics into account, but this is a small correction which we won’t focus on here.) All of our current telescopes collect photons, and as I just mentioned, when photons get close to a black hole, they fall in, so this means a detection with current technology will only be indirect. What are these indirect detections we have made? Well, general relativity makes numerous predictions about black holes. After we confirm enough of these predictions to a high enough precision, and without a viable alternative theory, we can safely conclude that we have detected black holes. This is similar to how many other areas of science work, like particle physics finding new particles through detecting a particle’s decay products, for example.

Without further ado, I hope the following experimental evidence will convince you that black holes permeate our universe (and if not black holes, then something even weirder and more interesting!)

1. **Sgr A*:** There is overwhelming evidence that there is a supermassive black hole at the center of our galaxy, the Milky Way. As a quick note, most of the black holes we have detected are broken into two categories, solar mass, where they are only a few times more massive than our sun (5-30 solar masses), or supermassive, where the mass is about solar masses. Some of the most convincing evidence comes from the picture below. Andrea Ghez and others tracked the orbits of several stars around the center of the Milky Way for over twenty years. We have learned that these stars orbit around a point-like object with a mass on the order of solar masses. Measurements in the radio spectrum show that there is a radio source located in the same location which we call Sagittarius A* (Sgr A*). Sgr A* is moving at less than and has a mass of at least solar masses. These bounds make it pretty clear that Sgr A* is the same object as what is at the focus of these orbits. A radio source is exactly what you would expect for this system because as dust particles get pulled towards the black hole, they collide and friction causes them to heat up, and hot objects radiate photons. These arguments together make it pretty clear that Sgr A* is a supermassive black hole at the center of the Milky Way!

2. **Orbit of S2: **During a recent talk that Andrea Ghez gave at Caltech, she said that S2 is “her favorite star.” S2 is a 15 solar mass star located near the black hole at the center of our galaxy. S2’s distance from this black hole is only about four times the distance from Neptune to the Sun (at closest point in orbit), and it’s orbital period is only 15 years. The Keck telescopes in Mauna Kea have followed almost two complete orbits of S2. This piece of evidence is redundant compared to point 1, but it’s such an amazing technological feat that I couldn’t resist including it.

3. **Numerical studies: **astrophysicists have done numerous numerical simulations which provide a different flavor of test. Christian Ott at Caltech is pretty famous for these types of studies.

4. **Cyg A: **Cygnus A is a galaxy located in the Cygnus constellation. It is an exceptionally bright radio source. As I mentioned in point 1, as dust falls towards a black hole, friction causes it to heat up and then hot objects radiate away photons. The image below demonstrates this. We are able to use the Eddington limit to convert luminosity measurements into estimates of the mass of Cyg A. Not necessarily in the case of Cyg A, but in the case of its cousins Active Galactic Nuclei (AGNs) and Quasars, we are also able to put bounds on their sizes. These two things together show that there is a huge amount of mass trapped in a small volume, which is therefore probably a black hole (alternative models can usually be ruled out.)

5. **AGNs and Quasars: **these are bright sources which are powered by supermassive black holes. Arguments similar to those used for Cyg A make us confident that they really are powered by black holes and not some alternative.

6. **X-ray binaries: **astronomers have detected ~20 stellar mass black holes by finding pairs consisting of a star and a black hole, where the star is close enough that the black hole is sucking in its mass. This leads to accretion which leads to the emission of X-Rays which we detect on Earth. Cygnus X-1 is a famous example of this.

7. **Water masers: **Messier 106 is the quintessential example.

8. **Gamma ray bursts**: most gamma ray bursts occur when a rapidly spinning high mass star goes supernova (or hypernova) and leaves a neutron star or black hole in its wake. However, it is believed that some of the “long” duration gamma ray bursts are powered by accretion around rapidly spinning black holes.

That’s only eight reasons but I hope you’re convinced that black holes really exist! To round out this list to include ten things, here are two interesting open questions related to black holes:

1. **Firewalls: **I mentioned this paradox at the beginning of this post. This is the cutting edge of quantum gravity which is causing hundreds of physicists to pull their hair out!

2. **Feedback: **there is an extremely strong correlation between the size of a galaxy’s supermassive black hole and many of the other properties in the galaxy. This connection was only realized about a decade ago and trying to understand how the black hole (which has a mass much smaller than the total mass of the galaxy) affects galaxy formation is an active area of research in astrophysics.

In addition to everything mentioned above, I want to emphasize that most of these results are only from the past decade. Not to mention that we seem to be close to the dawn of gravitational wave astronomy which will allow us to probe black holes more directly. There are also exciting instruments that have recently come online, such as NuSTAR. In other words, this is an **extremely exciting** time to be thinking about black holes–both from observational and theoretical perspectives–**we have data and a paradox**! In conclusion, black holes exist. They really do. And let’s all make a pact to read critically in the 21st century!

Cool resource from Sky and Telescope.

[* I want to thank my buddy Kaes Van't Hof for letting me crash on his couch in NYC last week, which is where I did most of this work. ** I also want to thank Dan Harlow for saving me months of confusion by sharing a draft of his notes from his course on firewalls at the Israeli Institute for Advanced Study's winter school in theoretical physics.]

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“[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 10* ^{8}* photons.

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).

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 × 10*^{14}*Hz**Photon energy: h*𝜈*= (6.626 × 10*^{-34}*J . s)(2 × 10*^{14}*Hz) = 10*^{-19}*J**Bit rate: 1 GB = 10*^{9}*bits/s**Number of bits per*H*: 10**Number of photons per*H*: (1 photon / 10*^{-19}*J) (10*^{-3}*J/s)(1 s / 10*^{9}*bits)(10 bits / 1*H*) = 10*^{8}

*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.*

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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: . *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 , which we call *time, *as well as the linear, self-adjoint operator , 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 , 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 :

s.append(’10’);

n++;

end

print s;

As the number of bits grows, one may wonder if the number of iterations (given above by ), can be further compressed to make the program even smaller. The answer is yes: The number in binary requires bits, but that binary number is a string of 0s and 1s, so it has its own Kolmogorov complexity, which may be smaller than . 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 . 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 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.

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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

– 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?

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?

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.

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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 , 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.

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

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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.

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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.

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 19^{th}-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?**

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?

We couldn’t answer his questions on the Sunday he asked them.

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.

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.*

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This summer I returned to the IQIM Summer Research Institute to continue my exploration of superconductors and gain even deeper research experience. This time around I have accompanied Caltech second year graduate student Kyle Chen in testing samples using the Scanning Tunneling Microscope (STM), some of which I helped form using Pulse Laser Deposition with Professor Feng last summer. I have always been curious about how we can have atomic resolution. This has been my big chance to have hands-on experience working with STM that makes it possible!

The Scanning Tunneling Microscope was invented by the late Heinrich Rohrer and Gerd Binnig at IBM Research in Zurich, Switzerland in 1981. STM is able to scan the surface contours of substances using a sharp conductive tip. The electron tunneling current through the tip of the microscope is exponentially dependent on the distance (few Angstroms) to the substance surface. The changing currents at different locations can then be compiled to produce three dimensional images of the topography of the surface on the nano-scale. Or conversely the distance can be measured while the current is held constant. STM has a much higher resolution of images and avoids the problems of diffraction and spherical aberration from lenses. This level of control and precision through STM has enabled scientists to use tools with nanometer precision, allowing scientists even to manipulate atoms and their bonds. STM has been instrumental in forming the field of nanotechnology and the modern study of DNA, semiconductors, graphene, topological insulators, and much more! Just five years after building their first STM, Rohrer and Binning’s work rightfully earned them the 1986 Nobel Prize in Physics.

Descending into the Sloan basement, Kyle and I work to prepare and scan several high temperature superconducting (HTSC) Calcium Doped YBCO samples in order better to understand the pairing mechanism that causes Cooper Pairs for superconductivity. In regular metals, the pairing mechanism via phonon lattice vibrations is fairly well understood by physicists. Meanwhile, the pairing mechanism for HTSC is still a mystery. We are also investigating how this pairing changes with doping, as well as how the magnetic field is channeled up vortices within HTSC.

One of our first tasks is to make probe tips for STM. Adding Calcium Chloride to de-ionized water, we are preparing a liquid conductive path to begin the chemical etching of the probe tip. Using a 10V battery, a wire bent into a ring is connected to the battery and placed in the Calcium Chloride solution. Then a thin platinum iridium wire, also connected to the voltage source, is placed at the center of the conductive ring. The circuit is complete and a current of about half an Ampere is used to erode uniformly the outer surface of the platinum iridium wire, forming a sharp tip. We examine the tip under a traditional microscope to scrutinize our work. Ideally, the tip is only one atom thick! If not, we are charged with re-etching until we reach a more suitable straight, uniform, sharp tip. As we work to prepare the platinum iridium tips, a stoic picture of Neils Bohr looks down at our work with the appropriate adjacent quotation, ” When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images. ” After making two or three nearly perfect tips, we clean and store them in the tip case and proceed to the next step of preparation.

We are now ready to clean the sample to be tested. Bromine etching removes any oxidation or impurities that have formed on our sample, leaving a top bromine film layer. We remove the bromine-residue layer with ethanol and then plunge further into the (sub)basement to load the sample into the STM casing before oxidation begins again. The STM in the Yeh Lab was built by Professor Nai-Chang Yeh and her students eleven years ago. There are multiple layers of vacuum chambers and separate dewars, each with its own meticulous series of steps to prepare for STM testing. At the center is a long, central STM tube. Surrounding this is a large cylindrical dewar. On the perimeter is an exterior large vacuum chamber.

First we must load the newly etched YBCO sample and tip into the central STM tube. The inner tube currently lays across a work bench beneath desk lamps. We must transfer the tiny tip from the tip case to just above the sample. While loading the tip with an equally minuscule flathead screwdriver, it became quite clear to me that I could never be a surgeon! The superconducting sample is secured in place with a small cover plate and screw. A series of electronic tests for resistance and capacitance must be conducted to confirm that there are no shorts in the numerous circuits. Next we must vacuum pump the inner cylindrical tube holding the sample, tip, and circuitry until the pressure is Bar. Then we “bake” the inner chamber, using a heater to expel any other gas, while the vacuum pump continues until we reach approximately Bar. The heater is turned off and the vacuum continues to pump until we reach Bar. This entire vacuum process takes approximately 15 hours…

During this span of time, I have the opportunity to observe the dark, cold STM room. The door, walls and ceiling are covered with black rubber and spongy padding to absorb vibration. The STM room is in the lowest level basement for the same reason. The vibration from human steps near the testing generates noise in the data, so every precaution is made to minimize noise. Giant cement blocks lay across the STM metal box to increase inertia and decrease noise. I ask Kyle what he usually does with this “down” time. We discuss the importance of reading equipment manuals to grasp a better understanding of the myriad of tools in the lab. He says he needs to continue reading the papers published by the Yeh Lab Group. In knowing what questions your research group has previously answered, one has a better understanding of the history and the direction of current work.

The next day, the vacuum-pumped inner chamber is loaded to the center of the STM dewar. We flush the surrounding chambers with nitrogen gas to extricate any moisture or impurities that may have entered since our last testing. Next we can set up the equipment for a liquid nitrogen transfer which lasts approximately 2 hours, depending on the transfer rate. As the liquid nitrogen is added to the system, we meticulously monitor the temperature of the STM system. It must reach 80 Kelvin before we again test the electronics. Eventually it is time to add the liquid helium. Since liquid helium is quite expensive, additional precautions are taken to ensure maximum efficiency for helium use. It is beautiful to watch the moisture in the air deposit in frost along the tubing connecting the nitrogen and helium tanks to the STM dewar. The stillness of the quiet basement as we wait for the transfer is calming. Again, we carefully monitor the temperature drop as it eventually reaches 4.2 Kelvin. For this research, STM must be cooled to this temperature because we must drop below the critical temperature of the sample in order to observe superconductivity. The lower the temperature, the more of the superconducting component manifests itself. Hence the spectrum will have higher resolution. Liquid nitrogen is first added because it can carry over 90% of the heat away due to its higher mass. Nitrogen is also significantly cheaper than liquid helium. The liquid helium is added later, because it is even cooler than liquid nitrogen.

After adding additional layers of rubber padding on top of the closed STM, we can move over to the computer that controls the STM tip. It takes approximately one hour for the tip to be slowly lowered within range for a tunneling current. Kyle examines the data from the approach to the surface. If all seems normal, we can begin the actual scan of the sample!

An important part of the lab work is trouble shooting. I have listed the ideal order of steps, but as with life, things do not always proceed as expected. I have grown in awe of the perseverance and ingenuity required for daily troubleshooting. The need to be meticulous in order to avoid error is astonishing. I love that some common household items can be a valuable tool in the lab. For example, copper scrubbers used in the kitchen serve as a simple conducting path around the inner STM chamber. Floss can be used to tie down the most delicate thin wires. I certainly have grown in my immense respect for the patience and brilliance required in real research.

I find irony in the quiet simplicity of recording and analyzing data, the stillness of carefully transferring liquid helium juxtaposed to the immense complexity and importance of this groundbreaking research. I appreciate the moments of simple quiet in the STM room, the fast paced group meetings where everyone chimes in on their progress, or the boisterous collaborative brainstorming to troubleshoot a new problem. The summer weeks in the Sloan basement have been a welcome retreat from the exciting, transformative, and exhausting year in the classroom. I am grateful for the opportunity to learn more about superconductors, quantum tunneling, vacuum pumps, sonicators, lab safety, and more. While I will not be bromine etching, chemically forming STM tips, or doing liquid helium transfers come September, I have a new-found love for the process of research that I will radiate to my students.

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