E=mc2

by David Bodanis

  Most of the other researchers who bothered with this had just shrugged it aside, but to Einstein (in a 1920 paper quoted in Folsing, p. 171), "The idea that these were two disparate situations was intolerable to me." For Einstein often said that one of his deepest ethical/religious beliefs was the ideal of social justice. What seems an unjustified or unfair distinction should, if one only examines it closely enough, be able to be resolved so that the unfairness no longer exists. It's the fairness principle of John Rawls, and all other believers in the objectionability of undeserved distinctions; a transposition outward, of the unified dominion, which a unitary deity might be expected to create.

  What Einstein did to resolve this dilemma of how Newton "contradicted" Maxwell was to take one of those right-angle jumps of the sort Faraday and Roemer had been so successful with before. He questioned the very terms in which the dilemma was posed! The definitions of length and time and simultaneity had been around so long— they'd been codified at least since Newton—that they seemed "basic" to common sense. But Einstein realized they all contained loaded assumptions about how measurements had to he made. Newton and Maxwell were being puuuuuuuulled apart. . . and Einstein let a change in the way of building up the definitions that both had been assuming snap to take up the slack.

  If I say a light beam should have passed a certain target pole by now but you say that's crazy, it's definitely going to take longer, that's no problem at all—so long asyour notion of longer is different from my notion of what that longer must be. What I see is then true, and it's not conflicting with what you see. Throughout special relativity, what had seemed contradictions are resolved by clarifying our perceptual terms.

  Was it a revolution? Einstein always insisted it wasn't, and that by shifting the core notions he was simply doing what was necessary to preserve the past. I'd take him at his word. Possibly his drive for continuity—for preserving the essence of a past—was at heart a desire for religious continuity; possibly it was his own respect for the great physicists of the past.

  I suspect it also was reinforced by all his years of traveling. First there had been the soft Swabian home, then a harsh Prussian-style school, in the setting of Catholic Bavaria; next came a few delightful teenage months in the freer air of Italy, followed by the intense mix of intellectual and romantic attachments in distant, isolated Aarau; after that, life in student Zurich, with the disappointments of a narrow, cold Polytechnic faculty in the background; then quickly, Bern and the rush of adult obligation—of wife, and children, and obeisance within a great civil service hierarchy. At that point Einstein was still only in his early 20s: Lorentz at that age had never been out of the Netherlands. Later, for Einstein, there would be more countries, more cities; ending only at Princeton, in a distant, barely understood America. In such traveling, such isolation, the one thing that travels intact is yourself.

  . . . different views about personal responsibility . . . : What type of theory is the theory of relativity that Einstein created? It's not like detailed laws such as the ones found in engineering texts, which might say that air resistance goes up as a certain power of an airplane's speed. Looked at in greater detail, such "laws" will break down, for their assumptions are based on only partial analyses. They're more just useful rules of thumb, carved out to conveniently summarize subsets of the physical world we're especially concerned with, but which go no further than that.

  Other principles, such as Newton's Third Law of Motion— the one about every action having an equal and opposite reaction—go deeper. They're what would be used in improving engineering rules of thumb about air resistance, for they're much more deeply embedded in the nature of an analytic system. Their application in such systems is, in principle, unlimited.

  Einstein's special theory of relativity is different yet again. It's not a particular result, which simply happens to go beyond Newton or Maxwell's work. Rather, it's a theory about theories: the specification of the two criteria—that the speed of light is the same to all observers; that no smoothly moving reference frame is inherently indistinguishable from any other—which any valid theory must fulfill. If those criteria hold, the theory being considered might be true. If not, then it is definitely false.

  Special relativity is simply a judgment machine. It's a meta-level commentary, just like the layered analyses of the Talmud; just like the Second Law of Thermodynamics.

  This juridical nature of Einstein's theory is often missed, for after enunciating his principle, Einstein himself— and then many others—went on to come up with particular results, such as E=mc2 or the observed slowing of time, which seem analogous to the derived particularities other theories generate. Yet this higher-order nature of the law is why the "m" in E=mc2 is so general, applying to every substance in the universe—from the carbon in your hand, to plutonium in a bomb, or the hydrogen inside the sun.

  "a temptation to superficiality . . . : Albrecht Folsing, Albert Einstein: A Biography (London: Viking Penguin, 1997), p. 102.

  . . . this gently self-teasing tone: In the letters of many artists of the time there's often a similar tone; a similarly bemused acceptance that there is a less than rational world of received rules within which we have to live. The fact that an entire knowledge-admiring academic system was mixed in with a society that had totally different standards—of Junker superiority; of Kaiserlich grandeur—roused intelligent cynicism among many of the young.

  "This should suffice to show . . . Albert Einstein never did attain.": The quotes are from his sister Maja's delightful short memoir, "Albert Einstein—A Biographical Sketch," in Collected Papers of Albert Einstein, Vol. 1. The Early Years: 1879-1902, trans. Anna Beck, consultant Peter Havas (Princeton, N.J.: Princeton University Press, 1987).

  Uncle Rudolf ("The Rich"): Ibid., p. 160.

  "he is oppressed by the thought. . .": Ibid., p. 164. It's Hermann Einstein's 1901 letter to Professor Ostwald again.

  Eventually a few other physicists . . . : Planck's student Max von Laue was the first to see the great professor who had written this paper. Von Laue was directed from the patent office reception room and along a corridor; a young man came out whom von Laue ignored; von Laue waited. Later the young man returned. It was Einstein; finally the two said hello. From von Laue's account in a 1952 letter in Carl Seelig, Albert Einstein: A Documentary Biography (trans. Mervyn Savill (London: Staples Press, 1956), p. 78.

  "I have to tell you . . .": Collected Papers of Albert Einstein, vol. 1. I've rearranged material from the letters given in documents 39, 72, 76, and 70.

  The myth that she had been responsible for . . . : The story was first promoted in In the Shadow of Albert Einstein, published in Serbo-Croat in 1969 by the retired schoolteacher Desanka Trbuhovic-Gjuric. It was developed in Andrea Gabor's Einstein's Wife (New York: Viking, 1995), and received a great public boost when Jill Ker Conway, onetime Smith College president, reviewed Gabor's book most favorably in The New York Times.

  Alas, the Times and Conway (and Gabor, and Trbuhovic-Gjuric) had the story totally wrong. Mileva was a good physics undergraduate, but no muse. See John Stachel's "Albert Einstein and Mileva Marie: A Collaboration that Failed to Develop" in Creative Couples in Science, ed. H. Pycior, N. Slack, and P. Abir-Am (New Brunswick, N.J.: Rutgers University Press, 1995). The real quality of their relation is best seen in Albert Einstein, Mileva Marie: The Love Letters, ed. Jurgen Renn and Robert Schulmann; trans. Shawn Smith (Princeton, N.J.: Princeton University Press, 1992).

  Compared with this . . . child's play: Banesh Hoffmann, Albert Einstein: Creator and Rebel (New York: Viking, 1972), p. 116.

  8. Into the Atom

  Their finding is so widely taught. . .: Rutherford first suspected that each atom would be a diffuse blob of electricity— since many physicists had gone to English schools, images of raisin puddings were common in the textbooks of the time. But when he created something like an ultra-miniature atomic bazooka and started shooting alpha particles into gold foil, a few ricocheted back and he k
new something solid was tucked away in there. But where?

  This was a great problem, for although Rutherford was one of the century's finest experimentalists, he was something of an embarrassment as a mathematician. He couldn't work out a plausible trajectory for what was happening to the particles that he'd shot in and which had then somehow curved around and roared back out. As a result, he ended up borrowing the mathematics of conic sections, which had been developed in classical times and used in the seventeenth century to track comet orbits. It worked to some extent—in time he did manage to get his Manchester results to seem to fit—but it also meant that for years students were taught that the atom really was like a miniature solar system. That doesn't make sense, however: there's no reason the electrons wouldn't crash inward after emitting radiation in their fast orbits; nor is there any physical analogue to the stability of the actual solar system, guaranteed by Newtonian inverse-square gravity. But such is the power of assumption-loaded mathematics (and also, who had a better idea?) that although the solar system model was eventually overthrown, what began with the mathematical weakness of Ernest Rutherford has carried on in popular mythology to become the default model most people carry of what an atom looks like.

  There were positively charged particles . . . : How could one tell there was a positive charge in the nucleus? The reason is the old law from high school classes: similar electric charges repel, and opposite charges attract. If you shot a positive particle into the center and it stuck, you'd guess there was a negative charge waiting there. But the incoming alpha particles Rutherford shot in were positively charged and deflected away from "something" hovering at the center of atoms. That "something" had to be positive as well.

  . . . the "Fewtron": Andrew Brown, The Neutron and the Bomb: A Biography of Sir James Chadwick (Oxford: Oxford University Press, 1997), p. 103.

  The reason they [the slowed neutrons] stuck so well . . . : The reference to quantum uncertainty is further discussed in the notes to Chapter 10.

  . . . his assistants lugged up buckets of water . . . : What worked in Fermi's research villa could work anywhere lots of neutron-slowing water gushed around radioactive clumps. In the early 1970s mining geologists were puzzled by peculiar ore specimens from a mine near the Oklo river in Gabon. Specialists from the French Atomic Energy Commission soon realized that this was where a series of natural uranium deposits had gone critical, over 1.8 billion years earlier. A natural aquifer had supplied the needed water; each of the reactions had continued for up to 100,000 years before dying down.

  George de Hevesy employed it . . . : De Hevesy's culinary defense was undertaken with lead and similar elements two decades before Fermi's work. See M. A. Tuve's "The New Alchemy," Radiology, vol. 35 (Aug. 1940), p. 180.

  9. Quiet in the Midday Snow

  "I have here . . . no position . . .": Sallie Watkins's essay "Lise Meitner: The Foiled Nobelist," in Rayner-Canham, A Devotion to Their Science (Toronto: McGill— Queen's University Press, 1997), p. 184.

  "Our Madame Curie": Philipp Frank, Einstein: His Life and Times (New York: Knopf, 1947), pp. 111-12.

  "[Hahn] would whistle large sections . . .": Ruth Lewin Sime, Lise Meitner: A Life in Physics (Berkeley: University of California Press, 1996), p. 35.

  "I've fallen in love . . .": Sime, Lise Meitner, p. 37.

  "Dear Herr Hahn! . . .": Ibid., pp. 69 and 67. The extracts are from letters of January 17, 1918, and August 6, 1917.

  . . . Meitner shifted once again . . . : There was a certain amount of envy from less successful Berlin peers when Meitner began concentrating on the neutron, and a certain amount of disgruntled gossip as well. It's rare to change a lab's research direction: all the equipment is set up for one sort of work; there are postgrads whose grants are contingent on that previous work, technicians who were trained for it, and sometimes even suppliers who've come to specialize in it. Economists call it the problem of sunk costs, and it's one of the main reasons that very few top labs stay at the top for long. In a more recent era, it's why computer industry monoliths have continually been wrong-footed by quick Silicon Valley startups. Despite her surface shyness, Meitner would have been a confident dot-com entrepreneur par excellence.

  "The Jewess endangers our institute . . .": For the Kurt Hess quote and associated details: Sallie Watkins's essay in A Devotion to Their Science, p. 183; also Sime, Lise Meitner, pp. 184-85.

  Hahn may have been slightly troubled . . . : There are many levels of culpability, and Hahn of course was never a Nazi. Indeed, several months after Hitler came to power, Hahn had suggested to Planck that there should be a protest against the way Jewish academics were being expelled. By the late 1930s, such public protests were impossible, but a number of other physicists made a point of discreetly helping individuals like Meitner: encouraging foreign colleagues to offer invitations to colloquia; making sure that such letters emphasized that all funds would be paid abroad (so that a visa could be withheld on the grounds that money would have to be taken out of Germany); perhaps arranging for such letters to be predated so they appeared to have been sent before any official expulsion from research institutes had taken place. The fact that Hahn did very little of this for his lifelong colleague is not a terrible sin: it just shows that he was not up to the level of the rare, more highly ethical individuals, such as his colleague Strassmann.

  What's more serious—or at least, what seems explicable only by Hahn's realizing he'd done something very wrong—was the way Hahn tried to rewrite the history of his relation with Meitner after the war: treating her as having been some sort of junior assistant when he was interviewed by Swedish newspapers in Stockholm in the week before his Nobel Prize ceremony in 1946; later, giving mocking, almost sighing references to how foolishly misguided her attempted advice had been. Meitner suspected it was all a way of Hahn exculpating himself—for if she'd hardly been there at all, how could he be charged with having treated her badly? See Sime, Lise Meitner, Chapters 8 and 14, and especially her note 26 on page 454.

  ". . . in the lurch": Ibid., p. 185.

  "Hahn says I should not . . .": Ibid.

  Hahn, as ever, seemed the slowest. . . : After the outlines of fission had been worked out, he still had troubles: "Bohr will perhaps think I'm a cretin," Hahn wrote to Meitner in July 1939, "but even after 2 of his long explanations I again don't understand it." As with Lawrence, though, the question is one of degree. Hahn was an intelligent enough man—he just wasn't at Meitner's level. What he was exceptionally good at, though, was judging when a field was ripe. That's indispensable. It was not entirely by chance that he "happened" to be at Rutherford's Montreal lab, just when it was possible for a skilled chemist like himself to discover a new element; nor that he was at the new institutes on the edge of Berlin when those were the most fruitful places for a chemist with his background to be.

  Peter Medawar called this importance of appropriate selection "the art of the soluble." The point is not that only easy problems are targeted; rather, "the art of research [is] the art of making difficult problems soluble by devising means of getting at them." Einstein when young was superb at this; Rutherford kept the ability his whole life. The Medawar quote is on page 2 of his justly lauded Pluto's Republic (Oxford: Oxford University Press, 1984).

  "Meitner's opinion and judgment . . .": Watkins, p. 185.

  Hahn's letter of December 19,1938, to Meitner: Sime, Lise Meitner, pp. 233-34.

  "Meitner was the intellectual leader . . .": Ibid., p. 241.

  "You see, you will do a good deed . . .": Ibid., p. 234.

  Robert Frisch: Many texts speak of someone named Otto Frisch, who confusingly seems to have been related-nephew perhaps?—to an earlier physicist named Robert Frisch. They're one and the same. As a young man, Robert Otto Frisch had used his first name, but when he later ended up working with Americans, for whom the name Robert was so common, Frisch decided being known by his middle name would be less confusing.

  "Fast, but not auntie": Otto Frisch, What
Little I Remember (Cambridge: Cambridge University Press, 1979), P. 33.

  The next morning, when he came down . . . : What happened at breakfast and then during their famous walk in the snow has been extensively recounted by the two participants. See the Frisch and Meitner items in the Guide to Further Reading, as well as the bibliographic notes at Sime, Lise Meitner, p. 455, and Richard Rhodes, The Making of the Atomic Bomb, p. 810, entry 257.

  ". . . that she could walk just as fast without": Frisch, What Little I Remember, p. 116.

  "so overwhelmingly new and surprising": Lise Meitner, "Looking Back," Bulletin of the Atomic Scientists (Nov. 1964), p. 4.

  "Fortunately [my aunt] remembered . . .": Frisch, What Little I Remember, p. 116. Meitner knew this from earlier published measurements of nuclear weights.

  The lahel fission . . .: The biological analogy was a common one: Rutherford had chosen the word nucleus for the center of an atom on the same basis.

  10. Germany's Turn

  Einstein's letter of August 2,1939: The letter is in most Einstein biographies or histories; see, e.g., Einstein: A Centenary Volume, ed. A. P. French (London: Heinemann, 1979), p.191, for a clear facsimile. The story of how Einstein came to sign the letter is given with exuberant detail in Leo Szilard, The Collected Works (Cambridge, Mass.: MIT Press, 1972), though with somewhat more accuracy in Eugene Wigner, The Recollections of Eugene P. Wigner (as told to Andrew Szanton) (New York: Plenum Press, 1992).