The age of the world

Some of the most iconic views of our planet returned by both living astronauts and robotic spacecraft in orbit throughout the space age. Credit: cc by NASA Goddard Space Flight Center via Flickr

Editor’s note: This essay was originally published in “Lutheran Partners” as a Handiwork column in 2006. The article is still timely though as many seek to downplay the attempts to publicly reaffirm the tenets of young earth creationism.

Before the rise of modern science there was no reason not to use Old Testament genealogies and other texts as straightforward historical data to get a date around 4000 B.C. for the world’s creation. Biblical criticism has since shown that we needn’t read the texts that way and science has found several methods for estimating ages. The earth is now thought to be about 4.6 billion years old.

How do we know this? One way of getting at the question not only involves fascinating science but gives insights into how scientists and science itself — including its mathematical dimension — work.

The phenomenon of radioactive decay was discovered at the end of the nineteenth century.  Some types of atomic nuclei are unstable and disintegrate into other types.  Half of any sample, large or small, of a given type of atom will decay in a time characteristic of that atom, called its half-life. The longer that half-life, the more slowly any given sample will decay. This is the basis for a number of techniques of radioactive dating, and I’ll sketch just one here.

The element uranium has several isotopes, atoms which have the same chemical properties but different nuclear masses. The most important are U238 and U235.  U238 is by far the most common form on earth today, with 138 atoms of it to 1 atom of U235.  This is of considerable political and economic importance because naturally occurring uranium must be enriched in the rarer form for nuclear weapons and many reactors.

Why is one form of uranium much rarer than the other? Both are radioactive (decaying through series of intermediates to stable isotopes of lead), and U235 disintegrates more rapidly than U238. The possibility suggests itself that there’s less U235 today because most of what was present initially has decayed while more of the U238 is still around.

The half-life of U235 is .7 billion years while that of U238 is over six times longer, 4.5 billion years. For a first estimate let’s assume that when uranium was first formed there were equal amounts of the two isotopes. Since U238 decays more slowly, let’s first ignore its decomposition. Then we note that after seven half-lives of U235 its abundance will have been diminished by a factor of ½ to the seventh power, or 1/128. This is close to the current U235/U238 ratio, 1/138. Thus if our hypotheses are correct, the earth’s uranium was made something more than 7 x .7 billion years ago. This gives an estimate of 4.9 billion years for the age of the earth’s uranium.

Careful readers will be critical of several things I’ve done here. U238 does decay and 128 isn’t equal to 138! But scientists often begin to attack a problem with a crude “back of the envelope” calculation. It can give an idea of the size of the effect that we’re looking for and tell us if it’s worth pursuing an idea further. Those who remember logarithms from algebra class can remedy the two deficiencies in my estimate and show that the correct result is close to 5.9, rather than 4.9, billion years.

But there’s a more fundamental concern. How do we know that there were equal amounts of the two isotopes to begin with? The answer is that we don’t. In fact there probably was more U235. We now think that the heavy elements like uranium are formed in stars which explode as supernovas, distributing the elements that have been built up by fusion reactions into the interstellar medium to become part of the next generation of stars and planetary systems. Nuclear theory indicates that about 65% more U235 than U238 would be formed in this way. Our estimate of age then works out to around 6.5 billion years if only one supernova event contributed. This is the age of the interstellar material from which the solar system eventually formed. The solar system itself, including the earth, is somewhat younger.

That result can still be challenged however. Maybe our theories of formation of the elements are wrong. Perhaps uranium was created at some point in the past with a quite different isotopic ratio.

Ah, but there’s another intriguing piece of information to consider. I said that the current U235/U238 ratio is 1/138, a value fairly uniform over the earth. But at Oklo, in the West African nation of Gabon, the proportion of U235 to U238 is lower by a small but significant amount. Investigations of conditions at Oklo and the discovery there of types of atoms that would result from nuclear fission have led to the conclusion that at some time in the past there were naturally occurring nuclear reactors! They would have functioned in a start and stop fashion: Groundwater served as a moderator for neutrons, allowing chain reactions to build up, and operation would have ceased when heat that was generated boiled the water off. Cooling and accumulation of more water would allow the cycle to start again. The fission of some U235 explains why the abundance of that isotope is lower today.

I said that this happened “at some time in the past” but we can be more precise. A reactor of this type would require uranium to contain something like 3% U235, and we can calculate how long ago the earth’s uranium would have had this composition. The result is that the Oklo reactors were in operation something more than 1.7 billion years in the past.

It’s remarkable that such natural reactors existed, as is the fact that at this remove we can understand their workings. I wish I could simply present this as an example of neat science but not everyone sees it that way. Some conservative Christians, “young earth creationists,” are deeply committed to the belief that the earth is only a few thousand years old and reject the billions of years that radioactive dating gives. They may claim that decay rates were much higher in the past, but there is no evidence for this.

Or they may fall back on the “apparent age” argument that God created the world only a few thousand years ago with isotopic abundances adjusted to make it look billions of years old. However, the Oklo data shows that God would also have had to tweak the isotopic abundances a bit at one site in Africa to make it look as if that place had some intermediate, though long, age. There is no strictly scientific or philosophical way of refuting that argument.  (Bertrand Russell pointed out that the world could have come into existence five minutes ago with all our memories and other records intact.)  But this makes God a deceiver, the fabricator of a world full of illusions. Belief in the goodness of creation, on the other hand, holds that God is the maker of a world that tells the truth about itself to honest investigators.

George Murphy received his Ph.D. in physics from Johns Hopkins for work on general relativity in 1972.  He taught at Westminster College (PA), The University of Western Australia and Luther College and did research for eleven years before entering Wartburg seminary. Ordained in 1983, he has served as a pastor in Lutheran and Episcopal congregations. His first article on theology and science was published in 1977 and he has since published six books and numerous articles and continues to speak and lead workshops in this area. His most recent book, Models of Atonement: Speaking about Salvation in a Scientific World (Lutheran University Press, 2013), discusses ways of understanding the saving work of Christ in an evolving world.

Further Reading

Cherry Lewis, The Dating Game (Cambridge, 2000), uses a biography of Arthur Holmes, a pioneer in the field, to tell the story of radioactive dating of the earth.
Alex P. Meshik, “The Workings of an Ancient Nuclear Reactor,” Scientific American, November 2005, deals with Oklo.

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