Fundamentals

  The first thing to notice is that ten minutes, in the subatomic world, is an eternity.

  By way of comparison, the lifetimes of hadrons that decay through strong interactions, by reshuffling quarks and gluons, are tiny fractions of a second. The strong force acts about 1027, or 1,000,000,000,000,000,000,000,000,000, times faster. By that standard, the instability introduced by the weak force, which causes neutron decay, takes a very long time to build up and become effective. In other words, it is a very weak instability. That is why we refer to its cause as the weak force.

  The elementary particle process that underlies neutron decay is the transformation of a d quark into a u quark (plus an electron and an antineutrino). Since neutrons are based on the quark combination (udd), while protons are based on the quark combination (uud), that transformation of quarks serves to transform neutrons into protons.

  Although the weak force is feeble, it can do things that the other forces can’t. Neither the strong force, nor the electromagnetic force, nor gravity can change one kind of quark into another kind. The weak force, on the other hand, has the ability to transform heavier quarks into lighter ones. All the “bonus particles” we mentioned in the previous chapter* are highly unstable, due to the weak force.

  The weak force acts upon quarks wherever they are. And so, specifically, the weak force can transform neutrons into protons not only when the neutrons are isolated, but also when they are within an atomic nucleus. After that happens, the new nucleus has one more proton and one less neutron than the old one. (The electron and the antineutrino escape.) Since the number of protons in an atomic nucleus ultimately determines the electrical character of the atom, and thus its chemistry, our process changes an atom of one chemical element into an atom of another. That is the sort of thing that alchemists aspired to do, but which the pioneers of modern chemistry said could not be done. The weak force performs natural alchemy.

  THE FUTURE OF COMPREHENSION

  Is That All There Is?

  Already in 1929, Paul Dirac, the great mathematical physicist who removed the guesswork from quantum electrodynamics, declared, “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known.”

  Dirac was referring to the laws of quantum electrodynamics, applied to matter assumed to be made from electrons, photons, and atomic nuclei. Through ninety years hosting thousands of new experiments, applications, and discoveries in atomic physics and chemistry, Dirac’s bold claim has not only survived, but become even truer, as the theory became more rigorous. And as the strong and weak forces came to be understood, the scope of fundamental understanding expanded—“a large part of physics” got much larger. The physics of 1929, for instance, had no clear ideas about how stars derive their energy or about what forces hold atomic nuclei together. Today, we know those things with confidence, thanks to thousands of stringent experimental tests.

  When Dirac continued, “And the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved,” modern supercomputers were not even a dream. With their help, we’re getting much better at solving the equations that fundamental understanding has provided for us. The equations of QED, QCD, general relativity, and the weak force, working in the framework of quantum theory, have powered many advances, including lasers, transistors, nuclear reactors, magnetic resonance imaging (MRI), and GPS.

  Chemists and materials engineers won’t be going out of business anytime soon, though. Once we go beyond a few simple cases, involving small molecules or perfect crystals, it isn’t practical to predict behavior though brute force calculation. Chemists and engineers rarely if ever deal with quarks and gluons. To make progress, people must invent approximations; introduce idealizations; build faster, more powerful computers; and do experiments.

  It’s a different question, though, whether “the difficulty lies only in the fact” that our fundamental equations can be hard to solve. Might there be big effects that they are missing altogether—or is that all there is?

  Our laws for the four fundamental forces, taken together, comprise what is sometimes called the “Standard Model” or (my preference) “the Core.” They work together like a well-oiled machine. There are good reasons to think that the Core—our fundamental laws for QED, QCD, gravitation, and the weak force, taken together—forms an adequate foundation for practical applications of physics and that it will remain the foundation for the foreseeable future.

  One reason is straightforward. The laws have now been tested with far greater precision and in a far wider range of conditions than are needed for practical applications in chemistry, biology, engineering, or even astrophysics (apart from early universe cosmology).

  Another reason is more theoretical. Quantum fields are powerful tools, but they are ornery ones. It is devilishly hard to use them in a mathematically consistent way. If you’re not careful, you will stumble into systems of equations that have no solutions. This gives the Core, which is heavily invested in quantum fields, a kind of rigidity. It is difficult to modify the Core without utterly wrecking it.

  You can add to the Core, but the additions must either involve new forms of matter that couple feebly to the matter we know, or else only modify behavior of elementary particles at “impractical”—that is, very high—energies. Axions, which we’ll discuss later, are an example of the former. Superstring theory, which postulates that our elementary particles are actually strings, is an example of the latter.* These sorts of additions might help to relieve the cosmological and aesthetic shortcomings of our fundamental equations, but they are unlikely to affect any of their practical applications.

  To paraphrase Dirac: That’s all there is, for practical purposes.

  Thankfully, though, there’s more to life than laying foundations—or being practical.

  Unifying the Forces

  The Core contains the seeds of its own transcendence.

  Three of the four forces—QED, QCD, and the weak force— are based on different kinds of charges.* We have fields that respond to the charges, and fields that can change some of the charges into others. (Color gluon fields change one kind of color charge into another, for example.) We have electric charge, three kinds of color charge, and two weak charges. What could be more natural than to imagine a larger framework, which treats all of those charges on the same footing, and allows transformations among all of them?

  That attractive idea faces a big problem: There is absolutely no evidence that the desired transformations are possible. On the contrary, they must occur very rarely, if at all. If it is possible to transform color charges into the other forms, then quarks will be able to change into electrons, and protons will be unstable. But people have looked very hard for proton decay, and they have never observed it.

  On the other hand, we have learned, in the theory of the weak interaction, a way to salvage beautiful equations that seem “too good for this world.” We can imagine an emptier world where the more beautiful equations hold, and then make it our world by filling it with an appropriate substance (the Higgs condensate).*

  Can we take that strategy further? Might the differences among the charges be due to the complicating influence of other cosmic media, made from heavier and more elusive Higgs-like particles?

  There is a beautiful reason to think so. It arises out of another key idea from the Core: asymptotic freedom. Asymptotic freedom is the weakening of the strong force at short distances. We discussed it earlier, without naming it. Asymptotic freedom was the key to discovering QCD, and it is the source of much of QCD’s predictive power. We can also calculate, using the same techniques, how the other forces change with distance. Those calculations lead to a marvelous result. We find that at extremely short distances, unification is achieved. The strengths of all four forces become equal. This is exactly what we predict to happen, in the unified f
ield theory. By looking at short distances we minimize the effect of the complicating medium. There we seem to glimpse, in calculated numbers, the ideal world we imagined.* In this way, Einstein’s vague dreams of a unified field theory have become specific, and even quantitative.

  The vision that fuels our drive toward unification is a natural, logical extension of central ideas from the Core: equations based on charges and their transformations, symmetry obscured by world-filling media, asymptotic freedom. Working together, these ideas explain a “coincidence” among the strengths of the forces (including gravity). If and when people observe proton decay, this vision will be vindicated. The search continues.

  Seeing Things Whole

  The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.

  —Hermann Weyl

  The idea that “the basic laws describe change” served, in our previous chapter, as the first guiding principle that leads to scientific understanding of how the world works. It has served us well. The fundamental laws of the Core have that character. They tell us what happens.

  But the boundary between what is and what happens is not entirely hard and fast. Eternal laws of change do not themselves change. They do not come to be, but simply are. And by drawing out their consequences, we can say a lot about enduring features of the world—or, in other words, what is—even though, on the face of it, they say only what happens.

  For example, when you ask what happens when you examine matter minutely, and discover that matter is made from a few ingredients, each with a few simple properties, you’ve crossed that boundary. When you ask what happens when you bring those ingredients together and let them settle down, and discover that matter is organized into the nuclei, atoms, and molecules that fill out the periodic table and the reference manuals of physics and chemistry, you’ve crossed it again.

  Still, the laws of the Core must be informed about the state of the universe at some time, before they can get about the business of constructing a world. They do not capture the God’s-eye view, which sees space-time as a whole, all at once. Their working material is not what Weyl called “the objective world,” but only slices of that world.

  General relativity teaches us that the separation of space-time into space and time is unnatural. Big bang cosmology, which we’ll take up in chapter 6, teaches us that the universe was remarkably simple, early on. These are big hints that we should look for more encompassing laws that will see things whole.

  5

  THERE’S PLENTY OF MATTER AND ENERGY

  In earlier chapters, we explored the abundance of space and of time. We reached, in both cases, four fundamental understandings. First, that the universe contains overwhelming riches. Second, that in practice only a tiny fraction of those riches is available to us. Third, that the fraction we are given remains, for human purposes, plentiful. And fourth, that we are far from fully exploiting what we are given. There is still plenty of room for growth.

  In this chapter, we will explore the abundance of matter and energy. Here, too, we will arrive at those four fundamental understandings.

  THE ABUNDANCE OF COSMIC ENERGY

  Let us begin with some comparisons, to get the measure of cosmic energy on human scales. A typical human adult takes in about 2,000 calories daily. That is roughly enough energy to run a 100-watt light bulb continuously. Over a year, it amounts to 3 billion joules. (A joule of energy, by definition, supplies a watt of power for one second, and there are about 30 million seconds in a year.) Let’s call that quantity of energy an AHUMEN—pronounced, of course, “a human”—for Annual Human Energy. Of that amount, about 20 percent is used to support brain activity.

  In 2020, world energy consumption was approximately 1.9 × 1011—that is, 190 billion—AHUMENs. Since the world population in 2020 was about 7.5 billion, that amounts to roughly 25 AHUMENs of energy consumed per human. This number, 25, is the ratio of total energy consumed to the amount of energy used in natural metabolism. It is an objective measure of how far humans have progressed, economically, beyond scratching out a bare subsistence. Americans, for comparison, consume roughly 95 AHUMENs per person.

  The annual energy output of our Sun is enough to supply roughly 500 trillion AHUMENs to each human. You should not fail to notice that 500 trillion is a great deal larger than 25, or even 95. Thus, fundamentally, there’s vast room for economic growth based on harvesting a larger fraction of our Sun’s energy output.

  Of course, the Sun’s output gets radiated in all directions. To capture a bigger fraction, we’d need to make significant investments of time and resources to put gigantic collection devices in space. Freeman Dyson and others have proposed engineering projects of that sort, called Dyson spheres.

  If, more modestly, we restrict ourselves to the portion of solar energy that makes it to Earth, then we find “only” about 10,000 times our present total energy consumption. That number provides a more realistic baseline from which to assess the economic potential of solar energy. Evidently, even without a Dyson sphere, there’s still plenty of room for growth.

  Here we have considered the energy emitted from our Sun. Earlier, in our survey of the universe, we came to see our Sun as just one star among many. With that in mind, we understand that the universe as a whole is awash in vastly more energy than humans will, for the foreseeable future, be able to access. What we can do, though, is capture tiny samples from those dispersed riches. That’s what astronomy is all about. Astronomy enriches our minds, if not our economy.

  This discussion of comparisons gives objective meaning to the claim that there’s plenty of matter and energy. There’s more than enough to make objects as complex and dynamic as humans and to support an extremely expansive human agenda.*

  FUNDAMENTALS AND HUMAN PURPOSES

  Dynamic Complexity

  By making simple comparisons, we have demonstrated that there is, for human purposes, plenty of energy in the universe. Now let us consider, from a more fundamental perspective, why there is.

  To do that, we must address two basic questions:

  What is it, in the physical universe, that embodies “human purposes”?

  Why does realizing that thing require so little energy, compared to what our Sun puts forth?

  The first question can be addressed at many different levels. If we try to define “human purposes” precisely, we risk a rapid plunge into murky depths of vague metaphysics. But if we ask what it is that is essential to what people do, and to what they are, in physical terms, then the answer that emerges is clearer than the question is. At that level, the heart of the matter is dynamic complexity. Although there’s no scientific consensus on precisely how to define complexity, we “know it when we see it,” in examples like these:

  To learn and to think, we change patterns of connections, secretions, and electrical impulses in our brains. To sense the world, we transform incoming patterns of electromagnetic radiation (sight), air pressure (hearing), local chemistry (taste and smell), and a few other data streams into that common brain currency. To move and to act on the world, we use muscle power, ultimately based on the synchronized contraction of well-organized protein molecules.

  In building temples, synagogues, mosques, or cathedrals, people draw up plans, gather materials, use construction tools and machinery, and employ builders and artists to create complex, “unnatural,” “spiritual” environments where none existed before.

  Music and ritual are purified expressions of dynamic complexity.

  Each of those quintessentially human activities involves, at its core, complex material patterns that change in time. In different cases, the patterned matter takes different forms, ranging from neural networks to vibrations in air; and it embodies different things, including tools, symb
ols, memories, signals, instructions, and actors. Dynamic complexity is the deep structure underlying them all.

  Here on Earth, through most of biological and human history, the physical realization of dynamic complexity has hinged upon making and breaking enormous numbers of chemical bonds, using power supplied by the Sun. Today, other possibilities are opening up, as I’ll discuss below. But Sun-powered making and breaking of chemical bonds is still the central method, and we should discuss it first.

  EXPLOSION BY CONSTRUCTION

  Atoms have many features that make them excellent pieces with which to build up interesting and intricate—that is, complex—creations:

  There are many kinds of atoms, one for each chemical element. All the atoms of any particular element are essentially identical.* Thus, they provide a wide stock of interchangeable parts.

  Atoms are available in enormous numbers. A typical human body contains an octillion or so, which is more than the number of stars in the visible universe.

  Atoms can combine together into bigger units—molecules—following the rules of quantum theory and the laws of electrodynamics. We say that the atoms are joined by chemical bonds to make a molecule.