# LIGO: Playing the long game, and winning big!

Wow. What a day! And what a story!

Kip Thorne in 1972, around the time MTW was completed.

It is hard for me to believe, but I have been on the Caltech faculty for nearly a third of a century. And when I arrived in 1983, interferometric detection of gravitational waves was already a hot topic of discussion here. At Kip Thorne’s urging, Ron Drever had been recruited to Caltech and was building the 40-meter prototype interferometer (which is still operating as a testbed for future detection technologies). Kip and his colleagues, spurred by Vladimir Braginsky’s insights, had for several years been actively studying the fundamental limits of quantum measurement precision, and how these might impact the search for gravitational waves.

I decided to bone up a bit on the subject, so naturally I pulled down from my shelf the “telephone book” — Misner, Thorne, and Wheeler’s mammoth Gravitationand browsed Chapter 37 (Detection of Gravitational Wave), for which Kip had been the lead author. The chapter brimmed over with enthusiasm for the subject, but to my surprise interferometers were hardly mentioned. Instead the emphasis was on mechanical bar detectors. These had been pioneered by Joseph Weber, whose efforts in the 1960s had first aroused Kip’s interest in detecting gravitational waves, and by Braginsky.

I sought Kip out for an explanation, and with characteristic clarity and patience he told how his views had evolved. He had realized in the 1970s that a strain sensitivity of order $10^{-21}$ would be needed for a good chance at detection, and after many discussions with colleagues like Drever, Braginsky, and Rai Weiss, he had decided that kind of sensitivity would not be achievable with foreseeable technology using bars.

Ron Drever, who built Caltech’s 40-meter prototype interferometer in the 1980s.

We talked about what would be needed — a kilometer scale detector capable of sensing displacements of $10^{-18}$ meters. I laughed. As he had many times by then, Kip told why this goal was not completely crazy, if there is enough light in an interferometer, which bounces back and forth many times as a waveform passes. Immediately after the discussion ended I went to my desk and did some crude calculations. The numbers kind of worked, but I shook my head, unconvinced. This was going to be a huge undertaking. Success seemed unlikely. Poor Kip!

I’ve never been involved in LIGO, but Kip and I remained friends, and every now and then he would give me the inside scoop on the latest developments (most memorably while walking the streets of London for hours on a beautiful spring evening in 1991). From afar I followed the forced partnership between Caltech and MIT that was forged in the 1980s, and the painful transition from a small project under the leadership of Drever-Thorne-Weiss (great scientists but lacking much needed management expertise) to a large collaboration under a succession of strong leaders, all based at Caltech.

Vladimir Braginsky, who realized that quantum effects limit the sensitivity of  gravitational wave detectors.

During 1994-95, I co-chaired a committee formulating a long-range plan for Caltech physics, and we spent more time talking about LIGO than any other issue. Part of our concern was whether a small institution like Caltech could absorb such a large project, which was growing explosively and straining Institute resources. And we also worried about whether LIGO would ultimately succeed. But our biggest worry of all was different — could Caltech remain at the forefront of gravitational wave research so that if and when LIGO hit paydirt we would reap the scientific benefits?

A lot has changed since then. After searching for years we made two crucial new faculty appointments: theorist Yanbei Chen (2007), who provided seminal ideas for improving sensitivity, and experimentalist Rana Adhikari (2006), a magician at the black art of making an interferometer really work. Alan Weinstein transitioned from high energy physics to become a leader of LIGO data analysis. We established a world-class numerical relativity group, now led by Mark Scheel. Staff scientists like Stan Whitcomb also had an essential role, as did longtime Project Manager Gary Sanders. LIGO Directors Robbie Vogt, Barry Barish, Jay Marx, and now Dave Reitze have provided effective and much needed leadership.

Rai Weiss, around the time he conceived LIGO in an amazing 1972 paper.

My closest connection to LIGO arose during the 1998-99 academic year, when Kip asked me to participate in a “QND reading group” he organized. (QND stands for Quantum Non-Demolition, Braginsky’s term for measurements that surpass the naïve quantum limits on measurement precision.) At that time we envisioned that Advanced LIGO would turn on in 2008, yet there were still many questions about how it would achieve the sensitivity required to ensure detection. I took part enthusiastically, and learned a lot, but never contributed any ideas of enduring value. The discussions that year did have positive outcomes, however; leading for example to a seminal paper by Kimble, Levin, Matsko, Thorne, and Vyatchanin on improving precision through squeezing of light. By the end of the year I had gained a much better appreciation of the strength of the LIGO team, and had accepted that Advanced LIGO might actually work!

I once asked Vladimir Braginsky why he spent years working on bar detectors for gravitational waves, while at the same time realizing that fundamental limits on quantum measurement would make successful detection very unlikely. Why wasn’t he trying to build an interferometer already in the 1970s? Braginsky loved to be asked questions like this, and his answer was a long story, told with many dramatic flourishes. The short answer is that he viewed interferometric detection of gravitational waves as too ambitious. A bar detector was something he could build in his lab, while an interferometer of the appropriate scale would be a long-term project involving a much larger, technically diverse team.

Joe Weber, whose audacious belief that gravitational waves are detectable on earth inspired Kip Thorne and many others.

Kip’s chapter in MTW ends with section 37.10 (“Looking toward the future”) which concludes with this juicy quote (written almost 45 years ago):

“The technical difficulties to be surmounted in constructing such detectors are enormous. But physicists are ingenious; and with the impetus provided by Joseph Weber’s pioneering work, and with the support of a broad lay public sincerely interested in pioneering in science, all obstacles will surely be overcome.”

That’s what we call vision, folks. You might also call it cockeyed optimism, but without optimism great things would never happen.

Optimism alone is not enough. For something like the detection of gravitational waves, we needed technical ingenuity, wise leadership, lots and lots of persistence, the will to overcome adversity, and ultimately the efforts of hundreds of hard working, talented scientists and engineers. Not to mention the courage displayed by the National Science Foundation in supporting such a risky project for decades.

I have never been prouder than I am today to be part of the Caltech family.

# Some like it cold.

When I reached IBM’s Watson research center, I’d barely seen Aaron in three weeks. Aaron is an experimentalist pursuing a physics PhD at Caltech. I eat dinner with him and other friends, most Fridays. The group would gather on a sidewalk in the November dusk, those three weeks. Light would spill from a lamppost, and we’d tuck our hands into our pockets against the chill. Aaron’s wife would shake her head.

“The fridge is running,” she’d explain.

Aaron cools down mechanical devices to near absolute zero. Absolute zero is the lowest temperature possible,1 lower than outer space’s temperature. Cold magnifies certain quantum behaviors. Researchers observe those behaviors in small systems, such as nanoscale devices (devices about 10-9 meters long). Aaron studies few-centimeter-long devices. Offsetting the devices’ size with cold might coax them into exhibiting quantum behaviors.

The cooling sounds as effortless as teaching a cat to play fetch. Aaron lowers his fridge’s temperature in steps. Each step involves checking for leaks: A mix of two fluids—two types of helium—cools the fridge. One type of helium costs about \$800 per liter. Lose too much helium, and you’ve lost your shot at graduating. Each leak requires Aaron to warm the fridge, then re-cool it. He hauled helium and pampered the fridge for ten days, before the temperature reached 10 milliKelvins (0.01 units above absolute zero). He then worked like…well, like a grad student to check for quantum behaviors.

Aaron came to mind at IBM.

Nick works at Watson, IBM’s research center in Yorktown Heights, New York. Watson has sweeping architecture frosted with glass and stone. The building reminded me of Fred Astaire: decades-old, yet classy. I found Nick outside the cafeteria, nursing a coffee. He had sandy hair, more piercings than I, and a mandate to build a quantum computer.

IBM Watson

“Definitely!” Nick fished out an ID badge; grabbed his coffee cup; and whisked me down a wide, window-paneled hall.

Different researchers, across the world, are building quantum computers from different materials. IBMers use superconductors. Superconductors are tiny circuits. They function at low temperatures, so IBM has seven closet-sized fridges. Different teams use different fridges to tackle different challenges to computing.

Nick found a fridge that wasn’t running. He climbed half-inside, pointed at metallic wires and canisters, and explained how they work. I wondered how his cooling process compared to Aaron’s.

“You push a button.” Nick shrugged. “The fridge cools in two days.”

IBM, I learned, has dry fridges. Aaron uses a wet fridge. Dry and wet fridges operate differently, though both require helium. Aaron’s wet fridge vibrates less, jiggling his experiment less. Jiggling relates to transferring heat. Heat suppresses the quantum behaviors Aaron hopes to observe.

Heat and warmth manifest in many ways, in physics. Count Rumford, an 18th-century American-Brit, conjectured the relationship between heat and jiggling. He noticed that drilling holes into canons immersed in water boils the water. The drill bits rotated–moved in circles–transferring energy of movement to the canons, which heated up. Heat enraptures me because it relates to entropy, a measure of disorderliness and ignorance. The flow of heat helps explain why time flows in just one direction.

A physicist friend of mine writes papers, he says, when catalyzed by “blinding rage.” He reads a paper by someone else, whose misunderstandings anger him. His wrath boils over into a research project.

Warmth manifests as the welcoming of a visitor into one’s lab. Nick didn’t know me from Fred Astaire, but he gave me the benefit of the doubt. He let me pepper him with questions and invited more questions.

Warmth manifests as a 500-word disquisition on fridges. I asked Aaron, via email, about how his cooling compares to IBM’s. I expected two sentences and a link to Wikipedia, since Aaron works 12-hour shifts. But he took pity on his theorist friend. He also warmed to his subject. Can’t you sense the zeal in “Helium is the only substance in the world that will naturally isotopically separate (neat!)”? No knowledge of isotopic separation required.

Many quantum scientists like it cold. But understanding, curiosity, and teamwork fire us up. Anyone under the sway of those elements of science likes it hot.

With thanks to Aaron and Nick. Thanks also to John Smolin and IBM Watson’s quantum-computing-theory team for their hospitality.

1In many situations. Some systems, like small magnets, can access negative temperatures.

# More than Its Parts

“The whole not only becomes more than but very different from the sum of its parts.”
– P. W. Anderson

It was a brainstorming meeting. We went from referencing a melodramatic viral Thai video to P. W. Anderson’s famous paper, “More is Different” to a vote-splitting internally produced Caltech video to the idea of extracting an edit out of existing video we already had from prior IQIM-Parveen Shah Productions’ shoots. And just like that, stepping from one idea to the next, hopping along, I pitched a theorist vs experimentalist “interrogation”. They must have liked it because the opinion in the room hushed for a few seconds. It seemed plausibly exciting and dangerously perhaps…fresh. But what I witnessed in the room was exactly the idea of collaboration and the “storm” of the brain. This wasn’t a conclusion we could likely have arrived to if all of us were sitting alone. There was a sense of the dust settling around the chaotic storm of the collective brain(s). John Preskill, Crystal Dilworth, Spiros Michalakis and I finally agreed on a plan of action going forward. And mind you, this of course was very far from the first meeting or email we had had about the video.

Capitalizing on the instant excitement, the emails started going around. Who will be the partners in crime? A combination of personality, representation, willingness and profile were balanced to decide the participants. We reached out to Gil Refael, David Hsieh, Nai-Chang Yeh, Xie Chen and Oskar Painter. They all said “yes”! It seemed deceivingly easy. And alas it came. Once the idea of the interrogation was unleashed; pitting them against one another or should I say “with” one another, brought about a bit of anxiety and confusion at first. “Wait, we’re supposed to fight on camera?” “But, our fields don’t match necessarily.” “No, no, it just doesn’t make sense.” I was prepared for the paranoia. It was natural and a bit less than what we got back when we pitched the high-fashion shoot for geeks video. I was taking them out of their comfort zone. It was natural. I abated the fears. I told them it was not going to be that controversial.

But I had to prep it to a certain level of “conflict” or “drama” so that what we got on camera, was at least some remnant of the initial emotional intention. The questions, the “tone” had to be set. Then we realized that it wasn’t just the meeting of the professorial brains but also the other researchers of the Institute that needed to be represented. And so, we also added some post docs and graduate students. Johannes Pollanen (now already an Assistant Professor at Michigan State University), Chandni Usha and Shaun Maguire. The idea of a nebulous conversation about theory vs practical or theory and practical seemed like a literal experiment of the very idea of the formation of the IQIM: putting the best brains in the field, in a sandbox, shaking them around to see the entangled interactions produced. It seemed too perfect.

The resulting video might not have produced the exact linear narrative I desired…but it was indeed “more than the sum of its parts”. It showed the excitement, the constant interaction, the curious conversations and the anxiety of being at the forefront, the cutting edge, where one is sometimes limited by another and sometimes enabled by the other, but most importantly, constantly growing and evolving. IQIM to me signifies that community.

Being accepted and integrated as a filmmaker itself is a virtue of that forced and encouraged collaboration and interaction.

And so we began. Before we filmed, I spent time with each duo, discussing and requesting a narrative and answers to some proposed questions.

Cinematographer, Anthony C. Kuhnz, and I were excited to shoot in Keith Schwab’s spacious lab, that had produced the memorable shot of Emma Wollman for our initial promo video. It’s space and background was exactly what we needed for the blurred backgrounds of this “brain space” we were hoping to create.

The lighting was certainly inspired by an interrogation scene but dampened for the dream state. We wanted to bring people into a behind the scenes discussion of some of the most brilliant minds in quantum physics, seeing the issues and challenges that face them; the exciting possibilities that they predict. The handheld camera and the dynamic pans from one to another were also inspired to communicate that transitional and collaborative “ball toss” energy. Once you feel that tangible creativity, then we go into the depths of what IQIM really is, how it creates its community within and without, the latter by focusing on the outreach and the educational efforts to spread the magic and sparkle of Physics.

I’m proud of this video. When I watch it, whether or not I understand everything being said, I do certainly want to be engaged with IQIM and that is the hope for others who watch it.

Nature is subtle and so is the effect of this video…as in, we hope that…we gotcha!

# Life, cellular automata, and mentoring

One night last July, IQIM postdoc Ning Bao emailed me a photo. He’d found a soda can that read, “Share a Coke with Patrick.”

Ning and I were co-mentoring two Summer Undergraduate Research Fellows, or SURFers. One mentee received Ning’s photo: Caltech physics major Patrick Rall.

“Haha,” Patrick emailed back. “I’ll share a Coke.”

Patrick, Ning, and I shared the intellectual equivalent of a six-pack last summer. We shared papers, meals, frustrations, hopes, late-night emails (from Patrick and Ning), 7-AM emails (from me), and webcomic strips. Now a senior, Patrick is co-authoring a paper about his SURF project.

The project grew from the question “What would happen if we quantized Conway’s Game of Life?” (For readers unfamiliar with the game, I’ll explain below.) Lessons we learned about the Game of Life overlapped with lessons I learned about life, as a first-time mentor. The soda fountain of topics contained the following flavors.

Update rules: Till last spring, I’d been burrowing into two models for out-of-equilibrium physics. PhD students burrow as no prairie dogs can. But, given five years in Caltech’s grassland, I wanted to explore. I wanted an update.

Ning and I had trespassed upon quantum game theory months earlier. Consider a nonquantum game, such as the Prisoner’s Dilemma or an election. Suppose that players have physical systems, such as photons (particles of light), that occupy superposed or entangled states. These quantum resources can change the landscape of the game’s possible outcomes. These changes clarify how we can harness quantum mechanics to process, transmit, and secure information.

How might quantum resources change Conway’s Game of Life, or GoL? British mathematician John Conway invented the game in 1970. Imagine a square board divided into smaller squares, or cells. On each cell sits a white or a black tile. Black represents a living organism; white represents a lack thereof.

Conway modeled population dynamics with an update rule. If prairie dogs overpopulate a field, some die from overcrowding. If a black cell borders more than three black neighbors, a white tile replaces the black. If separated from its pack, a prairie dog dies from isolation. If a black tile borders too few black neighbors, we exchange the black for a white. Mathematics columnist Martin Gardner detailed the rest of Conway’s update rule in this 1970 article.

Updating the board repeatedly evolves the population. Black and white shapes might flicker and undulate. Space-ship-like shapes can glide across the board. A simple update rule can generate complex outcomes—including, I found, frustrations, hopes, responsibility for another human’s contentment, and more meetings than I’d realized could fit in one summer.

Modeled by Conway’s Game of Life. And by PhD students.

Initial conditions: The evolution depends on the initial state, on how you distribute white and black tiles when preparing the board. Imagine choosing the initial state randomly from all the possibilities. White likely mingles with about as much black. The random initial condition might not generate eye-catchers such as gliders. The board might fade to, and remain, one color.*

Enthusiasm can fade as research drags onward. Project Quantum GoL has continued gliding due to its initial condition: The spring afternoon on which Ning, Patrick, and I observed the firmness of each other’s handshakes; Patrick walked Ning and me through a CV that could have intimidated a postdoc; and everyone tried to soothe everyone else’s nerves but occasionally avoided eye contact.

I don’t mean that awkwardness sustained the project. The awkwardness faded, as exclamation points and smiley faces crept into our emails. I mean that Ning and I had the fortune to entice Patrick. We signed up a bundle of enthusiasm, creativity, programming skills, and determination. That determination perpetuated the project through the summer and beyond. Initial conditions can determine a system’s evolution.

Long-distance correlations:  “Sure, I’d love to have dinner with you both! Thank you for the invitation!”

Lincoln Carr, a Colorado School of Mines professor, visited in June. Lincoln’s group, I’d heard, was exploring quantum GoLs.** He studies entanglement (quantum correlations) in many-particle systems. When I reached out, Lincoln welcomed our SURF group to collaborate.

I relished coordinating his visit with the mentees. How many SURFers could say that a professor had visited for his or her sake? When I invited Patrick to dinner with Lincoln, Patrick lit up like a sunrise over grasslands.

Our SURF group began skyping with Mines every Wednesday. We brainstorm, analyze, trade code, and kvetch with Mines student Logan Hillberry and colleagues. They offer insights about condensed matter; Patrick, about data processing and efficiency; I, about entanglement theory; and Ning, about entropy and time evolution.

We’ve learned together about long-range entanglement, about correlations between far-apart quantum systems. Thank goodness for skype and email that correlate far-apart research groups. Everyone would have learned less alone.

Long-distance correlations between quantum states and between research groups

Time evolution: Logan and Patrick simulated quantum systems inspired by Conway’s GoL. Each researcher coded a simulation, or mathematical model, of a quantum system. They agreed on a nonquantum update rule; Logan quantized it in one way (constructed one quantum analog of the rule); and Patrick quantized the rule another way. They chose initial conditions, let their systems evolve, and waited.

In July, I noticed that Patrick brought a hand-sized green spiral notepad to meetings. He would synopsize his progress, and brainstorm questions, on the notepad before arriving. He jotted suggestions as we talked.

The notepad began guiding meetings in July. Patrick now steers discussions, ticking items off his agenda. The agenda I’ve typed remains minimized on my laptop till he finishes. My agenda contains few points absent from his, and his contains points not in mine.

Patrick and Logan are comparing their results. Behaviors of their simulations, they’ve found, depend on how they quantized their update rule. One might expect the update rule to determine a system’s evolution. One might expect the SURF program’s template to determine how research and mentoring skills evolve. But how we implement update rules matters.

Caltech’s 2015 quantum-information-theory Summer Undergraduate Research Fellows and mentors

Life: I’ve learned, during the past six months, about Conway’s Game of Life, simulations, and many-body entanglement. I’ve learned how to suggest references and experts when I can’t answer a question. I’ve learned that editing SURF reports by hand costs me less time than editing electronically. I’ve learned where Patrick and his family vacation, that he’s studying Chinese, and how undergrads regard on-campus dining. Conway’s Game of Life has expanded this prairie dog’s view of the grassland more than expected.

I’ll drink a Coke to that.

Glossary: Conway’s GoL is a cellular automatonA cellular automaton consists of a board whose tiles change according to some update rule. Different cellular automata correspond to different board shapes, to boards of different dimensions, to different types of tiles, and to different update rules.

*Reversible cellular automata have greater probabilities (than the GoL has) of updating random initial states through dull-looking evolutions.

**Others have pondered quantum variations on Conway’s GoL.

# Quantum Information: Episode II: The Tools’ Applications

Monday dawns. Headlines report that “Star Wars: Episode VII” has earned more money, during its opening weekend, than I hope to earn in my lifetime. Trading the newspaper for my laptop, I learn that a friend has discovered ThinkGeek’s BB-8 plushie. “I want one!” she exclaims in a Facebook post. “Because BB-8 definitely needs to be hugged.”

BB-8 plays sidekick to Star Wars hero Poe Dameron. The droid has a spherical body covered with metallic panels and lights.Mr. Gadget and Frosty the Snowman could have spawned such offspring. BB-8 has captured viewers’ hearts, and its chirps have captured cell-phone ringtones.

ThinkGeek’s BB-8 plushie

Still, I scratch my head over my friend’s Facebook post. Hugged? Why would she hug…

Oh. Oops.

I’ve mentally verbalized “BB-8” as “BB84.” BB84 denotes an application of quantum theory to cryptography. Cryptographers safeguard information from eavesdroppers and tampering. I’ve been thinking that my friend wants to hug a safety protocol.

Charles Bennett and Gilles Brassard invented BB84 in 1984. Imagine wanting to tell someone a secret. Suppose I wish to coordinate, with a classmate, the purchase of a BB-8 plushie for our friend the droid-hugger. Suppose that the classmate and I can communicate only via a public channel on which the droid-hugger eavesdrops.

Cryptographers advise me to send my classmate a key. A key is a random string of letters, such as CCCAAACCABACA. I’ll encode my message with the string, with which my classmate will decode the message.

I have to transmit the key via the public channel. But the droid-hugger eavesdrops on the public channel. Haven’t we taken one step forward and one step back? Why would the key secure our information?

Because quantum-information science enables me to to transmit the key without the droid-hugger’s obtaining it. I won’t transmit random letters; I’ll transmit quantum states. That is, I’ll transmit physical systems, such as photons (particles of light), whose properties encode quantum information.

A nonquantum letter has a value, such as A or B or C.  Each letter has one and only one value, regardless of whether anyone knows what value the letter has. You can learn the value by measuring (looking at) the letter. We can’t necessarily associate such a value with a quantum state. Imagine my classmate measuring a state I send. Which value the measurement device outputs depends on chance and on how my classmate looks at the state.

If the droid-hugger intercepts and measures the state, she’ll change it. My classmate and I will notice such changes. We’ll scrap our key and repeat the BB84 protocol until the droid-hugger quits eavesdropping.

BB84 launched quantum cryptography, the safeguarding of information with quantum physics. Today’s quantum cryptographers rely on BB84 as you rely, when planning a holiday feast, on a carrot-cake recipe that passed your brother’s taste test on his birthday. Quantum cryptographers construct protocols dependent on lines like “The message sender and receiver are assumed to share a key distributed, e.g., via the BB84 protocol.”

BB84 has become a primitive task, a solved problem whose results we invoke in more-complicated problems. Other quantum-information primitives include (warning: jargon ahead) entanglement distillation, entanglement dilution, quantum data compression, and quantum-state merging. Quantum-information scientists solved many primitive problems during the 1990s and early 2000s. You can apply those primitives, even if you’ve forgotten how to prove them.

A primitive task, like quantum-entanglement distillation

Those primitives appear to darken quantum information’s horizons. The spring before I started my PhD, an older physicist asked me why I was specializing in quantum information theory. Haven’t all the problems been solved? he asked. Isn’t quantum information theory “dead”?

Imagine discovering how to power plasma blades with kyber crystals. Would you declare, “Problem solved” and relegate your blades to the attic? Or would you apply your tool to defending freedom?

Primitive quantum-information tools are unknotting problems throughout physics—in computer science; chemistry; optics (the study of light); thermodynamics (the study of work, heat, and efficiency); and string theory. My advisor has tracked how uses of “entanglement,” a quantum-information term, have swelled in high-energy-physics papers.

A colleague of that older physicist views quantum information theory as a toolkit, a perspective, a lens through which to view science. During the 1700s, the calculus invented by Isaac Newton and Gottfried Leibniz revolutionized physics. Emmy Noether (1882—1935) recast physics in terms of symmetries and conservation laws. (If the forces acting on a system don’t change in time, for example, the system doesn’t gain or lose energy. A constant force is invariant under, or symmetric with respect to, the progression of time. This symmetry implies that the system’s energy is conserved.) We can cast physics instead (jargon ahead) in terms of the minimization of a free energy or an action.

Quantum information theory, this physicist predicted, will revolutionize physics as calculus, symmetries, conservation, and free energy have. Quantum-information tools such as entropies, entanglement, and qubits will bleed into subfields of physics as Lucasfilm has bled into the fanfiction, LEGO, and Halloween-costume markets.

BB84, and the solution of other primitives, have not killed quantum information. They’ve empowered it to spread—thankfully, to this early-career quantum information scientist. Never mind BB-8; I’d rather hug BB84. Perhaps I shall. Engineers have realized technologies that debuted on Star Trek; quantum mechanics has secured key sharing; bakers have crafted cakes shaped like the Internet; and a droid’s popularity rivals R2D2’s. Maybe next Monday will bring a BB84 plushie.

The author hugging the BB84 paper and a plushie. On my wish list: a combination of the two.

# Discourse in Delft

A camel strolled past, yards from our window in the Applied-Sciences Building.

I hadn’t expected to see camels at TU Delft, aka the Delft University of Technology, in Holland. I breathed, “Oh!” and turned to watch until the camel followed its turbaned leader out of sight. Nelly Ng, the PhD student with whom I was talking, followed my gaze and laughed.

Nelly works in Stephanie Wehner’s research group. Stephanie—a quantum cryptographer, information theorist, thermodynamicist, and former Caltech postdoc—was kind enough to host me for half August. I arrived at the same time as TU Delft’s first-year undergrads. My visit coincided with their orientation. The orientation involved coffee hours, team-building exercises, and clogging the cafeteria whenever the Wehner group wanted lunch.

And, as far as I could tell, a camel.

Not even a camel could unseat Nelly’s and my conversation. Nelly, postdoc Mischa Woods, and Stephanie are the Wehner-group members who study quantum and small-scale thermodynamics. I study quantum and small-scale thermodynamics, as Quantum Frontiers stalwarts might have tired of hearing. The four of us exchanged perspectives on our field.

Mischa knew more than Nelly and I about clocks; Nelly knew more about catalysis; and I knew more about fluctuation relations. We’d read different papers. We’d proved different theorems. We explained the same phenomena differently. Nelly and I—with Mischa and Stephanie, when they could join us—questioned and answered each other almost perpetually, those two weeks.

We talked in our offices, over lunch, in the group discussion room, and over tea at TU Delft’s Quantum Café. We emailed. We talked while walking. We talked while waiting for Stephanie to arrive so that she could talk with us.

The site of many a tête-à-tête.

The copiousness of the conversation drained me. I’m an introvert, formerly “the quiet kid” in elementary school. Early some mornings in Delft, I barricaded myself in the visitors’ office. Late some nights, I retreated to my hotel room or to a canal bank. I’d exhausted my supply of communication; I had no more words for anyone. Which troubled me, because I had to finish a paper. But I regret not one discussion, for three reasons.

First, we relished our chats. We laughed together, poked fun at ourselves, commiserated about calculations, and confided about what we didn’t understand.

We helped each other understand, second. As I listened to Mischa or as I revised notes about a meeting, a camel would stroll past a window in my understanding. I’d see what I hadn’t seen before. Mischa might be explaining which quantum states represent high-quality clocks. Nelly might be explaining how a quantum state ξ can enable a state ρ to transform into a state σ. I’d breathe, “Oh!” and watch the mental camel follow my interlocutor through my comprehension.

Nelly’s, Mischa’s, and Stephanie’s names appear in the acknowledgements of the paper I’d worried about finishing. The paper benefited from their explanations and feedback.

Third, I left Delft with more friends than I’d had upon arriving. Nelly, Mischa, and I grew to know each other, to trust each other, to enjoy each other’s company. At the end of my first week, Nelly invited Mischa and me to her apartment for dinner. She provided pasta; I brought apples; and Mischa brought a sweet granola-and-seed mixture. We tasted and enjoyed more than we would have separately.

Dinner with Nelly and Mischa.

I’ve written about how Facebook has enhanced my understanding of, and participation in, science. Research involves communication. Communication can challenge us, especially many of us drawn to science. Let’s shoulder past the barrier. Interlocutors point out camels—and hot-air balloons, and lemmas and theorems, and other sources of information and delight—that I wouldn’t spot alone.

With gratitude to Stephanie, Nelly, Mischa, the rest of the Wehner group (with whom I enjoyed talking), QuTech and TU Delft.

During my visit, Stephanie and Delft colleagues unveiled the “first loophole-free Bell test.” Their paper sent shockwaves (AKA camels) throughout the quantum community. Scott Aaronson explains the experiment here.

# BTZ black holes for #BlackHoleFriday

Yesterday was a special day. And no I’m not referring to #BlackFriday — but rather to #BlackHoleFriday. I just learned that NASA spawned this social media campaign three years ago. The timing of this year’s Black Hole Friday is particularly special because we are exactly 100 years + 2 days after Einstein published his field equations of general relativity (GR). When Einstein introduced his equations he only had an exact solution describing “flat space.” These equations are notoriously difficult to solve so their introduction sent out a call-to-arms to mathematically-minded-physicists and physically-minded-mathematicians who scrambled to find new solutions.

If I had to guess, Karl Schwarzschild probably wasn’t sleeping much exactly a century ago. Not only was he deployed to the Russian Front as a solider in the German Army, but a little more than one month after Einstein introduced his equations, Schwarzschild was the first to find another solution. His solution describes the curvature of spacetime outside of a spherically symmetric mass. It has the incredible property that if the spherical mass is compact enough then spacetime will be so strongly curved that nothing will be able to escape (at least from the perspective of GR; we believe that there are corrections to this when you add quantum mechanics to the mix.) Schwarzchild’s solution took black holes from the realm of clever thought experiments to the status of being a testable prediction about how Nature behaves.

It’s worth mentioning that between 1916-1918 Reissner and Nordstrom generalized Schwarzschild’s solution to one which also has electric charge. Kerr found a solution in 1963 which describes a spinning black hole and this was generalized by Newman et al in 1965 to a solution which includes both spin (angular momentum) and electric charge. These solutions are symmetric about their spin axis. It’s worth mentioning that we can also write sensible equations which describe small perturbations around these solutions.

And that’s pretty much all that we’ve got in terms of exact solutions which are physically relevant to the 3+1 dimensional spacetime that we live in (it takes three spatial coordinates to specify a meeting location and another +1 to specify the time.) This is the setting that’s closest to our everyday experiences and these solutions are the jumping off points for trying to understand the role that black holes play in astrophysics. As I already mentioned, studying GR using pen and paper is quite challenging. But one exciting direction in the study of astrophysical black holes comes from recent progresses in the field of numerical relativity; which discretizes the calculations and then uses supercomputers to study approximate time dynamics.

Artist’s rendition of dust+gas in an “accretion disk” orbiting a spinning black hole. Friction in the accretion disk generates temperatures oftentimes exceeding 10M degrees C (2000 times the temperature of the Sun.) This high temperature region emits x-rays and other detectable EM radiation. The image also shows a jet of plasma. The mechanism for this plasma jet is not yet well understood. Studying processes like this requires all of tools that we have available to us: from numerical relativity; to cutting edge space observatories like NuSTAR; to LIGO in the immediate future *hopefully.* Image credit: NASA/Caltech-JPL

I don’t expect many of you to be experts in the history outlined above. And I expect even fewer of you to know that Einstein’s equations still make sense in any number of dimensions. In this context, I want to briefly introduce a 2+1 dimensional solution called the BTZ black hole and outline why it has been astonishingly important since it was introduced 23 years ago by Bañados, Teteilboim and Zanelli (their paper has been cited over 2k times which is a tremendous number for theoretical physics.)

There are many different viewpoints which yield the BTZ black hole and this is one of them. This is a  time=0 slice of the BTZ black hole obtained by gluing together special curves (geodesics) related to each other by a translation symmetry. The BTZ black hole is a solution of Einstein’s equations in 2+1d which has two asymptotic regions which are causally separated from each other by an event horizon. The arrows leading to “quantum states” come into play when you use the BTZ black hole as a toy model for thinking about quantum gravity.

One of the most striking implications of Einstein’s theory of general relativity is that our universe is described by a curved geometry which we call spacetime. Einstein’s equations describe the dynamical interplay between the curvature of spacetime and the distribution of energy+matter. This may be counterintuitive, but there are many solutions even when there is no matter or energy in the spacetime. We call these vacuum solutions. Vacuum solutions can have positive, negative or zero “curvature.

As 2d surfaces: the sphere is positively curved; a saddle has negative curvature; and a plane has zero curvature.

It came as a great surprise when BTZ showed in 1992 that there is a vacuum solution in 2+1d which has many of the same properties as the more physical 3+1d black holes mentioned above. But most excitingly — and something that I can’t imagine BTZ could have anticipated — is that their solution has become the toy model of all toy models for trying to understand “quantum gravity.

GR in 2+1d has many convenient properties. Two beautiful things that happen in 2+1d are that:

• There are no gravitational waves. Technically, this is because the Riemann tensor is fully determined by the Ricci tensor — the number of degrees of freedom in this system is exactly equal to the number of constraints given by Einstein’s equations. This makes GR in 2+1d something called a “topological field theory” which is much easier to quantize than its full blown gauge theory cousin in 3+1d.
• The maximally symmetric vacuum solution with negative curvature, which we call Anti de-Sitter space, has a beautiful symmetry. This manifold is exactly equal to the “group manifold” SL(2,R). This enables us to translate many challenging analytical questions into simple algebraic computations. In particular, it enables us to find a huge category of solutions which we call multiboundary wormholes, with BTZ being the most famous example.

Some “multiboundary wormhole” pictures that I made. The left shows the constant time=0 slice for a few different solutions and what you are left with after gluing according to the equations on the right. These are solutions to GR in 2+1d.

These properties make 2+1d GR particularly useful as a sandbox for making progress towards a theory of quantum gravity. As examples of what this might entail:

• Classically, a particle is in one definite location. In quantum mechanics, a particle can be in a superposition of places. In quantum gravity, can spacetime be in a superposition of geometries? How does this work?
• When you go from classical physics to quantum physics, tunneling becomes a thing. Can the same thing happen with quantum gravity? Where we tunnel from one spacetime geometry to another? What controls the transition amplitudes?
• The holographic principle is an incredibly important idea in modern theoretical physics. It stems from the fact that the entropy of a black hole is proportional to the area of its event horizon — whereas the entropy of a glass of water is proportional to the volume of water inside the glass. We believe that this reduction in dimensionality is wildly significant.

A few years after the holographic principle was introduced in the early 1990’s, by Gerard ‘t Hooft and Lenny Susskind, Juan Maldacena came up with a concrete manifestation which is now called the AdS/CFT correspondence. Maldacena’s paper has been cited over 14k times making it one of the most cited theoretical physics papers of all time. However, despite having a “correspondence” it’s still very hard to translate questions back and forth between the “gravity and quantum sides” in practice. The BTZ black hole is the gravity solution where this correspondence is best understood. Its quantum dual is a state called the thermofield double, which is given by: $|\Psi_{CFT}\rangle = \frac{1}{\sqrt{Z}} \sum_{n=1}^{\infty} e^{-\beta E_n/2} |n\rangle_1 \otimes |n \rangle_2$. This describes a quantum state which lives on two circles (see my BTZ picture above.) There is entanglement between the two circles. If an experimentalist only had access to one of the circles and if they were asked to try to figure out what state they have, their best guess would be a “thermal state.” A state that has been exposed to a heat-bath for too long and has lost all of its initial quantum coherence.

It is in this sense that the BTZ black hole has been hugely important. It’s also evidence of how mysterious Einstein’s equations still remain, even to this day. We still don’t have exact solutions for many settings of interest, like for two black holes merging in 3+1d. It was only in 1992 that BTZ came up with their solution–77 years after Einstein formulated his theory! Judging by historical precedence, exactly solvable toy models are profoundly useful and BTZ has already proven to be an important signpost as we continue on our quest to understand quantum gravity. There’s already broad awareness that astrophysical black holes are fascinating objects. In this post I hope I conveyed a bit of the excitement surrounding how black holes are useful in a different setting — in aiding our understanding of quantum gravity. And all of this is in the spirit of #BlackHoleFriday, of course.