A broader picture of Rutherford’s geophysicists

In his interesting article “Rutherford’s Geophysicists” (Physics Today, July 2010, page 42 ), Greg Good says, “Rutherford and others believed that the heat given off by radioactive elements derailed the arguments that Lord Kelvin had used to support a youthful Earth and to critique Charles Darwin’s theory of evolution by natural selection.” Given that this belief undoubtedly influenced the development of geophysics, I find it interesting that the primary error in Kelvin’s estimate was not his neglect of a heat source but rather his neglect of any means other than conduction for getting heat out of Earth. Indeed, if Earth had zero radiogenic heat sources, it would very likely convect, slowly eliminating the great heat produced from gravity when the planet formed. Kelvin’s tens of millions of years—roughly the typical age of the ocean floor—would still be a reasonable estimate for the conductive diffusion time of heat through the thermal boundary layer. This is not something related to Earth’s total age, because the mantle has overturned many times in Earth history.

At the time Kelvin proposed his argument, the fact that much of Earth is solid had not yet been well established. Therefore, the idea that Earth’s deep interior convected was not unreasonable, and later arguments about the ability of solids to flow would not have been a problem. He could have obtained a roughly correct answer for Earth’s age by merely dividing the planet’s total heat content by its total heat output; that calculation yields around 10 billion years for current estimates of the input numbers, and it would have been a perfectly reasonable thing to do for the understanding of cosmogony at that time. Of course, Kelvin had the misfortune to get a similar answer for the Sun’s age as he obtained for Earth; the method he used roughly works for Earth but fails badly for the Sun because he was understandably unaware of fusion.

Another great scientist, Harold Urey, is responsible for posing the question of how much of Earth’s heat flow comes from radiogenic heat production rather than secular cooling. The current estimate for the fraction derived from radiogenic heating is around one-half; the reason for that value is still hotly debated.