The Science Book

by Clifford A Pickover

  PEP is well-tested, and one of the most important principles in physics. According to author Michela Massimi, “From spectroscopy to atomic physics, from quantum field theory to high-energy physics, there is hardly another scientific principle that has more far-reaching implications than Pauli’s exclusion principle.” As a result of PEP, one can determine or understand electronic configurations underlying the classification of chemical elements in the Periodic Table as well as atomic spectra. Science-journalist Andrew Watson writes, “Pauli introduced this principle early in 1925, before the advent of modern quantum theory or the introduction of the idea of electron spin. His motivation was simple: there had to be something to prevent all the electrons in an atom collapsing down to a single lowest state. . . . So, Pauli’s exclusion principle keeps electrons—and other fermions—from invading each other’s space.”

  SEE ALSO Coulomb’s Law of Electrostatics (1785), Electron (1897), Bohr Atom (1913), Neutron Star (1933).

  Artwork titled “Pauli’s Exclusion Principle, or Why Dogs Don’t Suddenly Fall Through Solids.” PEP helps explain why matter is rigid, why we do not fall through solid floors, and why neutron stars resist collapsing under their humongous masses.

  1926

  Schrödinger’s Wave Equation • Clifford A. Pickover

  Erwin Rudolf Josef Alexander Schrödinger (1887–1961)

  “Schrödinger’s Wave Equation enabled scientists to make detailed predictions about how matter behaves, while being able to visualize the atomic systems under study,” writes physicist Arthur I. Miller. Schrödinger apparently developed his formulation while vacationing at a Swiss ski resort with his mistress who seemed to catalyze his intellectual and “erotic outburst,” as he called it. The Schrödinger Wave Equation describes ultimate reality in terms of wave functions and probabilities. Given the equation, we can calculate the wave function of a particle:

  Here, we need not worry about the details of this formula, except perhaps to note that ψ(r, t) is the wave function, which is the probability amplitude for a particle to have a given position r at any given time t. ∇2 is used to describe how ψ(r, t) changes in space. V(r) is the potential energy of the particle at each position r. Just as an ordinary wave equation describes the progression of a ripple across a pond, Schrödinger’s Wave Equation describes how a probability wave associated with a particle (e.g. an electron) moves through space. The peak of the wave corresponds to where the particle is most likely to be. The equation was also useful in understanding energy levels of electrons in atoms and became one of the foundations of quantum mechanics, the physics of the atomic world. Although it may seem odd to describe a particle as a wave, in the quantum realm such strange dualities are necessary. For example, light can act as either a wave or a particle (a photon), and particles such as electrons and protons can act as waves. As another analogy, think of electrons in an atom as waves on a drumhead, with the vibration modes of the wave equation associated with different energy levels of atoms.

  Note that the matrix mechanics developed by Werner Heisenberg, Max Born, and Pascual Jordan in 1925 interpreted certain properties of particles in terms of matrices. This formulation is equivalent to the Schrödinger wave formulation.

  SEE ALSO Wave Nature of Light (1801), Electron (1897), De Broglie Relation (1924), Heisenberg Uncertainty Principle (1927), Dirac Equation (1928), Schrödinger’s Cat (1935).

  Erwin Schrödinger on a 1000 Austrian schilling banknote (1983).

  1927

  Complementarity Principle • Clifford A. Pickover

  Niels Henrik David Bohr (1885–1962)

  Danish physicist Niels Bohr developed a concept that he referred to as complementarity in the late 1920s, while trying to make sense of the mysteries of quantum mechanics, which suggested, for example, that light sometimes behaved like a wave and at other times like a particle. For Bohr, writes author Louisa Gilder, “complementarity was an almost religious belief that the paradox of the quantum world must be accepted as fundamental, not to be ‘solved’ or trivialized by attempts to find out ‘what’s really going on down there.’ Bohr used the word in an unusual way: ‘the complementarity’ of waves and particles, for example (or of position and momentum), meant that when one existed fully, its complement did not exist at all.” Bohr himself in a 1927 lecture in Como, Italy, said that waves and particles are “abstractions, their properties being definable and observable only through their interactions with other systems.”

  Sometimes, the physics and philosophy of complementarity seemed to overlap with theories in art. According to science-writer K. C. Kole, Bohr “was known for his fascination with cubism—especially ‘that an object could be several things, could change, could be seen as a face, a limb, a fruit bowl,’ as a friend of his later explained. Bohr went on to develop his philosophy of complementarity, which showed how an electron could change, could be seen as a wave [or] a particle. Like cubism, complementarity allowed contradictory views to coexist in the same natural frame.”

  Bohr thought that it was inappropriate to view the subatomic world from our everyday perspective. “In our description of nature,” Bohr wrote, “the purpose is not to disclose the real essence of phenomena but only to track down, as far as it is possible, relations between the manifold aspects of experience.”

  In 1963, physicist John Wheeler expressed the importance of this principle: “Bohr’s principle of complementarity is the most revolutionary scientific concept of this century and the heart of his fifty-year search for the full significance of the quantum idea.”

  SEE ALSO Wave Nature of Light (1801), Heisenberg Uncertainty Principle (1927), Schrödinger’s Cat (1935), EPR Paradox (1935), Parallel Universes (1956).

  The physics and philosophy of complementarity often seemed to overlap with theories in art. Bohr was fascinated with Cubism, which sometimes allowed “contradictory” views to coexist, as in this artwork by Czech painter Eugene Ivanov.

  1927

  Food Webs • Michael C. Gerald with Gloria E. Gerald

  Al-Jahiz (781–868/869), Charles Elton (1900–1991), Raymond Lindeman (1915–1942)

  The concept of a food chain originated with Al-Jahiz, a ninth-century Arabic author of some two hundred books on a wide range of subjects including grammar, poetry, and zoology. In his zoology work, he discussed a struggle for existence among animals who hunt to obtain food and who are, in turn, hunted. Charles Elton, an Oxford faculty member, was among the most important animal ecologists of the twentieth century. In his classic 1927 text Animal Ecology, Elton laid out the basic principles of modern ecology, including, rather explicitly, food chains and food webs, which are now central themes in ecology.

  At its simplest level, a food cycle follows a linear relationship from the base of the food chain—a species that eats no other (typically, a plant)—to the final predator or ultimate consumer, which is typically three to six feeding levels in length. Elton recognized that this simple food chain depiction was a gross oversimplification of “who eats whom.” The food chain failed to account for real ecosystems, in which there are multiple predators and multiple preys, and the reality that a given animal might consume other animals if the preferred prey was not available. Moreover, some carnivores also eat plant material and are omnivores; conversely, herbivores occasionally eat meat. The food web, a concept now preferred to food chain, represents these highly complex interrelationships.

  In 1942, Raymond Lindeman postulated that the number of levels in a food chain is limited by trophic dynamics, or the effective transfer of energy from one part of the ecosystem to another. After food is consumed, energy is stored in the body of the consumer, and it travels in only one direction. Much of that energy is lost as heat (when the food is being utilized for basic needs), and the remainder eliminated as waste material. In general, only about 10 percent of the energy consumed is available at the next higher trophic (feeding) level. Thus, with each successive level up the chain, less energy is transmitted and, therefore, food chains rar
ely exceed four to five feeding levels.

  SEE ALSO Agriculture (c. 10,000 BCE) Ecological Interactions (1859), Insect Dance Language (1927).

  The food web is exemplified at Katmai National Park, Alaska, where this grizzly bear is a jawful away from eating a fish, which fed on a smaller fish or microscopic plants or animals floating in the water.

  1927

  Heisenberg Uncertainty Principle • Clifford A. Pickover

  Werner Heisenberg (1901–1976)

  “Uncertainty is the only certainty there is,” wrote mathematician John Allen Paulos, “and knowing how to live with insecurity is the only security.” The Heisenberg Uncertainty Principle states that the position and the velocity of a particle cannot both be known with high precision, at the same time. Specifically, the more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa. The uncertainty principle becomes significant at the small size scales of atoms and subatomic particles.

  Until this law was discovered, most scientists believed that the precision of any measurement was limited only by the accuracy of the instruments being used. German physicist Werner Heisenberg hypothetically suggested that even if we could construct an infinitely precise measuring instrument, we still could not accurately determine both the position and momentum (mass × velocity) of a particle. The principle is not concerned with the degree to which the measurement of the position of a particle may disturb the momentum of a particle. We could measure a particle’s position to a high precision, but as a consequence, we could know little about the momentum.

  For those scientists who accept the Copenhagen interpretation of quantum mechanics, the Heisenberg Uncertainty Principle means that the physical Universe literally does not exist in a deterministic form but is rather a collection of probabilities. Similarly, the path of an elementary particle such as a photon cannot be predicted, even in theory, by an infinitely precise measurement.

  In 1935, Heisenberg was a logical choice to replace his former mentor Arnold Sommerfeld at the University of Munich. Alas, the Nazis required that “German physics” must replace “Jewish physics,” which included quantum theory and relativity. As a result, Heisenberg’s appointment to Munich was blocked even though he was not Jewish.

  During World War II, Heisenberg led the unsuccessful German nuclear weapons program. Today, historians of science still debate as to whether the program failed because of lack of resources, lack of the right scientists on his team, Heisenberg’s lack of a desire to give such a powerful weapon to the Nazis, or other factors.

  SEE ALSO Bohr Atom (1913), Schrödinger’s Wave Equation (1926), Complementarity Principle (1927).

  LEFT: According to Heisenberg’s Uncertainty Principle, particles likely exist only as a collection of probabilities, and their paths cannot be predicted even by an infinitely precise measurement. RIGHT: German postage stamp, 2001, featuring Werner Heisenberg.

  1927

  Insect Dance Language • Michael C. Gerald with Gloria E. Gerald

  Karl von Frisch (1886–1982)

  Animals communicate with one another when seeking to locate food, mate, or signal an alarm in the presence of threats in their environment. A variety of animals use pheromones to facilitate various phases of their mating behavior. Not all communication occurs between members of the same animal species, such as the facial expression and body language of our pets. The odor from a skunk’s spray is a highly effective defensive weapon used to ward off bears and other potential predators, and it is sufficiently pungent that it can be detected by human noses at downwind distances of one mile (1.6 kilometers).

  Animal communication is not limited to vertebrates, with some of the most interesting examples occurring in insects. Pioneering studies on insect communications were conducted in the 1920s by the Nobel laureate Karl von Frisch, an Austrian ethnologist at the University of Munich. He observed that a distinctive “dance language” is used by European honeybee (Apis mellifera) foragers to inform other bees in the hive about the direction and distance of food. A “round dance,” in which the forager executes tight circles, is performed when food is close to the hive—less than 160–320 feet (50–100 meters)—whereas a “waggle dance,” resembling a figure-eight movement, signifies food at a distant location.

  European honeybees also use a complex chain of communication modes that involve all five senses in a fascinating courtship ritual, with each signaling and triggering a subsequent behavior by the partner: The male visually identifies the female and turns toward her. The female releases a chemical that is detected by the male’s olfactory system. He approaches the female and taps her with his limb that, in the process, picks up the chemical. In response, the male extends and vibrates his wings producing a “courtship song,” a form of auditory communication. Only after this entire sequence is successively and successfully completed will the female allow the male to perform copulation.

  SEE ALSO Ecological Interactions (1859), Neuron Doctrine (1891), Food Webs (1927).

  Dance language among certain insects—in particular, honeybees—is well developed and has been extensively studied. Here, the Apis cerana japonica honeybees surround their nest in Japan.

  1928

  Dirac Equation • Clifford A. Pickover

  Paul Adrien Maurice Dirac (1902–1984)

  As discussed in the entry on antimatter, the equations of physics can sometimes give birth to ideas or consequences that the discoverer of the equation did not expect. The power of these kinds of equations can seem magical, according to physicist Frank Wilczek in his essay on the Dirac Equation. In 1927, Paul Dirac attempted to find a version of Schrödinger’s Wave Equation that would be consistent with the principles of special relativity. One way that the Dirac Equation can be written is

  Published in 1928, the equation describes electrons and other elementary particles in a way that is consistent with both quantum mechanics and the Special Theory of Relativity. The equation predicts the existence of antiparticles and in some sense “foretold” their experimental discovery. This feature made the discovery of the positron, the antiparticle of the electron, a fine example of the usefulness of mathematics in modern theoretical physics. In this equation, m is the rest mass of the electron, ħ is the reduced Planck’s constant (1.054 × 10−34 J∙s), c is the speed of light, p is the momentum operator, x and t are the space and time coordinates, and Ψ(x,t) is a wave function. α is a linear operator that acts on the wave function.

  Physicist Freeman Dyson has lauded this formula that represents a significant stage in humanity’s grasp of reality. He writes, “Sometimes the understanding of a whole field of science is suddenly advanced by the discovery of a single basic equation. Thus it happened that the Schrödinger equation in 1926 and the Dirac equation in 1927 brought a miraculous order into the previously mysterious processes of atomic physics. Bewildering complexities of chemistry and physics were reduced to two lines of algebraic symbols.”

  SEE ALSO Electron (1897), Special Theory of Relativity (1905), Schrödinger’s Wave Equation (1926), Antimatter (1932).

  The Dirac equation is the only equation to appear in Westminster Abbey, London, where it is engraved on Dirac’s commemorative plaque. Shown here is an artist’s representation of the Westminster plaque, which depicts a simplified version of the formula.

  1928

  Penicillin • Clifford A. Pickover

  John Tyndall (1820–1893), Alexander Fleming (1881–1955), Howard Walter Florey (1898–1968), Ernst Boris Chain (1906–1979), Norman George Heatley (1911–2004)

  Reflecting on his discovery later in life, Scottish biologist Alexander Fleming recalled, “When I woke up just after dawn on September 28, 1928, I certainly didn’t plan to revolutionize all medicine by discovering the world’s first antibiotic, or bacteria killer. But I suppose that was exactly what I did.”

  When Fleming returned from a vacation, he noticed that mold had developed on his contaminated culture plate of the bacterium Staphylococc
us. He also noticed that the bacterial growth was inhibited near the mold, so he concluded that the mold was releasing a substance that repressed bacterial growth. He soon grew a pure mold culture in broth, determined the mold to be of the Penicillium genus, and referred to the antibiotic substance in the broth as penicillin. Interestingly, many ancient societies had noticed that mold could serve as a remedy, and Irish physicist John Tyndall even demonstrated the antibacterial action of the Penicillium fungus in 1875. However, Fleming was probably the first to suggest that this mold secreted an antibacterial substance and then isolate it. Later studies showed that penicillin works by weakening the cell walls of bacteria.

  In 1941, Australian pharmacologist Howard Florey, German biochemist Ernst Chain, and English biochemist Norman Heatley, while working together in England, were finally able to turn penicillin into a usable drug, showing that it cured infections in mice and people. The U.S. and British governments were determined to produce as much penicillin as possible to help their soldiers during World War II, and a moldy cantaloupe in Peoria, Illinois, produced more than two million doses before 1944. Penicillin was soon used to defeat major bacterial diseases, such as blood poisoning, pneumonia, diphtheria, scarlet fever, gonorrhea, and syphilis. Unfortunately, antibiotic-resistant bacterial strains have evolved, necessitating the quest for additional antibiotics.