1
OVER THE YEARS, I have seen my share of airports around the world, but Tirana’s Mother Teresa Airport looms the largest in my memory. It was the place where my scientific journey literally took wing.
In January 1994, I left my walled-off life in Albania for a new one in the United States. My journey followed a route I never could have imagined: I had won a full scholarship to study at an American university.
Several years prior, as Albania had begun to shake off the chains of Communism, the U.S. embassy and the American Cultural Center reopened their doors, which had been closed for almost fifty years. Soon thereafter, the United States offered its Fulbright Scholar Program to Albanians. I was preparing to graduate from the University of Tirana with a bachelor’s degree in physics and was deciding what to do next with both my life and career; I knew that I wanted to pursue an advanced degree, but Albania’s educational system didn’t offer a graduate physics program. Studying abroad was the only route.
The Fulbright program was widely advertised, and students were encouraged to apply. Based on my experience in Albania, where merit carried very little weight, and political connections were everything, I thought the idea that someone like me could receive a scholarship to study in the United States by filling out an application and taking some standardized tests was too good to be true. Urged by my friends, I completed the forms, but without much hope, so I was shocked when, a few months later, I received a letter congratulating me on winning a Fulbright scholarship to study advanced physics for one academic year at the University of Maryland in College Park. It was the first Fulbright awarded to an Albanian for science. It was also my first experience with the fairness of the merit-based U.S. system.
My parents and brother accompanied me to the airport to say goodbye. Besides math and family, my dad’s two other passions were mountain climbing and chess. As my mom’s and my brother’s eyes welled with tears, my dad couldn’t resist offering some last-minute advice. “Really good science is like climbing a mountain,” he said. “It takes superb skill, stamina, and the courage to never compromise your scientific integrity. But the view from the top is breathtaking and worth the sacrifice.” He added that, as in chess, “If you want to get it right, you must be at least three moves ahead of your opponent. You have to anticipate and prepare for what can go wrong, not only on the first move, but also on any of the possible combinations and outcomes of the second and third moves.” By this, he meant I should thoroughly scrutinize my ideas and whether they agreed or disagreed with the bigger picture so I could anticipate where they might go wrong.
As we hugged, I started to miss them already. My dad pulled back and looked at me, and in a shaky voice he told me what only parents are capable of saying to their children: “Do not look back. We will be fine.”
I boarded a Swissair plane, wondering what my new life would be like in a country where I knew no one, a sea and an ocean away from my childhood home. I could not have predicted that my one-year Fulbright would lead to acceptance to an American graduate school and, from there, to what has become a lifetime of study. Nor could I have guessed that the United States would become my new home.
Mist enveloped the plane and obscured the ground as we landed at Baltimore/Washington International Airport. I passed through customs and found someone from the University of Maryland office for International Student and Scholar Services waiting to greet me. Outside, large snowflakes were falling steadily. By the time we arrived at a hotel near the campus, the snow had turned gritty, and the storm transformed into a historic blizzard. All the airports, the city of Washington, DC, everything came to a standstill. As evening approached, I watched the fast-falling snow and icy roads as they glimmered eerily under the streetlights.
I spent my first week in the United States existing on doughnuts and filtered coffee that the hotel kindly provided in the lobby for all its stranded guests. The interwoven moments of quiet contemplation and wonder I experienced that first week (along with the sweetness provided by all those doughnuts!) would become a good metaphor for my new life in America.
Many things appear obvious in retrospect, but truth be told, I almost didn’t become a physicist. As a high school student in Albania, I hadn’t been able to decide whether to major in physics or math at the University of Tirana until a week before the selection deadline. I liked them both. I competed in the national Olympiads in math and in physics, hoping that would help solve my dilemma. As it happened, I won both, which made my choice even harder. So I flipped a coin: heads, physics; tails, math. It came up heads.
But although chance had landed me on the path of physics, I always knew I wanted to be in the world of numbers and hard sciences. At that time in Albania, the fields of social sciences, economics, and the humanities were mostly political dogma in disguise. History was our national version of Communist myths and fairy tales, and even the law school was just a name because there were no defense lawyers. For me, those fields held no temptation. Yet many of the students who were assigned to the natural sciences saw it as a punishment. The math and physics building was mockingly known as “the Winter Palace.”
I loved math, however, because its pure logic and precision removed all ambiguity and arbitrariness, a rare quality in Albanian life. I loved physics just as much because it combined math with creativity and intuition and, through ideas, applied math in a real setting. I ended up majoring in advanced physics in what was known as the five-year program; in the second year, I decided to sign up for the math program too.
Having a math degree in addition to a physics degree would have made absolutely no practical difference if, as seemed likely at that point, I spent my working life in Albania. But nevertheless, my parents supported me in my decision. I think my mom was happy that I was going to be fully occupied studying for two degrees and would have no time for partying; my dad, for his part, was delighted that I shared his passion for math.
My friends in Albania thought that doing math for fun was nuts, but once I migrated from the hotel to a small apartment and began navigating the sprawling campus at UMD, I found myself surrounded by students who were as passionate as I was about the subject and who were similarly determined to make the most of the educational opportunities available to them.
The University of Maryland physics department has a big graduate program. It offers an unusually large number of advanced courses in physics, along with many research programs, including world-class research groups in theoretical physics. During my Fulbright, I took full advantage of these opportunities and signed up for many more classes than required. I also applied to UMD’s graduate school so I could continue my studies after my fellowship ended. Fortunately, I was accepted.
Of the roughly two hundred physics graduate students at the University of Maryland, only three were women. But other than the severe gender gap, there was a great deal of diversity. For nearly all of my life in Albania, until the regime fell, I had seen only other Albanians; to be surrounded by students from so many backgrounds and places was a new and wonderful experience. Clearly, the world was bigger than I had seen.
By my second year at Maryland, I realized that I was drawn to the big questions about the universe, specifically to theoretical physics and cosmology, the study of the whole universe—a discipline of literally cosmic proportions.
In their working lives, theoretical physicists aim to decipher how nature functions, from the smallest conceivable particle to the largest distances. We do so by working with the current laws of nature and discovering new ones; using tested theories and, when necessary, replacing them with better ones; and solving mathematical equations on which these laws and theories are based to unwrap the next mystery. Like children, we love asking questions, from the basic to the most sophisticated; we come up with outrageous ideas and then mercilessly scrutinize and discard most of them after applying logical rigor and observational tests. We are known for our lack of everyday practical skills combined with our love of logical deduction and synthesis.
At Maryland, I joined the Gravitational Theory and Cosmology Group, one of several faculty-led groups organized around specific areas of research. Groups include postdocs and students. (One group member was Charles Misner, a celebrated physicist who worked on the foundations of gravity; he was a former student of John Wheeler and had been a classmate of Hugh Everett at Princeton University, both of whom we will meet later in this book.)
During one seminar offered by this group, I heard a statement that shocked me. The speaker walked us through what the chances were that our universe would come into existence and concluded that the odds that our universe would form in the way that it did, with a big bang at high energies, were nearly zero! In fact, it was possible to calculate the odds, which the eminent British mathematician and theoretical physicist Roger Penrose (later a Nobel Prize laureate) had done in the late 1970s.
When Penrose calculated the likelihood of our universe spontaneously forming, he got a staggering number: 1 in 10^10^123. Less than a one in a googolplex chance.
It was, to my mind, a completely ridiculous number.
Mathematicians joke that a googolplex is simply 1 followed by as many zeros as you can write before you get tired. The number is longer than the length of our entire universe.
If you are a cosmologist (and even if you aren’t), there’s something deeply distressing about Penrose’s conclusion. Was the creation of our universe such a special event, produced out of such a unique set of circumstances, that it has never been and will never be repeated? Were we the virtually impossible winner of some bizarre cosmic lottery?
Along with Stephen Hawking, Penrose went even further. He and Hawking derived from first principles a logical argument in a theorem (a proposition that can be proved mathematically) that if our universe has been expanding since its creation, then it must have started from a point in space of literally infinite energy density—what is known as a singularity.
Hawking and Penrose’s singularity theorem implied that scientists could never explore the actual moment of the universe’s creation because nothing, absolutely nothing, existed before creation. That meant we could never replicate or identify the conditions that caused it, that the creation of our own universe was truly beyond our ability to study.
Which, of course, made it a thoroughly intriguing question for me.
When I lived in Maryland, one of my favorite weekend activities was to spend whole afternoons at a large bookstore in Bethesda browsing books on any subject from literature to philosophy to art—anything, that is, but physics.
Physics was reserved for weeknights and weekdays. On weekday evenings, I read everything I could from the scientific literature, and I even tried to reproduce the calculations. I wanted to understand how Penrose had arrived at what to me seemed like a preposterous conclusion about our universe; I wanted to try to follow the arguments that had convinced his fellow scientists to embrace the view that nothing existed before our universe did.
Although I was intrigued by Penrose’s argument, I wasn’t persuaded by his conclusions. I kept returning to Penrose’s paper, dissecting and analyzing his reasoning, hoping either to be convinced or to find out where his reasoning might have taken a wrong turn. Certainly, I never thought that I would be able to solve the questions that Penrose and Hawking had walled off with their singularity theorem. I wasn’t delusional. I was merely curious.
I quickly learned that Penrose’s conclusion of a nearly zero chance of our universe coming into existence seemed rock solid. His finding was also deceptively simple. It was based on a fundamental law of nature—the second law of thermodynamics, which was predicated on the work of the esteemed nineteenth-century Austrian physicist Ludwig Boltzmann.
I had learned of Boltzmann’s many contributions to thermodynamics and atomic theory during my undergraduate studies in Albania. (Incidentally, the professor who taught me thermodynamics went on to become Albania’s president during the transition years.) However, it was not until later, when I started dismantling Penrose’s derivation—the solution he obtained by solving those equations—that I fully understood, and appreciated, the significance of his work.
Boltzmann’s discoveries were not simply a collection of equations bearing his name. They also formed a major stepping-stone in the development of modern physics: a breakthrough that revealed a crucially important relationship between the probability that an event would spontaneously come into existence and a concept known as entropy. Indeed, it was Boltzmann’s probability insight that led to Penrose’s ridiculous number—that the chances of our universe emerging randomly were nearly zero.
Simply put, Boltzmann’s concept of entropy quantifies disorder. Imagine a kids’ closet full of shirts in different sizes and colors. At a macroscopic level, the closet can be described perfectly well by its size, the color of its walls, and the number of shirts in it. One day, the parents decide on a rule for organizing the closet: all the shirts will be hung by size, from the smallest to the largest. Suppose the day after, the kids start hanging the shirts (or, more likely, throwing them on the closet floor) randomly. Unlike the parents’ system, the specific ordering of which—arrangement by size—is unique, the children’s system contains many different possibilities. But this information about the parents’ or the children’s arrangements is unaccounted for in the macroscopic description of the closet. In fact, every time the kids arrange the shirts differently and mess up the ordered closet, they create new configurations or, in physics jargon, new microstates. So, unlike the parents’ unique and tidy system, a disordered closet has many microstates, since there are so many ways to disorder it. Despite the fact that the specific details of disorder are not captured in the macroscopic description of the closet, we can still deduce that overall, a disordered closet is not special because it is far more likely to be found randomly than a tidy closet.
The missing information contained in the collection of these microstates is Boltzmann’s entropy. Entropy counts all the microstates that a system can possibly have without changing its macroscopic state, as in the closet example above. Entropy, therefore, measures what is hidden about a system. In the case of the closet, it minutely describes the fine details and disorder inside by means of a mathematical formula.
I already knew what Boltzmann’s entropy was, but what I was really curious about was how Penrose connected it to the probability, or improbability, of our universe randomly coming into existence. How was entropy related to the birth of the universe? How did knowledge of the probability of the universe quantitatively emerge from knowledge of its entropy?
The answer is etched on the headstone of Boltzmann’s grave in Vienna. At the very top, above a bust of the famous physicist, is an unusual epitaph—a mathematical formula:
S = k Log W
This is one of Boltzmann’s most famous equations, what is known as his entropy formula. In this equation, S is the entropy of the system we would study; for example, the children’s closet. W is the number of microstates of this system; in our example, it is the number of all the possible ways of arranging the shirts inside the closet. Ln is the natural logarithm.* And k is a constant number, known as Boltzmann’s constant, that makes the rest of the formula work. Simply put, entropy is proportional to (the log of) the number of microstates of a system. Or, equivalently, the number of available microstates of a system W is exponentially large with its entropy S.*
The formula on Boltzmann’s headstone provides the first microscopic understanding of entropy in terms of the bits—the microstates—that make up a system. But until I revisited it in graduate school, I had overlooked the real meaning of his insight: that the number of these bits, the number of the possible microstates available in a system (as calculated by its entropy), is nothing less than a direct measure of the probability that this system will occur.
For example, there were many different ways, many microstates (W), for disorganizing a closet, but only a few ways of making it tidy and ordered. Therefore, if I were to randomly look at the closet, my chances of finding it in an ordered state would be very slim. The same principle applies to larger systems, up to and including the universe itself.
Any macroscopic system, whether a closet or the whole universe, has its own set of microstates through which it can occur and be realized. If the universe at its creation moment has a large number of possible microstates through which it can come into existence, then the probability that it will randomly come into existence is high. Likewise, if the number of possible microstates through which a particular creation model can be realized is low, then the probability that it will occur is exponentially low.
Boltzmann’s formula (which connects the entropy of a system to its probability of existence) implied that, in order for our universe to be exponentially less likely to come into existence by chance than any other universe we can imagine, as Penrose had calculated, our universe must have started from an exquisitely ordered state of very low entropy.
As I kept trying to connect the dots in my understanding of Penrose’s derivation of the entropy of the universe, the story of our universe’s unlikely existence became even more interesting. How can we even know what the entropy of our universe is? What information would calculating its entropy require? The entropy of the universe at each moment counts all the microstates of the universe, all the possible arrangements of its components. It reveals how disordered our universe is and what is not known about it.
Suppose that the closet in the previous example is as large as the universe. The shirts correspond to all the atoms and photons and stars and galaxies—all the matter, energy, and radiation in the universe. The amount of these components at present is inferred from astrophysical observations of our universe. Yet each time we exchange two photons from different sides of the universe, we have a new arrangement, a new universe microstate. Each time a supernova explodes and spews all its material into the universe, we have a new microstate, although the macroscopic universe as a whole remains the same. As in the closet example, if scientists know the universe’s matter and energy content, they can count all the possible ways of spreading these bits around and calculate a system’s entropy. This is what Penrose did. And as it turns out, the entropy of our present universe is not that large.
But there is always a catch, and in the case of our universe, it was this: The probability of our existence depended not on the entropy of the present universe but rather on the entropy at the moment of creation. This is tricky to discern, of course, since we cannot observe the moment of creation. Yet in order to estimate our universe’s probability, Penrose had to find a way to deduce its entropy at its earliest moment. How did he achieve that? I had to find out.
In order to pinpoint the entropy of the universe at its creation, I needed to revisit what is probably the most important law of nature: the second law of thermodynamics.
The second law of thermodynamics states that the entropy of a system never decreases. Entropy always increases with time, no matter how much entropy you start with. In other words, the natural tendency for any system is to become more disordered, not less.
Imagine two adjacent rooms connected by an insulated door. Initially, the temperature in the first room is low (say, 40°F), and the temperature in the second room is high (say, 103°F). The second law of thermodynamics tells us what happens to the entropy of the rooms over time when the connecting door is opened.
As a result of air molecules moving between the two rooms, both rooms slowly reach the same average temperature. However, disorder grows, since we have more air molecules that have more space to roam around and create new arrangements. They can move from one room to the next and back. Heat is gradually transferred to the cold room, creating new microstates within both rooms. The more time passes, the more microstates are created in the two rooms, and the number keeps growing until the two rooms are the same temperature everywhere.
Furthermore, without external intervention, this process cannot be reversed. No matter how long we wait for the initially hot room to get hot again and the cold room to become cold again, it simply won’t happen! The two rooms cannot spontaneously return to their original states. In other words, the entropy of the adjoining rooms keeps increasing over time—irreversibly.
This behavior is the essence of the second law of thermodynamics. Entropy growth over time is universal and irreversible, no matter the system. And the tendency of any system in nature is to try to reach equilibrium by increasing its entropy over time. The same conclusion is inevitable if I apply it to the whole universe: the entropy of the system—the whole universe—will increase irreversibly over time.
We know the entropy of the present universe, since, through our space- and ground-based astrophysical observations and a measurement of its expansion, we can count all of its content (mass, energy, and radiation), and with the help of the second law of thermodynamics, we can deduce that the entropy at the moment of creation must have been smaller than the entropy of the present universe. But precisely how much smaller was the entropy of the universe at the earliest moment relative to the present? Simply asserting that the state of the universe then had a smaller entropy than it does now does not provide sufficient information for estimating the probability.
There was another wrinkle. Penrose’s argument for the ridiculously small probability of our universe’s having come into existence, calculated from the formula on Boltzmann’s headstone, depended solely on a number: the value for the entropy at the earliest moment in the life of the universe. Yet the second law of thermodynamics cannot provide an exact number for what the entropy was at the moment of creation. And this part of the puzzle became more complicated the further I delved into it.
Reconstructing the entropy of the universe at the moment of creation required tracking the cosmic evolution of the universe back in time, all the way to its inception. But therein lies the rub. The accepted narrative of the early universe given by the modern version of Big Bang theory (a story known as cosmic inflation), while wildly successful in explaining almost everything else about our universe, describes a universe of a very special origin, one of an exceptionally low-entropy state.
Cosmic inflation posits that in the blink of an eye, our tiny primordial universe, filled with high energy, became much bigger through a gargantuan explosion. It offers a compelling story for how a tiny universe can quite naturally grow large and later brim with life, and its exquisite agreement with observations helps explain why it remains widely accepted by scientists and the public to this day.
But Penrose’s paper raised lots of doubts about the theory of cosmic inflation. Our universe’s high-energy but very low-entropy initial state posited by the theory of cosmic inflation implies that the probability of our universe beginning in this manner was as small as it could possibly be. By pointing out this wrinkle in the cosmic-inflation theory, Penrose’s argument posed the greatest threat to the validity of cosmic inflation being the progenitor state of our universe.
This, in a nutshell, was the infamous problem of the origin of our universe.
My simple plan was to zoom in on the details of cosmic inflation and the process of what happened afterward. I wanted to familiarize myself with previous attempts at solving this problem and, especially, understand why and where those attempts failed. If the issue of our special origin was an artifact of cosmic inflation, then perhaps we needed to discard that theory and replace it with a better model of creation. As I wondered at the time, did the apparent unlikelihood of our universe coming into existence indicate a different problem, even a fundamental problem, with the generally accepted explanation of our origins? Or were we entirely missing the point and asking the wrong question? It turned out the answer to both was yes.