The answer is that this symmetry is “spontaneously broken.” The same background density of particles in empty space that causes a Z particle to appear massive, while a photon, which transmits electromagnetism, remains massless, provides a background that can physically respond to the weak charge of an object. For this reason one is no longer free to vary locally what one means by positive and negative weak charge and thus the gauge symmetry which would otherwise be present is not manifest. It is as if there were a background electric field in the universe. In this case, there would be a big difference between positive and negative charges in that one kind of charge would be attracted by this field and another kind would be repelled by it. Thus, the distinction between positive and negative charge would no longer be arbitrary. This underlying symmetry of nature would now be hidden.
The remarkable thing is that spontaneously broken gauge symmetries are not entirely hidden. As I have described, the effect of a background “condensate” of particles in empty space is to make the
W and Z particles appear heavy, while keeping the photon massless. The signature of a broken gauge theory is then the existence of heavy particles, which transmit forces that can act only over short distances—so-called short-range forces. The secret of discovering such an underlying symmetry that is broken is to look at the short-range forces and explore similarities with long-range forces—forces that can act over long distances, such as gravity and electromagnetism. This, in a heuristic sense at least, is exactly how the weak interaction was eventually “understood” to be a cousin of quantum electrodynamics, the quantum theory of electromagnetism.
Feynman and Murray Gell-Mann developed a phenomenological theory in which the weak interaction was put in the same form as electromagnetism in order to explore the consequences. Within a decade a theory unifying both electromagnetism and the weak interaction as gauge theories was written down. One of its central predictions was that there should be one part of the weak force that had never been previously observed. It would not involve interactions that mixed up the charge of particles, such as that which takes a neutral neutron and allows it to decay into a positive proton and a negative electron. Rather, it would allow interactions that would keep the charges of particles the same, just as the electric force can act between electrons without changing their charge. This “neutral interaction” was a fundamental prediction of the theory, which was finally unambiguously observed in the 1970s. This was perhaps the first case of a discovery of a symmetry that
predicted
the existence of a new force, rather than naming it in hindsight.
The weakness of the weak interaction is due to the fact that the gauge symmetry associated with it gets spontaneously broken. Thus—on length scales larger than the average distance between particles in the background condensate that affects the
properties of the W and Z particles—these particles appear very heavy and the interactions mediated by them are suppressed. If other, new gauge symmetries were to exist in nature that got spontaneously broken at even smaller distance scales, the forces involved could easily be too weak to have yet been detected. Perhaps there are an infinite number of them. Perhaps not.
It then becomes relevant to ask whether all the forces in nature must result from gauge symmetries, even if they are spontaneously broken. Is there no other reason for a force to exist? We do not yet have a complete understanding of this issue, but we think the answer is likely to be that there is none. You see, all theories that do not involve such a symmetry are mathematically “sick,” or internally inconsistent. Once quantum-mechanical effects are properly accounted for, it seems that an infinite number of physical parameters must be introduced in these theories to describe them properly. Any theory with an infinite number of parameters is no theory at all! A gauge symmetry acts to restrict the number of variables needed to describe physics, the same way a spherical symmetry acts to limit the number of variables needed to describe a cow. Thus, what seems to be required to keep various forces mathematically and physically healthy is the very symmetry that is responsible for their existence in the first place.
This is why particle physicists are obsessed with symmetry. At a fundamental level, symmetries not only describe the universe; they determine what is possible, that is, what
is
physics. The trend in spontaneous symmetry breaking has thus far always been the same. Symmetries broken at macroscopic scales can be manifest at smaller scales. As we have continued to explore ever smaller scales, the universe continues to appear more symmetrical. If one wishes to impose the human concepts of simplicity and beauty on nature, this must be its manifestation. Order
is
symmetry.
Symmetry considerations have taken us to the very limits of our knowledge about the world. But in the past twenty years or so they have begun to push us well beyond this limit, as physicists have wrestled to explore what symmetries might determine why the universe at its most fundamental scale behaves the way it does and whether the observed symmetries of nature may force us toward a totally new conception of physical reality.
Part of the motivation comes from the very connection between electromagnetism and gravity that I have just discussed and mentioned in the context of Herman Weyl’s attempt at unification. The recognition that both forces arise from a local symmetry of nature is very satisfying, but nevertheless there remains a fundamental difference between the two. Gravity is related to a symmetry of space, whereas electromagnetism and the other known forces of nature are not. The force we feel as gravity reflects an underlying curvature of space, whereas what we feel as electromagnetism does not. In 1919 this difference was addressed by a young Polish mathematician, Theodor Kaluza, who proposed that perhaps there was another dimension of space, beyond the three we directly experience. Could electromagnetism result from some underlying curvature in an otherwise unobserved extra dimension of space?
Remarkably, the answer turned out to be yes. As confirmed independently several years later by the Swedish physicist Oskar Klein, if one added a fifth dimension, which Klein suggested could be curled up in a circle so small that it would not be detectable by any existing experiments, then both electromagnetism and four-dimensional gravity could result from an underlying five-dimensional theory with five-dimensional symmetries, in which a curvature in our observed four dimensions would produce what we observe as gravity, and a curvature in the fifth dimension could produce what we observe as electromagnetism.
You would think that with such a remarkable result Kaluza and Klein would have become as famous as Einstein and Dirac, but it turned out that their theory, as beautiful as it was, also predicted an additional kind of gravitational force that was not observed, and thus this idea could not have been correct as they had formulated it. Nevertheless, the Kaluza-Klein unification remained in the back of theorist’s minds as the rest of twentieth-century physics unfolded.
In the 1970s and 1980s, as it became clear that all the other forces in nature were, like electromagnetism, described by gauge symmetries, physicists began to once again take up Einstein’s holy grail of unifying all the forces in nature, including gravity, in a single theory.
To tell the proper story of what unfolded would require a whole book, but fortunately I recently have written one, as have a host of others. Suffice it to say that physicists proposed in 1984 that if we extend our spacetime not by merely one dimension, but at least six additional dimensions, then one could embed all the observed symmetries associated with all the observed forces in nature,
including gravity
, in a way that also appeared to allow a consistent quantum theory of gravity, something that had thus far eluded all attempts, to be developed. The resulting “theory” became known as Superstring theory, because it was based in part on the assumption that all the particles we observe in nature are actually made up of string-like objects that can vibrate in the extra dimensions.
String theory has had its ups and downs over the past two decades, and the initial excitement of the 1980s has been tempered by the realization that one cannot apparently write down a single string theory that uniquely predicts anything like our world to exist and the realization that even more sophisticated kinds of mathematical symmetries may be necessary to make the theory
consistent, so that perhaps even the idea of fundamental strings themselves may be an illusion, with the more fundamental objects being something else. In fact, as I shall return to at the end of this book, the failure of string theory to predict anything resembling our universe has recently driven some theorists to suggest that there
may be no
fundamental physical explanation of why the universe is the way it is. It may just be an environmental accident!
I did not however, introduce ideas of string theory and extra dimensions here either to praise them or to bury them. The jury is certainly still out on all these issues. Rather, what is important to realize is that it is the search for symmetry that has driven theorists to explore these presently hypothetical new worlds. One physicist has termed the beauty associated with the symmetries of extra dimensions as “elegance.” Time will tell whether this beauty is truly that of nature or merely in the eye of the beholder.
Once again, I have gotten carried away with phenomena at the high-energy frontier. There are also many examples of how symmetries govern the dynamical behavior of our everyday world and that are unrelated to the existence of new forces in nature. Let’s return to these.
Until about 1950, the major place in which symmetry had manifested itself explicitly in physics was in the properties of materials such as crystals. Like Feynman’s chess board, crystals involve a symmetrical pattern of atoms located on a rigid crystal lattice. It is the symmetrical pattern of these atoms that is reflected in the beautiful patterns of crystal surfaces such as those of diamonds and other precious stones. Of more direct relevance to physics, the movements of electronic charges inside a crystal lattice, like pawns in a chess game, can be completely determined
by the symmetries of the lattice. For example, the fact that the lattice pattern repeats itself with a certain periodicity in space fixes the possible range of momenta of electrons moving inside the lattice. This is because the periodicity of the material inside the lattice implies that you can make a translation only up to a certain maximum distance before things look exactly the same, which is equivalent to not making any translation at all. I know that sounds a little like something you might read in
Alice in Wonderland
, but it does have a significant effect. Since momentum is related to the symmetry of physical laws under translations in space, restricting the effective size of space by this type of periodicity restricts the range of available momenta that particles can carry.
This single fact is responsible for the character of all of modern microelectronics. If I put electrons inside a crystal structure, they will be able to move freely about only within a certain range of momenta. This implies that they will have a fixed range of energies as well. Depending on the chemistry of the atoms and molecules in the crystal lattice, however, electrons in this energy range may be bound to individual atoms and not free to move about. Only in the case that this “band” of accessible momenta and energies corresponds to an energy range where electrons are free to flow does the material easily conduct electricity. In modern semiconductors such as silicon, one can, by adding a certain density of impurities that affect which energy range of electrons is bound to atoms, arrange for very sensitive changes in the conductivity of the materials to take place as external conditions vary.
Arguments such as these may in fact be relevant to the greatest mystery of modern condensed matter physics. Between 1911, when Onnes discovered superconductivity in mercury, and 1987, no material had ever been found that became superconducting at
temperatures higher than 20° above absolute zero. Finding such a material had long been the holy grail of the subject. If something could be found that was superconducting at room temperature, for example, it might revolutionize technology. If resistance could be overcome completely without the necessity for complex refrigeration schemes, a whole new range of electrical devices would become practical. In 1987, as I mentioned earlier, two scientists working for IBM serendipitously discovered a material that became superconducting at 35° above absolute zero. Other similar materials were soon investigated, and to date materials that become superconducting at over 100° above absolute zero have been uncovered. This is still a far cry from room-temperature superconductivity, but it is above the boiling point of liquid nitrogen, which can be commercially produced relatively cheaply. If this new generation of “high-temperature” superconductors can be refined and manipulated into wires, we may be on the threshold of a whole new range of technology.
What is so surprising about these new superconductors is that they do not resemble, in any clear fashion, preexisting superconducting materials. In fact, in these materials, superconductivity requires
introducing
impurities into the material. Many of these materials are, in fact,
insulators
in their normal state—that is, they do not conduct electricity at all.
In spite of frantic efforts by thousands of physicists, no clear understanding of high-temperature superconductivity yet exists. But the first thing they focused on was the symmetry of the crystal lattice in these materials, which appears to have a well-defined order. Moreover, it is made of separate layers of atoms that appear to act independently. Current can flow along these two-dimensional layers, but not along the perpendicular direction. It remains to be seen whether these particular symmetries of high-temperature
superconductors are responsible for the form of the interactions that results in a macroscopic superconducting state of electrons, but if history is any guide, that is the best bet.