Jeff Kimble explained to me why we should propose establishing the IQI. He knew I had used my slice of our shared DARPA grant to bring Alexei Kitaev to Caltech as a visiting professor, which had been wonderful. Recalling how much we had both benefited from Kitaev’s visit, Jeff remarked emphatically that “This stuff’s not free.” He had a point. To have more fun we’d need more money. Jeff took the lead in recruiting a large team of Caltech theorists and experimentalists to join the proposal we submitted, but the NSF was primarily interested in supporting the *theory* of quantum computation rather than the experimental part of the proposal. That was how I wound up in charge, though I continued to rely on Jeff’s advice and support.

This was a new experience for me and I worried a lot about how directing an institute would change my life. But I had one worry above all: space. We envisioned a thriving institute brimming over with talented and enthusiastic young scientists and visitors drawn from the physics, computer science, and engineering communities. But how could we carve out a place on the Caltech campus where they could work and interact?

To my surprise and delight, Jeff and I soon discovered that someone else at Caltech shared our excitement over the potential of IQI — Richard Murray, who was then the Chair of Caltech’s Division of Engineering and Applied Science. Richard arranged for the IQI to occupy office space in Steele Laboratory and some space we could configure as we pleased in Jorgensen Laboratory. The hub of the IQI became the lounge in Jorgensen, which we used for our seminar receptions, group meetings, and innumerable informal discussions, until our move to the beautiful Annenberg Center when it opened in 2009.

I sketched a rough plan for the Jorgensen layout, including furniture for the lounge. The furniture, I was told, was “NIC”. Though I was too embarrassed to ask, I eventually inferred this meant “Not in Contract” — I would need to go furniture shopping, one of my many burgeoning responsibilities as Director.

By this time, Ann Harvey was in place as IQI administrator, a huge relief. But furniture was something I thought I knew about, because I had designed and furnished a common area for the particle theory group a couple of years earlier. As we had done on that previous occasion, my wife Roberta and I went to Krause’s Sofa Factory to order a custom-made couch, love seat, and lounge chair, in a grayish green leather which we thought would blend well with the carpeting.

Directing an institute is not as simple as it sounds, though. Before the furniture was delivered, Krause’s declared bankruptcy! We had paid in full, but I had some anxious moments wondering whether there would be a place to sit down in the IQI lounge. In the end, after some delay, our furniture was delivered in time for the grand opening of the new space in September 2001. A happy ending, but not really the end of the story.

Before the move to Annenberg in 2009, I ordered furniture to fill our (much smaller) studio space, which became the new IQI common area. The Jorgensen furniture was retired, and everything was new! It was nice … But every once in a while I felt a twinge of sadness. I missed my old leather chair, from which I had pontificated at eight years worth of group meetings. That chair and I had been through a lot together, and I couldn’t help but feel that my chair’s career had been cut short before its time.

I don’t recall mentioning these feelings to anyone, but someone must have sensed by regrets. Because one day not long after the move another miracle occurred … my chair was *baaack*! Sitting in it again felt … good. For five years now I’ve been pontificating from my old chair in our new studio, just like I used to. No one told me how my chair had been returned to me, and I knew better than to ask.

Eventually the truth comes out. At my 60th birthday celebration last year, Stephanie Wehner and Darrick Chang admitted to being the perpetrators, and revealed the whole amazing story in their article on “Macroscopic Quantum Teleportation” in a special issue of *Nature Relocations*. Their breakthrough article was enhanced by Stephanie’s extraordinary artwork, which you really have to see to believe. So if your curiosity is piqued, please follow this link to find out more.

Why, you may wonder, am I reminiscing today about the story of my chair? Well, is an excuse really necessary? But if you must know, it may be because, after two renewals and 14 years of operation, I submitted the IQI Final Report to the NSF this week. Don’t worry — the Report is not really Final, because the IQI has become part of an even grander vision, the IQIM (which has given birth to this blog among other good things). Like my chair, the IQI is not quite what it was, yet it lives on.

The nostalgic feelings aroused by filing the Final Report led me to reread the wonderful volume my colleagues put together for my birthday celebration, which recounts not only the unforgettable exploits of Stephanie and Darrick, but many other stories and testimonials that deeply touched me.

Browsing through that book today, one thing that struck me is the ways we sometimes have impact on others without even being aware of it. For example, Aram Harrow, Debbie Leung, Joe Renes and Stephanie all remember lectures I gave when they were undergraduate students (before I knew them), which might have had some impact on their later research careers. Knowing this will make it a little harder to say no the next time I’m invited to give a talk. Yaoyun Shi has vivid memories of the time I wore my gorilla mask to the IQI seminar on Halloween, which inspired him to dress up as “a butcher threatening to cut off the ears of my students with a bloody machete if they were not listening,” thus boosting his teaching evaluations. And Alexios Polychronakos, upon hearing that I had left particle theory to pursue quantum computing, felt it “was a bit like watching your father move to Las Vegas and marry a young dancer after you leave for college,” while at the same time he appreciated “that such reinventions are within the spectrum of possibilities for physicists who still have a pulse.”

I’m proud of what the IQI(M) has accomplished, but we’re just getting started. After 14 years, I still have a pulse, and my chair has plenty of wear left. Together we look forward to many more years of pontification.

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Adding more fuel to “Red October”, I presented the final product to my teammates. With a communal nod of approval, we rushed over to the crowd.

“1, 2, 3, GO!”

It was the semi-finals. Teams Heil Hydra! and The Archimedean Hawks ignited their engines and set their vehicles onto the starting line. Nascar? F1? Nope, even better. Homemade steamboat races! Throughout the cheers and yelling, we discovered that more isn’t better. Flames were devouring Team Heil Hydra!’s Red October. Down went the ship. Despite the loss, the kids learned about steam as a source of energy, experimentation, and teamwork. Although it may have been hard to tell the first day, by the end of this fourth day of the camp, all students were visibly excited for another day of the InnoWorks summer program at Caltech.

What is InnoWorks? An engaging summer program aimed for middle school students with disadvantaged backgrounds, InnoWorks offers a free of charge opportunity to dig into the worlds of science, technology, engineering, mathematics, and medicine (STEM^2). In his own life experience, William Hwang (founder of InnoWorks) was blessed with the opportunities to attend several summer camps throughout his childhood, but he had a friend who did not share the same opportunities. Sparked with the desire to start something, Hwang founded the non-profit organization, United InnoWorks Academy. With the first program to begin in 2004, the InnoWorks Academy developed these summer programs to help provide underprivileged kids with hands-on activities, team-building activities, and fast-paced competitive missions. Starting with just 34 students and 17 volunteers in a single chapter, InnoWorks has now grown to more than a dozen university chapters that have hosted above 60 summer programs for 2,200 middle school students, all done with the help of over 1000 volunteers.

Monday, August 11th, 2014 marked the first day of Caltech’s 3rd annual summer InnoWorks program. Last year, my younger brother participated in the program and had such a great experience that he wanted to become a junior mentor this year. After researching the program and listening to my brother’s past experiences, I was ecstatic to accept this journey as a mentor for Caltech’s InnoWorks program. Allow me to take you on a ride through my team’s and my own experience of InnoWorks.

**First Day of Caltech InnoWorks 2014. **My first team member that I checked in was Elliot. “Are you ready for InnoWorks!?” Perhaps I was a little overly excited. I received a shrug and “What’re we eating for breakfast?” Not the response I was hoping for, but that was going to change. As the rest of my team, which included Frank, Megan, Ethan, and my junior mentor, Elan, arrived, I began peppering them with icebreakers left and right. Soon enough, we dubbed ourselves Heil Hydra! and by the end of the second day, I couldn’t get them to be quiet.

“What are we doing next?”

“Guys, GUYS! Let’s use the green pom-poms as chloroplasts.”

“Hey, the soap actually smells good.”

“Hm. If you add another rubber band, the cup won’t vibrate as much, and it makes a lower sound.”

Sometimes they would have endless questions, which was great! Isn’t that what science is all about?

Most of the days during camp were themed with a specific subject, including biology, chemistry, physics, and engineering. Before each activity, both mentors and junior mentors gave a brief, prepared introduction to the science used during the experimentation. Here’s a quick synopsis of some of the activities and the students’ experiences:

**Camera Obscura. **After a short explanation of light, and how a lens works, we split the room up into 3 groups to build their very own camera obscura, which is an optical device that projects an image of its surroundings onto a screen (or in our case, the ground). Using a mirror, a magnifying glass, some PVC piping, and a black tarp, the kids constructed a camera obscura. I was impressed by how many students encumbered the heat of the black tarp and concrete all in the name of science.

**Build Your Own Instrument. **The title says all. I let my junior mentor, Elan, lead the group in this activity. Tasked with creating an instrument based on accurate pitch of 3 whole note tones, creativity, efficiency, and performance, the students went straight to work. Children have endless imaginations. Give kids PVC pipes, rubber bands, balloons, cups, and paper clips, and they’ll make everything! Working together, the groups created an instrument (often more than one) to present in front of everyone. Teams were required to explain how their instrument created sound (vibrations), and attempt to play “Mary Had a Little Lamb” (which most succeeded). I came across paperclip rain sticks, PVC didgeridoos, test tube pan flutes, red solo cup drums, and even PVC balloon catapults and rubber band ballistas!

**Liquid Nitrogen. **One of the highlights of the camp was liquid nitrogen! We were very honored to have Glen Evenbly and Olivier Landon-Cardinal, IQIM postdocs, join us. After pouring the liquid into a bowl, Glen showed the kids how nitrogen gas enveloped the area. Liquid nitrogen’s efficiency as a coolant is limited by the fact that it boils immediately upon contact with a warmer object, surrounding the object with nitrogen gas on which the liquid surfs. This effect is known as the Leidenfrost effect, which applies to any liquid in contact with an object significantly hotter than its boiling point.

However, liquid nitrogen is still extremely cold, and when roses were placed into the bowl with liquid nitrogen, the pedals froze right before everyone’s eyes.

**Lego Mindstorms. **The last activity of the camp was building a lego robot and programming it to track and follow a black tape trail using its light sensor. Since each of my team members had experience with these lego kits, they went to work right away. Two of my students worked on building the robot, while the other two retrieved the pieces. After awhile, they prompted each other to switch roles.

Programming the robot was a struggle, but manipulating the code and watching the aftermath was all part of the experiment. After many attempted tries, the group was unable to accurately get the robot to follow the black line (some groups were successful!). However, without any outside help (including myself), Team Heil Hydra! programmed the robot to move and sing (can you guess?) “Mary Had a Little Lamb”. Teamwork for the win! Team spirit bloomed in my group – each day of camp my InnoWorkers agreed on a matching t-shirt color. As a mentor, I could not have been more proud.

I know that I am not only speaking for myself when I say that the InnoWorks family, the students, and the program itself has burrowed its way into my heart. I have watched these students develop teamwork skills, enthusiasm for learning new things, and friendships. I have heard these students speak the minimal amount on their first day, only to find that their chatterboxes won’t stop the last day. To overlook InnoWorks as just a science camp where students come to learn about science is an understatement. InnoWorks is where students experience, engage, and conduct science, where they learn not just about science, but also about collaboration, leadership, and innovation.

I must end on this last note: Heil Hydra!

*Editor’s Note: Ms. Rebekah Zhou is majoring in mathematics at CSU Fresno. In her spare time, she enjoys teaching piano and tutoring.*

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My senior spring in college, PFP manifested as “PHYS 001/002: Understanding the Universe: From Atoms to the Big Bang.” The tallness of this order failed to daunt Marcelo Gleiser, a cosmologist whose lectures swayed with a rhythm like a Foucault pendulum. From creation myths and Greek philosophers, we proceeded via Copernicus and Kepler to Newton and the Enlightenment, Maxwell and electromagnetism, the Industrial Revolution and thermodynamics, Einstein’s relativity, and WWII and the first quantum revolution, ending with particle physics and cosmology. The course provided a history credit I needed. It offered a breather from problem sets, sandwiching my biophysics and quantum-computation lectures. Pragmatism aside, PHYS 2 showcased the grandness of the physicist’s legacy—of my legacy. PHYS 2 sharpened my determination to do that legacy justice. To do it justice, most of us must pass tests. Here’s how PFP can help.

Reviewing basic physics can improve GRE scores. If thermodynamics has faded from memory, good luck calculating a Carnot engine’s efficiency. Several guides (and I) recommend reviewing notes and textbooks, working practice problems, simulating exams, and discussing material with peers.

Taking PFP, you will review for the GRE. A list of the topics on the Physics GRE appears here. Of the 14 mechanics topics, eight surfaced in PHYS 2. Taking PFP will force you to review GRE topics that lack of time (or that procrastination) might force you to skip. Earning credit for GRE prep, you won’t have to shoehorn that prep into your schedule at the expense of research. The Physics GRE covers basic physics developed during the past 500 years; so do many PFP courses.

The GRE, you might protest, involves more math than PFP. But GRE questions probe less deeply, and PFP can galvanize more reviews of math, than you might expect. According to Stanford’s Society of Physics Students, “Each [Physics GRE] question shouldn’t require much more than a minute’s worth of thought and computation.” Expect to use the Wave Equation and Maxwell’s Equations, not to derive the former from the latter. Some PFP instructors require students to memorize formulae needed on the GRE. PFP can verify whether your memory has interchanged the exponents in Kepler’s Third Law, or dropped the negative sign from the kinetic-energy term in Schrödinger’s Equation.

Even formulae excluded from PFP exams appear in PFP classes. In a PHYS 2 Powerpoint, Marcelo included Planck’s blackbody formula. Though he never asked me to regurgitate it, his review benefited me. Given such a Powerpoint, you can re-memorize the formula. Derive the Stefan-Boltzmann and Wien Displacement Laws. Do you remember how a blackbody’s energy density varies with frequency in the low-energy limit? PFP can catalyze your review of math used on the GRE.

While recapitulating basic physics, PFP can introduce “specialized” GRE topics. Examples include particle physics, astrophysics, and nuclear physics. Covered in advanced classes, these subjects might have evaded mention in your courses. Signing up for biophysics, I had to drop particle theory. PHYS 2 helped compensate for the drop. I learned enough about neutrinos and quarks to answer GRE questions about them. In addition to improving your score, surveying advanced topics in PFP can enhance your understanding of physics seminars and conversations. The tour can help you identify which research you should undertake. If you’ve tried condensed-matter and atmospheric research without finding your niche, tasting cosmology in PFP might point toward your next project. Sampling advanced topics in PFP, you can not only prepare for the GRE, but also enrich your research.

I am not encouraging you to replace advanced physics courses with PFP. I encourage you to complement advanced courses with PFP. If particle physics suits your schedule and intrigues you, enjoy. If you need to fulfill a history or social-sciences distribution requirement, check whether PFP can count. Consider PFP if you’ve committed to a thesis and three problem-set courses, you haven’t signed up for the minimum number of courses required by your college, and more problem sets would strangle you. Sleep deprivation improves neither exam scores nor understanding. Not that I sailed through PHYS 2 without working. I worked my rear off—fortunately for my science. Switching mindsets—pausing frustrating calculations to study Kepler—can refresh us. Stretch your calculational toolkit in advanced courses, and reinforce that toolkit with PFP.

In addition to reviewing basic physics and surveying specialized topics, you can seek study help from experts in PFP. When your questions about GRE topics overlap with PFP material, ask your instructor and TA. They’ll probably enjoy answering: Imagine teaching physics with little math, with one hand tied behind your back. Some students take your class not because they want to, but because they need science credits. Wouldn’t you enjoy directing a student who cares? While seeking answers, you can get to know your professor or TA. You can learn about his or her research. Maybe PFP will lead you to join that research. PFP not only may connect you to experts able to answer questions as no study guide can. PFP offers opportunities to enhance a course as few non-physics students can and to develop relationships with role models.

Those relationships illustrate the benefits that PFP extends beyond GREs. As mentioned earlier, surveying advanced topics can diversify the research conversations you understand. The survey can direct you toward research you’ll pursue. Further exposure to research can follow from discussions with instructors. Intermissions from problem sets can promote efficiency. Other benefits of PFP include enhancement of explanatory skills and a bird’s-eye view of the scientific process to which you’re pledging several years. What a privilege we enjoy, PFP shows. We physicists explore questions asked for millennia. We wear mantles donned by Faraday, Bernoulli, and Pauli. When integrals pour out our ears and experiments break down, PFP can remind us why we bother. And that we’re in fine company.

Physics for Poets can improve your Physics GRE score and reinforce your physics major. Surveying basic physics, PFP will force you to review GRE topics. PFP may introduce specialized GRE topics absent from most physics majors. Opportunities abound to re-memorize equations and to complement lectures with math. Questioning instructors, you can deepen your understanding as with no study guide. Beyond boosting your GRE score, PFP can broaden your research repertoire, energize your calculations, improve your explanatory skills, and inspire.

Good luck with the academic year, and see you in grad school!

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So what is the *technological singularity*? My personal translation is: are we on the verge of narcissistic flesh-eating robots stealing our lunch money while we commute to the ‘special school for slow sapiens’?

This is an especially hyperbolic view, and I want to be clear to distinguish ‘machine learning‘ from ‘artificial consciousness.’ The former seems poised for explosive growth but the latter seems to require breakthroughs in our understanding of the fundamental science. The two concepts are often equated when defining the singularity, or even artificial intelligence, but I think it’s important to distinguish these two concepts. Without distinguishing them, people sometimes make the faulty association: machine_learning_progress=>AI_progress=>artificial_consciousness_progress.

I’m generally an optimistic person, but on this topic, I’m especially optimistic about humanity’s status as machine overlords for at least the next ~100 years. Why am I so optimistic? Quantum information (QI) theory has a secret weapon. And that secret weapon is obviously Scott Aaronson (and his brilliant friends+colleagues+sidekicks; especially Alex Arkhipov in this case.) Over the past few years they have done absolutely stunning work related to understanding the computational complexity of linear optics. They colloquially call this work Boson sampling.

What I’m about to say is probably extremely obvious to most people in the QI community, but I’ve had conversations with exquisitely well educated people–including a Nobel Laureate–and very few people outside of QI seem to be aware of Aaronson and Arkhipov’s (AA’s) results. Here’s a thought experiment: does a computer have all the hardware required to simulate the human brain? For a long time, many people thought yes, and they even created a more general hypothesis called the “extended Church-Turring hypothesis.”

An interdisciplinary group of scientists has long speculated that quantum mechanics may stand as an obstruction towards this hypothesis. In particular, it’s believed that quantum computers would be able to efficiently solve some problems that are hard for a classical computer. These results led people, possibly Roger Penrose most notably, to speculate that consciousness may leverage these quantum effects. However, for many years, there was a huge gap between quantum experiments and the biology of the human brain. If I ever broached this topic at a dinner party, my biologist friends would retort: “but the brain is warm and wet, good luck managing decoherence.” And this seems to be a valid argument against the brain as a universal quantum computer. However, one of AA’s many breakthroughs is that they paved the way towards showing that a rather elementary physical system can gain speed-ups on certain classes of problems over classical computers. Maybe the human brain has a Boson sampling module?

More specifically, AA’s physical setup involves being able to: generate identical photons; send them through a network of beamsplitters, phase shifters and mirrors; and then count the number of photons in each mode through ‘nonadaptive’ measurements. This setup computes the permanent of a matrix, which is known to be a hard problem classically. AA showed that if there exists a polynomial-time classical algorithm which samples from the same probability distribution, then the polynomial hierarchy would collapse to the third level (this last statement would be very bad for theoretical computer science and therefore for humans; ergo probably not true.) I should also mention that when I learned the details of these results, during Scott’s lectures this past January at the Israeli Insitute of Advanced Studies’ Winter School in Theoretical Physics, that there was one step in the proof which was not rigorous. Namely, they rely on a conjecture in random matrix theory–but at least they have simulations indicating the conjecture should be true.

Nitty gritty details aside, I find the possibility that this simple system is gaining a classical speed-up compelling in the conversation about consciousness. Especially considering that finding permanents is actually useful for some combinatorics problems. When you combine this with Nature’s mischievous manner of finding ways to use the tools available to it, it seems plausible to me that the brain is using something like Boson sampling for at least one non-trivial task towards consciousness. If not Boson sampling, then maybe ‘Fermion smashing’ or ‘minimal surface finding’ or some other crackpottery words I’m coming up with on the fly. The point is, this result opens a can of worms.

AA’s results have bred new life into my optimism towards humanity’s ability to rule the lands and interwebs for at least the next few decades. Or until some brilliant computer scientist proves that human consciousness is in P. If nothing else, it’s a fun topic for wild dinner party speculation.

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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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