The Cosmic Landscape

by Leonard Susskind

  A short-range force of the flypaper type would be useless in binding electrons to the nucleus. The atom is a miniature solar system, and the all-important valence electrons are the most distant planets: the Plutos and Neptunes of the atom. Only a force that reaches out to large distances can keep them from flying off into the “outer space” beyond the boundaries of the atom.

  Long-range forces, the kind that grab from a distance, are uncommon. Of all the many different types of forces in nature, only two are long range. Both are familiar, the most familiar being gravity. When we jump off the earth, gravity pulls us back. It reaches out hundreds of millions of miles to hold the planets in their orbits around the sun and tens of thousands of light-years to keep the stars confined within galaxies. That’s the kind of force that is needed to tie the outer electrons to the central nucleus. Of course it’s not gravity that holds the atom together: it’s far too weak.

  Another familiar long-range force acts between a magnet and an iron paper clip. The magnet doesn’t have to be in direct contact with the paper clip to attract it. A strong magnet tugs on the clip even from a remote distance. But more relevant for the atom, the electric cousin of magnetic force is a long-range force that acts between electrically charged particles. Much like the gravitational force, except vastly stronger, the electric force binds the valence electrons the same way that gravity ties Pluto to the sun.

  As I explained in chapter 1, electric forces between charged particles are caused by photons that are exchanged between the charges.2 The ultralight photons (remember that they have no mass) are capable of jumping long distances to create long-range forces that bind the distant valence electrons to the nucleus. Remove the photon from the list, and there would be nothing to hold the atom together.

  The photon is very exceptional. It is the only elementary particle, other than the graviton, that has no mass. What if it were less exceptional and had mass? Feynman’s theory tells us how to compute the force when a hypothetical massive photon jumps between nucleus and electron. What one finds is that the heavier the photon, the less far it is able to jump. Were the photon mass even a tiny fraction of the electron mass, instead of being a long-range force, electric interactions would become short-range “flypaper forces,” totally incapable of holding on to the distant valence electrons. Atoms, molecules, and life are entirely dependent on the curious fact that the photon has no mass.

  The range of the electric force is not the only feature that is essential for atoms to work properly. The strength of the force (how hard it pulls on the electrons) is critical. The force holding the electron to the nucleus is not very large by the standards of ordinary human experience. It’s measured in billionths of a pound. What is it that determines the strength of electric forces between charged particles? Again, Feynman’s theory tells us. The other ingredients in a Feynman diagram, besides particles, are vertex diagrams. Remember that every vertex diagram has a numerical value—the coupling constant—and for photon emission the coupling constant is the fine structure constant α, a number about equal to the fraction 1/137. The smallness of a is the ultimate mathematical reason why electric forces are much weaker than their nuclear counterparts.

  What if the fine structure constant were bigger, say about one? This would create several disasters, one of which would endanger the nucleus. The nuclear force that holds the nucleons (protons and neutrons) together is a flypaper force: short range and strong. The nucleus itself is like a ball of sticky flies. Each nucleon is stuck to its nearest neighbors, but if it can just separate from the others by a tiny bit, it’s free to fly off.

  There is something working against the nuclear force, competing with it, to repel the protons from one another. The protons are, of course, electrically charged. They attract the negative electrons because they have the opposite charge (opposite charges attract; like charges repel). The neutrons are electrically neutral and, therefore, don’t play a role in the balance of electric forces. Protons, on the other hand, are positively charged and electrically repel one another. In fact if a nucleus has more than about one hundred protons, the repulsive long-range electric forces are enough to blow it apart.

  What would happen if the electric force were as strong as the nuclear force? Then all complex nuclei would be unstable. In fact the electric force could be a good deal weaker than the nuclear force and still endanger nuclei like carbon and oxygen. Why is the fine structure constant small? No one knows, but if it were big, there would be no one to ask the question.

  Protons and neutrons are no longer considered to be elementary particles. Each is composed of three quarks. As discussed in chapter 1, there are several different species of quarks labeled up, down, strange, charmed, bottom,andtop.While the names are quite meaningless, the differences between the types of quarks are important. A quick look at the list of particle masses in chapter 3 reveals that the quark masses vary over a huge range from roughly 10 electron masses for the up- and down-quarks to 344,000 electron masses for the top-quark. Physicists puzzled for some time about why the top-quark is so heavy, but recently we have come to understand that it’s not the top-quark that is abnormal: it’s the up- and down-quarks that are absurdly light. The fact that they are roughly twenty thousand times lighter than particles like the Z-boson and the W-boson is what needs an explanation. The Standard Model has not provided one.

  Thus, we can ask what the world would be like if the up- and down-quarks were much heavier than they are. Once again—disaster! Protons and neutrons are made of up- and down-quarks. (Particles made of strange-, charmed-, bottom-, and top-quarks play no role in ordinary physics and chemistry. They are of interest mainly to high-energy physicists.) According to the quark theory of protons and neutrons, the nuclear force (force between nucleons) can be traced to quarks hopping back and forth between these nucleons.3 If the quarks were much heavier, it would be much more difficult to exchange them, and the nuclear force would practically disappear. With no sticky flypaper force holding the nucleus together, there could be no chemistry. Luck is with us again.

  Remember that in terms of the Landscape, our universe rests in a valley where all the fortunate coincidences are true. But in generic regions of the Landscape, things can be very different. The fine structure constant could easily be larger, the photon massive, quarks heavier, or even worse, electrons, photons, or quarks might not be on the list. Any one of these would be enough to eliminate our presence.

  Even if all the standard particles existed with the right mass and the right forces, chemistry could still fail. One thing more is needed: electrons must be fermions. The fact that fermions are so exclusive—you can’t put more than one in a quantum state—is essential to chemistry. Without the Pauli exclusion principle, all electrons in an atom would sink down to the lowest atomic orbits, where they would be much more difficult to dislodge. Ordinary chemistry is completely dependent on the Pauli principle. If electrons suddenly turned into the more sociable bosons, life based on carbon chemistry would go poof. So you see that a world with ordinary chemistry is far from generic.

  Physicists often use words differently from the way they are ordinarily used. When you say that something exists, you probably mean that it can be found somewhere in the universe. For example, if I were to tell you that black holes exist, you might ask me where you can find one. Black holes do exist in the ordinary sense: they are actual astronomical objects found, for example, at the centers of galaxies. But suppose I told you tiny black holes no bigger than a speck of dust exist. Again you might ask where they are found. This time I would answer that there is none; it takes a huge amount of mass to squeeze itself into a black hole. No doubt you would get annoyed and say, “Stop pulling my leg. You told me they exist!”

  What physicists (especially of the theoretical variety) mean by the term exist is that the object in question can exist theoretically. In other words, the object exists as a solution to the equations of the theory. By that criterion perfectly cut diamonds a hundred miles in diamete
r exist. So do planets made of pure gold. They may or may not actually be found somewhere, but they are possible objects consistent with the Laws of Physics.

  Long-range weak forces and short-range strong forces, acting among fermions, lead to the existence of complex atoms like carbon, oxygen, and iron. That’s nice, but I mean it in the theoretical sense. “What more,” you may ask, “is needed to make sure that complex atoms exist in my ordinary sense? What is required to actually produce those atoms and make them abundant in the universe?” The answer is not so simple. Complex atomic nuclei are not likely to result from random collisions of particles, even in the early hot universe.

  In the first minutes after the Big Bang, there were no atoms or even nuclei. Hot plasma composed of protons, neutrons, and electrons filled all space. The high temperature prevented nucleons from sticking together to form nuclei. As the universe cooled, protons and neutrons stuck together and formed the primordial elements.4 But apart from tiny traces of other elements, only the very simplest of nuclei formed: hydrogen and helium.

  Moreover, as medieval alchemists discovered, it’s not easy to transmute one element into another. So where, then, did all the carbon, oxygen, nitrogen, silicon, sulfur, iron, and other familiar chemical elements come from? The answer is that the intensely hot nuclear furnace of a star can do what no alchemists ever could—transform the elements, one into another. The cooking process is nuclear fusion, the same kind of fusion that powers nuclear weapons. Fusion combines the hydrogen nuclei in all sorts of permutations and combinations. The results of these nuclear reactions were the familiar elements.

  The chain of nuclear reactions in stars that starts with the lightest elements and leads to iron is complicated. A couple of examples will illustrate the point. The most familiar example is the fusion reaction that begins with hydrogen and produces helium. Here is where the weak interactions (diagrams with W- and Z-bosons) come in. The first step is the collision of two protons.5 Many things can happen when two protons collide, but if you know the Feynman diagrams for the Standard Model, you can find one that ends up with a proton, a neutron, a positron, and a neutrino.

  The positron finds a wandering electron in the star, and together they self-destruct into photons that eventually become the star’s thermal energy (heat). The neutrino just zips away and disappears with almost the speed of light. That leaves one sticky proton and one sticky neutron that stick together to form an isotope of hydrogen called deuterium.

  Next, a third proton strikes the deuterium nucleus and sticks to it. The nucleus with two protons and a neutron is a form of helium called helium-three (3He), but it’s not the stable kind of helium that we use to fill balloons. That stuff is called helium-four (4He).

  The story continues: two 3He nuclei collide. All together that means four protons and two neutrons. But they don’t all stick together. Two of the protons fly off and leave a nucleus with two protons and two neutrons. That’s an ordinary 4He nucleus. You don’t need to remember all that. Very few physicists do.

  Most of the nuclear reactions that take place in stars consist of a single proton colliding with an already present nucleus and increasing its atomic weight by one unit. Sometimes the proton turns into a neutron by giving off a positron and a neutrino. Sometimes a neutron will become a proton, electron, and antineutrino. In any case, inside the star, step-by-step, the original hydrogen and helium nuclei turn into heavier elements.

  But what good are the complex elements locked up inside stars? Science-fiction stories might posit strange forms of life made of swirling hot plasma that thrive at millions of degrees, but real life needs a cooler environment. Sadly, the carbon and oxygen remained imprisoned in the star’s interior throughout the entire lifetime of the star.

  But stars don’t live forever.

  Eventually all stars, our sun included, will run out of fuel. At that point a star collapses under its own weight. Before the fuel runs out, stars are kept in equilibrium by the heat and pressure generated by nuclear reactions. There are two competing tendencies in the star. Like a nuclear bomb, it wants to explode, while at the same time gravity is trying to crush it under its own enormous weight. These two tendencies, exploding and imploding, are kept in balance as long as there is fuel to burn. But once the fuel runs out, there is nothing to resist the pull of gravity, and the star implodes.

  There are three possible endpoints to the implosion. A star like our sun is relatively light, and it will collapse only until it forms a white dwarf. A white dwarf is made of more or less ordinary material—protons, neutrons, and electrons—but the electrons are squeezed up against one another to a far greater degree than in ordinary materials. It’s the Pauli exclusion principle that keeps the electrons from collapsing even further. If all stars ended up as white dwarfs, the freshly cooked elements would remain imprisoned inside them.

  On the other hand, if the star is many times heavier than the sun, the force of gravity will be irresistible. The inevitable disastrous collapse will end in the most violent process imaginable—the formation of a black hole. Elements trapped in black holes would be even less available than those in white dwarfs.

  But there is a middle ground. Stars within a certain range of masses collapse past the white dwarf stage but not all the way to a black hole. In these stars the electrons, in a sense, get squeezed out, while the protons turn into neutrons, and the end result is a solid ball of incredibly dense neutron matter: a neutron star. Surprisingly, the weak interactions play an indispensable role. Each proton, as it becomes a neutron, gives off two particles, a positron and a neutrino. The positrons quickly combine with the electrons in the star and disappear.

  Such an event, called a supernova, is not a gentle one. A supernova can outshine an entire galaxy with a hundred billion stars!

  In everyday physics and chemistry, neutrinos are of no importance at all. They can pass through light-years of lead without disturbing it one bit. Neutrinos from the sun are continually passing through the earth, through our food and drink, and through our bodies with no effect at all. But our existence is totally dependent on them. The neutrinos flying out of the supernova implosion are so numerous that, despite their feebleness, they create an enormous pressure, pushing matter in front of them. The pressure exerted by the neutrinos blows off the outer layers of the collapsing star and, in the process, sprays out the complex nuclei that were cooked before the star collapsed. So as its final act, the star in its death throes donates its complex nuclei to fill the universe with matter.

  Our sun is a youngster. The universe is about fourteen billion years old, but the sun was born late in its history, only five billion years ago. By that time generations of stars had formed and died and there were already enough heavy elements to form the solar system. We are fortunate indeed that the ghostly neutrino exists—in the ordinary sense of the word.

  There are multiple ways that things could go wrong with the nuclear cooking. If there were no weak interactions or if neutrinos were too heavy, protons could not turn into neutrons during the cooking. The cooking of carbon is sensitive to the details of the carbon nucleus. One of the great scientific events of the twentieth century occurred when the cosmologist Fred Hoyle was able to predict one of these nuclear details just from the fact that we are here. In the early 1950s Hoyle argued that there is a “bottleneck” in the cooking of elements in stars like the sun. There appeared to be no way for the cooking to proceed past atomic number 4—helium. Nuclear cooking usually goes forward one proton at a time to form a heavier element, but there is no stable nucleus with atomic number 5, so there is no easy way to get past helium.

  There is one way out. Two helium nuclei can collide and stick together to form a nucleus with atomic number 8. That nucleus would be the isotope beryllium 8. Later, another helium nucleus could collide with the beryllium and form a nucleus with atomic number 12—good old carbon 12, the stuff of organic chemistry. But there is a fly in this ointment.

  Beryllium 8 is a very unstable isotope. I
t decays (falls apart) so rapidly that there is not enough time for the third helium nucleus to collide before the beryllium disappears—unless an unlikely coincidence occurs. If by accident there were an excited state—a so-called resonance—of the carbon nucleus with exactly the right properties, the probability for the beryllium to capture a helium nucleus would be much higher than expected. The likelihood of such a coincidence is very small, but when Hoyle suggested that such a coincidence might solve the problem of cooking the heavy elements, experimental nuclear physicists went right to work. And BINGO, the excited state was discovered with exactly the properties that Hoyle guessed. Just a small increase or decrease in the energy of the excited carbon nucleus, and all the work of making galaxies and stars would have been in vain; but as it is, carbon atoms—and thus, life—can exist.

  The properties of Hoyle’s carbon resonance are sensitive to a number of constants of nature, including the all-important fine structure constant. Just a few percent change in its value, and there would have been no carbon and no life.6 This is what Hoyle meant when he said that “it looks as if a super-intellect has monkeyed with physics as well as with chemistry and biology.”

  But again, it would do no good for the nuclear physics to be “just right” if the universe had no stars. Remember that a perfectly homogeneous universe would never give birth to these objects. Stars, galaxies, and planets are all the result of the slight lumpiness at the beginning. Early on, the density contrast was about 10–5 in magnitude, but what if it had been a little bigger or a little smaller? If the lumpiness had been much less, let’s say, 10–6, in the early universe, galaxies would be small and the stars, very sparse. They would not have had sufficient gravity to hang on to the complex atoms that were spewed out by supernovae; these atoms would have been unavailable for the next generation of stars. Make the density contrast a little less than that, and no galaxies or stars would form at all.