The Great Debate 2

M.V.N. Murthy, The Institute of Mathematical Sciences, Chennai 

Introduction
Conflicts in science can be fascinating and have occurred often enough. One such conflict in the 19th century led to one of the greatest debates in the history of science. It was all the more interesting because the protagonists were all eminent scientists and leaders beyond compare in their own fields.
The debate began when Charles Darwin the biologist, Sir Charles Lyell the geologist and Lord Kelvin the physicist, squared off on the question of the Age of the Earth in the latter half of the 19th century. It started with the Darwin's theory of evolution and could only be settled with the discovery of radioactivity.
In this second article we continue to trace the history of this debate which attracted the attention of not only physicists and astronomers, but also biologists and geologists as well and how the solution was found.

The great debate
From a physicist's point of view in the 19th century, the source of the energy in the Sun and the stars remained a major puzzle in science. In relation to this puzzle, there were several questions. The key questions were 
1. How old is life on Earth? Indeed there is no life on Earth without the Sun. The energy from the Sun is the ultimate source of every motion that takes place on Earth. This was a question of paramount importance to Charles Darwin. Furthermore, the Age of the Earth and not just how old is the life on the earth, itself was of great importance to the geologists.
2. Therefore what is the age of the Sun? The Sun must have existed for as long as or much longer than the time over which life forms have existed on Earth.
3. What powers the Sun? The age of the Sun crucially depends on how it is powered. How does the Sun produce vast amounts of energy necessary to support life forms on earth? How long is it going to keep doing so?
The first part of this article, published in the last issue, SepOct 2008, of JM, showed how Kelvin drastically underestimated the age of the Earth (he estimated it to be about 30 million years old) since he did not know about radioactivity. Radioactivity from natural sources on Earth is a major heat source, apart from sunlight.
Darwin's observations, on the other hand, persuaded him that the earth must be at least 300 million years old so that the natural selection that he observed had sufficient time to take place.
Today we know that Kelvin was wrong and the geologists and biologists were in fact right. In fact, the Sun is approximately 4.5 billion years old, much older even than Darwin's limit. What went wrong with Kelvin's estimate?
Radioactive decay of substances naturally occurring in rock causes changes in concentration of that substance over time, though in small amounts. Exotic elements can be introduced over time by this process. By studying the rates of decays of these materials in the laboratory, it is possible to find the approximate age of the rock sample.
Thus the age of the oldest terrestrial rock gives a lower limit for the age of the Earth---by assuming that a rock cannot have been in existence for longer than the Earth itself! In the beginning such an estimate of the age of the samples gave the age of the Earth to be about 2 billion years. This is much longer than the time required for natural selection to operate.
Thus the great debate of the 19th century, namely the age of the Earth, was settled by the discovery of radioactivity and consequent estimate of the age of the Earth by examining geological samples.

The age of the Sun
This however left the original puzzle about the age of the Sun unsolved. This puzzle was solved only after the discovery of the atomic nucleus and the tremendous energy locked up inside the nucleus. That is the story to be discussed in this article.
Immediately after the discovery of radioactivity, in 1904, Rutherford made the point that ``The discovery of radio-active elements, which in their disintegration liberate enormous amounts of energy [in the Sun], thus increases the possible limit of the duration of life on this planet, and allows the time claimed by geologist and biologist for the process of evolution".
This suggested that there may be hitherto unknown sources of energy. While the discovery of radioactivity opened up a new possibility for energy production in the Sun, it was in fact not to be the correct explanation. For one it did not depend on the temperature where as the astronomical observations showed that in fact it should. However, study of radioactivity led to other developments which play a central role in understanding how the Sun shines.
In a completely independent development, an important piece of puzzle was found when Einstein, in 1905, derived his famous relation E=mc2, as a consequence of the famous special theory of relativity. Here E is the energy, m is the mass and c=300,000 km/sec is the velocity of light. Because the velocity of light c is so large, even a tiny amount of mass would translate into an enormous amount of energy.
The enormous implication of this statement became clear soon after the startling discovery by Francis Aston in 1920. By this time Rutherford had established the existence of the nucleus and hence the structure of the atom. An atom is made up of electrons orbiting around a nucleus just as the planets go around the Sun. Almost the entire mass of the atom resides in the nucleus.
Aston measured the mass of the nucleus of the helium atom (also known as alpha-particle) and compared it with the sum of masses four hydrogen atoms. The mass of the helium nucleus was smaller compared to the sum of four hydrogen nuclei by a tiny amount, 0.7 %. The nucleus of hydrogen is nothing but a proton. Aston reasoned that if four protons were to fuse to form Helium the mass difference (in effect, the left-over mass) would appear as a huge amount of energy.
It was Arthur Eddington who, in 1920, suggested nuclear energy as the source of solar and stellar energy. He therefore could explain why the stars continued to burn for a very long time. With enormous foresight he stated "If, indeed, the sub-atomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring us a little nearer to fulfilment of our dream of controlling this latent power for the well-being of the human race--or for its suicide." 
(Unfortunately nuclear fusion weapons of today stand testimony to the foresight contained in Eddington's statement.) 
It was an inspired hypothesis, but only that, since at the time of Eddington physicists knew very little about the structure of the nucleus. The theory of quantum mechanics would be needed to understand nuclear fusion. It had to wait until George Gamow derived the quantum mechanical formula that explained how two positively charged protons come together in order to fuse, even though like charges repel.
In the stars such fusion happens in regions where the density and temperatures are huge compared to the surface values. The details of fusion processes were enunciated by Hans Bethe in 1939. Even a rough estimate based on Bethe's calculations gives about 10 billion years for the life time of the Sun (that is the period over which Sun continues to produce enormous quantities of energy) based on the quantity of hydrogen gas available in the Sun.
The actual lifetime calculated is now understood to be 9.6 billion years, using a detailed understanding of all the processes in the core of the Sun. In fact the present age of the Sun is about 5 billion years, just about halfway. Obviously this is much more than geologists and biologists had estimated and definitely many orders more than what the physicists had predicted based on gravitational contraction alone.
All this, however, was theory in need of experimental confirmation. One had to wait for another half a century before a conclusive proof of nuclear processes came along through the detection of the fusion products from the Sun. But that is another story.