What Does Any of This Have to Do With Physics?

 

30,000 mathematicians solving inconsequential questions.   That can be frustrating and hard to understand for an outsider.  Yet the search for knowledge is always thus.  This item share the struggle itself to the readerr along with some of the triumphs.

 

One true insight. Your knowledge of a given body of work may well have a screw loose.  I have experienced just that and setting that screw makes it all good forever.

 

Teachers do not know how to winkle out those problems..

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What Does Any of This Have to Do With Physics?

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Einstein and Feynman ushered me into grad school, reality ushered me out.

Bob Henderson

https://getpocket.com/explore/item/what-does-any-of-this-have-to-do-with-physics

“Have you ever been happy?”

My girlfriend asked me that question, after work over drinks at some shiny Manhattan bar, after another stressful day on the trading floor.


How to answer that? I knew she was talking about work, but how unhappy did she think I was? I took a sip of single malt scotch and scrolled back through time in my mind until I had it.


It was the spring of ’93, 16 years earlier, at the University of Rochester, where I went to graduate school for physics. An afternoon that I can play back like a home movie. It’s a bright sunny day in the wake of one of Rochester, New York’s typically brutal winters. The sky is blue, the clouds are cotton balls, and sunlight shimmers off the deep green leaves of the grass, bushes, and oak trees of campus, all freshly nourished by the recently melted snow. Undergraduates are out in shorts on the quad, some gathered on steps, others tossing Frisbees, all surrounded by ivy-covered halls of red brick and gray stone, including Bausch and Lomb Hall, home of the physics department. I’m in the dining room of the university’s Faculty Club, where the daylight is smothered by heavy velvet drapes. Maroon, I think, bordered by sunlight. Chandeliers sparkle above. There are seven or eight people sitting around the table, which is set with a white cloth and place settings decked out with multiple forks. A bottle of wine is making the rounds. The meal feels like what it is: a celebration. 

 





Bausch and Lomb Hall. Photo courtesy of the author.


It was the end of my second year of graduate school and I had what I’m sure was a very goofy grin on my face as I listened to the little pecan-colored man with the remarkably round head to my right. He wore wire-framed glasses and was smiling too. Actually Sarada Rajeev was always smiling, although his smile had several variations. There was the default smile he had on now, a smile of surprise that lifted his glasses in synchrony with his eyebrows, and a smile of discomfort where his eyes gave his true feelings away. But my favorite of all was the subversive smile he’d get after one of his own mischievous jokes, the one where his eyes would light up and meet yours until you were smiling too. Rajeev was an assistant professor of physics in his early 30s, just five years older than me. He had a soft voice, a quick wit, and a way of sauntering the department’s hallways—chin up and smiling—that prompted one of my classmates to admiringly comment on how “prosperous” he looked. Rajeev had arranged the lunch, having gathered all of his students and postdocs to welcome me into his group.


I’d met him for the first time a year earlier, after finding a slip of paper in my Bausch and Lomb mail cubby and on it a handwritten note:


“Mr. Henderson. If you’d like to discuss research in high-energy theory, please come by my office. – S.G. Rajeev.”


I was thrilled, even though I knew little about Rajeev. There were 15 of us in my class at Rochester and I was the only one who still hadn’t found a research advisor to take me on as an apprentice once classes were over. That was because I was the only one holding out for high-energy theory, aka theoretical particle physics—Rajeev’s specialty. High-energy theory is also sometimes called “fundamental physics” because it concerns the fundamental laws of nature that govern the way elementary particles, like electrons and quarks, act and interact, and therefore how everything made of those particles (which meant, as far as I knew, everything) behaves, too. I’d quit a good job as an electrical engineer in Southern California and come to Rochester with a dream of studying fundamental physics and pursuing its Holy Grail: a theory of quantum gravity that would reconcile quantum mechanics with Einstein’s general theory of relativity and therefore, as I understood things at the time, amount to a Theory of Everything.


Like Don Quixote, I was propelled on my quest by books, New Agey ones like The Tao of Physics and Zen and the Art of Motorcycle Maintenance, and biographies of physics greats like Einstein and Feynman, books that gave me the very welcome news that there were still frontiers to explore, even in the late 20th century, even for a bookish sort like me. Basically I was a naïve and dreamy kid who hadn’t yet hit any intellectual limits. My dad was an NYPD detective whose one pearl of career advice was, “You can do whatever you want.” And, at the time I switched to physics, I saw no reason to doubt him.


I staggered back into the hallway punch-drunk from all the new concepts that had just been pounded into my head.


Rajeev must have heard about me from one of the more senior theorists in the department who I’d already approached but who wasn’t taking students. So Rajeev wasn’t my first choice, but by the time I found his note he seemed like my only hope.


The next thing I knew I was crouched in a chair in Rajeev’s little office, with a notebook on my knee and focused with everything I had on an impromptu lecture he was giving me on an esoteric aspect of some mathematical subject I’d never heard of before. Zeta functions, or elliptic functions, or something like that. I’d barely introduced myself when he’d started banging out equations on his board. Trying to follow was like learning a new game, with strangely shaped pieces and arbitrary rules. It was a challenge, but I was excited to be talking to a real physicist about his real research, even though there was one big question nagging me that I didn’t dare to ask: What does any of this have to do with physics?


After a couple of hours, Rajeev turned to me with a look that I later realized must have been heightened scrutiny.


“Maybe, you could work it out?” he said, about a problem he’d just described but hadn’t solved.


Sure, I said, stuffing my notebook into my backpack, I could give it a try.


I staggered back into the hallway punch-drunk from all the new concepts that had just been pounded into my head. So it was only as I stepped out of Bausch and Lomb altogether and back into the bright of the quad that I added two and two together and got four. Rajeev had said little about his research or his group, and the only question he’d asked me was that one problem at the end.


Clearly it was a test.


That night, I took Rajeev’s problem home with me, to a house in a suburban neighborhood a few miles from campus, where I rented the second floor from an old woman who lived downstairs. My desk was in the bedroom and my pacing creaked the floorboards, which periodically prompted the boom-boom-boom of her broom on her ceiling as a rebuke to my stirring past the 11 p.m. end of prime time.


Eventually I settled down at my desk, and tiptoed whenever I had to get up for coffee or the bathroom.


I don’t remember the details of the problem, just that it involved proving some general property of elliptic functions (or zeta functions, or whatever) as opposed to being a brute force calculation. It was a little as if someone had just introduced you to right triangles, but not the Pythagorean theorem, and then asked if you could find some relationship between the sides. Solving it would take a creative spark. But what really threw me was realizing that I didn’t have any sense of how hard the problem was, how intricate the calculation would have to be to solve it, or whether Rajeev knew the answer himself, or even whether the thing had an answer at all. Damn, I thought to myself, Why didn’t I ask?


I figured I had until the next day, when I’d agreed to see Rajeev again. I’d plowed through page after page of my yellow pad all evening, but each time I tried a new direction I either got lost or lost heart in the thicket of jumbled symbols I’d scribbled on the page. I kept flipping through my notes, looking for some fact I’d missed. I was haunted by the possibility that the thing had no answer at all, and by the even more dismaying thought that the damn thing was simple and I just couldn’t see it. Am I stupid to keep trying or stupid to not be done yet? Either way …


I feared failing Rajeev’s test. All of my classmates had taken up with advisors who were, like most physicists, experimentalists, the researchers who do the hands-on work of, say, smashing particles together at accelerators to see what comes out. Theorists like Rajeev, or for that matter Einstein and Feynman, who instead do the noodling necessary to explain the results of experiments with math are fewer and further between. A couple of Rochester’s experimentalists had pressured me to drop my dream of doing theory because, they explained, theory was so ridiculously difficult and had so few jobs. But I’d brushed them off. The whole reason I’d quit my job and come to Rochester was to do theory and to pursue “The Grail.” Anything less would have felt like failure.


I made another pot of coffee and brought a mug back to my desk. I scribbled ever deeper into my yellow pad. I got more and more nervous and it got harder and harder to sit still. Every once in awhile I padded to the window, for a view that no longer changed.


Stray thoughts fluttered like butterflies through my mind, scattering my mental constructions to the wind. Sometimes they morphed into more sinister things, little black spidery things that hissed with a hectoring voice …


You’re not smart enough to do this.


See how you can’t hold a thought?


If you can’t even do this, how can you ever expect to make it as a theorist?


Pinpricks of sweat pierced the back of my neck and hands. My throat went dry. The hectoring voice questioned every decision I’d made that brought me to where I was. Quitting my cushy California job. Sending the experimentalists away. Waiting to start this damn problem until after dinner.


When the idea finally came, it was like a faint breath over my shoulder, unexplained magic from an unseen direction. I felt in my gut it was right, but still had to prove it. I was too excited to sit still. I held myself down in my chair. The damn thing was solvable after all. I was wet with sweat when I finished. When I looked back up at the window, it was glowing a rosy morning gold.


I’d have to keep up, keep moving. There was no time to stop just to appreciate the scenery.


A year later, at the Faculty Club lunch, I was finished with classes for good and chomping at the bit to start research with Rajeev. I’d just learned that I’d passed the department’s “prelim” exam with flying colors; I even received an award for my score. That made my joining Rajeev’s group official, but it felt like a formality after Rajeev’s own test the year before.


After lunch, we all filed out of the club and into the sunlight and shimmering green of campus. In my home-movie memory, I’m walking next to Rajeev on the path back to Bausch and Lomb. He’s twisting a toothpick in his mouth, deep in thought. I’m still grinning that goofy grin and can’t feel the ground. I’m high from the wine and the sun, but also from memories of the convoluted route it had taken me to get there, including a couple of other aborted careers before engineering. Finally I’d figured out who I was and where I belonged. Finally. I held back tears.


And this is where I’d freeze the frame. This was my happiest moment, and not just with work, but ever. There on that path with Rajeev and thinking to myself, for the first time in my life: There is nowhere I’d rather be, and nothing I’d rather be doing. Rajeev had just told me over dessert that the first project he wanted me to work on with him was a problem in quantum gravity.


And so began the undoing of “You can do whatever you want.”





***


That summer, I moved. A fellowship I’d had had run out, so I’d have to start earning my keep as a teaching assistant and living off a stipend that went from a subsistence wage to a sub-subsistence wage. I left the old woman’s house for the relative bargain of a basement of another house in a seedier neighborhood. Its tiny windows up by the ceiling furnished its one room with feeble light and a bug’s-eye view of weeds. Its concrete walls seeped with damp. The bed was a mattress on the floor, with a plastic tarp under it to keep it dry. I kept a pair of running shoes next to it, for whacking the giant centipedes that regularly wriggled by. Dad, who never seemed bothered by sleeping on the shared cots in his dingy police station, or by nights spent in the rat-infested warehouses where he moonlighted as a security guard, was incredulous the first time he came. “I don’t know how you can live like this,” he rasped in his Bronx accent, looking both concerned and amused.


Eh. Living in squalor was just part of the adventure.


And I’d be spending all my waking hours in Bausch and Lomb anyway, working on quantum gravity with Rajeev, exploring the sort of intellectual frontier that Zen and the Art of Motorcycle Maintenance had called the “high country of the mind.”


What will I find there? I wondered.


Answer: a series of surprises, each more disquieting than the last.


The first was how much Rajeev already knew about the problem, even before we started. And I don’t just mean background knowledge, but instead the actual answer to our project’s main question, at least in broad strokes.





If you were to picture Rajeev and me as explorers in the high country, facing some misty mountain range that we needed to cross, Rajeev was the one scanning the landscape, making mental calculations, and pointing the way. What struck me most was how he somehow knew that our ultimate destination, call it a river, lay on the other side. The “river” in our case was a detailed answer to the quantum gravity question Rajeev had posed over dessert at the Faculty Club. Its exact location and shape would remain a mystery until we’d found it, but Rajeev never doubted it was there.


That made me the scout. We’d convene in Rajeev’s little office and, like our first meeting, I’d focus on following his logic and asking questions while he paced back and forth, thought out loud, and banged out equations on the board. At some point, after three or four hours, he might say something like “What else could it be?” that signaled that he was happy enough with the direction he’d found to let me forge ahead on my own, meaning I’d spend the next day or two in my office doing the detailed calculations that he’d speculated would take us to the next landmark. Sometimes I’d find the route clear; other times an obstacle in the way. Either way, I’d report back and then we’d sink back into another session. Thus research advanced, by a system reminiscent of the directions on a shampoo bottle: Meet. Calculate. Repeat.


After a few months, we solved the problem and reached the river’s edge, which was right about where Rajeev had reckoned. We wrote and published a paper called “Quantum Gravity on a Circle and the Diffeomorphism Invariance of the Schrödinger Equation.” Rajeev put my name first, because “H” comes before “R.”


And here came the second surprise of my first research experience: that I could come all the way to a true frontier and still have so little clue where I was. There are terms in our paper (“Virasoro algebra,” “Yamabe problem”) that I could not define for you today, and not because I’ve forgotten. I understood our calculations, but there was so much more to knowing where you were than that, so much context that Rajeev had in his head but that I didn’t have time to learn because it was all I could do to simply keep up. The times I’d fallen behind, Rajeev had gone ahead on his own, done his own calculations and summarized for me what he found. I learned my lesson. If I wanted to forge frontiers rather than just following as a tourist, I’d have to keep up, keep moving, and only pause long enough to hack a few vines and clear a few weeds. There was no time to stop just to appreciate the scenery.


But even if I’d had …


I only would have appreciated more how Rajeev and I hadn’t come any closer to The Grail. This was yet another surprise: that not every part of the frontier is equally earthshaking and that some are sort of trivial. Despite how knotty our project seemed to me, our conclusions were of extraordinarily limited scope.


“Quantum Gravity on a Circle …”


The paper we wrote did indeed flesh out a consistent theory of quantum gravity, one in which the concept of distance is defined by the phase of a quantum mechanical wavefunction. It even predicted black holes. But—and this is a very big but—the theory could only be true in a hypothetical one-dimensional universe that’s shaped like a ring, in other words a world nothing at all like the three-dimensional one in which you and I live, pay taxes, and die.


What we’d created is called a “toy model”: an exact solution to an approximate version of an actual problem. This, I learned, is what becomes of a colossal conundrum like quantum gravity after 70-plus years of failed attempts to solve it. All the frontal attacks and obvious ideas have been tried. Every imaginable path has hit a dead end. Therefore researchers retreat, set up camp, and start building tools to help them attempt more indirect routes. Toy models are such tools. Rajeev’s river almost certainly didn’t run to The Grail. The hope was that some side stream of one of its many tributaries (Virasoro, Yamabe …) would.


Actually that was my hope, not Rajeev’s. Rajeev, I believe, just liked doing the math. The thing was a puzzle he could solve, so he solved it. For him that was enough.


I, of course, had my sights set on bigger game.


***


One morning in 1907, Einstein gazed out his Swiss Patent Office window at the skyline of Bern and imagined what it would feel like to fall off a roof. Weightless was his answer, and that rapturous realization led him to the general theory of relativity and its radical reinterpretation of gravity as a consequence of curved spacetime.


That was one of the stories that had inspired me into physics, a view from 150,000 feet of the high country, in all of its awe-inspiring, albeit hazy, glory. The idea that one could discover something deep about the universe by making a slightly offbeat observation about an ordinary occurrence. The possibility that I, too, might one day look out a window and see a path to The Grail.


Galileo called the universe a “great book,” that’s written in the “language of mathematics.” Einstein said he wanted to know the “thoughts of God.” Wow. It was statements like those that fed my hope that I’d one day read the universe like prose and discover whatever fundamental ingredients and eternal rules undergird its ever-shifting surface. And that maybe, just maybe, the answers to the “What?” and the “How?” might even give a clue to the “Why?”


It was fuzzy logic like that—and, of course, dreams of explorer glory—that brought me to Rochester. But those fantasies started drying up quick under the heat lamp of research with Rajeev and of having my expectations of enlightenment adjusted by our work and by the tales Rajeev told of his own physics heroes.


The echo of “You can do whatever you want” still rang in my ears.


One was William Hamilton, a 19th-century Irish physicist whose big contribution wasn’t a new theory but instead a new mathematical formulation of an old theory, Newton’s laws of motion. Hamilton’s math managed to make all the same predictions as Newton’s, but without the need for Newton’s notion of force. I was struck by the wrinkle this revealed in Galileo’s great book metaphor. If the universe was really a book written in math, I thought, then different mathematical descriptions of the same physical phenomenon should just be a simple matter of translation, like going from French to Greek; the fundamental ingredients of the universe wouldn’t change, only their names would.


But Hamilton’s discovery helped me see that that’s not the way physics really works. Instead, different mathematical descriptions describe the world in terms of fundamentally different things. Newton’s description includes force. Hamilton’s doesn’t. That wasn’t just translation; that was different characters and a different plot.


I saw the same in quantum mechanics. The Schrödinger formulation of the theory, for example, describes reality in terms of an entity called a wavefunction that undulates through space and collapses to a point whenever it’s observed. The Feynman formulation describes it in terms of strangely schizophrenic particles that somehow take every possible path when traveling from one place to another. And the Heisenberg formulation manages to make the same predictions as the other two, while steadfastly refusing to give any picture of “what’s really going on” underneath nature’s hood at all. And that’s just the start of a long list of formulations that invoke things like particles riding on mysterious waves and a multiverse of universes growing constantly like a colony of splitting amoebas. All of these formulations are consistent with what we know, and each can be translated to the others with math. Yet each paints a very different picture of what reality really is.


Even a Theory of Everything, I started to realize, might suffer the same fate of multiple interpretations. The Grail could just be a hall of mirrors, with no clear answer to the “What?” or the “How?”—let alone the “Why?”


Plus physics had changed since Big Al bestrode it. Mathematical as opposed to physical intuition had become more central, partly because quantum mechanics was such a strange multi-headed beast that it diminished the role that everyday, or even Einstein-level, intuition could play. So much for my dreams of staring out windows and into the secrets of the universe.


There’s an adage about quantum mechanics that’s sometimes attributed to Feynman, though God knows if he ever actually said it. I never heard Rajeev say it either, but it’s in line with what I took to be his own philosophy of physics, which is that one shouldn’t waste time on the kinds of mushy metaphysical musings that I’ve been going on about here, and to instead focus on the real business of doing actual physics.


The adage?


“Shut up and calculate!”


If only I could.


The most distressing surprise I encountered working with Rajeev didn’t come from the quantum gravity project, but another on which I collaborated with Rajeev’s other students and postdocs in addition to Rajeev himself. The surprise was how ill-equipped I was to calculate compared to those other students and, I soon realized, compared to all the other theory students in the department, all of whom seemed to be much more familiar than me with a vast landscape of math relevant to physics that I’d first encountered in my first meeting with Rajeev and that was then and still was now as foreign to me as Khartoum.


It didn’t help that none of the other theory students had a background remotely like mine. None were even from the United States. Most, like Rajeev himself, came from developing countries like China, India, Turkey, and Brazil. Several told me that their educational systems had challenged them with more rigorous curricula than what I’d experienced, and had given them head starts by focusing them on math and science earlier in their educations. Although it was also true that many of them, Rajeev included, had made math a hobby as teenagers, while I at that age was still fantasizing about following in the footsteps of my favorite private eyes on TV.


And yet, the echo of “You can do whatever you want” still rang in my ears. I’d been less prepared than many of my classmates in engineering school too, nearly flunked out my freshman year, but still graduated near the top of my class. So even if all these strangers from strange lands did have head starts, why couldn’t I just catch up? For me the solution was simple.


Just work harder.


***


If I did lose my marbles for a while, this is how it started. With cutting my time outside of Bausch and Lomb down to nine hours a day—just enough to pedal my mountain bike back to my bat cave of an apartment each night, sleep, shower, and pedal back in. With filling my file cabinet with boxes and cans of food, and carting in a coffee maker, mini-fridge, and microwave so that I could maximize the time spent at my desk. With feeling guilty after any day that I didn’t make my 15-hour quota. And with exceeding that quota frequently enough that I regularly circumnavigated the clock: staying later and later each night until I was going home in the morning, then in the afternoon, and finally at night again.


The longer and harder I worked, the more I realized I didn’t know.


Such a complete immersion into physics was fun—at first. I remember the first time I swiped my ID card to get into Bausch and Lomb’s library in the middle of the night, flipping the florescent lights on, and getting a contact high from the sheer volume of volumes. So much here! So much to learn! I remember the dozens of seminal papers I copied and optimistically organized into little piles on my desk, plus the books I collected, including a stack of Dover Classic math texts with enigmatic covers colored with kaleidoscopic diagrams. So many exotic places to explore! And I was thrilled to be free to explore, to wander, and to get wonderfully lost in whatever mazes the high country had to offer, fueled by my ready supply of coffee and boxed macaroni and cheese.


The university had a network of steam tunnels that crisscrossed the campus underground, with pipes to heat the buildings and paths to provide passage out of the weather. Daytime, they boiled with hordes of hurrying students. But at night they were deserted, pin-drop quiet and compellingly spooky. Some of their walls were lacquered with layers of graffiti, a psychedelic record of students’ sentiments over the eons. Some of their extremities terminated in the subterranean labs of other scientific departments. On breaks from my desk, I’d wander the tunnels, eyes peeled for the giant cockroaches that occasionally crept out from under the pipes. I’d study the graffiti like an anthropologist analyzing hieroglyphs and snoop in open labs searching for signs of discoveries. Nights split between wandering the physics landscape and wandering the tunnels felt like adventures into forgotten territory, like being Indiana Jones.


Until it started to feel like I was sinking in quicksand.


The longer and harder I worked, the more I realized I didn’t know. Papers that took days or weeks to work through cited dozens more that seemed just as essential to digest; the piles on my desk grew rather than shrunk. I discovered the stark difference between classes and research: With no syllabus to guide me I didn’t know how to keep on a path of profitable inquiry. Getting “wonderfully lost” sounded nice, but the reality of being lost, and of re-living, again and again, that first night in the old woman’s house, with all of its doubts and dead-ends and that horrible hissing voice was … something else. At some point, flipping the lights on in the library no longer filled me with excitement but with dread.


The gap between the other students and me didn’t seem to shrink much either. And the one between me and the physics giants I’d read about and couldn’t stop comparing myself to hadn’t shrunk at all. I’d once been encouraged, for example, by Feynman’s claim that his colleagues were sometimes exasperated by how slow he could be to understand their ideas. The reason, he explained, was that he’d build a model in his mind of their subject as he listened to them talk, adding to it piece by piece as they spoke. Picture a Tinkertoy machine growing bigger and more complex as Feynman kept asking questions to ensure each stick and pulley was put in its rightful place. It took time, but when all was said and done Feynman would have in his head a fully three-dimensional model of whatever the idea was. And that allowed him to tilt, spin, and examine it in his imagination as if he held it in his hands. One of Feynman’s collaborators called him a “magician” for the mysterious ways his mind seemed to work. But to hear Feynman tell it, he was just listening carefully and building those little models in his mind.


That’s how it is for me too! I thought when I first read that. I, too, had sometimes frustrated classmates and teachers with all my questions. I, too, often ended up seeing things they couldn’t see.





But that was in the context of classes in the past. Now, with Rajeev and the other theorists, that just wasn’t happening anymore.


My mental model building was hitting its limits. I’d sit there in Rajeev’s office with him and his other students, or in a seminar given by some visiting luminary, listening and putting each piece in place, and try to fix in memory what I’d built so far. But at some point I’d lose track of how the green stick connected to the red wheel, or whatever, and I’d realize my picture had diverged from reality. Then I’d try toggling between tracing my steps back in memory to repair my mistake and catching all the new pieces still flying in from the talk. Stray pieces would fall to the ground. My model would start falling down. And I would fall hopelessly behind.


A year or so of research with Rajeev, and I found myself frustrated and in a fog, sinking deeper into the quicksand but not knowing why. Was it my lack of mathematical background? My grandiose goals? Was I just not intelligent enough? Or maybe it was the type of research Rajeev had me doing. And what about Rajeev himself?


Writing this now, more than 20 years later, I have to dig really deep to get to the part of me that began to hate Rajeev. Deep down through layers of memory and reason that have since solidified into gratitude and affection for all the time he gave me, for all that I learned from him, and for the fact that he gave me a chance.


But I did start to hate him. For steaming ahead without looking back when I tripped and fell behind. For seeming oblivious to my frustrations generally. And for dashing my dreamy ideas of what doing physics would be like. Fuck him, I thought to myself, more than once. Maybe I’d be better off without him. “You can do whatever you want” just didn’t want to die.


The reality was that we weren’t chasing any grails.


So I did strike out on my own. A subject called random matrix theory was hot in physics at the time, applied to condensed matter phenomena and to the quantum behavior of classically chaotic systems. The relevant math was familiar to me from engineering. I figured I’d just dive in, learn the subject, and come out the other end with a publishable discovery. I pulled back from Rajeev’s group, stopped going to most of his meetings, renewed my 15-hour vow, and hunkered down in my office on my own.


And that smooth move cost me nearly a year.


More months of 15-hour days. More growing piles of papers and books. More microwaved meals and nights in the steam tunnels. But in the end, I never knew what I was looking for and I didn’t find it. Unlike Rajeev, I had no clue how to divine rivers beyond my view.


I turned 30 during this time and the milestone hit me hard. I was nearly four years into the Ph.D. program, and while my classmates seemed to be systematically marching toward their degrees, collecting data and writing papers, I had no thesis topic and no clear path to graduation. My engineering friends were becoming managers, getting married, buying houses. And there I was entering my fourth decade of life feeling like a pitiful and penniless mole, aimlessly wandering dark empty tunnels at night, coming home to a creepy crypt each morning with nothing to show for it, and checking my bed for bugs before turning out the lights.


The quicksand was up to my nostrils.


One morning I woke up with a truck on my chest—at least that’s what it felt like. I remember lying there on my floor-bound mattress, bug-killing shoes by my head, and realizing that I couldn’t move. I laid there for a long time, partly curious and partly afraid of what was happening to me. Then I realized I could move, just as long as it wasn’t back to Bausch and Lomb.


I left Rochester and the next month, or two, or whatever it was, is a blur. I just know I stayed with a friend in New York City. And that I drained his cupboard dry of booze. Then I came back to Rochester, feeling like I had nowhere else to go.


I dreaded going back to Rajeev. I was as ashamed and embarrassed as I’ve ever been. But there was also relief once I’d decided to do it, a lightness at the loss of a weight, as I finally and forever let go of “You can do whatever you want,” and accepted the idea of following someone else’s lead.


“Just tell me what to do,” I said to Rajeev, after explaining where I’d been all those months and why.


Rajeev took me back graciously, like the Prodigal Son.


“Now you know what makes theoretical physics so hard,” he said. “It’s not that the problems are hard, although they are. It’s that knowing which problems to try and solve is hard. That, in fact, is the hardest part.”


***


Two years later, I was writing my thesis. I’d moved out of my basement apartment to a second-floor studio farther from campus but with better light and smaller bugs. When I’d come back from my binge to Rochester and Rajeev, I was still suffering from some sort of post-theoretical-physics disorder and had to promise myself I’d stay only an hour to get back to my desk at all. One hour became two and eventually I was back in business again, although 15-hour days were now the exception rather than the rule.


My thesis topic was renormalization, a subject in quantum theory that Feynman helped found and that solves a critical problem quantum mechanics has when it’s married with Einstein’s special theory of relativity to produce quantum field theory, physics’ state-of-the-art description of the world, and the foundation for the Standard Model. The problem is that infinities infect the resulting theory, as if there were an errant division by zero, causing many of its predictions to be nonsensical. Renormalization is a recipe, a collection of recipes really, for subtracting those infinities away.


By staying laser-focused on renormalization, I learned the subject in some depth and was able to contribute more and more in my talks with Rajeev. Our meetings grew longer and longer. We’d meet after lunch, blow through the afternoon, and sometimes go well into the night. Rajeev’s wife would often call to remind him to come home for dinner. He’d whisper what sounded like compliance, but then would hang up and seem to forget the call ever happened, picking up with me right where he’d left off. There’d be a second call and sometimes a third. Sometimes Rajeev would give in. Other times his wife would give up. His mind was a hard thing to stop. I myself never tried. I always came to his office with a couple of granola bars stuffed in my pockets, just in case.


I loved seeing Rajeev’s mind in action. On the best days, I’d get a glimpse of his view of the physics landscape: a perspective from on high of a continent’s worth of alternating mountain ranges and plains, and wispy traces of various rivers in the distance. The view was thrilling and sometimes gave me a dizzy-high feeling, as if I really were at altitude. Sometimes Rajeev himself seemed to get a little high from the fumes of his own burning ideas and he’d start speculating where our work might lead us, if we stuck with it long enough. Possible solutions to longstanding conjectures in mathematics would be mentioned, along with Nobel-worthy breakthroughs in physics. “Hey, you never know!” he’d say, flashing his subversive smile.


But the reality was that we weren’t chasing any grails. We weren’t even developing a new theory. We were, like Hamilton, fleshing out an already established one, essentially staying in place on a trail in the landscape, digging holes, and trying to understand more deeply the place where we stood. In technical terms, we found new mathematical formulations of some quantum field theories that skirted the problematic infinities from the start, so that traditional renormalization procedures weren’t required. But still, like those traditional methods, ours avoided explaining the infinities’ source. And, as with the traditional approaches, you could argue we were just covering up holes in quantum field theory.


That’s why Feynman himself called renormalization a “shell game,” and why some physicists consider the sort of work Rajeev and I were doing distasteful—because it amounts to fleshing out a flawed, or at least incomplete, theory as opposed to boldly going in search of a better one, one that could include quantum gravity, the key to which may very well be buried somewhere deep in quantum field theory’s holes.


I actually tackled this viewpoint head-on in my thesis by quoting physics eminence Steven Weinberg’s response to the criticism that time spent on renormalization detracted from the greater glory of going for The Grail.


“It seems to me that this is analogous to saying that to balance your checkbook is to give up dreams of wealth and have a life that is intrinsically less exciting,” Weinberg said. “In a sense that’s true, but nevertheless it’s still something that you had better do once in awhile.”


Rajeev liked that line a lot. “It may not be the right time,” he’d say about discovering the next generation theory that could supersede the Standard Model and potentially provide a Theory of Everything. It took Hamilton and others several hundred years to fully flesh out Newton’s mechanics, and there were still open questions even in that field. Solving quantum gravity could take several hundred more.


By the time I finished my thesis, I’d convinced myself that physics was far from finding The Grail. But there were other reasons why I decided I’d have to make yet another career change, this time to Wall Street.


Not least was the job market. For six years I’d watched postdocs pass through the department with the seasons, like migrant workers come to pick beets. At one time, a single two-year assignment had been enough to qualify for a job as a professor. But now the norm was two or three postdocs, sometimes more, and even then the odds of landing a full-time job were slim. Every once in awhile I’d see the telltale sign of one who gave up: piles of books outside a Bausch and Lomb office in the hallway, a makeshift yard sale for those still clinging to the dream.


They all seemed at least as smart as me, and if I’d had any doubt about my standing among them, one moment in my final year brought it into terribly sharp relief. I was in Rajeev’s office with a group of other students and postdocs listening to our leader describe his latest idea. I got confused and asked a question. Then, when that didn’t clear things up, another. There may have been a third.


Rajeev had had enough.


“Do I need to explain fiber bundles to you again?” he said with a clenched jaw, the closest to angry I’d ever seen him—not even a smile of discomfort.


My face burned and I couldn’t speak. Rajeev finished the lecture, and I sat and stared through the blackboard, my thoughts a hot swirl of emotion and broken logic. I avoided Rajeev for at least a week after that. Fiber bundles are topological objects that were basic ingredients in Rajeev’s preferred way of framing quantum field theory, my supposed area of expertise. And yet, even as I was writing my thesis, my mental model of them was missing some screws.


As I put the final touches on my thesis, I weighed my options. I was broke, burned out, and doubted my ability to go any further in theoretical physics. But mostly, with The Grail now gone and the physics landscape grown so immense, I thought back to Rajeev’s comment about knowing which problems to solve and realized that I still didn’t know what, for me, they were.


***


Fifteen years later, in the autumn of 2012, I rolled into Rochester on a motorcycle laden with supplies for a cross-country trip, having just left my final job on Wall Street. I was hoping the trip would help me to clear my head and to decide what to do next. Rochester was my first stop, where I planned to meet Rajeev. We’d lost touch after I graduated, but I’d recently reached out and, to my surprise, he suggested we might do something together again in physics.


When I found him in his new office in Bausch and Lomb, Rajeev rubbed his round head and lamented the hair he’d lost in the intervening years. He wore a black turtleneck and black pants that made him look more like an artist than I remembered. His voice was even softer than I remembered too. Crossing the quad on the path to the Faculty Club for lunch, I struggled to hear him over the wind whishing through the brown leaves of the oak trees and the fallen ones skittering on the ground.


Back in his office after lunch, Rajeev offered me a chair and plopped down onto a couch. “I don’t know what you want to do,” he said, and I sat silent for an awkward moment considering ways to interpret that question. Then I asked him about Kerala, where he’s from, and we were off to the races. First about current events, then about history, and finally physics. We talked for hours, through the afternoon, until his window glowed orange with the setting sun. It was just like the old days, except this time Rajeev called his wife at dinnertime rather than the other way around.


We talked about what had happened in physics since I left. The Higgs boson had just been discovered, but that wasn’t such a surprise. More interesting, theoretically, was the finding that neutrinos have mass, which the Standard Model says they shouldn’t have. That and the discovery that the universe’s expansion is accelerating, implying the presence of dark energy, and the stark conclusion that most of the “stuff” in the universe may not be covered by the Standard Model at all. I harbored a hope that Rajeev would show an interest in this area, have some ideas. In some ways I hadn’t changed much. I was still inclined to go off chasing grails.


I realized it was as good a time as any to ask a question that had been burning in my brain for a long time, but which I’d never had the nerve to ask.


“What happened to me?” I started. I wanted to know why Rajeev thought I’d failed at physics. I had my own view and tipped my hand. I wanted to make it easier for Rajeev to say what I thought needed to be said, that I just wasn’t smart enough, not good enough at the math.


But Rajeev, true to form, had his own ideas.


Without naming names, he ticked through a catalog of his contemporaries who’d succeeded in theoretical physics even without having the towering mathematical intellect that I was sure it took and that Rajeev surely has. They’d made it, Rajeev explained, by focusing on problems that played to their strengths, or by taking advantage of computers, or by collaborating with peers who had complementary skills. Some socially gifted but not so mathematically talented types had gone quite far this way, earned a lot of renown. As Rajeev made his case, I realized he sounded familiar. In fact, he sounded a lot like me, the many times I’d been asked by young strivers how to break into Wall Street or how to succeed once there. Often I’d see my listener’s eyes glaze over as I gave them such practical advice and stressed how much work it took. So many people seemed to want some secret that wasn’t mine to give.

Gradually, I heard what Rajeev was saying but was too diplomatic to actually say, “You didn’t fail, Bob. You quit.”

That hit me like a brick. It hadn’t occurred to me, or I hadn’t let it occur to me, that if I’d really wanted it, I could have kept going, at least applied for a postdoc, whatever the odds. My mind wandered as I wondered whether and why I may not have wanted to do physics as much as I’d always imagined …


But Rajeev wasn’t finished.

“The hardest part of all,” he said, about theoretical physics, “is controlling your emotions.”

Another brick. It was clear he meant himself.

“You?” I asked.


Rajeev shot me a squinty look as if to ask was I really that dense. I had a fiber bundle flashback as he went on to explain.


Sound bites from that conversation echoed in my helmet as I twisted my bike’s throttle and left Rochester behind. I quit, as I cruised into Canada over Lake Erie. I quit, as I passed through Chicago and then through the farm fields of Wisconsin. I quit, across the flat nothingness of Nebraska. I quit, up into the snow-covered Rockies and back down through the melting heat of Moab, Needles, and Palm Springs.


Writers talk of the terror of facing a blank page, but it’s no different for theorists like Rajeev trying to choose which path to take. There are an infinite number to choose from, and most go nowhere or back from where you came. The clock is always ticking and you spend so much time in the dark that it can make you not only question your path, but your own self worth. It can make you feel stupid. Rajeev had once been a night person, but now, he told me, with two kids in the house, he awoke each day at 3 a.m. in order to have the quiet time he needed to do such wandering in the dark, undistracted. He confessed how stressful the work could be.


I was taken aback. To me, Rajeev had always seemed the happy mathematical warrior, blessed with a brain that enabled him to follow his bliss. Was it actually as stressful for him as it had been for me? Was my failure to follow through on physics more about emotions than math? These questions and the lessons I’d learned from Rajeev were on my mind as I crested a grassy hill outside of Malibu and got my first glimpse of the Pacific Ocean. That and how physics and writing and life are all essentially the same, and so are people. And, as I continued to consider how to navigate the open landscape of life ahead of me, how Rajeev had concluded our last conversation by conjecturing, as if he was contemplating the question for the first time, that theorists like him stay the stressful course of wandering in the dark and guessing which questions to ask is because, “They must really want to know the answers.”


Bob Henderson studied physics, worked on Wall Street, and is now an independent writer focused on science and finance.