by Max Tegmark
THE BOTTOM LINE
• Parallel universes are not a theory, but a prediction of certain theories.
• Eternal inflation predicts that our Universe (the spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang) is just one of infinitely many universes in a Level I multiverse where everything that can happen does happen somewhere.
• For a theory to be scientific, we need not be able to observe and test all its predictions, merely at least one of them. Inflation is the leading theory for our cosmic origins because it’s passed observational tests, and parallel universes seem to be a non-optional part of the package.
• Inflation converts potentiality into reality: if the mathematical equations governing uniform space have multiple solutions, then eternal inflation will create infinite regions of space instantiating each of those solutions—this is the Level II multiverse.
• Many physical laws and constants that are unchanged across a Level I multiverse may vary across the Level II multiverse, so students in Level I parallel universes learn the same things in physics class but different things in history class, while students in Level II parallel universes could learn different things in physics class as well.
• This could explain why many constants in our own Universe are so fine-tuned for life that if they differed by small amounts, life as we know it would be impossible.
• This would also give many numbers we’ve measured in physics a new meaning: they’re not telling us something fundamental about physical reality, but merely something about our location in it, forming part of our cosmic postal code.
• Although these parallel universes remain controversial, the main critique has shifted from “This makes no sense and I hate it” to “I hate it.”
Part Two
ZOOMING IN
7
Cosmic Legos
Everything we call real is made of things that cannot be regarded as real.
—Niels Bohr
No, this just doesn’t make sense! There’s got to be a mistake somewhere! I’m alone in my girlfriend’s dorm room in Stockholm, studying for my first college quantum-mechanics exam. The textbook says that small things such as atoms can be in several places at once, whereas big things such as people can’t. No way! I tell myself. We people are made of atoms, so if they can be in several places at once, surely we can, too! It also says that every time a person observes where an atom is, it randomly jumps to just one of the places where it previously was. But I can’t find any equation defining what exactly is supposed to count as an observation. Would a robot count as an observer? How about a single atom? And the book just said that every quantum system changes deterministically according to the so-called Schrödinger equation. Isn’t that logically inconsistent with this random-jumping business?
Flustered, I muster up the courage to knock on the door of our great expert, a physics professor on the Nobel Committee. Twenty minutes later, I emerge from his office feeling stupid, convinced that I’ve somehow misunderstood the whole thing. This marks the beginning of a long personal journey of mine that still continues, and leads to quantum parallel universes. It’s not until a couple of years later, when I move to Berkeley to do my Ph.D., that I realize that it wasn’t I who had misunderstood. I eventually learn that many famous physicists had been vexed by these problems with quantum mechanics, and I end up having lots of fun writing my own papers on the subject.
However, before telling you how I now think this all fits together (in Chapter 8), I want to take you back in time to really appreciate the craziness of quantum mechanics, and what all the fuss is about.
Figure 7.1: A pencil lead is made of graphite, which is made of layers of carbon atoms (this is a real image from a scanning tunneling microscope), which are made of protons, neutrons and electrons. The protons and neutrons are made of up and down quarks, which may in turn be vibrating strings. The refill pencil leads I bought to work on this book contain about 2 × 1021 atoms, so you could cut them in half at most 71 times.
Atomic Legos
Last time I asked my son Alexander what he wanted for his birthday, he said: “Surprise me! Anything is okay as long as it’s Legos.…” I, too, love Legos, and I feel that our Universe does as well: everything is made of the same basic building blocks, as illustrated in Figure 7.1. I find it quite remarkable that the same cosmic Lego set consisting of the eighty stable atoms from the periodic table1 can be used to build everything from rocks to rabbits, from stars to stereos—the only difference being how many Legos of each kind are used, and how they’re arranged.
The basic Lego idea of indivisible building blocks of course has a venerable history, with our owing the term atom to the ancient Greek word for “indivisible.” Indeed, Plato argued in his dialogue Timaeus that the four basic elements postulated at the time (earth, water, air and fire) consisted of four kinds of atoms, and that these atoms were invisibly small mathematical objects: cubes, icosahedra, octahedra and tetrahedra, respectively, i.e., four of Plato’s five eponymous solids (Figure 7.2). For example, he argued that the sharp corners of the tetrahedron explained why fire was painful, that the ball-like shape of the icosahedron explained water’s ability to flow, and that the unique ability of cubes to be compactly stacked explained Earth’s solidity. Although this cute theory was eventually demolished by observational facts, some aspects of it survive, such as his suggestions that each fundamental element consists of a specific kind of atom, and that properties of a substance are determined by properties of its atoms. Moreover, I’ll argue in Chapter 10 that the ultimate building blocks of our Universe are indeed mathematical in a different way than Plato suggested: not that our Universe is made of mathematical objects, but that it’s a part of a single mathematical object.
Figure 7.2: The five Platonic solids: tetrahedron, cube, octahedron, dodecahedron and icosahedron. Only the dodecahedron was excluded from Plato’s atomic theory; sometimes viewed as a cult object of mysterious mythical significance, it figures in art from ancient times through Salvador Dalí’s Sacrament of the Last Supper.
It took another two millennia for the modern theory of atoms to really catch on, and the famous Austrian physicist Ernest Mach refused to believe in the reality of atoms even in the early 1900s. He’d undoubtedly have been impressed by our current ability to image individual atoms (Figure 7.1) and even manipulate them.
* * *
1There are 80 kinds of stable atoms, containing all numbers of protons from 1 (hydrogen) through 82 (lead), except for 43 (technetium) and 61 (promethium), which are radioactive and unstable. Many of these atoms have more than one stable version corresponding to different numbers of neutrons (so-called isotopes); the total number of stable atomic isotopes is 257. There are about 338 isotopes found naturally here on Earth, if we also count about 30 isotopes with half lives longer than 80 million years and about 50 more short-lived ones.
Nuclear Legos
The very success of the atomic hypothesis naturally led to the question of whether atom was a misnomer: if macroscopic objects are all made of the smaller Legos that we call atoms, might they in turn be divisible into some form of smaller Legos that could be rearranged?
I find it extremely elegant that all the atoms in our periodic table are in fact made up of merely three kinds of smaller Lego blocks, even fewer than the four in Plato’s theory. We encountered them briefly in Chapter 3, and Figure 7.1 illustrates how these three—protons, neutrons and electrons—are arranged much like a miniature solar system with electrons orbiting the compact ball of protons and neutrons that we call the atomic nucleus. Whereas the Earth is kept in its orbit around the Sun by the attractive gravitational force between them, the electrons are kept in the atoms by the electrical force that attracts them to the protons (electrons have negative charge, protons have positive charge, and opposite charges attract). Since electrons also feel attracted to the protons in other atoms, they can help bind different atoms together i
nto the larger structures we know as molecules. If the atomic nuclei and the electrons get shuffled around without changing the number of each kind, then we call that a chemical reaction, regardless of whether it’s fast like a forest fire (which is mostly carbon and hydrogen atoms in wood and leaves combining with oxygen from the air to form carbon dioxide and water molecules) or slow like a growing tree (which is mostly the reverse reaction, powered by sunlight).
Over centuries, alchemists tried in vain to convert certain kinds of atoms into others, typically cheaper ones like lead into more expensive ones like gold. Why did they all fail? An atom is simply named according to the number of protons it contains (1 = hydrogen, 79 = gold, etc.), so what the alchemists failed to do was clearly to play Legos with the protons and move them from one atom to another. Why couldn’t they do it? We now know that they failed not because they tried something impossible, but merely because they didn’t use enough energy! Since the electric force causes equal charges to repel each other, the protons in atomic nuclei would fly apart unless some more powerful force held them together. The aptly named strong nuclear force does just this, and acts like a sort of nuclear Velcro that holds both protons and neutrons together as long as they get sufficiently close. It’s so strong that you need extreme violence to overpower it: whereas slamming two hydrogen molecules (each consisting of a pair of hydrogen atoms) together at 50 kilometers per second can break them apart so that their atoms get separated, you’d need to crash two helium nuclei (each consisting of two protons and two neutrons) together at the dizzying speed of 36,000 kilometers per second to stand a chance of breaking them apart into separate neutrons and protons—that’s about 12% of the speed of light, and fast enough to get you from New York to San Francisco in a tenth of a second.
In nature, such violent collisions happen when it gets extremely hot—millions of degrees. There were no atoms around in our early Universe except hydrogen plasma (single protons), since it was so hot that any protons or neutrons stuck together as heavier atoms were smashed apart. As our Universe gradually expanded and cooled, there was a brief period of a few minutes when collisions were still strong enough to overcome the electric repulsion between protons, but no longer strong enough to overpower the strong “Velcro” force that made them and neutrons stick together as helium: this was the period of Gamow’s Big Bang nucleosynthesis that we explored in Chapter 3. In the core of our Sun, the temperature is similarly in that magic range where hydrogen atoms can fuse into helium atoms.
The laws of economics tell us that atoms are expensive if they’re rare, and the laws of physics tell us that they’re rare if they require unusually high temperatures to make. Putting this together tells us that if atoms could talk, the priciest ones would tell the best stories. Garden-variety atoms such as carbon, nitrogen and oxygen (which together with hydrogen make up 96% of your body weight) are so cheap because garden-variety stars such as our Sun can produce them in their death throes, after which they can form new solar systems in a cosmic recycling event. Gold, on the other hand, is produced when a star dies in a supernova explosion so violent and rare that it, during a fraction of a second, releases about as much energy as all the other stars in our observable Universe combined. No wonder making gold eluded the alchemists.
Particle-Physics Legos
If everyday stuff is made of atoms and atoms are made of smaller pieces (neutrons, protons and electrons), then are these in turn made of some form of still smaller Legos? History has taught us the way to tackle this question experimentally: collide these smallest known building blocks together really hard and check if they break apart. This procedure has been tried with ever-larger particle colliders, but electrons still show no sign of being made of anything smaller despite having been smashed at 99.999999999% of the speed of light at the CERN Laboratory outside Geneva. Colliding protons, on the other hand, has revealed that both they and neutrons are made of smaller particles known as up quarks and down quarks. Two ups and a down make a proton (Figure 7.1), while two downs and an up make a neutron. Moreover, a slew of previously unknown particles have been produced in particle collisions (see Figure 7.3).
All of these new particles, with exotic names such as pions, kaons, Sigmas, Omegas, muons, tauons, W-bosons and Z-bosons, are unstable and decay into more familiar stuff in a split second, and clever detective work has revealed that all except the last four are made of quarks—not just ups and downs, but also four new unstable kinds known as strange, charm, bottom and top. The W- and the Z-bosons have been found responsible for transmitting the so-called weak force that’s involved in radioactivity, and are big fat cousins of the boson we know as the photon, the particle that light is made of and which transmits the electromagnetic force. Additional boson family members known as gluons have been discovered to glue the quarks together into larger particles, and the recently discovered Higgs boson endows other particles with mass. In addition, stable ghostlike particles known as electron neutrinos, muon neutrinos and tau neutrinos have been discovered—we encountered them in the last chapter, and they are so shy that they barely interact with other particles at all: if a neutrino crashes into the ground, it typically passes right through Earth and emerges unscathed on the other side, and continues into space. Finally, almost all of these particles have an evil twin called its antiparticle, which has the property that, if the two collide, they can annihilate each other in a burst of pure energy. Table 7.2 summarizes the key particles and related concepts that we discuss in this book.
Figure 7.3: The current standard model of particle physics (Image credit: CERN)
Click here to see a larger image.
So far, no evidence has been found that any of these bosons, quarks, leptons (that’s the family name for the electron, the muon, the tauon and the neutrinos) or their antiparticles are made of any smaller or more fundamental parts. However, since quarks are building blocks a full three levels down in the Lego hierarchy (Figure 7.1), you don’t need to be Sherlock Holmes to start wondering whether there are even more levels that we’re failing to discover simply because we don’t have enough energy in our particle accelerators. Indeed, as we hinted at in Chapter 6, string theory suggests precisely this: that if we could slam them together with vastly (perhaps ten trillion times) more energy than today, we’d discover that everything is made of tiny vibrating strings, and that different types of vibrations of the same basic type of strings would correspond to different types of particles a bit like different types of vibrations of a guitar string correspond to different musical notes. The rival theory known as loop quantum gravity suggests that everything is made not of strings, but of a so-called spin network of quantized loops of excited gravitational fields—that’s quite a mouthful there, and if you don’t fully understand what that means, don’t worry, since not even the most devoted practitioners of string theory and loop quantum gravity claim to fully understand their theories yet.… So what’s everything ultimately made of? Based on the current state-of-the-art experimental evidence, the answer is clear: we simply don’t know yet, but there’s good reason to suspect that everything we know of so far—including the very fabric of spacetime itself—is ultimately made up of some more fundamental building blocks.
Mathematical Legos
Even though we still don’t know the ultimate answer to the question of what everything is made of, we’ve discovered one more fascinating hint that I have to tell you about. To me, it feels pretty crazy that colliding two protons at the CERN Large Hadron Collider can produce a Z-boson weighing ninety-seven times as much as a proton. I used to think that mass was conserved: surely you can’t produce a cruise ship by colliding two Ferraris, since it would weigh more than both cars combined? However, if you think that it feels as fraudulent as a Ponzi scheme to create new particles like this, remember that Einstein taught us that energy E can be converted into mass m by the formula E = mc2, where c is the speed of light. So if you have loads of motion energy at your disposal in a particle collision, then part of t
hat energy is indeed allowed to take the form of new particles. In other words, the total energy is conserved (stays the same), but a particle collision repackages this available energy in new ways, which may include putting some into new particles that weren’t there to start with. The exact same thing happens with momentum:1 the total amount is conserved, but it gets redistributed during the collision just as in pool when the cue ball slows down while sending a stationary ball flying into a pocket. One of the most important discoveries in physics has been that there are additional quantities which, just as energy and momentum, appear to always be conserved: electric charge is the most familiar example, but there are also other kinds of conserved quantities known, with names such as isospin and color. There are also quantities that are conserved in many important circumstances, notably lepton number (the number of leptons minus the number of antileptons) and baryon number (the number of quarks minus the number of antiquarks, all divided by three so that neutrons and protons count as +1). Table 7.1 lists the amounts (called quantum numbers) of these quantities that various particles have. You’ll notice that many of them are whole numbers or simple fractions, and that three of the masses aren’t well measured.