Our Mathematical Universe

by Max Tegmark

  Quantum Suicide

  I used to feel that there were two kinds of physicists: the titans and the mere mortals. The titans were towering historical figures such as Newton, Einstein, Schrödinger and Feynman who possessed supernatural powers and were surrounded by legends and myths. The mere mortals were the physicists I’d met who, although perhaps brilliant, were clearly just ordinary people like you and me. And then there was John Wheeler. When I saw him in January 1996, I felt overwhelmed. There he was, eighty-four years old, in the Copenhagen cafeteria where we had our conference lunch. To me, he was the “last titan.” He’d worked with Niels Bohr on nuclear physics. He’d coined the term black hole. He’d pioneered spacetime foam. He’d had Feynman and Everett as grad students. He’d become one of my physics superheroes with his passion for wild ideas. And there he was, simply eating, like a mere mortal! I felt that I just had to introduce myself, or I’d never forgive myself, but I was extremely nervous as I approached his table. I’d been blown off before by people above me in the academic food chain: two different professors had turned their backs on me and walked away in mid-conversation, and yet they were mere mortals. So I was stunned by what happened. There I was, an inexperienced postdoc and a total nobody, yet Wheeler greeted me with a warm smile and invited me to join him for lunch! After hearing that I was interested in quantum mechanics, he told me about some new ideas he had about the subject of existence, and gave me a copy of some of his recent notes. He never talked down to me, and spoke to me in a way that made me feel like an equal even though clearly I wasn’t. A fortnight later, I even got an email from him—an email from a titan! He wrote:

  Figure 8.9: John Wheeler as I remember him (here, in 2004, holding a book from his ninetieth-birthday conference that I helped organize); flanked by his grad students Richard Feynman (around 1943), Hugh Everett (around 1957) and Wojciech Zurek (in 2007 by that Icelandic waterfall). (Image credits: Pamela Bond Contractor [Ellipses Enterprises], Mark Oliver Everett, Anthony Aguirre)

  It was a great pleasure and encouragement to talk to you in Copenhagen as I believe you share my belief that under and behind quantum mechanics lies some deep and wonderful principle yet to be discovered, as Einstein’s great geometric idea threw unexpected light on the power and scope of Newton’s supposedly all-embracing theory. The likelihood of such a discovery is surely proportional to our belief that there is something there to be discovered.

  He went on to encourage me to come to Princeton, writing, “I am eager to be able to talk to you every day.” At that time, I was deciding between postdoc offers—how could I possibly turn down Princeton after that? Once I’d moved to Princeton, I started visiting him regularly, and gradually got to know him better. He and his wife came to my housewarming party. He even signed my New Jersey marriage license—in my world, this felt like having God as a witness.

  In his office, he’d often get interrupted, so his favorite way to talk was while “doing orbits,” walking the third-floor corridors that looped around the inner courtyards of the Princeton University physics building. His colorful stories made history come alive for me, such as when he described how it felt to see the first hydrogen bomb go off, and to meet with Klaus Fuchs, who leaked nuclear-weapon secrets to the Soviet Union. He also gave me a more personal connection with the founding fathers of my field, who for him had been mere mortals.

  I showed him arguably my craziest paper ever, which explored the mathematical-universe idea that this book is leading up to, and he said he liked it. When the editor rejected it for being “too speculative” despite a positive referee report, he encouraged me to appeal the rejection, which worked. Later, we wrote an article together for Scientific American called “100 Years of Quantum Mysteries,” in which we tried to explain both quantum parallel universes and decoherence in plain English. When I asked him whether he really believed in quantum parallel universes, he said, “I try to find time to believe in them Mondays, Wednesdays and Fridays.”

  I very rarely cry, but I did in 2008 when I learned that John Wheeler had died. He really touched me and inspired me, and at his memorial service, it was palpable how many others felt the same way. At the open mike during the reception afterward, when people who felt compelled spoke of him, I said a few words about how much he’d meant to me. That if I had to sum it up in only one word, it would be inspiring. Inspiring that someone so brilliant and famous could be so nice, “treating everyone with equal dignity,” as another speaker aptly put it. And that he encouraged me to follow my heart and work on what I was really passionate about. And that the best testimony to how he had inspired people was to take a good look around the room and see how many amazing people had traveled from at least three continents to be there. The crowd felt like a veritable Who’s Who of physics.

  One afternoon when I was giving John a ride back home to Meadow Lakes, the retirement community where he lived, I excitedly started telling him about a totally crazy-sounding idea I’d just had, which I called “Quantum Suicide.” I’d spent a lot of time wondering whether there was an experiment that could convince you that Everett’s parallel universes were real, and had finally thought of one.

  Surprisingly, this experiment requires only rather low-tech equipment that’s readily available. However, it also requires you to be an unusually dedicated experimentalist, since it amounts to a repeated and faster version of Schrödinger’s cat experiment—with you as the cat. The apparatus is a “quantum machine-gun,” which fires depending on the outcome of a quantum measurement. Specifically, each time the gun is triggered, it places a particle in a superposition where it’s equally in two states at once (spinning clockwise and counterclockwise, say), then measures the particle. If the particle is found to be in the first of the two states, the gun fires, otherwise it merely makes an audible click. The details of the trigger mechanism are irrelevant1 as long as the time scale between the quantum measurement and the actual firing is much shorter than that characteristic of human perception, say, a hundredth of a second.

  Now suppose that you start this quantum machine-gun in an automatic mode where it’s triggered once every second. Regardless of whether you believe in Everett’s parallel universes or not, you’ll predict that you’ll hear a seemingly random sequence of shots and duds such as bang-click-bang-bang-bang-click-click-bang-click-click. Suddenly, you do something radical: you place your head in front of the gun barrel and wait. What do you expect to perceive next? That depends on whether Everett’s parallel universes are real or not! If not, then there’s only one outcome of each quantum measurement, so you’ll definitely be either dead or alive after the first second, with 50% probability for each. So you’d expect to perceive perhaps a click or two if you’re moderately lucky, then “game over,” nothing at all. The probability that you’ll survive n seconds is 1/2n, so your chance of lasting as long as a minute is less than one in a quintillion (10−18). If Everett’s quantum parallel universes are real, on the other hand, there will be two parallel universes after the first second: one where you’re alive and one where you’re dead and there’s blood all over the place. In other words, there’s exactly one copy of you having perceptions both before and after the trigger event, and since it occurred too fast to notice, the prediction is that you’ll hear click with 100% certainty. Wait a little longer, and you’ll find this quite striking: as soon as you put your head in the firing line, the seemingly random sequence of bangs and clicks gives way to just click-click-click-click-click-click-click, etc. After ten clicks, you conclude that you’ve ruled out wavefunction collapse with 99.9% confidence, in the sense that if wavefunction collapse really happened, then the probability of being dead by now would exceed 99.9%. After a minute, you’ll give it only a one-in-a-quintillion chance that Everett is wrong. To allay any concerns that the quantum machine-gun is broken, you remove your head from the firing line, and find that it, as if by magic, reverts back to firing intermittently.

  If you’re now convinced that Everett is right and bring a friend
to witness your experiment, then there’s a twist, however. Whereas you stay alive in only one parallel universe, she remains present in all of them, and typically sees you die after a few seconds. So the only thing you might succeed in convincing her of is that you were a mad scientist.

  John found this interesting. I said I thought that many physicists would undoubtedly rejoice if an omniscient genie appeared at their deathbed, and as a reward for lifelong curiosity granted them the answer to a physics question of their choice. But would they be as happy if the genie forbade them from telling anybody else? Perhaps the greatest irony of quantum mechanics is that if Everett was right, then the situation is quite analogous if, once you feel ready to die, you repeatedly attempt quantum suicide: you might experimentally convince yourself that the quantum parallel universes are real,2 but you can never convince anyone else!

  Well, you could of course convince your friends if you made the suicide experiment a collective one, say, by connecting the quantum trigger to a nuclear bomb, so that you’d end up only with parallel universes where you and your friends were all alive or all dead. But they probably wouldn’t be your friends afterward.

  * * *

  1For example, the particle could be a silver atom that has its spin measured by a so-called Stern-Gerlach apparatus, or it could be a photon that either does or doesn’t pass through a half-silvered mirror.

  2The British philosopher Paul Almond has an interesting counterargument to this claim, which I’ll tell you about in Chapter 11.

  Quantum Immortality?

  After I published a paper about the quantum-suicide idea, New Scientist and The Guardian ran articles about it, which generated a fair bit of attention, and it’s been fun for me to see the idea subsequently appearing in various science-fiction stories. As I mentioned earlier, many people tend to have similar ideas when the time is ripe, and sure enough, I later discovered that other people had thought along similar lines previously, perhaps starting with the Austrian mathematician Hans Moravec, who mentioned the idea in his 1988 artificial intelligence book Mind Children. As opposed to my earlier rediscoveries, however, I felt that this one actually had some impact, by helping get the idea more widely known.

  I soon got deluged with interesting email questions about quantum suicide that got me wondering more about the implications. Here’s my favorite one: can you think of all potentially lethal events in nature as quantum-suicide experiments, so that you should expect subjective immortality? You can answer this question with a simple experiment: wait and see! If one day, after a long sequence of seemingly unlikely coincidences, you find yourself to be the oldest living person on Earth, then that pretty much settles it! Note that you don’t expect to see other people get abnormally old, just as you don’t expect to see other people last long if they try the quantum-suicide experiment.

  So what do the laws of physics predict, assuming that Everett is right and the wavefunction never collapses? To be able to succeed, a successful quantum-suicide experiment needs to satisfy three criteria:

  1. The random-number generator must be quantum, not classical (deterministic), so that you really enter a superposition of dead and alive.

  2. It must kill you (or at least make you unconscious) on a time scale shorter than that on which you can become aware of the outcome of the quantum measurement—otherwise you’ll have a very unhappy version of yourself for a second or more who knows s/he is about to die for sure, and the whole effect gets destroyed.

  3. It must be virtually certain to really kill you, not just injure you.

  Most accidents and common causes of death clearly don’t satisfy all three criteria, suggesting that you won’t feel immortal after all. In particular, regarding criterion 2, under normal circumstances dying isn’t a binary thing where you’re either dead or alive—rather, there’s a whole continuum of states of progressively decreasing self-awareness. What makes the quantum suicide work is that it forces an abrupt transition. I suspect that when I get old, my brain cells will gradually give out (indeed, that’s already started happening…), so that I keep feeling self-aware, but less and less so. This will make the final stage of death quite anticlimactic, sort of like when an amoeba croaks.

  Criterion 3 places a limit on how long you can run your quantum-suicide experiment in practice before fluke events save your life. For example, my neighborhood gets a power failure on average once every few years, about once every 108 ≈ 227 seconds. This means that if my quantum machine-gun uses a power plug rather than battery power, I should expect to experience about twenty-seven straight clicks and then a power failure halting my experiment—because after that, there will be more parallel universes with me alive that have a disabled gun than a functioning gun. The longer I get the machine-gun to work, the crazier the flukes I should expect: for example, after to the tune of sixty-eight seconds’ worth of straight clicks, I should expect my machine-gun to get struck by a meteorite.… In Douglas Adams’s science-fiction spoof The Hitchhiker’s Guide to the Galaxy, there’s an “Infinite Improbability Drive” that makes you experience extremely unlikely events. Although such a device sounds like pure science fiction, it isn’t: the quantum machine-gun effectively acts like one!

  I find criterion 1 particularly interesting. Suppose your suicide device didn’t rely on quantum randomness, but on something like a coin toss, where you could actually predict whether you’d get heads or tails in principle, just not in practice, because you haven’t fully figured out how the coin was initially moving and done the math. Then if you started out with only one parallel universe, there would still only be one parallel universe after the first second, and you’d be either alive or dead depending on the initial position and motion of the coin, so you’d not feel subjectively immortal.

  However, what if the Level I multiverse from Chapter 6 is real? Then there would be infinitely many parallel universes to start with that contained you in subjectively indistinguishable mental states, but with imperceptibly slight differences in the initial position and velocity of the coin. After one second, you’d be dead in half of those universes, but no matter how many times the experiment is repeated, there would always be universes where you never got shot. In other words, this sort of macabre randomized-suicide experiment can reveal the existence of not merely Level III (quantum) parallel universes, but also of parallel universes more generally.

  I know. This stuff sounds seriously nuts. “Don’t try this at home,” as they say. Moreover, as I’ll explain in Chapter 11, I’ve now become convinced that neither quantum suicide nor quantum immortality actually works, because they depend crucially on something that I don’t think exists in nature: an infinitely divisible mathematical continuum. But who really knows? When one fateful day in the future, you think that your own life is about to end, remember this and don’t say to yourself, There’s nothing left now—because there might be. You might be about to discover firsthand that parallel universes really do exist.

  Multiverses Unified

  All animals are equal, but some animals are more equal than others.

  —George Orwell, Animal Farm, 1945

  I just couldn’t get this nagging thought out of my mind: were the Level I and Level III multiverses somehow really one and the same? Could they somehow be unified, just as Maxwell had unified electricity and magnetism into electromagnetism, and Einstein had unified space and time into spacetime? On one hand, their natures seemed quite different: the Level I parallel universes from Chapter 6 are far away in our good old three-dimensional space, while the Level III parallel universes from this chapter can be right here as far as these three dimensions are concerned, but separated from us in Hilbert space, the abstract space with infinitely many dimensions where the wavefunction lives. On the other hand, the Level I and Level III multiverses have a lot in common. Jaume Garriga and Alex Vilenkin had written a paper showing that the Level I parallel universes that may have been created by cosmological inflation contain all the same sequences of events that Everett’
s quantum parallel universes do, and so had I. Figure 8.10 illustrates that if a quantum event causes two events to happen in quantum superposition, effectively splitting your future into two parallel quantum branches, then the parallel quantum outcome that you’re now unaware of is also occurring right here in your particular quantum branch—just really far away in space.

  Figure 8.10: Comparison of Level I and Level III parallel universes. Whereas Level I parallel universes are far away in space, those of Level III are even right here, with quantum events causing classical reality to split and diverge into parallel storylines. Yet Level III adds no new storylines beyond levels I or II.

  Click here to see a larger image.

  There was also another source of nagging: Anthony Aguirre. Anthony is one of my best friends, and our lives are parallel in many ways: we both try to balance our careers with two young sons, we’re both obsessed with big questions, and together we’ve founded the Foundational Questions Institute, fqxi.org, a philanthropically funded organization that funds high-risk, high-reward physics research that conventional funding agencies shy away from. What was he nagging me about? “Are some parallel universes really more equal than others?” he’d ask.

  What he was getting at was that the explanation I gave for quantum probabilities earlier in this chapter works great when you have outcomes with equal probability (like the quantum card whose chances of falling face-up and face-down were both 50%), but not when the probabilities were unequal. For example, suppose you start with the card tilted by an extremely small amount, so that the probability (square of the wavefunction) is 2/3 for it falling face-up and 1/3 for it falling face-down. Then Figure 8.2 would still look the same: there are still 2 × 2 × 2 × 2 = 16 outcomes after four trials, and the most typical outcome is the card falling face-up 50% of the time, not 2/3 of the time. The way that Everett saved the day and nonetheless managed to predict a probability of 2/3 from this was by arguing that some of these outcomes had a larger measure of existence than others and that, specifically, this measure of existence could be calculated as the square of the wavefunction. This worked, and many authors have since given more elaborate arguments for why squaring the wavefunction is the right thing to do, but Anthony convinced me that this was an ugly blemish on Everett’s otherwise elegant argument. People often asked me if I believed that Everett’s parallel universes were real. Answering, “Yeah, but … eh … hrm … some are more real than others” sounded really lame.