The Story of Western Science

by Susan Wise Bauer

  Four years later, in one of his 1905 papers, Albert Einstein made use of Planck’s work to explain some previously perplexing properties of light. “If we had to characterize the principal idea of quantum theory in one sentence,” Einstein would later write, “we could say: it must be assumed that some physical quantities so far regarded as continuous are composed of elementary quanta.” Perhaps, Einstein theorized in 1905, light was not simply a continuous wave; perhaps it, too, was made up of individual particles.9

  Like Planck, Einstein treated quanta as a theoretical construct, a technical fix rather than a picture of physical reality. But the more phenomena that quantum theory explained, the more “real” it seemed to be.

  In 1913, the young Danish physicist Niels Bohr solved an atomic-level puzzle with the help of quantum theory. The puzzle had to do with the stability of the Rutherford model, which imagined electrons to be something like satellites circling the earth. If a satellite orbiting the earth lost some of its energy, it would spiral down and crash. When an atom emitted energy (as, for example, hydrogen atoms did, giving off light particles that some physicists had labeled photons), why did the orbits of the electrons not decay?

  Bohr proposed that the orbits of electrons are not continuous circles. Rather, they are quantized: an electron does not sail smoothly through atomic space, but rather jumps from discrete spot to discrete spot. When a hydrogen atom emits a photon, the electron loses energy, but it doesn’t spiral down; it “jumps” to a lower orbital path, one that is stable but takes less energy to maintain. The difference between the higher and lower orbits could be calculated. It corresponded exactly to the energy emitted by the atom.10

  Einstein praised Bohr’s results, but over the next decade or so, he and a whole cadre of other physicists became increasingly aware of just how odd the implications of quantum mechanics were. For example, in the new “Bohr-Rutherford model” of the atom, an electron could perform a “quantum leap” between orbits, rather than gliding smoothly through consecutive space. So, while making the leap, the electron was . . . nowhere.

  And this was only one of the paradoxes that arose when quantum theory was used to solve existing physical problems. Quantum theory, announced Max Planck in his Nobel Prize address of 1922, had the potential “to transform completely our physical concepts,” and this was a massive upset in the world of physics.11

  •

  In October of 1926, the Austrian physicist Erwin Schrödinger traveled to Bohr’s home city of Copenhagen to discuss those upsets in person.

  Schrödinger, two years Bohr’s junior, was at the height of a distinguished academic career. He was in line to be Max Planck’s successor as a lecturer in theoretical physics at Berlin University, and he had just published his own version of quantum theory—one that insisted on retaining waves to describe physical phenomena. Schrödinger appreciated the value of quantum theory in problem solving, but he was worried about doing away with waves. Without waves, an electron had no definite path, no trajectory through space; it could simply disappear and reappear, Cheshire Cat–like, with no way to predict the next place it would show up. Without waves, Schrödinger insisted, physics had no connection with reality, with the laws of electrodynamics, with our experience.

  Bohr refused to yield the point. Quantum jumps had nothing to do with the everyday physics that governed ordinary life; they could not be directly experienced, but they were no less “real.” According to Bohr’s then-assistant, the young German physicist Werner Heisenberg, Schrödinger finally said, in exasperation, “If we are going to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory.”12

  Schrödinger returned home, determined to resist the randomness and uncertainty of quantum jumps. Meanwhile, Heisenberg, still in Copenhagen, was figuring out just how those jumps could be better understood. The end point of a quantum jump, Heisenberg concluded, is impossible to calculate with certainty. We cannot predict exactly where a quantum particle will show up next; although we can calculate the probability of where it will reappear, we can only be certain of its new location once the particle has actually reappeared. But this, too, poses a problem: any instrument that is sensitive enough to measure the particle (for example, an electron microscope, which can locate particles by bouncing electrons off of them) will have to strike the reappearing particle, which will change its trajectory. In short, an exact measurement at a single point in time is, for all practical purposes, impossible. This conclusion, expressed mathematically, became known as the Heisenberg Uncertainty Principle.13

  Heisenberg was quick to point out that, for objects larger than a molecule, our uncertainty is minuscule. Less than minuscule: essentially nonexistent. Only at the subatomic level does the uncertainty play any part in our understanding of the material world. An electron orbiting the nucleus of a hydrogen atom might make an unexpected leap, but a goat grazing on a hillside isn’t going anywhere unpredictable at all.

  This didn’t reassure Schrödinger, who clung to the reality of predictable movement through space and time. His solution was an alternate quantum theory: wave mechanics. Wave mechanics turned Bohr’s version of quantum theory on its head. What if, Schrödinger proposed, the movements of electrons were not because waves were actually particles—but because particles were actually waves? What if electrons themselves were merely the manifestation of a particular phase in a wave’s existence?

  Later, Albert Einstein would explain wave mechanics using the analogy of a rubber cord, shaken so that a wave travels down it:

  We take in our hand the end of a very long flexible rubber tube, or a very long spring, and try to move it rhythmically up and down, so that the end oscillates. Then . . . a wave is created by the oscillation which spreads through the tube with a certain velocity. . . .

  26.2 EINSTEIN’S TUBE

  Now another case. The two ends of the same tube are fastened. . . . What happens now if a wave is created at one end of the rubber tube or cord? The wave begins its journey as in the previous example, but it is soon reflected by the other end of the tube. We now have two waves: one created by oscillation, the other by reflection; they travel in opposite directions and interfere with each other. It would not be difficult to trace the interference of the two waves and discover the one wave resulting from their superposition; it is called the standing wave.14

  The standing wave had nodes, places where the waves canceled each other out. Electrons, far from being discrete entities, moved along the waveforms but were observable (appearing discrete) only at the places farthest from the nodes—where the standing wave was greatest.

  Mathematically, Schrödinger’s wave mechanics and Bohr’s quantum leaps (which became known as the “Copenhagen interpretation”) actually ended up yielding very similar results. The difference between them was, at base, a philosophical one. Schrödinger’s wave mechanics could not predict the position of an electron, at any given time, with much more certainty than Bohr’s Copenhagen theory; but Schrödinger had held on to a mechanical explanation that, while no more observable than quantum jumps, still resembled an effect that could be acted out in the real world. He had on his side Max Planck, and also Albert Einstein, who remained until the end of his life deeply skeptical of the Copenhagen interpretation, and wary of those “spookish long-distance effects” that had no discernible physical cause.

  26.3 EINSTEIN’S WAVES

  In fact, Einstein read, and approved of, Schrödinger’s 1935 paper “The Present Situation in Quantum Mechanics,” in which Schrödinger proposed a thought experiment intended to point out the invalidity of the Copenhagen interpretation.

  Imagine that a cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discha
rges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

  It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.15

  In other words, Schrödinger continued to believe that quantum theory could not simply be sequestered into a conveniently separate closet marked “subatomic.” Whatever message it conveyed to us about the movement of electrons was the same message it was conveying about the rest of reality.

  Einstein agreed. After reading an early draft of the paper, he wrote to Schrödinger, “Your cat shows that we are in complete agreement. . . . [A box that] contains the living as well as the dead cat just cannot be taken as a description of a real state of affairs.”16

  •

  Thirty years earlier, there had been no such thing as quantum theory at all; now there were two vigorous, well-supported quantum theories, with plenty of adherents to both.

  It was out of the conflict between the two theories that Schrödinger’s 1944 book What Is Life? arose. In it, Schrödinger dealt with the overlap between quantum physics and biology, the common ground between the study of ourselves and the study of the cosmos. Using quantum theory to account for the behavior of orbiting electrons, Schrödinger showed how this behavior affected the formation of chemical bonds, and how those chemical bonds then affected cell behavior, genetics, evolutionary biology.

  Like the works of Julian Huxley and Ernst Mayr, What Is Life? was a synthesis—an effort to show that quantum theory was not all about spookish, long-distance effects. Its success can be measured by the number of physicists who were inspired, after reading it, to migrate over into biological research. “No doubt molecular biology would have developed without What Is Life?” writes Schrödinger’s biographer, Walter Moore, “but it would have been at a slower pace, and without some of its brightest stars. There is no other instance in the history of science in which a short semipopular book catalyzed the future development of a great field of research.”17

  “Semipopular” is an accurate description; What Is Life? was not a groundbreaking twentieth-century work of quantum theory. Pure quantum theory was mostly impenetrable to anyone except physicists. In fact, physics had been in danger of becoming a mountaintop pursuit, its discoveries expressed in a mathematical language so rarefied that only a few could keep up.

  But for Schrödinger, quantum mechanics had to be able to speak about the reality that is accessible to our senses. Sooner or later, quantum mechanics would affect the cat.

  MAX PLANCK

  “The Origin and Development of the Quantum Theory”

  (1922)

  Planck’s brief essay, the written version of his Nobel Prize address, provides a fascinating glimpse into the development and early direction of quantum theory. The original English translation, by H. T. Clarke and L. Silberstein, is widely available online, as well as in paperback reprints.

  Max Planck, “The Origin and Development of the Quantum Theory,” trans. H. T. Clarke and L. Silberstein, Clarendon Press (e-book, 1922; paperback reprint available from Forgotten Books, 2013, ISBN 978-1440037849).

  ERWIN SCHRÖDINGER

  What Is Life?

  (1944)

  The standard edition is published by Cambridge University Press and includes Schrödinger’s short essay on consciousness, “Mind & Matter.”

  Erwin Schrödinger, What Is Life?: The Physical Aspect of the Living Cell; with, Mind & Matter; & Autobiographical Sketches, Cambridge University Press (paperback and e-book, 1992, ISBN 978-1107604667).

  * * *

  * For those interested in greater precision: Einstein’s calculations were ostensibly about the motions of molecules, but his conclusions also affected two measurements, known as Avogadro’s Number and Boltzmann’s Constant, that were directly related to atomic theory. Avogadro’s Number can be used to calculate the number of atoms in a given unit of a substance, and Boltzmann’s Constant can predict the amount of thermal energy that those atoms carry. For a fuller explanation, see John S. Rigden, Einstein 1905: The Standard of Greatness (Harvard University Press, 2005), 57ff.

  † This wasn’t quite right; atoms as a whole are not electrically neutral, but Thomson believed that they were, which led him to his next conclusion.

  ‡ A more technical but still readable explanation of Planck’s investigations can be found in Bruce Rosenblum and Fred Kuttner, Quantum Enigma: Physics Encounters Consciousness, 2nd ed. (Oxford University Press, 2011), 55ff.

  TWENTY-SEVEN

  The Triumph of the Big Bang

  Returning to the question of beginnings, and contemplating the end

  The nebulae are all rushing away from our stellar system,

  with velocities that increase directly with distances.

  —Edwin Hubble, The Realm of the Nebulae, 1937

  I find myself forced to assume that the nature of the

  Universe requires continuous creation—the perpetual

  bringing into being of new background material.

  —Fred Hoyle, The Nature of the Universe, 1950

  In the beginning, there was an explosion.

  —Steven Weinberg, The First Three Minutes:

  A Modern View of the Origin of the Universe, 1977

  While quantum physicists peered closer and closer inward, astronomers extended their gaze outward to the skies.

  Once again, Einstein’s work helped to shape the ongoing investigations. If general relativity was a valid theory, three phenomena should be observable. First, the perihelion of Mercury should have shifted over time to a specific degree; Einstein himself had demonstrated this.* Second, starlight should bend as it passed the sun; Arthur Eddington had measured the bend in 1919.

  And third, there was the predicted redshift.

  Forty years before Einstein, the British astronomer William Huggins had used wavelength changes in starlight to demonstrate that stars were moving, both toward and away from the earth—a visual version of the Doppler effect.† If Einstein’s general theory of relativity was correct, astronomers should be able to detect a very specific kind of wavelength change in the light coming from massive bodies such as the sun. The mass curves space-time, meaning that light particles have to work harder to move away—as if the particles were scrambling up a smooth, curved wall, rather than skating away on a level surface. Because the particles are expending more energy (actually traveling a longer distance), their radiation shifts down to a lower frequency—put visually, toward the red end of the spectrum.

  Detecting this “redshift” was not simple, as Einstein himself mused. “The spectral lines of sunlight, as compared with the corresponding spectral lines of terrestrial sources of light, must be somewhat displaced towards the red,” he wrote, “[but] it is difficult to discover whether the inferred influence of the gravitational potential really exists.” In the decades after 1916, numerous attempts were made to demonstrate redshift in the light coming both from the sun and from Venus, but scientists argued over the interpretation of the data. “The difficulty of deciding for or against the Einstein shift in the sun lies in the conflicting nature of the evidence itself,” concluded the British astronomer John Evershed in 1919; redshift, after all, could be affected by pressure, temperature, or (as Huggins had demonstrated) movement.1

  The problem of the redshift, and inconclusive data results, bedeviled Einstein’s theory of relativity for years. But measuring re
dshift became a regular part of astronomical observations. And in the 1930s the astronomer Edwin Hubble was measuring redshift when his calculations led him to a new conclusion.

  The universe was much, much larger than we had previously suspected. And it was not, as Albert Einstein himself had concluded, in a stable and static state.

  •

  Fifteen years earlier, a young Edwin Hubble had been finishing up his doctoral dissertation, a photographic study of the fuzzy celestial patches known as nebulae (from the Latin word for “mist”). Nebulae had been observed for centuries, but the limited range of telescopes made it impossible to see exactly where and what they were. Hubble had used a cutting-edge 24-inch reflecting telescope to photograph the nebulae, but although he was able to map their locations with some accuracy, he could only speculate about the nature of the luminescent clouds.

  His speculation was a radical one: “Perhaps,” Hubble wrote, “we see clusters of ‘galaxies.’”2

  Up until this point, scientists knew of only one galaxy—our own. The Milky Way had been named by the Greeks (kyklos galaktikos, “milky circle”), and since Galileo it had been known to contain uncounted stars. Little was known, though, about what might lie beyond its borders (wherever those might be). Galaxy might well be identical to universe.

  Some astronomers had theorized that there might be other galaxies, or “island universes” floating outside our own, and Hubble’s telescopic observations inclined him to think that nebulae might be those galaxies. But the photographs were inconclusive, and World War I interrupted his research. Just after receiving his doctorate, Hubble joined the US Army and headed overseas.