Chapter One: Quantum Uncertainty
In 1900, Lord Kelvin spoke of the triumphs of physics and how Newton's theory of motion could be extended to embrace the phenomena of light and heat. His address went on to mention "two clouds" that obscured the "beauty and clearness" of the theory: the first involved the way light travels through space, the second was the problem of distributing energy equally among vibrating molecules. The solution Kelvin proposed, however, proved to be way off the mark. Ironically, what Kelvin had taken to be clouds on the horizon were in fact two bombshells about to create a massive explosion in twentieth century physics. Their names were relativity and quantum theory, and both theories had something to say about light.
Light, according to physicists like Kelvin, is a vibration, and like every other vibration it should be treated by Newton's laws of motion. But a vibration, physicists argued, has to be vibrating in something. And so physicists proposed that space is not empty but filled with a curious jelly called "the luminiferous ether.” But this meant that the speed of light measured in laboratories on earth-the speed with which vibrations appear to travel through the ether-should depend on how fast and in what direction the earth is moving through the ether. Because the earth revolves around the sun this direction is always varying, and so the speed of light measured from a given direction should vary according to the time of year. Scientists therefore expected to detect a variation in the speed of light measured at various times of the year, but very accurate experiments showed that this was not the case. No matter how the earth moves with respect to the background of distant stars, the speed of light remains the same.
This mystery of the speed of light and the existence, or nonexistence, of the ether was only solved with Einstein's special theory of relativity, which showed that the speed of light is a constant, independent of how fast you or the light source is traveling.
The other cloud on Kelvin's horizon, the way in which energy is shared by vibrating molecules, was related to yet another difficult problem-the radiation emitted from a hot body. In this case, the solution demanded a revolution in thinking that was just as radical as relativity theory-the quantum theory.
Bohr and Einstein
Special relativity was conceived by a single mind-that of Albert Einstein. Quantum theory, however, was the product of a group of physicists who largely worked together and acknowledged the Danish physicist Niels Bohr as their philosophical leader. As it turns out, the tensions between certainty and uncertainty that form the core of this book are nowhere better illustrated than in the positions on quantum theory taken by these two great icons of twentieth century physics, Einstein and Bohr. By following their intellectual paths we are able to discover the essence of this great rupture between certainty and uncertainty.
When the two men debated together during the early decades of the twentieth century they did so with such passion for truth that Einstein said that he felt love for Bohr. However, as the two men aged, the differences between their respective positions became insurmountable to the point where they had little to say to each other. The American physicist David Bohm related the story of Bohr's visit to Princeton after World War II. On that occasion, the physicist Eugene Wigner arranged a reception for Bohr that would also be attended by Einstein. During the reception, Einstein and his students stood at one end of the room and Bohr and his colleagues at the other.
How did this split come about? Why, with their shared passion for seeking truth, had the spirit of open communication broken down between the two men? The answer encapsulates much of the history of twentieth century physics and concerns the essential dislocation between certainty and uncertainty. The break between them involves one of the deepest principles of science and philosophy-the underlying nature of reality. To understand how this happened is to confront one of the great transformations in our understanding of the world, a leap far more revolutionary than anything Copernicus, Galileo, or Newton produced. To find out how this came about we must first take a tour through twentieth century physics.
Relativity
Einstein's name is popularly associated with the idea that "everything is relative.” This word "relative" has today become loaded with a vast number of different associations. Sociologists, for example, speak of "cultural relativism," suggesting that what we take for "reality" is to a large extent a social construct and that other societies construct their realities in other ways. Thus, they argue, "Western science" can never be a totally objective account of the world for it is embedded within all manner of cultural assumptions. Some suggest that science is just one of the many equally valid stories a society tells itself to give authority to its structure; religion being another.
In this usage of the words "relative" and "relativism" we have come far from what Einstein originally intended. Einstein's theory certainly tells us that the world appears different to observers moving at different speeds, or who are in different gravitational fields. For example, relative to one observer lengths will contract, clocks will run at different speeds, and circular objects will appear ellipsoidal. Yet this does not mean that the world itself is purely subjective. Laws of nature underlie relative appearances, and these laws are the same for all observers no matter how fast they are moving or where they are placed in the universe. Einstein firmly believed in a totally objective reality to the world and, as we shall see, it is at this point that Einstein parts company with Bohr.
Perhaps a note of clarification should be added here since that word "relativity" covers two theories. In 1905, Einstein (in what was to become known as the special theory of relativity) dealt with the issue of how phenomena appear different to observers moving at different speeds. He also showed that there is no absolute frame of reference in the universe against which all speeds can be measured. All one can talk about is the speed of one observer when measured relative to another. Hence the term "relativity."
Three years later the mathematician Herman Minkowski addressed the 80th assembly of German National Scientists and Physicians at Cologne. His talk opened with the famous words: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” In other words, Einstein's special theory of relativity implied that space and time were to be unified into a new four-dimensional background called space-time.
Einstein now began to ponder how the force of gravity would enter into his scheme. The result, published in 1916, was his general theory of relativity (his earlier theory now being a special case that applies in the absence of gravitational fields). The general theory showed how matter and energy act on the structure of space-time and cause it to curve. In turn, when a body enters a region of curved space-time its speed begins to change. Place an apple in a region of space-time and it accelerates, just like an apple that falls from a tree on earth. Seen from the perspective of General Relativity the force of gravity acting on this apple is none other than the effect of a body moving through curved space-time. The curvature of this space-time is produced by the mass of the earth.
Now let us return to the issue of objectivity in a relative world. Imagine a group of scientists here on earth, another group of scientists in a laboratory that is moving close to the speed of light, and a third group located close to a black hole. Each group observes and measures different phenomena and different appearances, yet the underlying laws they deduce about the universe will be identical in each of the three cases. For Einstein, these laws are totally independent of the state of the observer.
This is the deeper meaning of Einstein's great discovery. Behind all phenomena are laws of nature, and the form of these laws, their most elegant mathematical expression, is totally independent of any observer. Phenomena, on the other hand, are manifestations of these underlying laws but only under particular circumstances and contexts. Thus, while phenomena appear different for different observers, the theory of relativity allows scientists to translate, or transform, one phenomenon into another and thus to return to an objective account of the world. Hence, for Einstein the certainty of a single reality lies behind the multiplicity of appearance.
Relativity is a little like moving between different countries and changing money from dollars into pounds, francs, yen, or euros. Ignoring bank charges, the amount of money is exactly the same, only its physical appearance-the bank notes in green dollars or pounds, yen, euros, and so on changes. Similarly a statement made at the United Nations is simultaneously translated into many different languages. In each particular case the sound of the statement is quite different but the underlying meaning is the same. Observed phenomena could be equated to statements in different languages, but the underlying meaning that is the source of these various translations corresponds to the objective laws of nature.
This underlying reality is quite independent of any particular observer. Einstein felt that if the cosmos did not work in such a way it would simply not make any sense and he would give up doing physics. So, in spite of that word "relativity," for Einstein there was a concrete certainty about the world, and this certainty lay in the mathematical laws of nature. It is on this most fundamental point that Bohr parted company with him.
Blackbody Radiation
If Einstein stood for an objective and independent reality what was Niels Bohr's position? Bohr was an extremely subtle thinker and his writings on quantum theory are often misunderstood, even by professional physicists! To discover how his views on uncertainty and ambiguity evolved we must go back to 1900, to Kelvin's problem of how energy is distributed amongst molecules and an even more troubling, related issue, that of blackbody radiation.
A flower, a dress, or a painting is colored because it absorbs light at certain frequencies while reflecting back other frequencies. A pure black surface, however, absorbs all light that falls on it. It has no preference for one color over another or for one frequency over another. Likewise, when that black surface is warmer than its surroundings it radiates its energy away and, being black, does so at every possible frequency without preferring one frequency (or color) over another.
When physicists in the late nineteenth century used their theories to calculate how much energy is being radiated, the amount they arrived at, absurdly, was infinite. Clearly this was a mistake, but no one could discover the flaw in the underlying theory.
Earlier that century the Scottish physicist James Clerk Maxwell had pictured light in the form of waves. Physicists knew how to make calculations for waves in the ocean, sound waves in a concert hall, and the waves formed when you flick a rope that is held fixed at the other end. Waves can be of any length, with an infinite range of gradations. In the case of sound, for example, the shorter the wavelength-the distance between one crest and the next-the higher the pitch, or frequency, of the sound because the shorter the distance between wave crests, the more crests pass a particular point, such as your ear, in a given length of time. The same is true of light: long wavelengths lie toward the red end of the spectrum, whereas blue light is produced by higher frequencies and shorter wavelengths.
By analogy with sound and water waves, the waves of light radiated from a hot body were assumed to have every possible length and every possible frequency; in other words, light had an infinite number of gradations from one wavelength to the next. In this way an infinity crept into the calculation and emerged as an infinite amount of energy being radiated.
The Quantum
In 1900, Max Planck discovered the solution to this problem. He proposed that all possible frequencies and wavelengths are not permitted, because light energy is emitted only in discrete amounts called quanta. Rather than continuous radiation emerging from a hot body, there is a discontinuous, and finite, emission of a series of quanta.
With one stroke the problem of blackbody radiation was solved, and the door was opened to a whole new field that eventually became know as quantum theory. Ironically Einstein was the first scientist to apply Planck's ideas. He argued that if light energy comes in the form of little packages, or quanta, then when light falls on the surface of a metal it is like a hail of tiny bullets that knock electrons out of the metal. In fact this is exactly what is observed in the "photoelectric effect," the principle behind such technological marvels as the "magic eye.&rd