The Age of the Earth 1

1. The Age of the Earth 1 Kelvin’s challenge to geology

2. Kelvin, Huxley

3. Darwin, T.C. Chamberlain

4. Lyell and Darwin • Darwin relied on Lyell’s position concerning the age of the earth. • He calculated, in the first edition of the Origin, how long the ‘denudation’ (erosion) of a region of England called the Weald (which goes back to the Carboniferous) had taken. • The figure he arrived at was (by our standards today) pretty good: 300 million years. • But he was soon to regret his boldness in actually specifying a number.

5. Kelvin • The most famous physicist of his time. • Kelvin made important contributions to the development of thermodynamics. • In particular, he identified/contributed to the expression of the second law (that entropy always increases– connected to the fact that heat always flows from hotter to cooler). • But this brings us back to the kind of calculation of the earth’s age that Buffon attempted. • Similarly, it suggests the possibility of calculating how long the sun could radiate energy at its present rate.

6. The Problem • Kelvin arrived at a simple model of the earth: • It had solidified pretty well all at once (until that point, it would be kept uniformly hot & mixed by convection currents). • From that point it would behave like any hot sphere, beginning at the melting temperature and gradually radiating heat outwards to space (temperature there is just above absolute zero). • There is plenty of evidence that temperature increases as we dig or drill deeper into the earth; this was well-known. • The calculations for temperature profiles over time of a solid, uniform sphere depend only on the initial temperature, the heat capacity and conductivity of the material. • The upshot is that there are limits to how old the earth is on this model, and when he applied it, Kelvin arrived first at an upper limit of 400 million years and a lower limit of 40 million years; he preferred about 100 million as the best estimate

7. The Sun • Helmholtz had proposed a gravitational theory of the sun’s energy. • Beginning with small bodies spread out through space, which then come together under the influence of gravity, we can calculate the amount of energy available to ‘power’ the sun. • This gravitational theory allows far more energy in total than any form of combustion could (the sun would go out within some thousands of years if it were a burning lump of coal). • Kelvin adopted this theory & concluded that the sun could provide something like the present level of energy for something like 100 million years, with 500 million as an outside limit. • Again, the main point for Kelvin was that the time was limited—he rejected Lyell’s appeal to ‘drafts on the bank of time’ as irresponsible. • Darwin was roundly criticized for his own calculation, which non-uniformitarians and fans of Kelvin dismissed as ‘absurd’.

8. Comparing ways of measuring time • Geologists had various processes: erosion, sedimentation,… • Each process produces a kind of cumulative measure, just like an hour-glass. • If we can combine a rate with a measure of how much of the process has taken place, we will get a time. • This kind of measure is pretty elastic—it’s hard to say just how fast or slow erosion or sedimentation is over the long run (even if we measure the sediment carried by a river over a year, we still need to know how much area that sediment is spread over to build sedimentary rock). • It’s also hard to measure just how much erosion or sedimentation has occurred (even if we add up the thicknesses of sedimentary rocks to form a column, it’s hard to be sure we’ve got it all, with no overlaps).

9. The Geological Estimates • Many of these estimates were made following Kelvin’s initial work. • They tended to come out roughly in agreement with Kelvin’s 100 million years. • But they are clearly pretty elastic. • On the other hand, if we can specify maximum rates and minimum accumulations with good confidence, we can put a lower limit on the time required.

10. The Physical Estimates • Kelvin’s methods depended on Kelvin’s models. • Kelvin’s model of the earth treated it as solid. There was real evidence for this, but the evidence was not conclusive. • John Perry added convection below the surface to Kelvin’s model of the earth– the result was a huge increase in the time available. • Also, of course, any source of heat that could replace the heat lost to space would put the calculations out of whack. • But Kelvin was right in terms of the physics known at the time: There was no credible source of energy that could do it.

11. The Sun • The models of the sun were much simpler– they didn’t depend on solidity. They only depended on the gravitational theory of the sun’s energy. It would be quite difficult to find, in 19th century physics, a way of ‘packing more energy in’. • So the limit of 100 million years for the sun, which was later reduced to something like 25 million (1899). Later calculations based on new figures, some from King and with support from another hard-liner, Tait, reduced Kelvin’s estimate of the age of the earth to 40 million or less.

12. Reaction • Huxley had resisted Kelvin’s calculations from the outset, pointing out that they depended on substantial and unproven assumptions, and that even if there were limits to time, nothing in the geologists’ evidence suggested those limits had made a difference to the history we now see in geological record . • These new limits, which were laid down in the 1890’s, sparked a resistance amongst geologists. • James Croll and T.C. Chamberlain were supporters of this kind of calculation, but they were also convinced that the geological evidence showed the earth could not be that young. • So we’re at an impasse.

13. Pecking order • When two sciences seem to disagree about a question that both have something to say about, what do we do? Who should we believe? • Kelvin’s view was that geology should take its time from physics and make whatever adjustments it had to. • Chamberlain and Croll held that geology should deal with its own evidence, develop and work on it independently, and hold its ground. • Perry offered a compromise, but it couldn’t help with the sun’s energy.

14. Upshot • Radioactivity & Rutherford: “Behold, the old boy beamed.” • The energy released in radioactive decay is much much higher than that produced by the burning of a similar mass of material. • This can replace heat lost by the earth and (much more important) provide a source of energy that could power the sun for much longer than Kelvin had allowed.

15. Better yet • As radioactivity came to be better understood (including isotopes & their relations, nuclear physics in general, half-lives etc.) it became evident that we could use these elements as geological clocks. • Holmes and others developed the techniques. • The upshot is the present measures of geological ages and the overall age of the earth, which have been very stable since the middle of the 20th Century.