E=mc2

by David Bodanis

  "the problem haunted me day and night" and "I expressed to a friend that I liked one of the other girls . . .": Cecilia Payne-Gaposchkin, pp. 122 and 111.

  "I always wanted to learn the calculus . . .": George Greenstein, "The Ladies of Observatory Hill," in Portraits of Discovery (New York: Wiley, 1998), p. 25.

  Her work was more complicated than our example: The new theory was from the Indian theorist Meg Nad Saha. There's excellent background in "Quantum Physics and the Stars. 2: Henry Norris Russell and the Abundance of the Elements in the Atmospheres of the Sun and Stars," by D. V. DeVorkin and R. Kenat, Journal of the History of Astronomy, 14 (1983), pp. 180-222; for briefer explanations see Greenstein, pp. 15-16, and Payne's autobiography, p. 20. On the extraordinary emergence of individuals such as Saha (and Raman and Bose) in India after 1920—and then their remarkable lack of achievement, after a first burst of world-class work was done—see Chandrasekhar's remarks in Kameshwar Wali, Chandra: A Biography of S. Chandrasekhar (Chicago: University of Chicago Press, 1992), pp. 246-53. The breakthroughs, Chandra thought, were part of the prideful self-expression that Gandhi's anti-British resistance encouraged; the subsequent collapse was due to haughty, prickly academic empire building by each suddenly famous researcher—a bane Indian science has suffered ever since.

  "The enormous abundance [of hydrogen] . . .": Cecilia Payne-Gaposchkin, p. 20.

  [the sun] pumps 4 million tons of hydrogen into pure energy each second: How can one possibly work out such things? The hottest noon heat in Death Valley is due to about one thousand watts of solar radiation hitting a square yard of the Earth's atmosphere directly overhead; if extended to cover the whole planet, that means the total amount of light energy hitting the Earth is 150 quadrillion watts.

  To see how much mass is lost within the sun to create that energy for Earth, remember that c2 is a tremendously large multiplier: We live in such a tiny, "low-speed" niche within the universe that our view of the single mass-energy entity is terribly skewed, so that the "mass" aspect of it seems to loom in the foreground, encompassing tremendous power. Since Energy equals mass times c2, then mass equals Energy divided by c2. In other words, m=E/c2. If you substitute 150 quadrillion watts for E and 670 million mph for c, the result is about 4.5 pounds. That's all: The light and heat that arrives on Earth is produced from a mere 4½ pounds of hydrogen going out of existence on the sun.

  That, incidentally, is how to work out such figures as the one at the start of this chapter, that the sun explodes the equivalent of so many Hiroshima-sized bombs each second. If the sun were at the center of a huge sphere, with the Earth as just a tiny dot on the inner surface of that sphere, then the full surface area of that sphere would be much greater than that of the Earth. It would be about 2 billion times larger, and since the Sun's fires do spray in all directions, suffusing the entire surface of such an imagined sphere with light, then the amount of mass the Sun "loses" each second is that much greater as well. The amount is eight billion pounds of mass. The bomb over Hiroshima in 1945 achieved its destruction by fully transforming under half a pound of mass into energy, which is how one can conclude that the mass our Sun is exploding into energy each second is equivalent to over 16 billion such bombs.

  15. Creating the Earth

  "The blow was delivered . . .": Fred Hoyle, Home Is Where the Wind Blows: Chapters from a Cosmologist's Life (Oxford: Oxford University Press, 1997), p. 48.

  "I pointed out . . .": Ibid., p. 49.

  "Each morning, I ate breakfast. . .": Ibid., p. 50.

  . . . from the faces he saw there . . . : One was Nick Kemmer, who'd been working on Britain's own atomic project before he'd suddenly disappeared; another was the brilliant mathematician Maurice Pryce, who'd also mysteriously vanished from the Admiralty Signal Establishment. See Ibid., pp. 227-28.

  Implosion was a powerful technique on Earth: The overlaps were reflected in recruitment. The head of the theoretical section at Los Alamos, for example, was Hans Bethe—the same man who, in 1938, had "completed" the work of Payne and others, perfecting the equations that describe fusion reactions in the sun.

  . . . there were hundreds of open-air tests: Which is how pre-World War I German battleships—or at least parts of them—have come to land on the moon.

  In 1919 the Imperial German battlefleet had surrendered to Britain, and was in the confines of the huge Royal Navy anchorage at Scapa Flow, up in Scotland. After a number of months of anxious waiting, the German admiral mistakenly came to believe that the British were about to seize his fleet. The admiral sent out a priorly agreed-upon coded signal, and the entire grand fleet scuttled itself. But Scapa Flow isn't especially deep—this is why it was chosen as an anchorage—and so hundreds of thousands of tons of high-quality steel was now waiting in those waters, only a few yards or tens of yards down. In the 1920s and 1930s, portions of the fleet were salvaged: divers welding the holes, then giant air bladders installed, and some of the half-submerged giants towed all the way to receiving docks at Rossyth in the Firth of Forth.

  After 1945, what remained took on a special value. It takes a lot of air to make steel, and all post-Hiroshima steel has some of the radiation from open-air atomic explosions. Pre-1945 steel doesn't. To this day, three battleships and four light cruisers from the kaiser's once-grand fleet rest in Scapa Flow (and intrepid readers can dive to see them, setting out from Stromness in the Orkneys). There's no advantage in using them for ordinary purposes—it's much cheaper to make fresh steel—but for extremely sensitive radiation monitors, as on spacecraft, such pre-Hiroshima sources are indispensable. Equipment that Apollo left on the moon, as well as part of the Galileo probe that reached Jupiter, and even the Pioneer probe now past the orbit of Pluto and on its way to distant star systems, all carry remnants of the kaiser's navy, via this salvaged steel from Scapa Flow. The story is well told by Dan van der Vat, in The Grand Scuttle: The Sinking of the German Fleet at Scapa Flow in 1919 (London: Hodder and S tough ton, 1982).

  It's not the most sensible of energy choices . . . : The early cost calculations were also distorted by the belief that since the weight of fuel used would go down by a factor of over 1 million, then generating costs would have to be much lower, at least in some proportion. But fuel is only a small part of an electricity generating station's costs. Firms still need to purchase the land and build the turbines and train the staff and pay their salaries and build cooling systems and install transmission stations and maintain the transmission cables. Many nuclear engineering executives knew they were offering unrealistic cost projections when the first big push for commercial reactors got going in 1960s America; the fact that their designs then had stabilized around a scaled-up version of Rickover's model suitable for the confined spaces of submarines did not add to the merits. In fairness, though, nuclear electricity is free of carbon dioxide emissions (aside from what's involved in ore extraction or site construction), and more recent designs really are fail-safe, making a further Chernobyl event impossible.

  16. A Brahmin Lifts His Eyes Unto the Sky

  In a further 5 billion years, the . . . fuel will be gone: Once again, this is the domain of E=mc2; it allows us to foresee how long our solar system will last. The sun's mass can be symbolized as M°. Only 10 percent of that is hydrogen in a form available for burning, and as we've seen, only 0.7 percent of that will actually transfer "through" E=mc2 and pour out as energy. This means the mass actually used will be 0.007 (1/10) X (M°), which comes out to 1.4 X 1030 grams.

  The total energy we can hope to get from that mass is E=mc2, which in this case is E=(1.4 X 1030 grams) X (670 million mph)2. Multiply it out, and the maximum energy the sun can supply till its fuel is used up—under the assumptions above—is, in common units, 1.3 X 1051 ergs.

  How long will that total last? It simply depends on the rate at which it's being used. The sun pours out energy—or "shines"—at the rate of 4 X 1035 ergs each second. (This is the sort of figure computable by the reasoning in the note pegged to p. 135, whi
ch worked backwards from the amount of sunlight arriving per square yard.) Multiply the total energy the sun can produce till it depletes itself, by this rate at which the depletion is taking place, and the result is 3.2 X 1017 seconds. When that number of seconds is gone, our sun's existence is over (given the approximations of mass availability and constant luminosity we're using). The Earth will either be burned, or absorbed, or flung loose. In slightly more wieldy units, 3.2 X 1017 seconds is about 10 billion years. Since we're about halfway along in the solar process, that's the reason we can assert there are about 5 billion years left.

  "Some say the world will end in fire . . . : From The Poetry of Robert Frost, ed. Edward Connery Lathem (New York: Holt, Rinehart and Winston, 1969), p. 220.

  In a small enough star, the buildup of pressure is low enough . . . : In "normal" stars, the extra pressure just forces much of the matter inside to move faster, but in stars already under great pressure, this matter is moving so fast that the energy can't go into raising the speed. As with our imagined space shuttle example from Chapter 5, the energy could only end up increasing its mass. The point is well elaborated in Kip Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy (New York: Norton, 1994), pp. 151 and 156-76; Chandra's reasoning is touched on in Wali, Chandra, p. 76.

  "He was a missionary . . .": Wali, Chandra, p. 75.

  "stellar buffoonery . . .": Ibid., p. 142. Wali's Chapters 5 and 6 give the details of Eddington's attack, as well as its influence on Chandra's later career; see also Chandrasekhar's own dignified 1982 remarks, at pp. 130-37 of his Truth and Beauty: Aesthetics and Motivations in Science (Chicago: University of Chicago Press, 1987).

  . . . very little of ordinary matter will be left. . . . : In this book we've mostly looked at E=mc2 as describing a bridge or tunnel that goes in one direction, starting on the mass side and transforming across to energy. But when Robert Recorde drew his typographically innovative '===' in the 1550s, he meant it to be a pathway held open in both directions. Neither side was favored.

  This reverse journey doesn't happen under normal circumstances— shine two flashlight beams at each other and solid objects won't pop into existence and start tumbling from the air. But in the early moments of the universe, temperatures and pressures were so high that pure light did regularly take this reverse journey along the equals sign bridge, and get compressed into mass.

  It didn't occur all at once, as if the universe were a celestial bathtub now suddenly poured full. Much of the newly formed mass kept on exploding back into pure energy. Only when the universe was an aged structure, a ponderous full second or more old, did the transformations stop. But by this time there had been a net accumulation on the mass side of the 1905 equation—and the substance that became the ancestor of us all was in existence. Other considerations were at play as well; the story is well enlarged upon in Alan Guth, The Inflationary Universe (London: Jonathan Cape, 1997).

  Epilogue. What Else Einstein Did

  "I was sitting on a chair . . .": The Quotable Einstein, ed. Alice Calaprice (Princeton, N.J.: Princeton University Press, 1996), p. 170.

  "the happiest thought of my life": From an unpublished manuscript Einstein wrote for Nature in 1920.

  "Do not worry . . .": Albert Einstein, the Human Side, Helen Dukas and Banesh Hoffmann (Princeton, N.J.: Princeton University Press, 1979), p. 8.

  "Attention was called . . .": Arthur Eddington, Space, Time and Gravitation (Cambridge: Cambridge University Press, 1920), p. 114.

  "Dear Russell . . .": The telegram from the mathematician J. E. Littlewood appears on p. i n of The Autobiography of Bertrand Russell, vol. II (London: George Allen and Unwin, 1968).

  "There was a dramatic quality . . .": The visitor was Russell's collaborator Alfred North Whitehead: Science in the Modern World (London, 1926), p. 13.

  "This is the most important result . . .": Albrecht Folsing, Albert Einstein: A Biography (London: Penguin, 1997), P. 444.

  Henry Crouch . . . golfing specialist: Meyer Berger, The Story of The New York Times, 1851-1951 (New York: Simon &Schuster, 1951), pp. 251-52.

  . . . but English anti-Semites . . . : The quote is from The Collected Writings of John Maynard Keynes, Vol. X: Essays in Biography (London: Macmillan; New York: St. Martin's Press, for the Royal Economic Society, 1972), p. 382. The occasion was Keynes's visit to Berlin in June 1926, where he lectured at the University; he met Einstein at a dinner afterwards. "It is not agreeable," Keynes remarked, "to see a civilization so under the ugly thumbs of its impure Jews."

  ". . . village of puny demi-gods upon stilts": The comment was to his long-time correspondent, Queen Elizabeth of Belgium. See The Quotable Einstein, p. 25.

  "Had I known . . .": Antonina Vallentin, The Drama of Albert Einstein (New York: Doubleday, 1954), p. 278.

  Then, as the years went on . . . : To some extent, what happened to Einstein is a common effect. Great artists and composers often do their top work as they get old, but scientists don't. Partly this could be because it's intellectually too difficult to hold complex ideas in one's head. Even in drama, the play Oedipus at Colonus, which Sophocles wrote when very old, has a crudeness of construction that would be not useful in a physical theory. But Beethoven wrote complex works into his fifties, and The Tempest was written in Shakespeare's late forties. There's something more going on in science—and for Einstein, the slippage was more extreme than almost anyone else's. It's a lengthy topic-there are important insights from Macauly and even Spielberg, which we'll explore on the Web site.

  [A] . . . young assistant once asked him . . . : Einstein, A Centenary Volume, ed. A. P. French (London: Heinemann, 1979), p. 32. The assistant was Ernst Strauss, who worked with Einstein from 1944 to 1948. The same volume, p. 211, has Einstein's account of how very different it had been when he was younger and could "scent out the paths that led to the depths, and to disregard everything else, all the many things that clutter up the mind, and divert it from the essential."

  "Discovery in the grand manner . . .": Banesh Hoffmann, Albert Einstein, Creator and Rebel (New York: Viking, 1972), p. 222.

  Appendix. Follow-up of Other Key Participants

  "If I were King . . .": Du Châtelet's preface to her translation of Mandeville's "The Fable of the Bees"; in Esther Ehrman, Mme du Châtelet (Berg Publishers, 1986), p. 61.

  "The gift of leading a harmonious life . . .": Albert Einstein/Michele Besso, Correspondence 1903-1955, trans. Pierre Spezialli (Paris: Hermann, 1972), p. 537.

  "I had then to start. . .": Richard Rhodes, The Making of the Atomic Bomb (New York: Simon & Schuster, 1986), p. 356.

  "A real genius . . .": Rhodes, The Making of the Atomic Bomb, p. 448.

  "The radioactivity was minuscule . . .": Emilio Segre, A Mind Always in Motion (Berkeley: University of California Press, 1994), p. 215.

  . . . deHevesy went back to the jar . . . : Adventures in Radioisotope Research: The Collected Papers of George Hevesy, vol. 1 (London: Pergamon Press, 1962), pp. 27, 28.

  "Why, fellows, you don't want . . .": Nuel Phar Davis, Lawrence and Oppenheimer (London: Jonathan Cape, 1969), p. 351.

  "Microphones installed?": Jeremy Bernstein, ed., Hitler's Uranium Club: The Secret Recordings at Farm Hall (Woodbury, N.Y.: American Institute of Physics, 1996), p. 75. See also the introduction by Sir Charles Frank to Operation Epsilon: The Farm Hall Transcripts (Bristol: Institute of Physics, 1993) for various practicalities of the recording, including his aplomb when questioned about "some unexplained wires in the back of a cupboard."

  "We have tried to make a machine . . .": Bernstein, Hitler's Uranium Club, p. 211.

  Berlin Auer company: Samuel Goudsmit, Alsos: The Failure in German Science (Woodbury, N.Y., 1996), pp. 56-65.

  "there was literally no time for research": Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections, ed. Katherine Haramundanis (Cambridge: Cambridge University Press, 2nd ed. 1947), p. 225.

  "Icelandic was a minor challenge": George Greenstein, "The Ladi
es of Observatory Hill," in Portraits of Discovery (New York: Wiley, 1998), p. 17.

  "Fred won't resign . . .": Fred Hoyle, Home Is Where the Wind Blows: Chapters from a Cosmologist's Life (Oxford: Oxford University Press, 1997), p. 374.

  "I am almost ashamed . . .": Kameshwar Wali, Chandra: A Biography of S. Chandrasekhar (Chicago: University of Chicago Press, 1992), p. 95.

  Guide to Further Reading

  Faraday and Energy

  The best way to get to know Michael Faraday as a person is to skim through his collected letters, either the version edited by L. P. Williams et al., The Selected Correspondence of Michael Faraday 2 vols. (Cambridge and New York: Cambridge University Press, 1971), or the more comprehensive The Correspondence of Michael Faraday, ed. Frank A. J. L. James (London: Institution of Electrical Engineers, ongoing from 1991). There's the teenager racing along the London streets in a rainstorm one night, exulting in the gush of water on his body; later there's the earnest young assistant, furious at Humphry Davy's wife for treating him as a servant on a trip to the Continent; finally, decades after, we see the grand old man of British science, distraught at realizing his memory is fading ever faster, and that the concentration he'd once been able to bring to bear on any subject is now gone.

  There's a good look at the way religion entered into his life and approach, in Geoffrey Cantor's Michael Faraday, Sandemanian and Scientist: A Study of Science and Religion in the Nineteenth Century (London: Macmillan; New York: St. Martin's Press, 1991) while Michael Faraday: His Life and Work, by Silvanus P. Thompson (London: Cassell, 1898), is my favorite overall biography, catching the tone of the times in a way later writers find difficult. The more recent Faraday Rediscovered: Essays on the Life and Work of Michael Faraday, ed. David Gooding and Frank A. J. L. James (London: Macmillan, 1985; New York: American Institute of Physics, 1989) corrects a number of Thompson's errors, and also is a good introduction to the major scientific discoveries. One of the most exciting chapters annotates an almost minute-by-minute account, based on Faraday's notebooks, of that crucial September 1821 experiment.