Virtual particles play a particularly important and interesting role in what is called self-interaction. This is the name given to the phenomenon of virtual particles being emitted and then reabsorbed by the same particle. Picture a girl walking down the street, repeatedly tossing and catching a ball as she walks. Or better, a juggler tossing and catching an assortment of objects as he cycles across the stage. Even these images are insufficient to convey the reality of self-interaction, because the very nature of a fundamental particle, including its mass, is dictated by its swarm of virtual particles. A free particle’s tendency to interact with itself displays most clearly our contemporary view of the submicroscopic world—a view of continual chaotic activity, from which no particle can be isolated.
A first guess about the world line of a single free particle (a proton, for instance), sitting motionless and alone in free space, might be an uninteresting vertical line in a spacetime diagram. As far as macroscopic observation goes, that is the whole story—an unchanging, unmoving particle tracing out its straight course through time. Can the proton decay into a pair of other particles, thereby causing its world line to fork into two others, making the diagram a little more interesting? No, that won’t work. Energy conservation and baryon number conservation prohibit it.1 But what can happen—and, we believe, does happen, continually and insistently—is the emission and reabsorption of endless virtual particles by our lonely, isolated proton. According to the Heisenberg uncertainty principle, nature is willing to overlook a violation of the law of energy conservation, provided the violation lasts a short enough time. The more flagrant the violation, the briefer its duration must be. So if we imagine a super-microscope that allows us to view, close-up, what the proton is doing, we would see that it is in a great state of agitation, emitting and reabsorbing a plethora of particles, and itself existing part of the time as a neutron. Its world line looks not like a straight vertical line but more like the result of a kitten tearing apart a skein of yarn.
Yet the proton’s dervish dance of creation and annihilation of other particles is not without discipline. It is hemmed in by the requirement that some quantities, such as charge and color and quark number, remain conserved even in the tiniest increments of space and time.
Since even a single particle alone is in such a continual state of agitation, one can ask about the still simpler situation of plain empty space. Field theory provides the answer that empty space, far from being truly void, is a rather lively place. Transitory violations of energy conservation permit particles to be formed out of nothing and vanish again. The name “physical vacuum” has been given to space filled continually with all of these momentary comings and goings, to distinguish it from the unreal “bare vacuum.”
The vision that I am outlining here is really a vision of chaos: the chaos provoked by the fundamental events of annihilation and creation underlying an order imposed by the conservation laws. This theme of order and chaos illustrates as clearly as anything can the complete revolution in our view of the world that has been brought about by the advances of physical science in the twentieth century.
Briefly stated, the new view is a view of chaos beneath order—or, what is the same thing, of order imposed upon a deeper and more fundamental chaos. This is in startling contrast to the view developed and solidified in the three centuries from Kepler to Einstein, a view of order beneath chaos. In spite of the haphazard and unpredictable nature of the world around us, ran the old argument, nature’s basic laws are fundamentally simple and orderly, and therefore the behavior of nature at the submicroscopic level is fundamentally simple and orderly too. The building blocks of the universe are elementary objects, colorless, unemotional, identical, comprehensible, and predictable, moving in calculable paths, interacting in a known way with other elementary objects.
A modern computing machine illustrates fairly well this classical view of elementary simplicity and orderliness. The basic units of the machine, such as its transistors, are simple objects, each capable of performing only a very elementary function in a predictable and easily controllable way. The electrical engineer might be excused for waxing rhapsodic about the magnificent beauty and simplicity of a transistor and of the laws governing its action. The ordinary citizen might be excused for regarding it as, on the whole, a rather dull object. But both must agree that when millions of simple units are connected together in the right way, a complicated organism comes into existence, with a rich and rewarding variety of functions and behavior patterns. A few million is a small enough number that the engineer can still undertake to predict just what the machine will do under all circumstances, but even the engineer will be astonished by the complexity engendered by mere size.
Such was the view of the physical world until quantum mechanics showed itself. Simple objects and simple laws—a basic, underlying orderliness—lay beneath the rich chaos and complexity of the world of our senses. To lay bare the orderliness and probe to ever deeper and simpler layers of reality had been the task of science, a task carried on with unprecedented speed and success in the most recent few centuries of mankind’s existence.
But, in the twentieth century and extending into this one, the theories of relativity and quantum mechanics and the experimental evidence from the world of fundamental particles have combined to reveal a deeper-lying and more fundamental chaos. Particles are found to have a transitory existence; empty space is a beehive of disordered activity; laws of probability have replaced laws of certainty; an isolated particle is engaged in a constant frenzied dance whose steps are random and unpredictable; a principle of uncertainty prevents too close scrutiny or precisely accurate measurements in the world of the very small.
This is not to say that the older idea of simplicity in the small and complexity in the large has been wholly abandoned. An electron is still a simple object, even if far from inert; nature’s most fundamental laws still appear to govern the submicroscopic world; and the complexity of size and organization is still very real. The revolution has appeared primarily in shifting the source of order from the elementary interactions and activity of particles to the overriding constraints of conservation laws. The present picture of the world is that of a nearly limitless chaos governed only by a set of constraining laws, a world in which apparently everything that can happen, subject only to the straitening effect of these conservation laws, does happen. The fields and particles of the submicroscopic world must be regarded as an unruly lot who carry on in every conceivable way that is not absolutely forbidden by the overriding restriction of a conservation principle.
Is this fundamental chaos of nature a temporary phenomenon in science that will be replaced by a deeper order in the future? Perhaps. There is no evidence at all upon which to base an answer to this question, but two main possibilities need to be cited. On the one hand, an elementary event of creation and annihilation, which now appears to occur catastrophically at a single point in spacetime, may, upon closer inspection, prove to be a swift but smooth, and more orderly, unrolling of a chain of events. The probability of quantum mechanics may prove to rest only upon the great complexity of the things we now regard as simple. On the other hand, our view of the world of the very small could easily become more chaotic, not less so. Lying dormant thus far in our view of the world is spacetime itself. While fields and particles come and go, space and time lie inert, providing the stage upon which the actors play their roles. There is some reason to believe that the future theory of particles may involve space and time as actors, not merely as stage.2 If so, weird convolutions of space and time and/or the quantization of spacetime may contribute more to the chaos in our view of the world.
In whatever direction the future theory of particles proceeds, I must emphasize that present theory is much more likely to be supplemented than to be rejected. Just as Newtonian mechanics is still entirely adequate for describing the motion of planets, present theories of particles are likely to remain adequate for describing all those features of the particle world that have been understood quantitatively so far. Nevertheless, it is the deepest theory that most strongly affects our image of the world, and this image may be drastically altered in the future.
In the seventeenth century, humans looked upward and outward into the universe and were humbled as the Earth took its diminutive place as a speck of matter in a corner of the cosmos. Now we look downward and inward and find new reasons for humility. Where we might have expected to find some firm lumps of matter as the building blocks of mankind and our world, we find a chaos of annihilation and creation, a swarm of transitory bits of matter, and the tenuous substance of wave fields. Where we might have expected to find laws of certainty, we find laws of probability, and seem to see the hand of chance working at every turn—chance that any particles are stable, chance that the neutron can live forever within a nucleus, chance that we are free of the threat of annihilation by antiparticles. Above the chaos and the probability stand the conservation laws, imposing their order upon the undisciplined energy of the universe to make possible the marvelously intricate, incredibly organized structures of the world around us.
1 It is possible that baryon number is “not quite” conserved. Searches for proton decay will continue.
2 When it comes to black holes and gravitational radiation, spacetime is already an important part of the action.