Units for which the average reader has no instinct or training, such as the curie, dol, mho, and gauss (the measure of magnetic field), should be avoided completely. Kilometers are all right, and so, in general, are meters and kilograms. Even here, there are exceptions. When you watch the Olympic Games, do you, like me, have to convert the pole vault from meters to feet before you have a real idea of how high the bar is set? Do you know if a long jump of nine meters is poor, good, or a world record?
There is one golden rule: numbers are there not to prove how smart you are, but to provide information to the reader. Since this book is written for anyone who wants to use a reasonable amount of science in stories, it's not unfair of me to assume the same of my potential reader. But if you yourself have to sit down and work out how big something is in a particular unit, you should probably look for another way to get your point across.
Technical vocabulary, like the occasional number, adds a feeling of solidity to a story. It should be used sparingly. And get the term right, or don't use it at all. Do not say "quasar" if you mean "quark," confuse momentum with energy, or employ "light-year" as though it is a unit of time.
As for the notation in which very large or small numbers are written, in this book I will assume that you, the reader, are familiar with expressions such as 10+27, or 5.3x10-16. Even so, I advise you to avoid this form of notation whenever possible.
That point was brought home to me many years ago at, of all places, NASA headquarters. We were in the middle of a presentation, and casually throwing around expressions like 1012 and 10-8, when a member of the audience (who happened to be NASA's Head of International Affairs) pointed at one of the numerical tables and said, "What are those little figures written above the tens?"
As we said when we left, "Thank God he's not designing the spacecraft."
Find an alternative in your storytelling to scientific notation. You never know whom you may lose when you use it.
CHAPTER 2
The Realm of Physics
Physics is the study of the properties of matter and energy. We begin with physics, not because it is easier, harder, or more important than other sciences, but because it is, in a specific sense, more fundamental.
More fundamental, in that from the laws of physics we can construct the laws of chemistry; from the laws of chemistry and the laws of physics together we can in turn build the laws of biology, of properties of materials, of meteorology, computer science, medicine, and anything else you care to mention. The process cannot be reversed. We cannot deduce the laws of physics from the laws of chemistry, or those of biology.
In practice, we have a long way to go. The properties of atoms and small molecules can be calculated completely, from first principles, using quantum theory. Large molecules present too big a computational problem, but it is considered to be just that, not a failure of understanding or principles. In the same way, although most biologists have faith in the fact that, by continuing effort, we will at last understand every aspect of living systems, we are a huge distance away from explaining things such as consciousness.
A number of scientists, such as Roger Penrose, believe that this will never happen, at least with current physical theories (Penrose, 1989, 1994; see also Chapter 13). Others, such as Marvin Minsky, strongly disagree; our brains are no more than "computers made of meat." Some scientists, believers in dualism, strongly disagree with that, asserting the existence of a basic element of mind quite divorced from the mechanical operations of the brain (Eccles, 1994).
Furthermore, there is a "more is different" school of scientists, led by physicist Philip Anderson and evolutionary biologist Ernst Mayr. Both argue (Anderson, 1972; Mayr, 1982) that one cannot deduce the properties of a large, complex assembly by analysis of its separate components. In Mayr's words, "the characteristics of the whole cannot (even in theory) be deduced from the most complete knowledge of the components, taken separately or in other partial combinations." For example, study of single cells would never allow one to predict that a suitable collection of those cells, which we happen to call the human brain, could develop self-consciousness.
Who is right? The debate goes on, with no end in sight. Meanwhile, this whole area forms a potential gold mine for writers.
2.1 The small world: atoms and down. It was Arthur Eddington who pointed out that, in size, we are slightly nearer to the atoms than the stars. It's a fairly close thing. I contain about 8 x 1027 atoms. The Sun would contain about 2.4 x 1028 of me. We will explore first the limits of the very small, and then the limits of the very large.
A hundred years ago, atoms were regarded as the ultimate, indivisible elements that make up the universe. That changed in a three-year period, when in quick succession Wilhelm Röntgen in 1895 discovered X-rays, in 1896 Henri Becquerel discovered radioactivity, and in 1897 J.J. Thomson discovered the electron. Each of these can only be explained by recognizing that atoms have an interior structure, and the behavior of matter and radiation in that sub-atomic world is very different from what we are used to for events on human scale.
The understanding of the micro-world took a time to appear, and it is peculiar indeed. In the words of Ilya Prigogine, a Nobel prize-winner in chemistry, "The quantum mechanics paradoxes can truly be said to be the nightmares of the classical mind."
The next step after Röntgen, Becquerel and Thomson came in 1900. Some rather specific questions as to how radiation should behave in an enclosure had arisen, questions that classical physics couldn't answer. Max Planck suggested a rather ad hoc assumption that the radiation was emitted and absorbed in discrete chunks, or quanta (singular, quantum; hence, a good deal later, quantum theory). Planck introduced a fundamental constant associated with the process. This is Planck's constant, denoted by h, and it is tiny. Its small size, compared with the energies, times, and masses of the events of everyday life, is the reason we are not aware of quantum effects all the time.
Most people thought that the Planck result was a gimmick, something that happened to give the right answer but did not represent anything either physical or of fundamental importance. That changed in 1905, when Albert Einstein used the idea of the quantum to explain another baffling result, the photoelectric effect.
Einstein suggested that light must be composed of particles called photons, each with a certain energy decided by the wavelength of the light. He published an equation relating the energy of light to its wavelength, and again Planck's constant, h, appeared. (It was for this work, rather than for the theory of relativity, that Einstein was awarded the 1921 Nobel Prize in physics. More on relativity later.)
While Einstein was analyzing the photoelectric effect, the New Zealand physicist Ernest Rutherford was studying the new phenomenon of radioactivity. The usual notion of the atom at the time was that of a sphere with electrical charges dotted about all over inside it, rather like raisins in a cake. Rutherford found his experiments were not consistent with such a model. Instead, an atom seemed to be made up of a very dense central region, the nucleus, surrounded by an orbiting cloud of electrons. In 1911 Rutherford proposed this new structure for the atom, and pointed out that while the atom itself was small—a few billionths of an inch—the nucleus was tiny, only about a hundred thousandth as big in radius as the whole atom. In other words, matter, everything from humans to stars, is mostly empty space and moving electric charges.
The next step was taken in 1913 by Niels Bohr. He applied the "quantization" idea of Planck and Einstein—the idea that things occur in discrete pieces, rather than continuous forms—to the structure of atoms proposed by Rutherford.
In the Bohr atom, electrons can only lose energy in chunks—quanta—rather than continuously. Thus they are permitted orbits only of certain energies, and when they move between orbits they emit or absorb radiation at specific wavelengths (light is a form of radiation, in the particular wavelength range that can be seen by human eyes). The electrons can't have intermediate positions, because to get there they would need to
emit or absorb some fraction of a quantum of energy; by definition, fractions of quanta don't exist. The permitted energy losses in Bohr's theory were governed by the wavelengths of the emitted radiation, and again Planck's constant appeared in the formula.
It sounded crazy, but it worked. With his simple model, applied to the hydrogen atom, Bohr was able to calculate the right wavelengths of light emitted from hydrogen.
More progress came in 1923, when Louis de Broglie proposed that since Einstein had associated particles (photons) with light waves, wave properties ought to be assigned to particles such as electrons and protons. He tried it for the Bohr atom, and it worked.
The stage was set for the development of a complete form of quantum mechanics, one that would allow all the phenomena of the subatomic world to be tackled with a single theory. In 1925 Erwin Schrödinger employed the wave-particle duality of Einstein and de Broglie to come up with a basic equation that applied to almost all quantum mechanics problems; at the same time Werner Heisenberg, using the fact that atoms emit and absorb energy only in finite and well-determined pieces, produced another set of procedures that could also be applied to almost every problem.
Soon afterwards, in 1926, Paul Dirac, Carl Eckart, and Schrödinger himself showed that the Heisenberg and Schrödinger formulations can be viewed as two different approaches within one general framework. In 1928, Dirac took another important step, showing how to incorporate the effects of relativity into quantum theory.
It quickly became clear that the new theory of Heisenberg, Schrödinger, and Dirac allowed the internal structure of atoms and molecules to be calculated in detail. By 1930, quantum theory, or quantum mechanics as it was called, became the method for performing calculations in the world of molecules, atoms, and nuclear particles. It was the key to detailed chemical calculations, allowing Linus Pauling to declare, late in his long life, "I felt that by the end of 1930, or even the middle, that organic chemistry was pretty well taken care of, and inorganic chemistry and mineralogy—except the sulfide minerals, where even now more work needs to be done" (Horgan, 1996, p. 270).
2.2 Quantum paradoxes. Quantum theory was well-formulated by the end of the 1920s, but many of its mysteries persist to this day. One of the strangest of them, and the most fruitful in science fiction terms, is the famous paradox that has come to be known simply as "Schrödinger's cat." (We are giving here a highly abbreviated discussion. A good detailed survey of quantum theory, its history and its mysteries, can be found in the book In Search of Schrodinger's Cat; Gribbin, 1984.)
The cat paradox was published in 1935. Put a cat in a closed box, said Schrödinger, with a bottle of cyanide, a source of radioactivity, and a detector of radioactivity. Operate the detector for a period just long enough that there is a fifty-fifty chance that one radioactive decay will be recorded. If such a decay occurs, a mechanism crushes the cyanide bottle and the cat dies.
The question is: Without looking in the box, is the cat alive or dead? Quantum indeterminacy insists that until we open the box (i.e., perform the observation) the cat is partly in the two different states of being dead and being alive. Until we look inside, we have a cat that is neither alive nor dead, but half of each.
There are refinements of the same paradox, such as the one known as "Wigner's friend" (Eugene Wigner, born in 1902, was an outstanding Hungarian physicist in the middle of the action in the original development of quantum theory). In this version, the cat is replaced by a human being. That human being, as an observer, looks to see if the glass is broken, and therefore automatically removes the quantum indeterminacy. But suppose that we had a cat smart enough to do the same thing, and press a button? The variations—and the resulting debates—are endless.
With quantum indeterminacy comes uncertainty. Heisenberg's uncertainty principle asserts that we can never know both of certain pairs of variables precisely, and at the same time. Position and speed are two such variables. If we know exactly where an electron is located, we can't know its speed.
With quantum indeterminacy we also have the loss of another classical idea: repeatability. For example, an electron has two possible spins, which we will label as "spin up" and "spin down." The spin state is not established until we make an observation. Like Schrödinger's half dead/half alive cat, an electron can be half spin up and half spin down pending a measurement.
This has practical consequences. At the quantum level an experiment, repeated under what appear to be identical conditions, may not always give the same result. Measurement of the electron spin is a simple example, but the result is quite general. When we are dealing with the subatomic world, indeterminacy and lack of repeatability are as certain as death and taxes.
Notice that the situation is not, as you might think, merely a statement about our state of knowledge; i.e., we know that the spin is either up or down, but we don't know which. The spin is up and down at the same time. This may sound impossible, but quantum theory absolutely requires that such "mixed states" exist, and we can devise experiments which cannot be explained without mixed states. In these experiments, the separate parts of the mixed states can be made to interfere with each other.
To escape the philosophical problem of quantum indeterminacy (though not the practical one), Hugh Everett and John Wheeler in the 1950s offered an alternative "manyworlds theory" to resolve the paradox of Schrödinger's cat. The cat is both alive and dead, they say—but in different universes. Every time an observation is made, all possible outcomes occur. The universe splits at that point, one universe for each outcome. We see one result, because we live in only one universe. In another universe, the other outcome took place. This is true not only for cats in boxes, but for every other quantum phenomenon in which a mixed state is resolved by making a measurement. The change by measurement of a mixed state to a single defined state is often referred to as "collapsing the wave function."
An ingenious science fiction treatment of all this can be found in Frederik Pohl's novel The Coming of the Quantum Cats (Pohl, 1986).
Quantum theory has been defined since the 1920s as a computational tool; but its philosophical mysteries continue today. As Niels Bohr said of the subject, "If you think you understand it, that only shows you don't know the first thing about it."
To illustrate the continuing presence of mysteries, we consider something which could turn out to be the most important physical experiment of the century: the demonstration of quantum teleportation.
2.3 Quantum teleportation. Teleportation is an old idea in science fiction. A person steps into a booth here, and is instantly transported to another booth miles or possibly light-years away. It's a wonderfully attractive concept, especially to anyone who travels often by air.
Until 1998, the idea seemed like science fiction and nothing more. However, in October 1998 a paper was published in Science magazine with a decidedly science-fictional title: "Unconditional Quantum Teleportation." In that paper, the six authors describe the results of an experiment in which quantum teleportation was successfully demonstrated.
We have to delve a little into history to describe why the experiment was performed, and what its results mean. In 1935, Einstein, Podolsky, and Rosen published a "thought experiment" they had devised. Their objective was to show that something had to be wrong with quantum theory.
Consider, they said, a simple quantum system in which two particles are coupled together in one of their quantum variables. We will use as an example a pair of electrons, because we have already talked about electron spin. Einstein, Podolsky, and Rosen chose a different example, but the conclusions are the same.
Suppose that we have a pair of electrons, and we know that their total combined spin is zero. However, we have no idea of the spin of either individual electron, and according to quantum theory we cannot know this until we make an experiment. The experiment itself then forces an electron to a particular state, with spin up or spin down.
We allow the two electrons to separate, until they are an arbitrarily
large distance apart. Now we make an observation of one of the electrons. It is forced into a particular spin state. However, since the total spin of the pair was zero, the other electron must go into the opposite spin state. This happens at once, no matter how far apart the electrons may be.
Since nothing—including a signal—can travel faster through space than the speed of light, Einstein, Podolsky, and Rosen concluded that there must be something wrong with quantum theory.
Actually, the thought experiment leads to one of two alternative conclusions. Either there is something wrong with quantum theory, or the universe is "nonlocal" and distant events can be coupled by something other than signals traveling at or less than the speed of light.
It turns out that Einstein, Podolsky, and Rosen, seeking to undermine quantum theory, offered the first line of logic by which the locality or nonlocality of the universe can be explored; and experiments, first performed in the 1970s, came down in favor of quantum theory and a nonlocal universe. Objects, such as pairs of electrons, can be "entangled" at the quantum level, in such a way that something done to one instantaneously affects the other. This is true in principle if the electrons are close together, or light-years apart.
To this time, the most common reaction to the experiments demonstrating nonlocality has been to say, "All right. You can force action at a distance using `entangled' particle pairs; but you can't make use of this to send information." The new experiment shows that this is not the case. Quantum states were transported (teleported) and information was transferred.
The initial experiment did not operate over large distances. It is not clear how far this technique can be advanced, or what practical limits there may be on quantum entanglement (coupled states tend to decouple from each other, because of their interactions with the rest of the universe). However, at the very least, these results are fascinating. At most, this may be the first crack in the iron straitjacket of relativity, the prodigiously productive theory which has assured us for most of the 20th century that faster-than-light transportation is impossible.
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