by Max Tegmark
Such weirdness amplification clearly happens whenever we make quantum measurements: if you measure the position of a single atom that’s in two places at once1 and write the result on a piece of paper, then the particle position will determine the motion of your hand, and your pencil will therefore end up in two places at once.
Last but not least, such weirdness amplification happens regularly even within your brain. Whether a given neuron fires at a given time depends on whether the sum of all its input signals exceeds a certain threshold, and this can make neural networks highly unstable, much like the weather and the balanced pencil. This was exactly what was happening on the opening page of this book, when I was biking to school and decided whether to look right. Suppose my snap decision was such a close call that it came down to whether a single calcium atom would enter a particular synaptic junction in my prefrontal cortex, causing a particular neuron to fire an electrical signal that would trigger a whole cascade of activity by other neurons in your brain which collectively encode Let’s look! So if that calcium atom started in two slightly different places at once, then half a second later, my pupils would have been pointing in two opposite directions at once, and before long, my entire body will be in two different places at once, one of them being the morgue, making this my own version of the Schrödinger’s cat experiment—with me in the role of the cat.…
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1One classic experiment that does this involves sending a single silver atom through a so-called Stern-Gerlach apparatus, which will put it in two different places depending on its spin.
Quantum Confusion
So there I was in my girlfriend’s dorm room in Stockholm, deeply frustrated and confused. Now you know why. My first quantum exam was coming up, and the more I thought about the Copenhagen interpretation that my textbook presented as obvious and absolute truth, the more disturbed I felt. Quantum weirdness clearly couldn’t be confined to the microworld. Schrödinger’s cat was out of the bag. I didn’t mind the weirdness per se, but here’s what really bothered me back then: suppose that you personally perform Schrödinger’s cat experiment. If that textbook is right, then the cat’s wavefunction collapses and it becomes definitely dead or definitely alive at the instant when you personally look at it. But what if I’m standing outside your lab and consider the wavefunction describing all the particles that make up the cat, you and everything else in your lab? Surely all those particles should obey the Schrödinger equation regardless of whether they’re part of a living being or not? And in that case, the book implies that the cat’s wavefunction collapses only when I myself enter the lab and observe what’s going on, not at the earlier time when you took a look. And in that case, before I looked, you yourself would have been in a superposition of feeling guilty about killing the cat and relieved that it made it. In other words, at best the Copenhagen interpretation was incomplete, refusing to answer the question of when precisely the wavefunction collapsed. At worst, it was inconsistent, since the wavefunction of our whole Universe would never collapse from the viewpoint of someone in a parallel universe who could never observe us.
Please join me in the next chapter to explore what quantum mechanics is really telling us about the nature of reality. Perhaps we Swedes have a genetic predisposition toward badmouthing our southwestern neighbors, but when I think about the Copenhagen interpretation, I just can’t get this Hamlet quote out of my mind: “Something is rotten in the state of Denmark.”
THE BOTTOM LINE
• Everything, even light and people, seems to be made of particles.
• These particles are purely mathematical objects in the sense that their only intrinsic properties are mathematical properties—numbers with names like charge, spin and lepton number.
• These particles don’t obey the classical laws of physics.
• Mathematically, the state of these particles (which should perhaps be called “wavicles”) can’t be described by six numbers (representing their position and velocity), but by a wavefunction, describing the extent to which they are in different places.
• This gives them properties both of traditional particles (they’re either here or there) and of waves (they can be in several places at once in a so-called superposition).
• Particles aren’t allowed to be in only one place (the Heisenberg uncertainty principle), which prevents atoms from collapsing.
• The future behavior of particles is described not by Newton’s laws, but by the Schrödinger equation.
• This equation shows that innocent microscopic superpositions can get amplified into crazy macroscopic superpositions such as Schrödinger’s cat, and you personally being in two places at once.
• The textbook formulation postulates that the wavefunction sometimes “collapses,” violating the Schrödinger equation and introducing fundamental randomness into nature.
• Physicists argue passionately about what this all means.
• The textbook formulation of quantum mechanics is either incomplete or inconsistent.
8
The Level III Multiverse
When you come to a fork in the road, take it.
—Yogi Berra
“Wow—it’s beautiful down there!” The San Francisco Bay glistened in the evening sun, and I felt even more excited than when my parents gave me my first-ever magic set. I was glued to my window, trying to make out all the famous landmarks I was seeing for the very first time. Since saving up enough money as a cheese salesman to take the train to Spain at age seventeen, I’d fallen more and more in love with travel. Since reading Feynman in college, I’d fallen more and more in love with physics. Now, after twenty-three years of living with ice and snow, I’d get to spend four years doing both! In what seemed to me one of the coolest places on Earth, and the perfect place to have crazy ideas.
Through a wild stroke of luck, I’d been admitted to Berkeley for physics grad school, and even though my expectations were perhaps unreasonably high, those four years ended up superseding them on all counts. I found Berkeley to be every bit as inspiring, wild and crazy a place as I’d hoped. I ended up with an Australian girlfriend the very day after I arrived. I found it convenient to hail from an obscure country that most people couldn’t find on the map: my nationality allowed me to be as crazy as I wanted, quickly earning the nickname “Mad Max,” and get away with it—people would give me the benefit of the doubt and assume that this was normal behavior in Sweden. Not that I needed to make excuses. A student who ended up living across the street from me would only attend class naked, and made national news when he got expelled. A physics classmate with whom I did homework problems doubled as a porn actor to help finance his studies. The guy across the hall from me in International House got arrested with a gun and a list of names of “People to Destroy.”1 So if your most crazy traits were being Swedish and having strange physics ideas, you blended right in.
Back in high school, my friend Magnus Bodin had inspired me with his contrarian philosophy. Since everyone else sent their letters in rectangular envelopes, he made triangular ones. Ever since, when I see the majority do things one way, I instinctively look for alternatives. For example, all my classmates spent ages on electromagnetism homework during our first year, so I talked our professor into letting me skip this in return for an oral exam at the end of the course. Instead, I spent endless hours in the library feeding my curiosity, learning all sorts of amazing physics that wasn’t in the textbooks—and which has kept helping me to this day. It also freed me up to pursue research on the side.
For the first time in my life, I made friends who shared my obsession with crazy physics questions, and it felt amazing to sit up late at night with these kindred souls speculating about the ultimate nature of reality. Justin Bendich, whose scruffy appearance reminded me of Shaggy from Scooby-Doo, was a gold mine of information and would give thoughtful answers to even my wackiest questions. Bill Poirier was obsessed with information theory, and together we came up with a cool informatio
n theory–based improvement of the Heisenberg uncertainty principle that had us extremely excited until I found an article about it in the library. I felt like the luckiest guy on the planet: I’d figured out what I really, really wanted to do, and I was doing it.
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1The student newspaper The Daily Cal published a quote from me, followed by “according to a Swedish student who lived across the hall and requested to remain anonymous,” and for days afterward, my friends would come up and say: “Hey, Max, you look so anonymous today!”
The Level III Multiverse
My new teachers were inspiring, too. I learned quantum mechanics much more thoroughly from Eugene Commins, whose dry humor livened up the blackboards full of equations. I once raised my hand and asked, “Isn’t that like adding apples and pears?”—a common Swedish expression. “No,” he replied. “It’s like adding apples and oranges.”
Although his one-year course taught me many useful technical tools, it never answered my burning quantum questions. In fact, it didn’t even ask them, leaving me stuck struggling with them on my own. Was quantum mechanics inconsistent? Did the wavefunction really collapse? If so, when? If not, then why didn’t we see things in two places at once, and where did the randomness and probabilities of quantum mechanics come from?
I’d heard that, back in 1957, Princeton grad student Hugh Everett III had proposed a truly radical answer involving parallel universes, and I was curious to learn the details. However, this idea was generally ignored and rarely taught. Although I met a few people who had heard of it, none of them had actually read his Ph.D. thesis describing it, which was buried in an out-of-print book. All our library had was a radically abbreviated version where the parallel-universe business was never explicitly mentioned. But in November 1990, my searches paid off, and I finally found that elusive book. Rather appropriately, I found it in a Berkeley store specializing in radical publications, where they also carried titles such as The Anarchist’s Cookbook.
Everett’s Ph.D. thesis totally blew me away. I felt like scales had fallen from my eyes. Suddenly it all made sense to me! Everett had been bothered by exactly the same things that bothered me, but rather than just leaving it at that, he’d pushed ahead, explored possible solutions, and discovered something remarkable. When you have a radical idea, it’s so easy to say to yourself, “Of course that can’t work,” and drop it. But if you hold the thought just a little longer and ask yourself, “Well, why exactly can’t it work?” and find that you’re struggling to come up with a logically watertight answer, then you might be onto something big.
So what was Everett’s radical idea? It’s amazingly simple to state:
The wavefunction never collapses. Ever.
In other words, the wavefunction that fully describes our Universe just changes deterministically at all times, always governed by the Schrödinger equation, regardless of whether there are observations taking place or not. So the Schrödinger equation rules supreme, without ifs, ands or buts. This means that you can think of Everett’s theory as “Quantum Mechanics Lite”: take the usual textbook version of the theory and simply drop the postulate that talks about wavefunction collapse and probabilities.
This surprised me, because the rumors I’d heard suggested that Everett postulated crazy-sounding stuff like parallel universes and that our Universe would split into parallel universes whenever you made an observation. Indeed, even today, many of my physics colleagues still think that this is what Everett assumed. Reading Everett’s book taught me a lesson not only in physics but also in sociology: I learned the importance of going back and checking the source material for yourself rather than relying on secondhand information. It’s not only in politics that people get misquoted, misinterpreted and misrepresented, and Everett’s Ph.D. thesis is a great example of something that, to first approximation, everyone in physics has an opinion about and almost nobody has read.1
I just couldn’t put his book down. His logic was beautiful: he didn’t assume any of that crazy-sounding stuff, but it all followed as consequences of his assumption! At first it seemed so simple that it couldn’t possibly work. After all, Niels Bohr and his collaborators were smart people and had invented wavefunction collapse for a reason, to explain why experiments seemed to have definite outcomes. But Everett realized something amazing: even if experiments didn’t have definite outcomes, it would still seem as though they did!
Figure 8.1 shows an example of how I think about this. In this thought experiment that I’ll call “Quantum Cards,” you take a card with a perfectly sharp bottom edge, balance it on a table, and bet $100 that it’s going to land face-up when it falls. You keep your eyes closed until you hear that the card has fallen, then look to see whether you’ve won or lost your bet. According to classical physics, it will in principle stay balanced forever.2 According to the Schrödinger equation, it will fall down in a few seconds even if you do the best possible job balancing it, because the Heisenberg uncertainty principle states that it can’t be in only one position (straight up) without moving. Yet since the initial state was left-right symmetric, the final state must be so as well. This implies that it falls down in both directions at once, in superposition.
When you open your eyes and look at the card, you’re making an observation. So according to the Copenhagen interpretation, the wavefunction would collapse and you’d see the card either face-up or face-down, with 50% probability for each outcome. You’d be either smiling about easy profits or cursing yourself for being tricked into wasting a hundred bucks on a silly physics experiment—and the laws of physics wouldn’t predict which, since it would have been caused by inherent randomness in nature. And according to Everett? Well, to him, there was nothing magical about observation: it was just a physical process like any other, but one characterized by transfer of information—in this case from the card to your brain. If the wavefunction had described the card as only face-up, you’d have gotten happy, and vice versa. Combining these facts with the Schrödinger equation, he could easily calculate exactly what would happen to the wavefunction: it would change to describe a superposition of two different configurations of the particles that made up you and the card: one where the card was face-up and you were cheerful, and one where it was face-down and you were disappointed. There are three key insights here:
1. The experiment puts your mind into two states at once. It’s basically a nonlethal version of Schrödinger’s cat experiment, with you in the role of the cat.
2. These two mind states are completely unaware of each other.
3. The state of your mind becomes linked with the state of the card, in such a way that everything is consistent. (The wavefunction doesn’t describe any particle configuration where you perceive the card face-up when it’s face-down.)
Figure 8.1: The Quantum Cards thought experiment: At 10:00 a.m., you balance a card on its edge, bet $100 on it falling face-up, and close your eyes. Ten seconds later, the card has fallen down both to the left and to the right in quantum superposition, so the wavefunction describes the card being in two places at once. Another ten seconds later, you’ve opened your eyes and looked at the card, so the wavefunction describes your being happy and sad at once. Although there’s still only one wavefunction and one quantum reality (within which particles making up both the card and you are in two places at once), Everett realized that this is in practice as if our Universe has split into two parallel universes (bottom), with a definite outcome in each of them.
Click here to see a larger image.
It’s easy to prove that the Schrödinger equation always keeps things consistent like this. For example, if your broke friend enters the room and asks you what’s up, the state of all the particles (making up the card, you and your friend) evolves into a quantum superposition of “card down/you sad/friend empathizes” and “card up/you happy/friend asks you for loan.”
Putting all this together, as illustrated in Figure 8.1, Everett realized that even though there’s still only on
e wavefunction and one quantum reality (within which many of the particles making up our Universe are in two places at once), this is in practice as if our Universe has split into two parallel universes! At the end of this experiment, there will be two different versions of you, each subjectively feeling just as real as the other, but completely unaware of each other’s existence.
This was when my head really started to spin, because the Quantum Cards experiment is just one particular example of how microscopic quantum weirdness gets amplified into macroscopic quantum weirdness. As we discussed in the last chapter, such amplification of small differences into big differences happens virtually all the time, like when a cosmic ray–particle hit does/doesn’t give someone a cancerous mutation, when today’s atmospheric conditions do/don’t evolve into a Category 4 hurricane next year, or when you use your neurons to make decisions. In other words, parallel-universe splitting is happening constantly, making the number of quantum parallel universes truly dizzying. Since such splitting has been going on ever since our Big Bang, pretty much any version of history that you can imagine has actually played out in a quantum parallel universe, as long as it doesn’t violate any physical laws. This makes vastly more parallel universes than there are grains of sand in our Universe. In summary, Everett showed that if the wavefunction never collapses, then the familiar reality that we perceive is merely the tip of an ontological iceberg, constituting a minuscule part of the true quantum reality.