Lord Kelvin's Heat Loss Model as a Failed Scientific Clock
By Matthew Rognstad
Some of the great scientists, carefully ciphering the evidences furnished by geology, have arrived at the conviction that our world is prodigiously old, and they may be right but Lord Kelvin is not of their opinion. He takes the cautious, conservative view, in order to be on the safe side, and feels sure it is not so old as they think. As Lord Kelvin is the highest authority in science now living, I think we must yield to him and accept his views.
-Mark Twain, Letters from the Earth (Burchfield, ix)
When Charles Darwin set sail on the H.M.S. Beagle on December 27, 1831, he took with him a copy of Charles Lyell's Principles of Geology. Lyell was one of the most outspoken proponents of the idea of uniformitarianism, which held that the same geological processes occurring today have existed largely in their present state throughout all of geologic time. From the uniformitarian perspective, it was obvious that the Earth must have existed for an utterly immense period of time; the measured rates of geologic change, e.g. erosion and uplift, were far too slow to create the modern shape of Earth's surface without millions and millions of years. Lyell's argument for age not only convinced Darwin, but it also greatly influenced his thinking on the origin of species by providing a timescale large enough to make natural selection plausible (Lewis, 19). Lyell carefully avoided attempts to quantify Earth's age (Lewis, 25). This led some to conclude that he was actually asserting that Earth was infinitely old. Darwin, however, was not so prudent; in the first edition of his Origin of Species, he estimated that it took 300 million years to erode the Weald, a chalk deposit in southern England (Hallam, 106; Lewis, 25). Though Darwin only intended to provide a rough estimate in order to emphasize the point, his statement became the subject of much controversy (Hallam, 107)-so much so that it was modified and eventually removed entirely from later editions (Hallam, 113; Lewis, 26).
Among those who objected to Darwin's argument was William Thomson, a young physicist from Glasgow University who would later become Lord Kelvin (Lewis, 34). Kelvin was widely regarded as the best physicist of his time; his expertise on thermodynamics was particularly revered (Dalrymple, 33; Hallam, 108; Lewis, 34). It made sense that Kelvin would approach the age question from the perspective of his primary field of study. Accordingly, he thought Darwin's estimate of the Weald chalk erosion to be "absurd" (Hallam, 108). Keep in mind that Darwin's 300 million years only addressed the erosion of the chalk; it did not encompass the time required for the chalk to be deposited. Nor did it address the great majority of geologic time since the Weald sits at the top of the geologic column. The net result of the argument was that Earth must have existed for billions of years (Lewis, 25) or, in other words, be of almost limitless age (Hallam, 108). Kelvin's estimates of the age of the Earth, and his attendant attacks on Darwin and uniformitarianism, were seen as dispositive for nearly five decades (Dalrymple, 29; Hallam, 108). The following explanations (1) of Kelvin's method, (2) its significance through history, and (3) modern invocations of Kelvin by creationists will help shed light on the larger conflict over the age of the Earth.
Kelvin's primary attack on geologic dating was that measurements of the rates of geologic processes were highly uncertain, if it was possible to measure them at all (Hallam, 110). Accordingly, Kelvin sought to apply the knowledge of physics to the problem. Given that temperature increases the further one descends below Earth's surface, Kelvin concluded that Earth was slowly cooling. He set out to calculate the time required for the Earth to cool, and thereby solidify, from an initially molten state. The idea that Earth had begun as an incredibly hot sphere of liquid dates back to Descartes and Leibnitz. This assumed initial condition was the linchpin for Kelvin's entire method (Hallam, 110). Bits of material at the surface would sink before solidifying, creating convection currents that kept the Earth at a uniform temperature until solidification began at the core (Hallam, 110; Knopf, 445). Kelvin needed to know: (1) the temperature at Earth's core, (2) the temperature gradient with regard to depth below the surface, and (3) the thermal conductivity of rocks. The gradient was established to be around one degree Fahrenheit for every fifty feet. Kelvin made his own measurements of conductivity. The problem was determining the temperature at the core. This is where Kelvin's theory of solidification enters the picture. Because the core was thought to be solid rock, its temperature could not exceed the melting point of rocks (Hallam, 110). He constructed the following equation:
dθ / dx = S / h √(π t)
The temperature gradient is expressed by dθ / dx; h is the thermal conductivity; x is the distance below the surface, and θ is the temperature (Holmes, 445). In 1862, Kelvin arrived at a likely age of 100 million years. Because of uncertainties in the data, the lower and upper limits were 20 million and 400 million years (Dalyrmple, 26; Hallam, 111).
The historical impact of Kelvin's judgment was profound. The timeframe he provided was too short for observed geological processes to create Earth's current geography (Knopf, 16) and did not allow enough time for evolution to explain the diversity of life (60). Though Kelvin made several blistering attacks on geology, most geologists were too intimidated by Kelvin's stature to defend themselves (Lewis, 35). Dalrymple explains that Kelvin was one of if not the single most imposing scientific figure of the day (33). Physics was then a more established and prestigious field than geology (Hallam, 108). Kelvin derived his estimate from quantitative and repeatable measurements, physical principles of natural laws, and elegant math (Dalrymple, 33). That method, combined with his arguments about the uncertainty of geologic data, provided Kelvin with a tremendous amount of ethos. He was enthusiastic and authoritative, and this made him an exceptionally difficult opponent for Lyell and Darwin (Hallam, 108); Darwin referred to Kelvin as his "sorest trouble" (Dalrymple, 113; Lewis, 35). The end result was that most scientists sought agreement rather than conflict with Kelvin (Lewis, 36). Archibald Geikie (Hallam, 112), James Croll (112, 116), Lyell (116), and Samuel Haughton (118) all adjusted their theories to make allowances for Kelvin. Additionally, P.G. Tait (115), T. Mellard Reade (117), Clarence King (119), and John Joly (119) all reached conclusions concordant with Kelvin through their own methods.
Eventually, however, criticism started to mount, and Kelvin became increasingly dogmatic in his assertions. Thomas Huxley attacked Kelvin's underlying data. Plugging bad values into a perfect equation will result in bad results-in modern parlance, "garbage in, garbage out" (Hallam, 115). Osmond Fisher, a pioneering geophysicist, challenged Kelvin's assumption of a solid Earth. If the interior were plastic, convection currents would fundamentally undermine Kelvin's entire model (120). Geikie and Croll rejected the arrogance of the mathematical physicists and argued that there must be some flaw in Kelvin's reasoning (121). Huxley (115) and Fisher (120) also leveled charges of arrogance. G.H. Darwin attacked Kelvin's ideas about tides retarding Earth's rotation; the underlying charge was that Kelvin attributed far too much certainty to speculative findings (121). John Perry, an accomplished mathematician and Kelvin's former assistant, also attacked Kelvin's assumptions, arguing that the mantle was partly liquid, and therefore conduction-the core of Kelvin's model-was less responsible for heat transfer than convection (121).
Kelvin was forced to respond and did so in an 1897 address. Based on new measurements of the melting point of rocks, Kelvin adjusted his estimate down to 20 million years. Based on this new data, he was increasingly confident and omitted the cautionary statements from his earlier works (121). Geikie, who had initially accepted Kelvin's 100 million year estimate because he believed geologic processes could complete their work within that timeframe, now turned on Kelvin when it became obvious that 20 million years was far insufficient and declared the independence of geologists from the autocratic pronouncements of the mathematical physicists like Kelvin and Tait (122). T.C. Chamberlain, a distinguished glacial geologist, also reacted strongly against Kelvin's updated estimate. He argued that the Earth had never been a molten sphere; rather Earth had formed from the slow accumulation of solid material like asteroids. There was good reason to doubt Kelvin's fundamental assumptions, and therefore phrases like "certain truth" (123) and "no other possible alternative" (Dalrymple, 36) were completely out of line. Most importantly, he attacked Kelvin's assumption about a closed system of dwindling initial heat by offering the possibility that the then-unknown internal structure of atoms could contain massive amounts of potential energy (Dalyrmple, 36; Hallam, 123).
That prescient comment foretold the coming of radioactivity and atomic physics. Once it was discovered that radioactive isotopes are abundant in rocks and that radioactive decay releases tremendous amounts of heat, Kelvin's assumption of a closed system and dwindling initial heat proved to be demonstrably false (Dalrymple, 37; Hallam, 124; Knopf, 16; Lewis, 47-48). Kelvin's assumption of a solid Earth and heat transfer only by conduction also proved incorrect; the mantle does flow, and convection is the key method of heat transfer within the Earth (Dalrymple, 37). As Burchfield explains, radioactivity undermined the foundations for virtually all of Kelvin's dating work (218). Lord Kelvin initially rejected the idea that radioactivity could emit significant heat, but he publicly abandoned this theory at the British Association Meeting of 1904 (Lewis, 55). In a debate two years later, however, it was clear that he never truly accepted radioactivity as the primary source of Earth's internal heat (55). Accordingly, Kelvin never published a retraction of his overall theory, though he did privately concede to J.J. Thomson that the discovery of radioactivity rendered several of his assumptions unworkable (Hallam, 124).
In spite of the flaws in his age models, modern creationists invoke Kelvin with surprising regularity. Usually he is presented as a "creation scientist" (Answers in Genesis; Christian Answers Network). There is, however, some dissembling about what "creation scientist" means. Does it mean a scientist who happens to be a Christian? A scientist who believes in biblical literalism and a young Earth? Or maybe a Christian whose work focuses on attempting to scientifically support the idea of a young Earth? Kelvin was undeniably a Christian, but he certainly did not believe in the literal truth of the Bible or in a young Earth. He specifically applauded geologists for destroying the validity of dating methods based on the Mosaic chronology (Hallam, 114). The more creative invocations of Kelvin focus on his attacks against evolution. As Paul Ackerman argues:
Lord Kelvin tore the evolutionists' position to shreds with simple and straightforward physical arguments that the earth and solar system were not old enough for life to have arisen by Darwin's proposed evolutionary process... Lord Kelvin had the theory of evolution on the ropes and had seemingly dealt the knockout blow. What happened? The discovery of atomic radiation changed the whole picture. Evolutionists suddenly took new courage as the phenomenon of atomic radiation seemed to provide the necessary answer to Kelvin's challenge.
Ackerman then goes on to argue that the sun is not powered by nuclear fusion. Another creationist, David Coppedge, gets even more creative:
He often expressed awe at the beauty, design and orderliness of creation and natural law. But he also recognized the rise of Darwinism both for its bad science and evil influence. Accordingly, he contested the arguments of Huxley and others that the earth was millions of years old. In a well-known interchange with Huxley, he calculated mathematically that the earth and the sun could not be that old, based on his own knowledge of thermodynamics. His argument for a maximum age for the earth was made before the discovery of thermonuclear reactions, and has been largely discounted unfairly on that basis. (In actuality, the age of the earth and sun are difficulties for evolution even today, and his arguments are largely ignored.)
Actually Kelvin did believe the Earth was millions of years old, just not as many millions as Darwin initially thought. Some creationists even try to affirm the validity of Kelvin's method as disproving evolution. John Woodmorappe argues that Kelvin still disproves Darwin because radioactivity can supposedly only account for sixty percent of Earth's internal heat. Kelvin's entire method was based on assumptions that Earth is a closed system, is uniformly hot throughout, is made of the same material throughout, and is completely solid. Every one of those assumptions has proven to be wrong. Radioactivity disproves Kelvin even if it cannot explain all the heat inside the Earth. In fact, Dalrymple points out that radioactivity is not the whole story when it comes to Earth's temperature. Heat generation and loss are incredibly complex and are not attributable to any single factor (Dalrymple, 37). Even if radioactivity were the only factor, then based on the amount of heat it produces according to young Earth creationists, Earth is still 2.7 billion years old (Woodmorappe). Making that argument or endorsing Kelvin's 20-400 million year age does nothing to support the idea of a 6,000 year old Earth. That is probably why these creationists seldom mention Kelvin's estimate of the age of the Earth; they just say he attacked Darwin and an old Earth, and let the people reading their material come to their own incorrect conclusions. The tendency is to focus on Kelvin's negative attacks on biology and geology while willfully ignoring his affirmative arguments about the age of the Earth. By using Kelvin to indict several natural sciences while asserting the 6,000 year time scale that Kelvin explicitly rejected, Ackerman, Coppedge, and Woodmorappe purposefully misrepresent one of the leading scientists of the 19th Century in order to support a narrow ideological agenda.
Lord Kelvin exerted profound influence in the debate over the age of the Earth. His theory dominated the scientific debate for over forty years. By applying scientific principles to attempts to quantify the date of Earth's formation, he opened the doors to this important area of scientific study.
- Ackerman, Paul D. 1986. Is the sun shrinking? Chapter 6 in Ackerman, Paul D. It's a Young World After All. http://www.creationism.org/ackerman/AckermanYoungWorldChap06.htm Last updated: 2002. Accessed: October 18, 2005.
- Answers in Genesis. No date. Creation scientists and other biographies of interest. http://www.answersingenesis.org/Home/Area/bios/default.asp Accessed: October 18, 2005.
- Burchfield, Joe D. 1975. Lord Kelvin and the age of the Earth, Science History Publications, New York, 260 p.
- Christian Answers Network. 1998. Do real scientists believe in creation? http://www.christiananswers.net/q-eden/edn-scientists.html Accessed: October 18, 2005.
- Coppedge, David F. 2000. The world's greatest creation scientists. http://creationsafaris.com/wgcs_3.htm Accessed: October 18, 2005.
- Dalrymple, G.Brent. 2004. Ancient Earth, ancient skies: The age of the Earth and its cosmic surroundings, Stanford University Press, Stanford, California, 247 p.
- Hallam, Anthony. 1989. Great geological controversies, Oxford University Press, New York. 244 p.
- Holmes, Arthur. June 1931. Radioactivity and geologic time. Part IV (pp. 124-459) in Knopf, Adolph Schuchert, Charles, Kovarik, Alois F., Holmes, Arthur, & Brown, Ernest W. Physics of the Earth IV: The age of the Earth, National Research Council of the National Academy of Sciences, Washington, D.C., 487 p.
- Lewis, Cherry. 2000. The dating game: One man's Search for the age of the Earth, Cambridge University Press, Cambridge, United Kingdom, 253 p.
- Woodmorappe, John. April 4, 1999. Lord Kelvin revisited on the young age of the Earth. Answers in Genesis Technical Journal, 13(1). http://www.answersingenesis.org/tj/v13/i1/kelvin.asp Accessed: October 18, 2005.