Our Mathematical Universe

by Max Tegmark

  One evening back in high school, I started reading Agatha Christie’s detective novel Death on the Nile. Although I was painfully aware that my alarm clock would go off at seven a.m., I couldn’t for the life of me put it down until the mystery had been solved, around four a.m. I’ve been inexorably drawn to detective stories ever since I was a kid, and when I was around twelve, I started a detective club with my classmates Andreas Bette, Matthias Bothner and Ola Hansson. We never captured any criminals, but the idea of solving mysteries captured my imagination. To me, the question “What is reality?” represents the ultimate detective story, and I consider myself incredibly fortunate to be able to spend so much of my time pursuing it. In the chapters ahead, I’ll tell you about other occasions when my curiosity has kept me up in the wee hours of the morning, totally unable to stop reading until the mystery was resolved. Except that I wasn’t reading a book, but what my hand was writing, and what I was writing was a trail of mathematical equations that I knew would ultimately lead me to an answer.

  Some Responses to “What Is Reality?”

  The question has a meaningful answer. Elementary particles in motion

  Earth, wind, fire, air and quintessence

  Atoms in motion

  Elementary particles in motion

  Strings in motion

  Quantum fields in curved spacetime

  M-theory (substitute your favorite capital letter…)

  A divine creation

  A social construct

  A neurophysiological construct

  A dream

  Information

  A simulation (à la The Matrix)

  A mathematical structure

  The Level IV Multiverse

  The question lacks a meaningful answer. There is a reality, but we humans can’t fully know it: we have no access to what Immanuel Kant called “das Ding an sich.”

  Reality is fundamentally unknowable.

  Not only don’t we know it, but we couldn’t express it if we did.

  Science is nothing but a story (postmodern answer by Jacques Derrida and others).

  Reality is all in our head (constructivist answer).

  Reality doesn’t exist (solipsism).

  I’m a physicist, and I’m taking a physics approach to the mysteries of reality. To me, this means starting with great questions such as “How big is our Universe?” and “What’s everything made of?” and treating them exactly like detective mysteries: combining clever observations and reasoning and persistently following each clue wherever it leads.

  The Journey Begins

  A physics approach? Isn’t that a great way to turn something exciting into something boring? When the person sitting next to me on a plane asks what I do, I have two options. If I feel like talking, I’ll say, “Astronomy,” which infallibly triggers an interesting conversation.1 If I don’t, I’ll say, “Physics,” at which point they typically say something like “Oh, that was my worst subject in high school,” and leave me alone for the rest of the flight.

  Indeed, physics was also my least-favorite subject in high school. I still remember my very first physics class. With a monotonous and sedative voice, our teacher announced that we were going to learn about density. That density was mass divided by volume. So if the mass was blah and the volume was blah, then we could calculate that the density was blah blah. After that point, all I remember is a big blur. And that whenever his experiments failed, he’d blame humidity and say, “It worked this morning.” And that some friends of mine couldn’t figure out why their experiment wasn’t working until they discovered that I’d mischievously attached a magnet underneath their oscilloscope.…

  When the time came to apply for college, I decided against physics and other technical fields, and ended up at the Stockholm School of Economics, focusing on environmental issues. I wanted to do my small part to make our planet a better place, and felt that the main problem wasn’t that we lacked technical solutions, but that we didn’t properly use the technology we had. I figured that the best way to affect people’s behavior was through their wallets, and was intrigued by the idea of creating economic incentives that aligned individual egoism with the common good. Alas, I soon grew disillusioned, concluding that economics was largely a form of intellectual prostitution where you got rewarded for saying what the powers that be wanted to hear. Whatever a politician wanted to do, he or she could find an economist as advisor who had argued for doing precisely that. Franklin D. Roosevelt wanted to increase government spending, so he listened to John Maynard Keynes, whereas Ronald Reagan wanted to decrease government spending, so he listened to Milton Friedman.

  Then my classmate Johan Oldhoff gave me the book that changed everything: Surely You’re Joking, Mr. Feynman! I never got to meet Richard Feynman, but he’s the reason I switched to physics. Although the book wasn’t really about physics, dwelling more on topics such as how to pick locks and how to pick up women, I could read between the lines that this guy just loved physics. Which really intrigued me. If you see a mediocre-looking guy walking arm in arm with a gorgeous woman, you probably wonder if you’re missing something. Presumably, she’s seen some hidden quality in him. Suddenly I felt the same way about physics: what did Feynman see that I’d missed in high school?

  I just had to solve this mystery, so I sat down with volume 1 of The Feynman Lectures on Physics, which I found in Dad’s bookcase, and started reading: “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words?”

  Whoa—this guy was nothing like my high-school physics teacher! Feynman continued: “I believe it is that […] all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart but repelling upon being squeezed into one another.”

  A lightbulb went off in my head. I read on and on and on, spellbound. I felt like I was having a religious experience. I finally got it! I had the epiphany that explained what I’d been missing all along, and what Feynman had realized: physics is the ultimate intellectual adventure, the quest to understand the deepest mysteries of our Universe. Physics doesn’t take something fascinating and make it boring. Rather, it helps us see more clearly, adding to the beauty and wonder of the world around us. When I bike to work in the fall, I see beauty in the trees tinged with red, orange and gold. But seeing these trees through the lens of physics reveals even more beauty, captured by the Feynman quote that opens this chapter. And the deeper I look, the more elegance I glimpse: we’ll see in Chapter 3 how the trees ultimately come from stars, and we’ll see in Chapter 8 how studying their building blocks suggests their existence in parallel universes.

  At this time, I had a girlfriend studying physics at the Royal Institute of Technology, and her textbooks seemed so much more interesting than mine. Our relationship didn’t last, but my love for physics did. Since college was free in Sweden, I enrolled in her university without telling the Stockholm School of Economics administrators about my secret double life. My detective investigation had officially begun, and this book is my report a quarter of a century later.

  So what is reality, then? My goal with this audaciously titled chapter isn’t to arrogantly try to sell you on an ultimate answer (although we’ll explore intriguing possibilities in the last part of the book), but rather to invite you along on my personal journey of exploration, and to share with you my excitement and reflections about these mind-expanding mysteries. Like me, I think you’ll conclude that whatever reality is, it’s wildly different from what we once thought, and a fascinating enigma at the very heart of our everyday lives. I hope you will, like me, find that this places everyday problems such as parking tickets and heartaches in a refreshing perspective, making it easier to take them in stride and focus on enjoying life and its mysteries to the fullest.

  When I first discussed my ideas for this book with John Bro
ckman, now my book agent, he gave me clear marching orders: “I don’t want a textbook—I want your book.” So this book is a scientific autobiography of sorts: although it’s more about physics than it’s about me, it’s certainly not your standard popular science book that attempts to survey physics in an objective way, reflecting the community consensus and giving equal space to all opposing viewpoints. Rather, it’s my personal quest for the ultimate nature of reality, which I hope you’ll enjoy seeing through my eyes. Together, we’ll explore the clues that I personally find the most fascinating, and try to figure out what it all means.

  We’ll begin our journey by surveying how the whole context of the question “What is reality?” has been transformed by recent scientific breakthroughs, with physics shedding new light on our external reality from the largest (Chapters 2–6) to the smallest (Chapters 7–8) scales. In Part I of the book, we’ll pursue the question “How big is our Universe?” and seek its ultimate conclusion by traveling out to ever-larger cosmic scales, exploring both our cosmic origins and two types of parallel universes, finding hints that space is in a sense mathematical. In Part II of the book, we’ll relentlessly pursue the question “What’s everything made of?” by journeying into the subatomic microcosm, examining a third kind of parallel universe and finding hints that the ultimate building blocks of matter are also in a sense mathematical. In Part III of the book, we’ll take a step back and consider what all this might mean for the ultimate nature of reality. We’ll begin by arguing that our failure to understand consciousness doesn’t stand in the way of a complete understanding of the external physical reality. We’ll then delve into my most radical and controversial idea: that the ultimate reality is purely mathematical, demoting familiar notions such as randomness, complexity, and even change to the status of illusions, and implying that there’s a fourth and ultimate level of parallel universes. We’ll wrap up our journey in Chapter 13 by returning home, exploring what this all means for the future prospects of life in our Universe, for us humans, and for you personally. You’ll find our travel planner in Figure 1.3 with my reading tips. A fascinating journey awaits us. Let’s begin!

  Figure 1.3: How to read this book. If you’ve read lots of modern popular-science books and feel that you already understand curved space, our Big Bang, the cosmic microwave background, dark energy, quantum mechanics etc., then you may consider skipping Chapters 2, 3, 4 and 7 after reviewing the “Bottom Line” boxes that follow them, and if you’re a professional physicist, you might consider skipping Chapter 5 as well. But many concepts that may sound familiar are startlingly subtle, and if you can’t answer all of questions 1–16 in Chapter 2, I hope you’ll learn from the early material as well and see how the later chapters logically build on it.

  Click here to see a larger image.

  THE BOTTOM LINE

  • I feel that the most important lesson physics has taught us about the ultimate nature of reality is that, whatever it is, it’s very different from how it seems.

  • In Part I of this book, we’ll zoom out and explore physical reality on the largest scales, from planets to stars, galaxies, superclusters, our Universe and two possible levels of parallel universes.

  • In Part II of the book, we’ll zoom in and explore physical reality on the smallest scales, from atoms to their even more fundamental building blocks, encountering a third level of parallel universes.

  • In Part III, we’ll take a step back and examine the ultimate nature of this strange physical reality, investigating the possibility that it’s ultimately purely mathematical, specifically a mathematical structure that’s part of a fourth and ultimate level of parallel universes.

  • Reality means very different things to different people. I use the word to mean the ultimate nature of the outside physical world that we’re part of, and ever since I was a kid, I’ve been inspired and fascinated by the quest to understand it better.

  • This book is about my personal journey to explore the nature of reality—please join me!

  * * *

  1This conversation sometimes begins: “Oh, astrology! I’m a Virgo.” When I’ve instead given the more precise answer “Cosmology,” I’ve gotten answers such as “Oh, cosmetology!”—with follow-up questions about eyeliner and mascara.

  Part One

  ZOOMING OUT

  2

  Our Place in Space

  Space … is big. Really big. You just won’t believe how vastly hugely mind-bogglingly big it is.

  —Douglas Adams, in The Hitchhiker’s Guide to the Galaxy

  Cosmic Questions

  He raises his hand, and I gesture to him that it’s okay to ask his question. “Does space go on forever?” he asks.

  My jaw drops. Wow. I’ve just finished a little astronomy presentation at Kids’ Corner, my kids’ after-school program in Winchester, and this extremely cute group of kindergartners is sitting on the floor, looking at me with big inquisitive eyes, awaiting a response. And this five-year-old boy just asked me a question I can’t answer! Indeed, a question that nobody on our planet can answer. Yet it’s not a hopelessly metaphysical question, but a serious scientific question for which theories I’ll soon tell you about make definite predictions, and one on which ongoing experiments are shedding further light. In fact, I think it’s a truly great question about the fundamental nature of our physical reality—as we’ll see in Chapter 5, this question will lead us to two different kinds of parallel universes.

  I’d been growing progressively more misanthropic over the years by following world news, but in just a few seconds, this kindergartner managed to give a major boost to my faith in the potential of humankind. If a five-year-old can say such profound things, then imagine what we grown-ups have the potential to accomplish together in the right circumstances! He also reminded me of the importance of good teaching. We’re all born with curiosity, but at some point, school usually manages to knock that out of us. I feel that my main responsibility as a teacher isn’t to convey facts, but to rekindle that lost enthusiasm for asking questions.

  I love questions. Especially big ones. I feel so fortunate to be able to spend much of my time tackling interesting questions. That I can call this activity work and make a living from it is just luck beyond my wildest expectations. Here’s my top-sixteen list of questions that I often get asked:

  1. How could space not be infinite?

  2. How could an infinite space get created in a finite time?

  3. What’s our Universe expanding into?

  4. Where in space did our Big Bang explosion happen?

  5. Did our Big Bang happen at a single point?

  6. If our Universe is only 14 billion years old, how can we see objects that are 30 billion light-years away?

  7. Don’t galaxies receding faster than the speed of light violate relativity theory?

  8. Are galaxies really moving away from us, or is space just expanding?

  9. Is the Milky Way expanding?

  10. Do we have evidence for a Big Bang singularity?

  11. Doesn’t creation of the matter around us from almost nothing by inflation violate energy conservation?

  12. What caused our Big Bang?

  13. What came before our Big Bang?

  14. What’s the ultimate fate of our Universe?

  15. What are dark matter and dark energy?

  16. Are we insignificant?

  Let’s tackle these questions together. We’ll answer eleven of them in the next four chapters, and find interesting twists on the remaining five. But first, let’s return to that kindergartner’s question, which will form a central theme of this entire first part of the book: Does space go on forever?

  How Big Is Space?

  My dad once gave me the following advice: “If you have a tough question that you can’t answer, first tackle a simpler question that you can’t answer.” In this spirit, let’s begin by asking what the minimum size is that space must have without contradicting our observations. Figure 2.1 illust
rates that the answer to this question has increased dramatically over the centuries: we now know our space to be at least a billion trillion (1021) times bigger than the largest distances our hunter-gatherer ancestors knew about—which was essentially how far they walked in a lifetime. Moreover, the figure shows that this expansion of our horizons wasn’t a one-shot deal, but something that recurred repeatedly. Every time we humans have managed to zoom out and map our Universe on larger scales, we’ve discovered that everything we previously knew about was part of something greater. As illustrated in Figure 2.2, our homeland is part of a planet, which is part of a solar system, which is part of a galaxy, which is part of a cosmic pattern of galactic clustering, which is part of our observable Universe, which we’ll argue is part of one or more levels of parallel universes.

  Figure 2.1: Our lower bound on the size of our Universe has kept growing, as we’ll describe in this chapter. Note that the vertical scale is extreme, increasing tenfold with every tick mark.

  Like an ostrich with its head in the sand, we humans have repeatedly assumed that all we could see was all that existed, hubristically imagining ourselves at the center of everything. In our quest to understand the cosmos, underestimation has thus been a persistent theme. However, the insights illustrated in Figure 2.1 reflect also a second theme, which I find inspiring: we’ve repeatedly underestimated not only the size of our cosmos, but also the power of our human mind to understand it. Our cave-dwelling ancestors had just as big brains as we have, and since they didn’t spend their evenings watching TV, I’m sure they asked questions like “What’s all that stuff up there in the sky?” and “Where does it all come from?” They’d been told beautiful myths and stories, but little did they realize that they had it in them to actually figure out the answers to these questions for themselves. And that the secret lay not in learning to fly into space to examine the celestial objects, but in letting their human minds fly.