# Explaining Quantum Physics to Newton… in 140 characters

Sir Isaac Newton is considered by many as the greatest physicist of all time. But despite Newton’s contributions to classical physics, the man never even fathomed that the world was actually governed by the equations of quantum mechanics. We think it is time to right that wrong. With your help, we plan to send a Tweet back in time (something about time machines restricts quantum telegraphs to 140 characters) that explains what quantum is all about to Sir Isaac. This mini competition is taking place on our Twitter account over @IQIM_Caltech and ends on November 5th, 2015. The prize is a one-year digital subscription to Scientific American.

For more details, please see below. This mini competition is part of Quantum Shorts, a flash fiction competition conceived and executed by our friends at the Center for Quantum Technologies.

Let the games begin!

# Nothing has been done yet. The world is your oyster…still.

The three things that come to mind when I watch Simon’s video are: travel, perspective and discomfort. They remind me of some of the things I also said in my TEDx talk titled “Get Uncomfortable Now”.

Simon’s video exemplifies a lot of what I feel is true in filmmaking as well. He goes running to clear his mind and get more creative, I take long walks when I’m stuck at a point in my screenplays or edits. He travels to learn more about what’s out there, I travel to absorb culture as well, he tries diversity of experiences to enrich his mind, so do I in a selfish desire to enrich every character I write or direct; all with the ultimate goal of growth & transience: emotional, physical, mental.

Simon also says something very exciting in the film, “there’s so much left to do out there”, a thought that isn’t expressed that often, the idea that “I can do something novel right here in the lab” makes the chance of innovation, success and achievement very tangible; achievable. That honesty, excitement and drive is important to be repeated in an otherwise very jaded and intimidated world. The belief in the power of the individual driving forward and having the potential to change the status quo, in the lab and outside, is critical.

It was hard to get Simon to narrow it down to the one hobby that drove him. After Debaleena’s video being internal and about family, we knew we wanted something more external. Filming in Griffith park is usually a nightmare but that early morning, we got everything we wanted minus possibly a clearer view of downtown LA, thanks to Marcia Brown’s usual detailed planning.

The shoot was complete with a steadicam operator, running videos and even the spotting of a snake!

The most memorable thing for me are Simon’s slow motion shots that highlight the sound of foot steps, of pushing forward, step by step, one ahead of the other; that basic contact that lunges us into the future. There was something very “grounding” about watching that, no pun intended.

Without further ado, here’s the video:

# “Experimenting” with women-in-STEM stereotypes

When signing up for physics grad school, I didn’t expect to be interviewed by a comedienne on a spoof science show about women in STEM.

Last May, I received an email entitled “Amy Poehler’s Smart Girls.” The actress, I read, had co-founded the Smart Girls organization to promote confidence and creativity in preteens and teens. Smart Girls was creating a webseries hosted by Megan Amram, author of Science…for Her! The book parodies women’s magazines and ridicules stereotypes of women as unsuited for science.

Megan would host the webseries, “Experimenting with Megan,” in character as an airhead. She planned to interview “kick-ass lady scientists/professors/doctors” in a parody of a talk show. Would I, the email asked, participate?

I’m such a straitlaced fogey, I never say “kick-ass.” I’m such a workaholic, I don’t watch webshows. I’ve not seen Parks and Recreation, the TV series that starred Amy Poehler and for which Megan wrote. The Hollywood bug hasn’t bitten me, though I live 30 minutes from Studio City.

But I found myself in a studio the next month. Young men and women typed on laptops and chattered in the airy, bright waiting lounge. Beyond a doorway lay the set, enclosed by fabric-covered walls that prevented sounds from echoing. Script-filled binders passed from hand to hand, while makeup artists, cameramen, and gophers scurried about.

Being interviewed on “Experimenting with Megan.”

Disney’s Mouseketeers couldn’t have exuded more enthusiasm or friendliness than the “Experimenting” team. “Can I bring you a bottle of water?” team members kept asking me and each other. “Would you like a chair?” The other women who interviewed that day—two biologist postdocs—welcomed me into their powwow. Each of us, we learned, is outnumbered by men at work. None of us wears a lab coat, despite stereotypes of scientists as white-coated. Each pours herself into her work: One postdoc was editing a grant proposal while off-set.

I watched one interview, in which Megan asked why biologists study fruit flies instead of “cuter” test subjects. Then I stepped on-set beside her. I perched on an armchair that threatened to swallow my 5’ 3.5” self.* Textbooks, chemistry flasks, and high-heeled pumps stood on the bookshelves behind Megan.

The room quieted. A clapperboard clapped: “Take one.” Megan thanked me for coming, then launched into questions.

Megan hadn’t warned me what she’d ask. We began with “Do you like me?” and “What is the ‘information’ [in ‘quantum information theory’], and do you ever say, ‘Too much information’?” Each question rode hot on the heels of the last. The barrage reminded me of interviews for not-necessarily-scientific scholarships. Advice offered by one scholarship-committee member, the year before I came to Caltech, came to mind: Let loose. Act like an athlete tearing down the field, the opposing team’s colors at the edges of your vision. Savor the challenge.

I savored it. I’d received instructions to play the straight man, answering Megan’s absurdity with science. To “Too much information?” I parried that we can never know enough. When I mentioned that quantum mechanics describes electrons, Megan asked about the electricity she feels upon seeing Chris Hemsworth. (I hadn’t heard of Chris Hemsworth. After watching the interview online, a friend reported that she’d enjoyed the reference to Thor. “What reference to Thor?” I asked. Hemsworth, she informed me, plays the title character.) I dodged Chris Hemsworth; caught “electricity”; and stretched to superconductors, quantum devices whose charges can flow forever.

Academic seminars conclude with question-and-answer sessions. If only those Q&As zinged with as much freshness and flexibility as Megan’s.

The “Experimenting” approach to stereotype-blasting diverges from mine. High-heeled pumps, I mentioned, decorated the set. The “Experimenting” team was parodying the stereotype of women as shoe-crazed. “Look at this stereotype!” the set shouts. “Isn’t it ridiculous?”

As a woman who detests high heels and shoe shopping, I prefer to starve the stereotype of justification. I’ve preferred reading to shopping since before middle school, when classmates began frequenting malls. I feel more comfortable demonstrating, through silence, how little shoes interest me. I’d rather offer no reason for anyone to associate me with shoes.**

I scarcely believe that I appear just after a “sexy science” tagline and a hot-or-not quiz. Before my interview on her quantum episode, Megan discussed the relationship between atoms and Adams. Three guests helped her, three Hollywood personalities named “Adam.”*** Megan held up cartoons of atoms, and photos of Adams, and asked her guests to rate their hotness. I couldn’t have played Megan’s role, couldn’t imagine myself in her (high-heeled) shoes.

But I respect the “Experimenting” style. Megan’s character serves as a foil for the interviewee I watched. Megan’s ridiculousness underscored the postdoc’s professionalism and expertise.

According to online enthusiasm, “Experimenting” humor resonates with many viewers. So diverse is the community that needs introducing to STEM, diverse senses of humor have roles to play. So deep run STEM’s social challenges, multiple angles need attacking.

Just as diverse perspectives can benefit women-in-STEM efforts, so can diverse perspectives benefit STEM. Which is why STEM needs women, Adams, shoe-lovers, shoe-haters…and experimentation.

With gratitude to the “Experimenting” team for the opportunity to contribute to its cause. The live-action interview appears here (beginning at 2:42), and a follow-up personality quiz appears here.

*If you’re 5′ 3.5″, every half-inch matters.

**Except when I blog about how little I wish to associate with shoes.

***Megan introduced her guests as “Adam Shankman, Adam Pally, and an intern that we made legally change his name to Adam to be on the show.” The “intern” is Adam Rymer, president of Legendary Digital Networks. Legendary owns Amy Poehler’s Smart Girls.

# The enigma of Robert Hooke

In 1675, Robert Hooke published the “true mathematical and mechanical form” for the shape of an ideal arch.  However, Hooke wrote the theory as an anagram,

Its solution was never published in his lifetime.  What was the secret hiding in these series of letters?

An excerpt from Hooke’s manuscript “A description of helioscopes, and some other instruments”.

The arch is one of the fundamental building blocks in architecture.  Used in bridges, cathedrals, doorways, etc., arches provide an aesthetic quality to the structures they dwell within.  Their key utility comes from their ability to support weight above an empty space, by distributing the load onto the abutments at its feet.  A dome functions much like an arch, except a dome takes on a three-dimensional shape whereas an arch is two-dimensional.  Paradoxically, while being the backbone of the many edifices, arches and domes themselves are extremely delicate: a single misplaced component along its curve, or an improper shape in the design would spell doom for the entire structure.

The Romans employed the rounded arch/dome—in the shape of a semicircle/hemisphere–in their bridges and pantheons.  The Gothic architecture favored the pointed arch and the ribbed vault in their designs.  However, neither of these arch forms were adequate for the progressively grander structures and more ambitious cathedrals sought in the 17th century.  Following the great fire of London in 1666, a massive rebuilding effort was under way.  Among the new public buildings, the most prominent was to be St. Paul’s Cathedral with its signature dome.  A modern theory of arches was sorely needed: what is the perfect shape for an arch/dome?

Christopher Wren, the chief architect of St. Paul’s Cathedral, consulted Hooke on the dome’s design.  To quote from the cathedral’s website [1]:

The two half-sections [of the dome] in the study employ a formula devised by Robert Hooke in about 1671 for calculating the curve of a parabolic dome and reducing its thickness.  Hooke had explored this curve the three-dimensional equivalent of the ‘hanging chain’, or catenary arch: the shape of a weighted chain which, when inverted, produces the ideal profile for a self-supporting arch.  He thought that such a curve derived from the equation y = x3.

A figure from Wren’s design of St. Paul’s Cathedral. (Courtesy of the British Museum)

How did Hooke came about the shape for the dome?  It wasn’t until after Hooke’s death his executor provided the unencrypted solution to the anagram [2]

Ut pendet continuum flexile, sic stabit contiguum rigidum inversum

which translates to

As hangs a flexible cable so, inverted, stand the touching pieces of an arch.

In other words, the ideal shape of an arch is exactly that of a freely hanging rope, only upside down.  Hooke understood that the building materials could withstand only compression forces and not tensile forces, in direct contrast to a rope that could resist tension but would buckle under compression.  The mathematics describing the arch and the cable are in fact identical, save for a minus sign.  Consequently, you could perform a real-time simulation of an arch using a piece of string!

Bonus:  Robert published the anagram in his book describing helioscopes, simply to “fill up the vacancy of the ensuring page” [3].  On that very page among other claims, Hooke also wrote the anagram “ceiiinosssttuu” in regards to “the true theory of elasticity”.  Can you solve this riddle?

[1] https://www.stpauls.co.uk/history-collections/the-collections/architectural-archive/wren-office-drawings/5-designs-for-the-dome-c16871708
[2] Written in Latin, the ‘u’ and ‘v’ are the same letter.
[3] In truth, Hooke was likely trying to avoid being scooped by his contemporaries, notably Issac Newton.

This article was inspired by my visit to the Huntington Library.  I would like to thank Catherine Wehrey for the illustrations and help with the research.

# Beware global search and replace!

I’m old enough to remember when cutting and pasting were really done with scissors and glue (or Scotch tape). When I was a graduate student in the late 1970s, few physicists typed their own papers, and if they did they left gaps in the text, to be filled in later with handwritten equations. The gold standard of technical typing was the IBM Correcting Selectric II typewriter. Among its innovations was the correction ribbon, which allowed one to remove a typo with the touch of a key. But it was especially important for scientists that the Selectric could type mathematical characters, including Greek letters.

IBM Selectric typeballs

It wasn’t easy. Many different typeballs were available, to support various fonts and special characters. Typing a displayed equation or in-line equation usually involved swapping back and forth between typeballs to access all the needed symbols. Most physics research groups had staff who knew how to use the IBM Selectric and spent much of their time typing manuscripts.

Though the IBM Selectric was used by many groups, typewriters have unique personalities, as forensic scientists know. I had a friend who claimed he had learned to recognize telltale differences among documents produced by various IBM Selectric machines. That way, whenever he received a referee report, he could identify its place of origin.

Manuscripts did not evolve through 23 typeset versions in those days, as one of my recent papers did. Editing was arduous and frustrating, particularly for a lowly graduate student like me, who needed to beg Blanche to set aside what she was doing for Steve Weinberg and devote a moment or two to working on my paper.

It was tremendously liberating when I learned to use TeX in 1990 and started typing my own papers. (Not LaTeX in those days, but Plain TeX embellished by a macro for formatting.) That was a technological advance that definitely improved my productivity. An earlier generation had felt the same way about the Xerox machine.

But as I was reminded a few days ago, while technological advances can be empowering, they can also be dangerous when used recklessly. I was editing a very long document, and decided to make a change. I had repeatedly used $x$ to denote an n-bit string, and thought it better to use $\vec x$ instead. I was walking through the paper with the replace button, changing each $x$ to $\vec x$ where the change seemed warranted. But I slipped once, and hit the “Replace All” button instead of “Replace.” My computer curtly informed me that it had made the replacement 1011 times. Oops …

This was a revocable error. There must have been a way to undo it (though it was not immediately obvious how). Or I could have closed the file without saving, losing some recent edits but limiting the damage.

But it was late at night and I was tired. I panicked, immediately saving and LaTeXing the file. It was a mess.

Okay, no problem, all I had to do was replace every \vec x with x and everything would be fine. Except that in the original replacement I had neglected to specify “Match Case.” In 264 places $X$ had become $\vec x$, and the new replacement did not restore the capitalization. It took hours to restore every $X$ by hand, and there are probably a few more that I haven’t noticed yet.

Which brings me to the cautionary tale of one of my former graduate students, Robert Navin. Rob’s thesis had two main topics, scattering off vortices and scattering off monopoles. On the night before the thesis due date, Rob made a horrifying discovery. The crux of his analysis of scattering off vortices concerned the singularity structure of a certain analytic function, and the chapter about vortices made many references to the poles of this function. What Rob realized at this late stage is that these singularities are actually branch points, not poles!

What to do? It’s late and you’re tired and your thesis is due in a few hours. Aha! Global search and replace! Rob replaced every occurrence of “pole” in his thesis by “branch point.” Problem solved.

Except … Rob had momentarily forgotten about that chapter on monopoles. Which, when I read the thesis, had been transformed into a chapter on monobranch points. His committee accepted the thesis, but requested some changes …

Rob Navin no longer does physics, but has been very successful in finance. I’m sure he’s more careful now.

# Bits, bears, and beyond in Banff

Another conference about entropy. Another graveyard.

Last year, I blogged about the University of Cambridge cemetery visited by participants in the conference “Eddington and Wheeler: Information and Interaction.” We’d lectured each other about entropy–a quantification of decay, of the march of time. Then we marched to an overgrown graveyard, where scientists who’d lectured about entropy decades earlier were decaying.

This July, I attended the conference “Beyond i.i.d. in information theory.” The acronym “i.i.d.” stands for “independent and identically distributed,” which requires its own explanation. The conference took place at BIRS, the Banff International Research Station, in Canada. Locals pronounce “BIRS” as “burrs,” the spiky plant bits that stick to your socks when you hike. (I had thought that one pronounces “BIRS” as “beers,” over which participants in quantum conferences debate about the Measurement Problem.) Conversations at “Beyond i.i.d.” dinner tables ranged from mathematical identities to the hiking for which most tourists visit Banff to the bears we’d been advised to avoid while hiking. So let me explain the meaning of “i.i.d.” in terms of bear attacks.

The BIRS conference center. Beyond here, there be bears.

Suppose that, every day, exactly one bear attacks you as you hike in Banff. Every day, you have a probability p1 of facing down a black bear, a probability p2 of facing down a grizzly, and so on. These probabilities form a distribution {pi} over the set of possible events (of possible attacks). We call the type of attack that occurs on a given day a random variable. The distribution associated with each day equals the distribution associated with each other day. Hence the variables are identically distributed. The Monday distribution doesn’t affect the Tuesday distribution and so on, so the distributions are independent.

Information theorists quantify efficiencies with which i.i.d. tasks can be performed. Suppose that your mother expresses concern about your hiking. She asks you to report which bear harassed you on which day. You compress your report into the fewest possible bits, or units of information. Consider the limit as the number of days approaches infinity, called the asymptotic limit. The number of bits required per day approaches a function, called the Shannon entropy HS, of the distribution:

Number of bits required per day → HS({pi}).

The Shannon entropy describes many asymptotic properties of i.i.d. variables. Similarly, the von Neumann entropy HvN describes many asymptotic properties of i.i.d. quantum states.

But you don’t hike for infinitely many days. The rate of black-bear attacks ebbs and flows. If you stumbled into grizzly land on Friday, you’ll probably avoid it, and have a lower grizzly-attack probability, on Saturday. Into how few bits can you compress a set of nonasymptotic, non-i.i.d. variables?

We answer such questions in terms of ɛ-smooth α-Rényi entropies, the sandwiched Rényi relative entropy, the hypothesis-testing entropy, and related beasts. These beasts form a zoo diagrammed by conference participant Philippe Faist. I wish I had his diagram on a placemat.

“Beyond i.i.d.” participants define these entropies, generalize the entropies, probe the entropies’ properties, and apply the entropies to physics. Want to quantify the efficiency with which you can perform an information-processing task or a thermodynamic task? An entropy might hold the key.

Many highlights distinguished the conference; I’ll mention a handful.  If the jargon upsets your stomach, skip three paragraphs to Thermodynamic Thursday.

Aram Harrow introduced a resource theory that resembles entanglement theory but whose agents pay to communicate classically. Why, I interrupted him, define such a theory? The backstory involves a wager against quantum-information pioneer Charlie Bennett (more precisely, against an opinion of Bennett’s). For details, and for a quantum version of The Princess and the Pea, watch Aram’s talk.

Graeme Smith and colleagues “remove[d] the . . . creativity” from proofs that certain entropic quantities satisfy subadditivity. Subadditivity is a property that facilitates proofs and that offers physical insights into applications. Graeme & co. designed an algorithm for checking whether entropic quantity Q satisfies subadditivity. Just add water; no innovation required. How appropriate, conference co-organizer Mark Wilde observed. BIRS has the slogan “Inspiring creativity.”

Patrick Hayden applied one-shot entropies to AdS/CFT and emergent spacetime, enthused about elsewhere on this blog. Debbie Leung discussed approximations to Haar-random unitaries. Gilad Gour compared resource theories.

Conference participants graciously tolerated my talk about thermodynamic resource theories. I closed my eyes to symbolize the ignorance quantified by entropy. Not really; the photo didn’t turn out as well as hoped, despite the photographer’s goodwill. But I could have closed my eyes to symbolize entropic ignorance.

Thermodynamics and resource theories dominated Thursday. Thermodynamics is the physics of heat, work, entropy, and stasis. Resource theories are simple models for transformations, like from a charged battery and a Tesla car at the bottom of a hill to an empty battery and a Tesla atop a hill.

My advisor’s Tesla. No wonder I study thermodynamic resource theories.

Philippe Faist, diagrammer of the Entropy Zoo, compared two models for thermodynamic operations. I introduced a generalization of resource theories for thermodynamics. Last year, Joe Renes of ETH and I broadened thermo resource theories to model exchanges of not only heat, but also particles, angular momentum, and other quantities. We calculated work in terms of the hypothesis-testing entropy. Though our generalization won’t surprise Quantum Frontiers diehards, the magic tricks in my presentation might.

At twilight on Thermodynamic Thursday, I meandered down the mountain from the conference center. Entropies hummed in my mind like the mosquitoes I slapped from my calves. Rising from scratching a bite, I confronted the Banff Cemetery. Half-wild greenery framed the headstones that bordered the gravel path I was following. Thermodynamicists have associated entropy with the passage of time, with deterioration, with a fate we can’t escape. I seem unable to escape from brushing past cemeteries at entropy conferences.

Not that I mind, I thought while scratching the bite in Pasadena. At least I escaped attacks by Banff’s bears.

With thanks to the conference organizers and to BIRS for the opportunity to participate in “Beyond i.i.d. 2015.”

# The mentors that shape us

I was in awe of Wheeler. Some students thought he sucked.

I immediately changed it to…

I was in awe of Wheeler. Some students thought less of him.

And next, when I saw John write about himself,

Though I’m 59, few students seemed awed. Some thought I sucked. Maybe I did sometimes.

I massaged it into…

Though I’m 59, few students seemed awed. Some thought I was not as good. Maybe I wasn’t sometimes.

When John published the post, I read it again for any typos I might have missed. There were no typos. I felt useful! But when I saw that all mentions of sucked had been restored to their rightful place, I felt like an idiot. John did not fire a strongly-worded email back my way asking for an explanation as to my taking liberties with his own writing. He simply trusted that I would get the message in the comfort of my own awkwardness. It worked beautifully. John had set the tone for Quantum Frontier’s authentic voice with his very first post. It was to be personal, even if the subject matter was as scientifically hardcore as it got.

So when the time came for me to write my first post, I made it personal. I wrote about my time in Los Alamos as a postdoc, working on a problem in mathematical physics that almost broke me. It was Matt Hastings, an intellectual tornado, that helped me through these hard times. As my mentor, he didn’t say things like Well done! Great progress! Good job, Spiro! He said, You can do this. And when I finally did it, when I finally solved that damn problem, Matt came back to me and said: Beyond some typos, I cannot find any mistakes. Good job, Spiro. And it meant the world to me. The sleepless nights, the lonely days up in the Pajarito mountains of New Mexico, the times I had resolved to go work for my younger brother as a waiter in his first restaurant… those were the times that I had come upon a fork on the road and my mentor had helped me choose the path less traveled.

When the time came for me to write my next post, I ended by offering two problems for the readers to solve, with the following text as motivation:

This post is supposed to be an introduction to the insanely beautiful world of problem solving. It is not a world ruled by Kings and Queens. It is a world where commoners like you and me can become masters of their domain and even build an empire.

Doi-Inthananon temple in Chiang Mai, Thailand. A breathtaking city, host of this year’s international math olympiad.

It has been way too long since my last “problem solving” post, so I leave you with a problem from this year’s International Math Olympiad, which took place in gorgeous Chiang Mai, Thailand. FiverThirtyEight‘s recent article about the dominance of the US math olympic team in this year’s competition, gives some context about the degree of difficulty of this problem:

Determine all triples (a, b, c) of positive integers such that each of the numbers: ab-c, bc-a, ca-b is a power of two.

Like Fermat’s Last Theorem, this problem is easy to describe and hard to solve. Only 5 percent of the competitors got full marks on this question, and nearly half (44 percent) got no points at all.

But, on the triumphant U.S. squad, four of the six team members nailed it.

In other words, only 1 in 20 kids in the competition solved this problem correctly and about half of the kids didn’t even know where to begin. For more perspective, each national team is comprised of the top 6 math prodigies in that country. In China, that means 6 out of something like 100 million kids. And only 3-4 of these kids solved the problem.

The coach of the US national team, Po-Shen Loh, a Caltech alum and an associate professor of mathematics at Carnegie Mellon University (give him tenure already) deserves some serious props. If you think this problem is too hard, I have this to say to you: Yes, it is. But, who cares? You can do this.

Note: I will work out the solution in detail in an upcoming post, unless one of you solves it in the comments section before then!

Update: Solution posted in comments below (in response to Anthony’s comment). Thank you all who posted some of the answers below. The solution is far from trivial, but I still wonder if an elegant solution exists that gives all four triples. Maybe the best solution is geometric? I hope one of you geniuses can figure that out!