Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe (25 page)

Since their inception, ideas about the process of the formation of the elements have been linked intimately to those on the enormous
energy sources
of stars. Recall that Helmholtz and Kelvin proposed that the Sun’s power comes from slow contraction and the associated release of gravitational energy. However, as Kelvin had clearly demonstrated, this reservoir could provide for the Sun’s radiation for only a limited time: no more than a few tens of millions of years. This limit was disturbingly at odds with geological and astrophysical evidence that was pointing with increasing accuracy to ages of billions of years for both the Earth and the Sun. Eddington was fully aware of this glaring discrepancy. In his address to the British Association for the Advancement of Science meeting in Cardiff, Wales, on August 24, 1920, he made the following prescient statement:

Only the inertia of tradition keeps the contraction hypothesis alive—or rather, not alive, but an unburied corpse. But if we decide to inter the corpse, let us frankly recognize the position in which we are left. A star is drawing on some vast reservoir of energy by means unknown to us.
This
reservoir can scarcely be other than the subatomic energy which, it is known, exists abundantly in all matter
[emphasis added].

Despite his enthusiasm for the idea that stars could derive their power from four hydrogen nuclei fusing together to assemble a helium nucleus, Eddington had no specific mechanism for this process to actually take place. In particular, the problem of the mutual electrostatic repulsion, mentioned above, had to be solved. Here is the obstacle: Two protons (the nuclei of hydrogen atoms) repel each other electrostatically because both have positive electric charges. This Coulomb force (named after the French physicist Charles-Augustin de Coulomb) has a long range, and it is therefore the dominant force between protons at distances larger than the size of the atomic nucleus. Within the nucleus, however,
the strong, attractive nuclear force takes over, and it can overcome the electric repulsion. Consequently, in order for protons in the cores of stars to fuse together as envisioned by Eddington, they need to have sufficiently high kinetic energies in their random motions to overcome the “Coulomb barrier” and allow them to interact via the attractive nuclear force. The apparent snag in Eddington’s hypothesis was that the temperature calculated for the center of the Sun was not high enough to impart protons with the necessary energy. In classical physics, this would have been a death sentence for this scenario; particles with insufficient energy to overcome such a barrier just cannot make it. Fortunately, quantum mechanics—the theory that describes the behavior of subatomic particles and light—came to the rescue. In quantum mechanics, particles can behave like waves, and all processes are inherently probabilistic. Waves are not precisely localized like particles but are spread out. In the same way that some parts of an ocean wave crashing against a seawall can splash to the other side, there is a certain (albeit small) probability that even protons with insufficient energy to overcome their Coulomb barrier would still interact.
Using this quantum mechanical effect of “tunneling” through barriers, physicist George Gamow and, independently, the
two teams of Robert Atkinson and Fritz Houtermans, and Edward Condon and Ronald Gurney, demonstrated in the late 1920s that under the conditions prevailing in stellar interiors, protons could indeed fuse.

Physicists Carl Friedrich von Weizsäcker in Germany, and Hans Bethe and Charles Critchfield in the United States, were the first to elaborate the precise nuclear reactions network through which four hydrogen nuclei coalesce to form a helium nucleus.
In a remarkable paper published in 1939, Bethe discussed two possible energy-producing paths in which hydrogen could convert into helium. In one, known as
the proton-proton (p-p) chain, two protons first combine to form deuterium—the isotope of hydrogen with one proton and one neutron in its nucleus—followed by the capture of an additional proton that transforms the deuterium into an isotope of helium. The second mechanism, known as the carbon-nitrogen (CN) cycle, was a cyclic reaction in which carbon and nitrogen nuclei acted only as catalysts. The net result was still the fusion of four protons to form one helium nucleus, accompanied by the release of energy. While Bethe thought originally that the CN cycle was the main mode by which our own Sun produces its energy, experiments at the Kellogg Radiation Laboratory at Caltech showed later that it was the p-p chain that mostly powered the Sun, with the CN cycle starting to dominate energy production only in more massive stars.

You have probably noticed that, as its name implies, the CN cycle requires the presence of carbon and nitrogen atoms as catalytic agents. Yet Bethe’s theory fell short of demonstrating how carbon or nitrogen formed in the universe in the first place. Bethe did consider the possibility that carbon could be synthesized from the fusion of three helium nuclei together. (A helium nucleus contains two protons, and a carbon nucleus, six.) However, after completing his calculations, he asserted,
“There is no way in which nuclei heavier than helium can be produced permanently in the interior of stars under the present conditions”—that is, with densities and temperatures such as those encountered in most Sun-like stars. Bethe concluded: “We must assume that the heavier elements [than helium]
were built up
before
the stars reached their present state of temperature and density.”

Bethe’s pronouncement created a serious conundrum, since astronomers and Earth scientists were concluding at the time that the different chemical elements had to have, by and large, a common origin. In particular, the fact that atoms such as carbon, nitrogen, oxygen, and iron appeared to have approximately the same relative abundances all across the Milky Way galaxy clearly hinted at the existence of some universal formation process. Consequently, if they were to accept Bethe’s adjudication, physicists had to come up with some common synthesis that could have operated before present-day stars reached their equilibrium.

Just as the theory seemed to be heading toward a paralyzing impasse, the versatile George Gamow (usually known to his colleagues as Geo) and his PhD student Ralph Alpher advanced what appeared to be a brilliant idea: Perhaps the elements could have been formed in the initial, extremely hot and dense state of the universe known as the big bang. The concept itself was genius in its clarity. In the primeval, dense fireball, Gamow and Alpher argued, matter consisted of a highly compressed neutron gas. They referred to this primordial substance as
ylem
(from the ancient Greek
yle
and the medieval Latin
hylem
, both meaning “matter”). As these neutrons started decaying into protons and electrons, all the heavier nuclei could, in principle, be produced by the successive capture of one neutron at a time from the remaining sea of neutrons (and the subsequent decay of those neutrons into protons, electrons, and antineutrinos). Atoms were supposed to march in this way up the periodic table, climbing one step with each consecutive neutron capture. The entire process was assumed to be controlled by the probability for particular nuclei to capture another neutron, and also by the expansion of the universe (discovered in the late 1920s, as we’ll discuss in the next chapter). The cosmic expansion determined the overall decrease of the density of matter with time, and thereby the slowing down of the nuclear reaction rates. Alpher carried out most of the computations, and
the results were published in the April 1, 1948,
issue of the
Physical Review
. (April Fool’s Day was Gamow’s favorite publication date.) The always-whimsical Geo noticed that if he could add Hans Bethe (who had nothing to do with the calculations) as a coauthor of the paper, the three names—Alpher, Bethe, Gamow—would correspond to the first three letters of the Greek alphabet: alpha, beta, gamma. Bethe agreed for his name to be included, and the paper is
often referred to as the “alphabetical article.” Later in the same year, Alpher collaborated with physicist Robert Herman to predict the temperature of the residual radiation from the big bang, known today as the
cosmic microwave background.
(Geo, who never abandoned his lifelong interest in punning, joked in his book
The Creation of the Universe
that Robert Herman
“stubbornly refuses to change his name to Delter”—to correspond to delta, the fourth letter in the Greek alphabet.)

As ingenious as the scheme of Alpher and Gamow was, it soon became clear that while nucleosynthesis in a hot big bang could indeed account for the relative abundances of the isotopes of hydrogen and helium (and some lithium and traces of beryllium and boron), it ran into insuperable problems producing the heavier elements. The challenge is easy to understand using a simple mechanical metaphor: It is very difficult to climb a ladder when some of the rungs are missing.
In nature, there are no stable isotopes with an atomic mass of 5 or 8
. That is, helium has only stable isotopes with atomic masses of 3 and 4; lithium has stable isotopes with atomic masses of 6 and 7; beryllium’s only truly stable isotope has an atomic mass of 9 (atomic mass 10 is unstable but long lived), and so on. Atomic masses of 5 and 8 are missing. Consequently, helium (atomic mass, 4) cannot capture another neutron to produce a nucleus that would be sufficiently long lived to continue the neutron-capture scheme. Lithium has a similar difficulty because of the gap at atomic mass 8. The mass gaps therefore frustrated further progress along the Gamow and Alpher approach.
Even the great physicist Enrico Fermi, who examined the problem in some detail with a colleague, concluded with disappointment that synthesis in the big bang was “incapable of explaining the way in which the elements have been formed.”

Fermi’s conclusion that carbon and heavier elements could not be produced in the big bang combined with Bethe’s assertion that these elements could not be produced in stars such as the Sun created a perplexing mystery: Where and how were the heavy elements synthesized? This was the point at which Fred Hoyle entered the picture.

In the late fall of 1944, Hoyle’s wartime activities in naval radar took him to the United States, where he used the opportunity to meet with one of the most influential astronomers of the time, Walter Baade, at the Mount Wilson Observatory in California. At the time, this observatory contained the largest telescope in the world. From Baade, Hoyle learned how enormously dense and hot the cores of massive stars can become during the late stages in their lives. Examining those extreme conditions, he realized that at temperatures approaching a billion degrees, protons and helium nuclei could easily penetrate the Coulomb barriers of other nuclei, resulting in such a high frequency of nuclear reactions and back-and-forth exchanges that the entire ensemble of particles could reach a state known as
statistical equilibrium
.

In nuclear statistical equilibrium, while nuclear reactions continue to occur, each reaction and its inverse occur at the same rate, so that there is no further overall net change in the abundances of the elements. Consequently, Hoyle argued, he could use the powerful methods of the branch of physics known as statistical mechanics to estimate the relative abundances of the various chemical elements. To actually perform the calculations, however, he needed to know the masses of all the nuclei involved, and that information was not available to him during the war years. Hoyle had to wait until the spring of 1945 to obtain a table of the masses from nuclear physicist Otto Frisch. The result of the ensuing calculation
was an epoch-making paper published in 1946, in which Hoyle delineated the framework of a theory for the formation of the elements from carbon and higher
in stellar interiors. The idea was mind boggling: Carbon, oxygen, and iron did not always exist (in the sense of having been formed in the big bang). Rather, these atoms, all of which are essential for life, were forged inside the nuclear furnaces of stars. Think about this for a moment: The individual atoms that currently form the two strands of our DNA may have originated billions of years ago in the cores of different stars. Our entire solar system was assembled some 4.5 billion years ago from a mixture of ingredients cooked inside previous generations of stars. Astronomer Margaret Burbidge, who was to collaborate with Hoyle a decade later, gave a wonderful description of her experience of listening to Hoyle at a meeting of the Royal Astronomical Society in 1946: “
I sat in the RAS auditorium in wonder, experiencing that marvelous feeling of the lifting of a veil of ignorance as a bright light illuminates a great discovery.”

Scrutinizing the consequences of his embryonic theory, Hoyle was gratified to discover a marked peak in the abundances of the elements neighboring iron in the periodic table, just as the observations seemed to indicate. This consistency of the “iron peak,” as it came to be known, indicated to Hoyle that he was doing something right. However, those missing rungs in the ladder—the absence of stable nuclei at atomic masses 5 and 8—continued to beleaguer any attempt to construct a detailed (as opposed to a skeletal) network of nuclear reactions that would produce all the elements.

To circumvent the mass-gap problem, Hoyle decided in 1949 to reexamine the possibility (previously aborted by Bethe) of fusing three helium nuclei to create the carbon nucleus, and he assigned this problem to one of his PhD students. Since helium nuclei are also known as alpha particles, the reaction is usually referred to as the
triple alpha
(3α) process. As it so happened,
that particular student decided to ditch his PhD work before completing it (he was Hoyle’s only student to ever do so), but he failed to cancel his formal registration. The rules of academic etiquette set for such cases by the University of Cambridge were clear: Hoyle was not allowed even to touch the problem until either the student or an independent researcher published the results. Eventually, two astrophysicists
published results, although the work of one of them went almost entirely unnoticed.