Authors: David Bodanis
E=mc2 (31 page)
Despite this, Einstein remained defensive about his link. In a reply to a Japanese newspaper in 1952, he wrote: "My participation in the production of the atomic bomb consisted of one single act: I signed a letter to President Roosevelt." In a 1955 letter to a French historian, Einstein elaborated:
Now you seem to believe that I, poor fellow that I am, by discovering and publishing the relationship between mass and energy, made an important contribution. . . . You suggest that I should . . . in 1905, have foreseen the possible development of atomic bombs. But this was quite impossible since the accomplishment of a "chain reaction" was dependent on the existence of empirical data that could hardly have been anticipated in 1905. . . . [E]ven if such knowledge had been available, it would have been ridiculous to attempt to conceal the particular conclusion resulting from the Special Theory of Relativity. Once the theory existed, the conclusion also existed.
The popular belief linking his work with the bomb encompasses, I suspect, the awe that even without willing the bomb, Einstein had, in this sense, foreseen it. The quotes are from
Einstein on Peace,
ed. Otto Nathan and Heinz Norden (New York: Simon & Schuster, 1960), pp. 583 and 622-23.
14. The Fires of the Sun
"fled down the stairs . . .": All quotes from
Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections,
ed. Katherine Haramundanis (Cambridge: Cambridge University Press, 2nd ed., 1996). "fled down the stairs," pp. 119-20; "bicycling," p. 121; "safely lying on her back," p. 72. "[R]ows of braying young men" is not a direct quote, but the reference is from p. 118.
. . . the original gas clouds . . . : Not all condensing clouds reach a sufficient density to ignite: the planet Jupiter is one example of such an inrushing cloud that was just a few times too small to achieve thermonuclear burning. It's possible that there are a great number of free-floating planets or larger unignited objects, eternally drifting sunless across our galaxy.
"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 c
2
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 c
2
, then mass equals Energy divided by c
2
. In other words, m=E/c
2
. 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=mc
2
; 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=mc
2
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 10
30
grams.
The total energy we can hope to get from that mass is E=mc
2
, which in this case is E=(1.4 X 10
30
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 10
51
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 10
35
ergs each second. (This is the sort of figure computable by the reasoning in the note pegged to p. 135, which 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 10
17
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 10
17
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=mc
2
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.