To Explain the World: The Discovery of Modern Science (38 page)

This did not mean that chemists would hand over their problems to physicists, and retire. As Dirac well understood, for all but the smallest molecules the Schrödinger equation is too complicated to be solved, so the special tools and insights of chemistry remain indispensable. But from the 1920s on, it would be understood that any general principle of chemistry, such as the rule that metals form stable compounds with halogen elements like chlorine, is what it is because of the quantum mechanics of nuclei and electrons acted on by electromagnetic forces.

Despite its great explanatory power, this foundation was itself far from being satisfactorily unified. There were particles: electrons and the protons and neutrons that make up atomic nuclei. And there were fields: the electromagnetic field, and whatever then-unknown short-range fields are presumably responsible for the strong forces that hold atomic nuclei together and for the weak forces that turn neutrons into protons or protons into neutrons in radioactivity. This distinction between particles and fields began to be swept away in the 1930s, with the advent of quantum field theory. Just as there is an electromagnetic field, whose energy and momentum are bundled in particles known as photons, so there is also an electron field, whose energy and
momentum are bundled in electrons, and likewise for other types of elementary particles.

This was far from obvious. We can directly feel the effects of gravitational and electromagnetic fields because the quanta of these fields have zero mass, and they are particles of a type (known as bosons) that in large numbers can occupy the same state. These properties allow large numbers of photons to build up to form states that we observe as electric and magnetic fields that seem to obey the rules of classical (that is, non-quantum) physics. Electrons, in contrast, have mass and are particles of a type (known as fermions) no two of which can occupy the same state, so that electron fields are never apparent in macroscopic observations.

In the late 1940s quantum electrodynamics, the quantum field theory of photons, electrons, and antielectrons, scored stunning successes, with the calculation of quantities like the strength of the electron’s magnetic field that agreed with experiment to many decimal places.
*
Following this achievement, it was natural to try to develop a quantum field theory that would encompass not only photons, electrons, and antielectrons but also the other particles being discovered in cosmic rays and accelerators and the weak and strong forces that act on them.

We now have such a quantum field theory, known as the Standard Model. The Standard Model is an expanded version of quantum electrodynamics. Along with the electron field there is a neutrino field, whose quanta are fermions like electrons but with zero electric charge and nearly zero mass. There is a pair of quark fields, whose quanta are the constituents of the protons and neutrons that make up atomic nuclei. For reasons that no one understands, this menu is repeated twice, with much heavier quarks and much heavier electron-like particles and their neutrino partners. The electromagnetic field appears in a unified “electroweak” picture along with other fields responsible for the
weak nuclear interactions, which allow protons and neutrons to convert into one another in radioactive decays. The quanta of these fields are heavy bosons: the electrically charged W
⁺
and W
⁻
, and the electrically neutral Z
⁰
. There are also eight mathematically similar “gluon” fields responsible for the strong nuclear interactions, which hold quarks together inside protons and neutrons. In 2012 the last missing piece of the Standard Model was discovered: a heavy electrically neutral boson that had been predicted by the electroweak part of the Standard Model.

The Standard Model is not the end of the story. It leaves out gravitation; it does not account for the “dark matter” that astronomers tell us makes up five-sixths of the mass of the universe; and it involves far too many unexplained numerical quantities, like the ratios of the masses of the various quarks and electron-like particles. But even so, the Standard Model provides a remarkably unified view of all types of matter and force (except for gravitation) that we encounter in our laboratories, in a set of equations that can fit on a single sheet of paper. We can be certain that the Standard Model will appear as at least an approximate feature of any better future theory.

The Standard Model would have seemed unsatisfying to many natural philosophers from Thales to Newton. It is impersonal; there is no hint in it of human concerns like love or justice. No one who studies the Standard Model will be helped to be a better person, as Plato expected would follow from the study of astronomy. Also, contrary to what Aristotle expected of a physical theory, there is no element of purpose in the Standard Model. Of course, we live in a universe governed by the Standard Model and can imagine that electrons and the two light quarks are what they are to make us possible, but then what do we make of their heavier counterparts, which are irrelevant to our lives?

The Standard Model is expressed in equations governing the various fields, but it cannot be deduced from mathematics alone. Nor does it follow straightforwardly from observation of nature. Indeed, quarks and gluons are attracted to each other by forces that increase with distance, so these particles can never be observed
in isolation. Nor can the Standard Model be deduced from philosophical preconceptions. Rather, the Standard Model is a product of guesswork, guided by aesthetic judgment, and validated by the success of many of its predictions. Though the Standard Model has many unexplained aspects, we expect that at least some of these features will be explained by whatever deeper theory succeeds it.

The old intimacy between physics and astronomy has continued. We now understand nuclear reactions well enough not only to calculate how the Sun and stars shine and evolve, but also to understand how the lightest elements were produced in the first few minutes of the present expansion of the universe. And as in the past, astronomy now presents physics with a formidable challenge: the expansion of the universe is speeding up, presumably owing to dark energy that is contained not in particle masses and motions, but in space itself.

There is one aspect of experience that at first sight seems to defy understanding on the basis of any unpurposeful physical theory like the Standard Model. We cannot avoid teleology in talking of living things. We describe hearts and lungs and roots and flowers in terms of the purpose they serve, a tendency that was only increased with the great expansion after Newton of information about plants and animals due to naturalists like Carl Linnaeus and Georges Cuvier. Not only theologians but also scientists including Robert Boyle and Isaac Newton have seen the marvelous capabilities of plants and animals as evidence for a benevolent Creator. Even if we can avoid a supernatural explanation of the capabilities of plants and animals, it long seemed inevitable that an understanding of life would rest on teleological principles very different from those of physical theories like Newton’s.

The unification of biology with the rest of science first began to be possible in the mid-nineteenth century, with the independent proposals by Charles Darwin and Alfred Russel Wallace of the theory of evolution through natural selection. Evolution was already a familiar idea, suggested by the fossil record. Many of those who accepted the reality of evolution explained it as a
result of a fundamental principle of biology, an inherent tendency of living things to improve, a principle that would have ruled out any unification of biology with physical science. Darwin and Wallace instead proposed that evolution acts through the appearance of inheritable variations, with favorable variations no more likely than unfavorable ones, but with the variations that improve the chances of survival and reproduction being the ones that are likely to spread.
*

It took a long time for natural selection to be accepted as the mechanism for evolution. No one in Darwin’s time knew the mechanism for inheritance, or for the appearance of inheritable variations, so there was room for biologists to hope for a more purposeful theory. It was particularly distasteful to imagine that humans are the result of millions of years of natural selection acting on random inheritable variations. Eventually the discovery of the rules of genetics and of the occurrence of mutations led in the twentieth century to a “neo-Darwinian synthesis” that put the theory of evolution through natural selection on a firmer basis. Finally this theory was grounded on chemistry, and thereby on physics, through the realization that genetic information is carried by the double helix molecules of DNA.

So biology joined chemistry in a unified view of nature based on physics. But it is important to acknowledge the limitations of this unification. No one is going to replace the language and methods of biology with a description of living things in terms of individual molecules, let alone quarks and electrons. For one thing, even more than the large molecules of organic chemistry, living things are too complicated for such a description. More important, even if we could follow the motion of every atom in a plant or animal, in that immense mass of data we would lose
the things that interest us—a lion hunting antelope or a flower attracting bees.

For biology, like geology but unlike chemistry, there is another problem. Living things are what they are not only because of the principles of physics, but also because of a vast number of historical accidents, including the accident that a comet or meteor hit the Earth 65 million years ago with enough impact to kill off the dinosaurs, and going back to the fact that the Earth formed at a certain distance from the Sun and with a certain initial chemical composition. We can understand some of these accidents statistically, but not individually. Kepler was wrong; no one will ever be able to calculate the distance of the Earth from the Sun solely from the principles of physics. What we mean by the unification of biology with the rest of science is only that there can be no freestanding principles of biology, any more than of geology. Any general principle of biology is what it is because of the fundamental principles of physics together with historical accidents, which by definition can never be explained.

The point of view described here is called (often disapprovingly) “reductionism.” There is opposition to reductionism even within physics. Physicists who study fluids or solids often cite examples of “emergence,” the appearance in the description of macroscopic phenomena of concepts like heat or phase transition that have no counterpart in elementary particle physics, and that do not depend on the details of elementary particles. For instance, thermodynamics, the science of heat, applies in a wide variety of systems: not just to those considered by Maxwell and Boltzmann, containing large numbers of molecules, but also to the surfaces of large black holes. But it does not apply to everything, and when we ask whether it applies to a given system and if so why, we must have reference to deeper, more truly fundamental, principles of physics. Reductionism in this sense is not a program for the reform of scientific practice; it is a view of why the world is the way it is.

We do not know how long science will continue on this reductive path. We may come to a point where further progress
is impossible within the resources of our species. Right now, it seems that there is a scale of mass about a million trillion times larger than the mass of the hydrogen atom, at which gravity and other as yet undetected forces are unified with the forces of the Standard Model. (This is known as the “Planck mass”; it is the mass that particles would have to possess for their gravitational attraction to be as strong as the electrical repulsion between two electrons at the same separation.) Even if the economic resources of the human race were entirely at the disposal of physicists, we cannot now conceive of any way of creating particles with such huge masses in our laboratories.

We may instead run out of intellectual resources—humans may not be smart enough to understand the really fundamental laws of physics. Or we may encounter phenomena that in principle cannot be brought into a unified framework for all science. For instance, although we may well come to understand the processes in the brain responsible for consciousness, it is hard to see how we will ever describe conscious feelings themselves in physical terms.

Still, we have come a long way on this path, and are not yet at its end.
⁶
This is a grand story—how celestial and terrestrial physics were unified by Newton, how a unified theory of electricity and magnetism was developed that turned out to explain light, how the quantum theory of electromagnetism was expanded to include the weak and strong nuclear forces, and how chemistry and even biology were brought into a unified though incomplete view of nature based on physics. It is toward a more fundamental physical theory that the wide-ranging scientific principles we discover have been, and are being, reduced.

Acknowledgments

I was fortunate to have the help of several learned scholars: the classicist Jim Hankinson and the historians Bruce Hunt and George Smith. They read through most of the book, and I made many corrections based on their suggestions. I am deeply grateful for this help. I am indebted also to Louise Weinberg for invaluable critical comments, and for suggesting the lines of John Donne that now grace this book’s front matter. Thanks, too, to Peter Dear, Owen Gingerich, Alberto Martinez, Sam Schweber, and Paul Woodruff for advice on specific topics. Finally, for encouragement and good advice, many thanks are due to my wise agent, Morton Janklow; and to my fine editors at HarperCollins, Tim Duggan and Emily Cunningham.

Technical Notes

The following notes describe the scientific and mathematical background for many of the historical developments discussed in this book. Readers who have learned some algebra and geometry in high school and have not entirely forgotten what they learned should have no trouble with the level of mathematics in these notes. But I have tried to organize this book so that readers who are not interested in technical details can skip these notes and still understand the main text.