You don't need something to get something more. That's what emergence means. Life can emerge from physics and chemistry plus a lot of accidents. The human mind can arise from neurobiology and a lot of accidents, the way the chemical bond arises from physics and certain accidents. It doesn't diminish the importance of these subjects to know they follow from more fundamental things plus accidents.

—Murray Gell-Mann1

PION EXCHANGE AND THE STRONG FORCE

With the incredible success of quantum electrodynamics, it was natural to apply the same methods of relativistic quantum field theory to the nuclear forces. Recall from chapter 8 that in 1932 Hans Bethe and Enrico Fermi had proposed that particles interact by exchanging other particles. In 1934, physicist Hideki Yukawa suggested that two nucleons (protons or neutrons) interact by the exchange of a particle called the meson. Note that this was well before the photon-exchange mechanism was applied with such great success in quantum electrodynamics.

Yukawa's model specified that the mass of an exchanged particle is inversely proportional to the range of the force that is mediated by that particle.2 Because the photon is massless, the electromagnetic force has unlimited range, and so light can reach us from great distances. Because the range of the strong nuclear force is only about a femtometer (10^–15 meter), Yukawa estimated the mass of the meson to be about two hundred times heavier than the electron but still much less massive than the proton.³

In 1936, Carl D. Anderson discovered the particle we now call the muon in cosmic rays. This particle was produced by the primary cosmic rays hitting the top of the atmosphere. At first, it was thought that the observed particle was Yukawa's meson, since its mass was 207 times the mass of the electron, almost exactly as predicted. However, it was soon realized that the muon was not strongly interacting and so could not be responsible for the nuclear force. Any strongly interacting particles produced in the upper atmosphere would quickly lose most of their energy colliding with the nuclei of atoms in the atmosphere. By contrast, muons easily reach sea level and penetrate deep into the ground. One muon passes through every square centimeter of our bodies every minute. As previously mentioned, the muon is essentially a heavy electron.

In 1947, a better candidate for Yukawa's meson was found in cosmic rays at high altitude. This particle is now called the pi meson or pion. The pion is strongly interacting, and few reach sea level. The pion occurs in three varieties: π⁺ with charge +1, π^– with charge –1, and π⁰ with charge 0. The mass of the π⁰ is 135 MeV, while the mass of each charged pion is 140 MeV. These masses actually fit the Yukawa model better than the muon mass. Pion exchange makes possible the variety of nucleon-nucleon interactions shown in figure 10.1.

However, all attempts to construct a QED-like theory for the strong interaction, with the pion taking the place of the photon, were a failure. I should know. I spent several years trying to make the model work. The reason photon exchange is such a good first approximation to the electromagnetic interaction between electrons is that the force strength is weak. The electromagnetic force strength is given by a dimensionless quantity α = e²/c called, for historical reasons, the fine-structure constant, where e is the unit electric charge. Although it has a slow dependence on energy, this is generally ignored since α has a value 1/137 over the range of energies with which most scientists deal.

The point here is that every time an electromagnetic interaction vertex appears in a Feynman diagram, a factor of α² enters into the calculation of the probability amplitude for the reaction, where you square the probability amplitude to get the probability. So the second-order diagrams in figure 9.2 are less probable than single photon exchange, and higher-order diagrams (some have been calculated) are even more unlikely.

In the case of the strong-interaction diagrams involving pions and nucleons, the corresponding interaction strength α_S is greater than 1, and each succeeding order of Feynman diagrams is more probable than the previous. In chapter 11, we will see how this problem was ultimately solved.

THE FERMI THEORY OF THE WEAK FORCE

The weak nuclear force is responsible for those processes termed beta decay, in which an electron and neutrino are emitted. In chapter 8, we found that the primary energy source of the sun, the conversion of hydrogen into helium, involves the weak nuclear force.

In the case of nuclear processes, the basic weak interaction is neutron decay,

(₁p¹ is the same as ₁H¹). Nuclear beta decay occurs when a neutron inside a nucleus decays. Most nuclei are stable, however, because their binding energies prevent their decay products from escaping the nucleus. Radioactive nuclei are the exceptions.

In 1934, Fermi developed a model of beta decay that was based on the diagram shown in figure 10.2.

Note that the interaction occurs at a point, implying that the range of the force is zero.

The Fermi model worked fairly well and was improved on over the years. However, the weak force was unlikely to have exactly zero range, and it seemed reasonable to assume an exchange process, such as illustrated in figure 10.3, where the exchanged particle W is a postulated weak boson that mediates the weak interaction. The weak interaction strength α_w is very small, so single W exchange suffices.

However, searches for a weak boson in the 1960s came up with nothing. This was not unexpected because the range of the weak force is even shorter than the strong force and so the W was probably too massive to be produced with the existing accelerators of the day. But its day would come.

THE PARTICLE EXPLOSION

Besides the muon and pion, cosmic-ray experiments in the 1950s revealed several additional particles whose behavior was strange, and so they were called strange particles. These included four K-mesons or kaons: the charged K⁺ and K^–, each with a mass of 494 MeV and two neutral kaons, each with a mass of 498 MeV. In addition, three types of particles heavier than nucleons called hyperons were found. These strange particles were assigned a new quantum number called strangeness, which appeared to be conserved in strong interactions but not in weak interactions. For example, charged kaons were produced in oppositely charged pairs in cosmic rays, never singly, which was explained by assigning the two particles of the pair opposite strangeness. Strangeness was assumed to be conserved in the interaction that produced the pairs. (See further discussion of strangeness conservation below.)

In the 1960s, new accelerators at the Lawrence Radiation Laboratory in Berkeley, California (now the Lawrence Berkeley Laboratory), the Brookhaven National Laboratory on Long Island, and the CERN laboratory in Geneva (now the European Center for Particle Physics) went into operation. They produced hundreds of new particles that were clearly not composed of other known particles. I participated in these events as a graduate student at the University of California at Los Angeles (UCLA) and then, after graduating in 1963, as an assistant professor of physics at the University of Hawaii where two colleagues and I set up a particle-physics research group, which still thrives today.

Almost all the new particles were strongly interacting and called hadrons. The exceptions were a second heavy electron, the tauon, which joined the electron and muon in a non-strongly interacting class called leptons. All three had charge –1. Included in the lepton class were three types of neutrinos, one associated with each charged lepton: the electron neutrino, muon neutrino, and tauon neutrino. Each lepton had an antiparticle partner.

The heavy electrons and all the new hadrons were very short-lived and did not occur in nature except momentarily when produced in the upper atmosphere by high-energy cosmic-ray collisions. However, the cosmic-ray “beam” was not controllable, and accelerators provided a much more efficient source and a better ability to examine the particle properties. The primary device used to detect these particles was the now-obsolete bubble chamber, although other instruments contributed as well.

Hadrons were divided into two categories: baryons, such as the proton and neutron, that had half-integral spin; and mesons, such as the pions and K-mesons, that had zero or integral spin. I did my doctoral thesis at UCLA on the interaction of K⁺ mesons, interacting with deuterium (heavy hydrogen) in a bubble chamber located at the Bevatron accelerator in Berkeley.

With a bubble chamber, we could photograph the paths of charged particles by the trails of bubbles they left in a superheated fluid, which produced beautiful images that enabled us to observe and measure the momenta and energies of the particles produced in a reaction. In the next chapter, we will review the attempts to bring order to this chaos of new particles, and how by the 1970s particle physicists had succeeded spectacularly with what was modestly called the standard model of particles and forces.

First, however, I need to cover another two important developments that occurred in the late 1950s: (1) the observation of several new conservation principles and (2) the discovery of broken symmetries in the weak interaction.

NEW CONSERVATION PRINCIPLES

Reactions involving the new particles were found empirically to obey a set of new conservation rules in addition to the familiar ones—energy, momentum, angular momentum, electric change, and nucleon number.

Recall from chapter 8 that the number of nucleons, that is, protons and neutrons, in a nuclear reaction is the same before and after the reaction takes place. This was no longer the case for the new particles. Instead, it was found that the number of baryons was conserved. To show this, let me generalize the notation introduced in chapter 8 so that a particle X is denoted by _ZX^B, where Z is the electric charge in units of the proton charge e and B is the baryon number. Both Z and B are conserved in all reactions observed so far.

For example,

where ₀π⁰ is the neutral pion, ₁p¹ is the proton, ₁K⁰ is the K-meson with charge +e, and ₀A¹ is the electrically neutral lambda hyperon.

The proton, neutron, and hyperons have B = +1, while their corresponding antiparticles have B = –1. The mesons and leptons have B = 0.

This example also serves to illustrate the conservation of strangeness, S, mentioned previously. The pion and proton have S = 0, the K-meson has S = +1, and the lambda has S = –1, so strangeness is conserved in the above reaction.

On the other hand, reactions such as

are observed, where _–1π⁰ is the negatively charged pion. This violates strangeness conservation. However, this is a weak interaction, whereas the previous is a strong interaction. We conclude that strangeness is conserved in strong interactions but not in weak interactions. Note that charge and baryon number are still conserved.

While other conservation principles were discovered as more particles were produced at higher energies, I will mention just one more here—lepton number conservation.

Recall that three negatively charged leptons—the electron, the muon, and the tauon—were found, and each was associated with a neutrino. These have been assigned a lepton number L = –1, while their corresponding antiparticles have L = +1. The hadrons (baryons and mesons) have L = 0.

Consider neutron beta decay,

This exhibits charge, baryon number, and lepton number conservation.

While no violation of baryon number or lepton number conservation has been observed, as we will see in chapter 12 both must have been violated in the early universe to account for the large excess (by a factor of a billion) that exists for matter over antimatter.

BROKEN SYMMETRIES

Not everything we witness in the world is symmetrical. While we often think of Earth as a sphere, it does not possess perfect spherical symmetry. That is, Earth is not the same viewed from all angles. Earth's rotation causes it to bulge at the equator and flatten at the poles, which breaks spherical symmetry and makes Earth an oblate spheroid. On the other hand, it is roughly symmetric about its axis of rotation. We say that Earth has axial symmetry but broken spherical symmetry.

Similarly, when we look in a mirror, the face we see is not the same one others see when they look straight at us. Our faces break left-right or mirror symmetry. We might call that “broken mirror symmetry.”

Broken symmetry is a feature of the familiar phase transitions we experience in everyday life. When water vapor condenses into liquid water and liquid water freezes into ice, each transition is a broken symmetry. Similarly, when a magnetite, a form of iron oxide that is naturally magnetic, is very hot, it will be nonmagnetic. Then, when it is cooled below a critical temperature, it becomes magnetic. Say the magnetite is shaped in a sphere. Above the critical temperature, it has spherical symmetry, which is then broken at lower temperature as the direction of the magnetic field singles out a special direction in space.

Until the 1950s, it was thought that fundamental chemical, nuclear, and elementary particle processes possess mirror symmetry, technically known as parity symmetry. That is, a reaction always seemed to occur at the same rate as the equivalent reaction viewed in a mirror. As you know, right and left are interchanged in a mirror. The parity operation exchanges left and right and is designated by the letter P.

In 1956, puzzling observations involving kaons in cosmic rays led to the suggestion by two young Chinese physicists working in the United States, Tsung Dao Lee and Chen Ning Yang, that parity symmetry was broken in weak interactions. The violation of parity symmetry was observed in the beta decay of cobalt-60 nuclei in 1956 by a team led by another Chinese physicist in the United States, Madame Chen-Shiung Wu.

The operation of changing a particle to an antiparticle, originally called charge-conjugation, is designated by the letter C. Until 1964 the combined operation CP, where you exchange particles with their antiparticles and left with right, seemed to be invariant for all chemical, nuclear, and particle reactions. However, that year CP symmetry was found to be violated in neutral kaon decays by Princeton physicists James Cronin and Val Fitch.

A symmetry that can be shown to follow from the axioms of quantum field theory is CPT, which combines C, P, and the time-reversal operation, T. Thus, the violation of CP leads to the conclusion that T is violated as well. In 1998, evidence for direct T violation independent of CP was found in neutral kaon decays.

However, as mentioned in chapter 5, it is incorrect to conclude that the source of the arrow of time, and thus the second law of thermodynamics, lies in these discoveries. As we have seen, the arrow of time is a statistical definition that applies for systems of many particles. While, as I have emphasized, so-called irreversible events on the macroscopic scale are still in principle reversible, the probability for the reverse process is so small as to be unlikely to occur in the age of the universe.

By contrast, the kaon reactions on the submicroscopic scale we are talking about here can occur in either direction. The violation of time-reversal symmetry does not mean time reversal is impossible. It just means that the rate in one direction is different than the rate in the other. In the case of kaon decays, the difference is typically only one part in a thousand.

In any case, these observations of a small amount of symmetry breaking are limited to weak interactions. You can take any reaction and, according to our best knowledge, predict that the CPT inverse will occur at the same rate.

“NUCLEAR DEMOCRACY” AND THE TAO OF PHYSICS

There is one more story I need to cover before we get to the standard model. As we have seen, in the 1960s accelerators of ever-increasing energies were producing hoards of new, short-lived particles that were clearly not composed of electrons and nucleons and could not all be “elementary.” Quantum field theory was having a lot of trouble explaining them and began to be questioned. An attempt was made to do away with the idea of elementary particles altogether and replace it with a new “bootstrap” theory in which all the particles are somehow made up of each other. The leading proponent was a brilliant, Hollywood-handsome professor from the University of California at Berkeley named Geoffrey Chew. He called the notion “nuclear democracy.” In this picture, there are no elementary particles. Or, if you wish, they are all elementary.

This was not as crazy as it sounds. Consider figure 10.4, where the arrows on incoming and outgoing nucleons in the π⁺-exchange diagram in figure 10.1 have been reversed. Recall that an antiparticle going one direction in time is empirically indistinguishable from the corresponding particle going backward in time. In figure 10.4 (a), we have an antineutron colliding with a proton, producing a pion, which then decays back into an antineutron and a proton. So, in a sense, the pion is sometimes a nucleon-antinucleon pair.

In figure 10.4 (b), we can see how a proton can spend some of its time as a pion and a neutron. The mathematical attempt to implement the bootstrap idea was called S-matrix theory.⁴

In the early 1970s, an Austrian physicist named Fritjof Capra was working on S-matrix theory with Chew at Berkeley. Hanging around Berkeley's famous marijuana-fogged coffeehouses, Capra learned about Eastern mysticism and proceeded to write a bestselling book called The Tao of Physics, published in 1975.⁵ In the book, Capra claimed that many of the ideas of modern physics, especially quantum mechanics, could be found in the teachings of Eastern mysticism.

Capra viewed the bootstrap idea as particularly compatible with the mystical notion of “oneness.”⁶ The traditional reductionist physics, as exemplified by atomism, was now to be replaced with a new holistic physics in which there are no parts, just one indivisible whole.

The Tao of Physics marked the beginning of a movement called the “New Age” in which, in part, quantum physics is used to justify a new kind spirituality ostensibly based on science.⁷ I have covered this story in detail in two books, The Unconscious Quantum⁸ and Quantum Gods.⁹ Here I will stick to the physics.

By the time The Tao of Physics was published in 1975, S-matrix theory had failed to produce any significant testable predictions while reductionist physics had been restored by the new standard model of particles and forces. Again, I was personally involved in that effort.

Once again, atomism and reductionism reigned supreme. Since its introduction, the standard model has agreed with all observations and is only now being severely tested at the Large Hadron Collider (LHC) at the CERN laboratory in Geneva. These tests are unlikely to overthrow atoms and the void.

Not only did the standard model restore atomism and reductionism by introducing a new set of elementary particles, it also reestablished the integrity of relativistic quantum field theory. The standard model provided a completely relativistic, renormalizable scheme in which equations can be written down that fully describe all that is known about the fundamental particles and forces of nature. As we will see, the key ingredient was the application of a symmetry principle called gauge invariance.