Uncertainty & Causality

The following is an excerpt from The Red Limit, The Search for the Edge of the Universe" by Timothy Ferris ©1977, 1983 Harper Collins:

A physicist named Max Plank developed quantum theory in response to the "blackbody" problem that plagues experimenters. The experiment in question consisted of observing the radiation of heated gas in a neutral ("black") enclosure. By hooking up a spectrometer and temperature-measuring device, an experimenter could chart the intensity with which the gas radiated energy at various wavelengths. When this experiment was performed, it gave results that conflicted with the predictions of classical theory. Each gas tested yielded a curve-wavelength against temperature-that had a characteristic "blackbody" contour, with its peak clearly related to the temperature of the gas, but the shape of the curve and location of the peak were not those predicted by existing physics. Attempts to reconcile theory and observation failed. Ultimately Planck realized that only by breaking with the scientific tradition in which he had been raised could he account for the blackbody results. After months of what he called the most intense work of his career, he derived the formula since called Planck's law." It has accurately predicted the behavior of radiated energy in laboratory jars, in the sun and stars and, apparently, in the universe at large-the cosmic background radiation discovered by Penzias and Wilson conforms to a Planck curve.

Plank saw that atoms radiate energy not in a smooth continuum, as had been assumed, but in discrete packets he called "quanta" (after the Latin "quantus," for "how much"). Quantum theory holds that nature acts, in a sense, like a bank teller who can pay out a penny or two pennies but not a penny and a half. "There is no way out," Planck told his students. We have to become accustomed to the quantum theory, and we shall see that it will penetrate into more and more fields of our physics."

Nineteenth-century science viewed matter and energy as two different worlds, each with its own set of "laws." Matter was said to be composed of particles, energy of waves. Planck's theory violated this well-established distinction by portraying energy as composed of "particles," the quanta. Within a generation, the Parisian physicist Louis de Broglie showed that matter could be viewed as waves, just as energy could look like particles. Indeed, De Broglie said in his Nobel Prize address n 1929, "to describe the properties of matter, as well as those of light, we must employ waves and corpuscles simultaneously."

The general reaction among researchers was to say, well, fine, particle theory and wave theory can both be applied to matter or energy, but ultimately nature must be one or the other. Which is it really? Particles or waves? Must of the theorizing and experimentation of early twentieth-century physics revolved around this question.

Two schools emerged and briefly coexisted. They represented the old wave-particle question in new clothing. Physicists who were intellectually more comfortable with a particle universe proved that the waves could be interpreted as probabilities: The ultimate reality was particles, in their view, and the waves reflected the probability of finding particles at each given point along, say, a ray of light. Einstein pioneered this position, in an early paper explaining light as composed of quanta he called photons. Those favoring wave theory, notably the Viennese physics Erwin Schrödinger, demonstrated with equal plausibility that waves were what counted, that particles were an illusion. Each side delighted in inventing experiments that made the other's position seem dubious. At this both sides were equally successful. Schrödinger, followed by Dirac, then demonstrated that the two schools were mathematically equivalent, that they amounted to different ways of saying the same thing.

But what was nature really? A swarm of particles? An ocean of waves?

The twenty-six-year-old physicist Werner Heisenberg, studying under Niels Bohr in Copenhagen, concluded that the paradox of waves and particles could be resolved only by taking the role of the observer, the physicist, into account. This step led Heisenberg to establish the uncertainty principle, and it is fair to say that science has not been the same since.

As Heisenberg recalled it, he was set on the path to the uncertainty principle by a remark Einstein had made in a private talk the previous year. Einstein was disturbed by what he thought to be Heisenberg's almost ruthless refusal to concern himself with elements of the physical world other than those that could be observed. Specifically, Einstein was concerned about a paper by the young Heisenberg that failed to accept the notion that electrons orbit the nucleus of atoms. Heisenberg refused to talk about electron orbits because no electron had ever been observed in orbit, and in all likelihood none ever could be.

"But surely you don't believe," Einstein said, as Heisenberg remembered the conversation, "that none but observable magnitudes must go into a physical theory?"

"Isn't that precisely what you have done with relativity?" Heisenberg asked. "After all, you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference system or the system at rest, are relevant to the determination of time."

"Possibly I did use this kind of reasoning," Einstein said, "but it is nonsense all the same. . . . It is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory that decides what we can observe. . . ."

Late one night in February 1927, Heisenberg walked in Copenhagen's Faelled Park, thinking about Einstein's remark, "It is the theory that decides what we can observe." That certainly seemed to describe the question of wave theory versus particle theory; one could see the subatomic world as waves or particles, whichever one looked for. What if the question of which was "real" could never be finally decided? What if the sort of things physicists observed in the subatomic realm was determined less by "reality" than by the methods they used to observe? Heisenberg knew, for example, that one could not observe an electron in an atom without knocking it out of the atom: The radiation needed to "illuminate" the electron for observation-in practice, gamma rays were employed for this purpose-would knock it out of orbit. This had been the bone of contention with Einstein, who thought of the orbit as "real" even though an electron could not be observed in orbit. Heisenberg wondered whether this limitation of observation might be the real issue. Perhaps we can never observe the "real" world on such a small scale. If we cannot, Heisenberg felt, then speculation about what that world was "really" like was not, in this situation at least, a matter that science could decide.

Back in his flat, Heisenberg attempted to determine just how much uncertainty was built into the situation. If a physicist wants to know exactly where a "particle" is at a given moment, he must interfere with it-wallop it with gamma rays or some other form of radiation-to find out, and in the process he will change its behavior, knocking it onto a new path. The price of knowing its position is that he must relinquish knowledge of how it might have behaved if he had let it alone. If, on the other hand, he wants to know the particle's behavior in space and time, how fast it is going and in what direction-and it is this behavior of great numbers of "particles" that generates "waves"-he must wait and see; a track in a cloud chamber or an oscilloscope will tell him where the particle went, after the fact. The price of that observation is that the physicist cannot know exactly where the particle was at a given moment. The trade-off, Heisenberg realized, is fundamental. The subatomic world is grainy with inexactitude, is build of little uncertainty "boxes" we macroscopic observers can never peer into. We can squeeze the box one way to make things look like particles, or the other way to see waves, according to how we set up each experiment, but we cannot reduce the area inside the box. When Heisenberg computed the "amount" of uncertainty inside the box, he founded it defined by Planck's constant.

When Bohr returned to Copenhagen-he had been away on a skiing trip-and was presented with Heisenberg's new theory, he went to work extrapolating it. The result was his "principle of complementarity." Bohr demonstrated that the uncertainty principle was implied by fundamental laws of conservation of energy and momentum. Wave and particle models were complementary aspects of the same reality. The "real" nature of the microscopic world, it appeared to Heisenberg and Bohr and has appeared ever since, cannot be captured in a microscopic model.

I have attempted this shamelessly oversimplified account of early quantum physics in order to suggest that something of deep importance was going on in science. Science was beginning to leave behind it need to visualize, and with it was discarding some other trappings of traditional science, including the doctrines of force and causation.

Scientific theories must be logical, must be expressible in terms of mathematics, the most rigorous logical system known. But in practice, theories also have had to "make sense" in terms of ordinary experience. The scientist, looking at nature, draws on more of his human experience than just mathematics. Science is full of metaphors, good and bad, as is poetry.

Because humans are visually oriented (so much so that the retina is regarded by neurophysiologists as part of the brain), models of nature typically have been visualizable, have made sense to the "mind's eye." This luxury was lost when physics penetrated to the subatomic world, where the "objects" being studied are not much larger than a wave of light and cannot be seen at all. Heisenberg realized that for science to go on, the inherent limitation on the relationship of the scientist to what he or she observed would have to become an acknowledged part of science.

With the fall of visualization came the fall, or at least decline, of causation and force, two concepts that had long been part of science. The logician positivist Rudolph Carnap traced the two doctrines to a common origin. They arose, he said, "as a kind of projection of human experience into the world of nature.

"When a table is pushed, tension is felt in the muscles," Carnap wrote. "When something similar is observed in nature, such as one billiard ball striking another, it is easy to imaging that one ball is having an experience analogous to our experience of pushing the table. The striking ball is the agent. It does something to the other ball that makes it move. It is easy to see how men of primitive cultures could suppose that elements in nature were animated, as they themselves were, by souls that willed certain things to happen. This is especially understandable with respect to natural phenomena that cause great harm. A mountain would be blamed for causing a landslide. A tornado would be blamed for damaging a village."

With the advent of twentieth-century physics, both force and causation appear to have been expunged from at least part of science. Einstein did away with the "force" long thought necessary to keep the planets moving in their orbits. For centuries it appeared that something-perhaps God-must push the planets along in their paths. Newton explained planetary motions in terms of a force of universal gravitation but apologized for doing so. In relativity, planets are said to follow their orbits because the orbits describe geodesics, paths of greatest efficiency, in space and time. No force holds them in orbit or pushes them along. In quantum physics causation fails because, given enormous swarms of matter/energy on a tiny scale, the experimenter can predict the behavior of "particles" only in terms of probabilities. Einstein, who helped introduce the statistical approach to physics, felt it was only an expedient and that a cause-and-effect explanation of the behavior of every particle could be worked out if one had sufficient equipment and patience. But Heisenberg showed that a complete cause-and-effect account of subatomic behavior could never be attained by us in the macroscopic world; we are prevented by the uncertainty principle from ever tracing the individual interactions of even a small group of subatomic "particles." Therefore-and this assertion is as much philosophy as science-it is said to be useless to talk about causation operating in a realm where we can never see or examine it at work. We might as well accept that the probabilities are real.

The decline of determinism may have been made possible in the West by the decline of God's perceived role in the cosmos. For centuries God was assigned the role of prime causer ("unmoved over," in Aristotle's phrase). Thomas Aquinas was able to construct an impressive proof of the existence of God by placing Him at the head of the cosmic causal chain. With the rise of technology, attention focused on the supposed machinery of nature, and God was increasingly relegated to the role of a creator who set the machinery in motion but now seldom had to look after it, like a successful entrepreneur who need no longer show up regularly at the office. By the beginning of this century, when the machine age began its slow termination, God had withdrawn so far from the scene as to be unable to defend nature against a noncausal philosophy of science.

Although talk of causation survives in modern science, something of the scientific world view has been changed at the root by the quantum principle. Atoms are ubiquitous, and if the subatomic world is nondeterministic, the broader universe must forever present to us an element of change. It cannot be the precise machine science once portrayed it to be. For many young physicists, the fall of causation was liberating; science had discarded a heavy piece of needless luggage and could proceed afresh. Reading Heisenberg or De Broglie, one gets the sense of adventure that the seventy-century Buddhist Fa-Tsang expressed when he wrote, "Now that we understand that causes are really not causes, any arising will be wonderful."

Einstein, however, did not share in this enthusiasm. He never accepted the contention that because the subatomic world must appear to us in probabilities, it really is built upon probabilities. Einstein had been one of the first to demand that the role of the observer be considered in physical theories, but he would not agree that limitation upon observation must be considered the same thing as limitations upon nature. "God does not play dice," he said.

Einstein became isolated from the quantum physics he had helped found. As De Broglie wrote in the early 1950s, "Theoretical physicists are present divided into two apparently irreconcilable groups. On the one hand, Einstein and his followers are trying to develop general relativity theory, while by far the great majority of theorists, attracted by atomic problems, are trying to develop quantum physics quite independent of general relativity and that of quanta, should so utterly ignore each other." Max Born wrote of Einstein, "when out of his own work a synthesis of statistical and quantum principles emerged which seemed to be acceptable to almost all physicists, he kept himself aloof and skeptical. Many of us regard this as a tragedy-for him, as he gropes his way in loneliness, and for us who miss our leader and standard-bearer."

As he lived out his final years in a white frame house on Mercer Street in Princeton, Einstein found himself set apart-enshrined, really-both my his minority position in the philosophy of science and by the international celebrity that had befallen him. His kindly face and rumpled sweaters had become symbols of incomprehensible wisdom. "Because of a peculiar popularity which I have acquired, anything I do is likely to develop into a ridiculous comedy," he wrote an old friend, the Queen Mother of Belgium. To Born he wrote sadly, "In our scientific expectation we have grown antipodes. You believe in God playing dice and I in perfect laws in the world of things existing as real objects, which I try to grasp in a wildly speculative way."

Einstein died on April 18, 1955. A beautiful tribute he wrote for Max Planck, the founder of quantum physics, in 1932, might serve Einstein himself as well:

"Many kinds of men devote themselves to science," Einstein wrote, "and not all for the sake of science herself. There are some who come into her temple because it offers them the opportunity to display their particular talents. To this class of men science is a kind of sport in the practice of which they exult, just as an athlete exults in the exercise of his muscular prowess. There is another class of men who come into the temple to make an offering of their brain pulp in the hope of securing a profitable return. These men are scientists only by the chance of some circumstance which offered itself when making a choice of career. If the attending circumstances had been different, hey might have become politicians or captains of business. Should an angel of God descend and drive from the temple of science all those who belong to the categories I have mentioned, I fear the temple would be nearly emptied. But a few worshippers would still remain-some from former times and some from ours. To these latter belongs our Planck. And that is why we love him."

"The Red Limit, The Search for the Edge of the Universe" by Timothy Ferris ©1977, 1983 Harper Collins

What is it that you can say you are certain of? . . . According to Heisenberg, nothing.

So then what is it we can know? . . . Nothing.

If there is no causality in the universe then everything is simply a happening.

When we experience we affect the outcome. We have no way of knowing what would have occurred had we not been there.

Observing is not a passive act. What we call observing is actually perceiving. We not only affect the outcome we create the outcome.

The instant you try to say something about it it's only a record of the experience . . . and the record and the thing itself is totally different.