A Hot Young Earth: My Answer to the Annual Edge Question

Each year, literary agent and science salonista John Brockman poses a question about science and gets a slew of answers from scientists, writers, and other folks. This year’s question is


Brockman got 187 responses, totaling some 126,700 words. A book, you say! Well, if this year is like previous ones, this year’s answers will indeed become a book. But in the meantime, you can browse the answers for yourself, perhaps plucking out those of your favorite people. (Fellow Discover blogger cosmologist Sean Carroll chooses Einstein’s explanation of gravity, for example.)

I found this year’s question particularly thought-provoking. Why is it that we call an equation or a theory “beautiful”? They don’t have pretty hazel eyes. They aren’t desert landscapes. I’m not sure of the answer. Scientific explanations seem to be beautiful if they give sense to confusing complexity in a very short space. Or maybe we just like the feeling we get when we consider how our puny human brains can interpret the universe.

For a lot of physicists, the beauty of an equation seems to be a good hint that it’s probably true. But I’m always a bit suspicious of beauty as a guide to the natural world. A number of contributors selected Darwin’s theory of evolution as their favorite explanation, and there’s no doubt that’s both beautiful and true. But there have been some wonderfully beautiful accounts of the natural world that have proven awesomely wrong. I was reminded of this fact while working on a new version of my evolution textbook (this one’s for biology majors). I was re-researching how scientists first came to appreciate the vast age of our planet, and realized it was a bit more complicated than I had previously appreciated. So that’s what I chose as my answer, which I’m reprinting here in full:

A Hot Young Earth: Unquestionably Beautiful and Stunningly Wrong

Around 4.567 billion years ago, a giant cloud of dust collapsed in on itself. At the center of the cloud our Sun began to burn, while the outlying dust grains began to stick together as they orbited the new star. Within a million years, those clumps of dust had become protoplanets. Within about 50 million years, our own planet had already reached about half its current size. As more protoplanets crashed into Earth, it continued to grow. All told, it may have taken another fifty million years to reach its full size—a time during which a Mars-sized planet crashed into it, leaving behind a token of its visit: our Moon.

The formation of the Earth commands our greatest powers of imagination. It is primordially magnificent. But elegant is not the word I’d use to describe the explanation I just sketched out. Scientists did not derive it from first principles. There is no equivalent of E=mc2 that predicts how the complex violence of the early Solar System produced a watery planet that could support life.

In fact, the only reason that we now know so much about how the Earth formed is because geologists freed themselves from a seductively elegant explanation that was foisted on them 150 years ago. It was unquestionably beautiful, and stunningly wrong.

The explanation was the work of one of the greatest physicists of the nineteenth century, William Thompson (a k a Lord Kelvin). Kelvin’s accomplishments ranged from the concrete (figuring out how to lay a telegraph cable from Europe to America) to the abstract (the first and second laws of thermodynamics). Kelvin spent much of his career writing equations that could let him calculate how fast hot things got cold. Kelvin realized that he could use these equations to estimate how old the Earth is. “The mathematical theory on which these estimates are founded is very simple,” Kelvin declared when he unveiled it in 1862.

At the time, scientists generally agreed that the Earth had started out as a ball of molten rock and had been cooling ever since. Such a birth would explain why rocks are hot at the bottom of mine shafts: the surface of the Earth was the first part to cool, and ever since, the remaining heat inside the planet has been flowing out into space. Kelvin reasoned that over time, the planet should steadily grow cooler. He used his equations to calculate how long it should take for a molten sphere of rock to cool to Earth’s current temperature, with its observed rate of heat flow. His verdict was a brief 98 million years.

Geologists howled in protest. They didn’t know how old the Earth was, but they thought in billions of years, not millions. Charles Darwin—who was a geologist first and then a biologist later—estimated that it had taken 300 million years for a valley in England to erode into its current shape. The Earth itself, Darwin argued, was far older. And later, when Darwin published his theory of evolution, he took it for granted that the Earth was inconceivably old. That luxury of time provided room for evolution to work slowly and imperceptibly.

Kelvin didn’t care. His explanation was so elegant, so beautiful, so simple that it had to be right. It didn’t matter how much trouble it caused for other scientists who would ignore thermodynamics. In fact, Kelvin made even more trouble for geologists when he took another look at his equations. He decided his first estimate had been too generous. The Earth might be only 10 million years old.

It turned out that Kelvin was wrong, but not because his equations were ugly or inelegant. They were flawless. The problem lay in the model of the Earth to which Kelvins applied his equations.

The story of Kelvin’s refutation got a bit garbled in later years. Many people (myself included) have mistakenly claimed that his error stemmed from his ignorance of radioactivity. Radioactivity was only discovered in the early 1900s as physicists worked out quantum physics. The physicist Ernst Rutherford declared that the heat released as radioactive atom broke down inside the Earth kept it warmer than it would be otherwise. Thus a hot Earth did not have to be a young Earth.

It’s true that radioactivity does give off heat, but there isn’t enough inside the planet is to account for the heat flowing out of it. Instead, Kelvin’s real mistake was assuming that the Earth was just a solid ball of rock. In reality, the rock flows like syrup, its heat lifting it up towards the crust, where it cools and then sinks back into the depths once more. This stirring of the Earth is what causes earthquakes, drives old crust down into the depths of the planet, and creates fresh crust at ocean ridges. It also drives heat up into the crust at a much greater rate than Kelvin envisioned.

That’s not to say that radioactivity didn’t have its own part to play in showing that Kelvin was wrong. Physicists realized that the tick-tock of radioactive decay created a clock that they could use to estimate the age of rocks with exquisite precision. Thus we can now say that the Earth is not just billions of years old, but 4.567 billion.

Elegance unquestionably plays a big part in the advancement of science. The mathematical simplicity of quantum physics is lovely to behold. But in the hands of geologists, quantum physics has brought to light the glorious, messy, and very inelegant history of our planet.

[Post-script: Thanks to responses from readers, I can see how this essay is confusing. I added some passages from the papers I cite below down in the comment thread, which I hope can clear things up a bit.]

[Update: For an up-to-date review of the age and formation of the Earth, see this paper [abstract, free pdf] For a great look at Kelvin’s work, see this piece in American Scientist or the more technical paper on which it was based (free pdf).]

[Image: Photo by Hawaiian Sea – http://flic.kr/p/8AyKnC via Creative Commons]

31 thoughts on “A Hot Young Earth: My Answer to the Annual Edge Question

  1. I have read of this story at different times and always came away a little annoyed and sad for Kelvin. He had a brilliant mind, but it seemed that the older he got, the less he was willing to take into account new data.

    He seemed, from what I know on the matter, to be of the thought that all that could be known was soon to be known. That there was no need to look at other people’s silly new ideas. While I hope I am somewhat wrong on this, if it is accurate, then I see it as a ‘hardening’ of a mind that, because of the name attached, became as Aristotle was before him. Someone to be cited but not questioned. He was made worse by the fact that he still lived and was harsh of a critic to anything new and far to little of the scientific community was willing to stand against him. Either because of their own pride or fear of being ousted themselves, I am unsure.

    Whatever the case, I am glad to see your take on the matter. It is a good lesson in being open to new data as well as remembering that the universe is, as J.D.S. Haldane put it “[…]not only queerer than we suppose, but queerer than we can suppose”, and to be honest, I rather like it like this. It always gives me new often stunningly beautiful new ideas to wonder over, even if they can get a bit messy at times.

  2. I like that.

    Kelvin was using his theories correctly but getting the incorrect result because of unknown variables. It shows the dangers of assuming you are correct because the theory looks good, the need to pay attention to all of the evidence/data. And how new data can lead to new understanding either through breaking a theory or breaking an answer.

  3. Hmm… First you say that Kelvin’s calculations based on a static ball of rock gave the Earth’s age as 10 million years. You then say that “This stirring of the Earth” increases the flow of heat from the interior “It also drives heat up into the crust at a much greater rate than Kelvin envisioned.”
    So, according to your view, Kelvin’ age of the Earth would be too long and so the Earth must be even younger! Obviously, the evidence shows it is actually much older, so your description of the source and transport of heat within the Earth is flawed.
    I understand that current thinking is that the heat is generated by a combination of radioactive decay and gravitation (The interior is still in the process of differentiating between heavier and lighter components).
    Any actual geologists here care to chip in?

    [CZ: It may help for me to quote a lengthy passage from the American Scientist article I cited. The authors are writing here about a scientist named John Perry realized in the late 1800s why Kelvin might be wrong–even though plate tectonics had yet to be discovered:

    Perry discovered the flaw in Kelvin’s argument in 1894 but, reluctant to embarrass his patron, tried first to convince Kelvin face to face and by private correspondence. He was brushed off, either because Kelvin did not understand Perry’s approach or because he was not interested. In 1895, therefore, Perry decided to go public, and he wrote to the journal Nature: “I have sometimes been asked by friends interested in geology to criticize Lord Kelvin’s calculation of the probable age of the earth. I have usually said that it is hopeless to expect that Lord Kelvin should have made an error in calculation.” Instead of focusing on Kelvin’s math, Perry suggested that one should examine his assumptions.
    In Kelvin’s model, the thermal gradient near the surface of the Earth (or, in the thought experiment given above, of the turkey) drops as the cooled outer skin thickens with age. If the Earth were much older than about 100 million years, this skin would be so thick that the thermal gradient would be much lower than is observed. Perry realized that there is a simple way to stop the skin from thickening: He proposed that heat might be transferred much more efficiently in the interior of the Earth than at the surface. If this were so, the deep interior could provide a large store of heat, which would keep the surface temperature gradient high for a long time, and Kelvin’s estimate of the age of the Earth would be too low, potentially by a large multiple.
    Perry had various suggestions as to how this might happen, but, for our purposes, his most important argument was that convection in the fluid, or partly fluid, interior of the Earth could transfer heat much more effectively than does diffusion. He pointed out that if only a thin outer skin of the planet is solid and if the rest of the Earth is a convecting fluid, then the interior would be well mixed and at the same temperature throughout. Perry’s model thus replaces the thought-experiment turkey with a turkey-sized bottle of, say, hot cider. Only the outer few millimeters of this object are solid (the glass of the bottle), and convection churns the interior. Thus the temperature gradient at the surface can stay high for a very long time.
    Perry’s calculation shows that if the Earth has a conducting lid of 50 kilometers’ thickness, with a perfectly convecting fluid underneath, then the measured thermal gradients near the surface are consistent with any age up to 2 billion or 3 billion years. Recognizing that heat transfer in the mantle cannot be perfectly efficient, Perry subsequently modeled the deep interior as a solid with high “quasi-diffusivity,” His results agreed with the original simple calculation in suggesting that the Earth could be several billions of years old. Full calculations of convection in the mantle (which were impossible until the advent of computers) confirm that Perry’s reasoning was sound.
    In other words, Perry was able to reconcile a physical calculation of Earth’s thermal evolution with the great age that geologists required. Perry needed nothing more than to introduce the idea that heat moved in the deep interior of the Earth more readily than it moved in the outermost layers. Yet to this day, most geologists believe that Kelvin’s (understandable) mistake was not to have known about Earth’s internal radioactivity.]

  4. Alas, I thought I understood exactly where this essay was headed, but I ended up very confused.

    In your essay you assert that Lord Kelvin’s real error was assuming earth so be solid when the reality was that the earth has various forms of flow going on, including both viscous or slow solid flow within the mantle and true liquid flow in the core.

    But convection always, to my best knowledge, _speeds up_ heat dissipation rather than slowing it down. I’ve scratched my head and just cannot figure out why invoking liquid and viscous flows would do anything but make Lord Kelvin’s estimate _too long_, rather than too short.

    I don’t mean to nitpick, but might you be able to address this point? I’ll be the first to admit I may be completely missing something, but if so, I’m darned if I know what it is.

    Is it possible that this is still a mystery? I’m pretty sure that heat budgets for certain moons such as Saturn’s Enceladus (http://www.space.com/11063-saturn-moon-enceladus-heat-power.html) remain more-or-less unexplained, or at least not explained well. Is this true even for Earth?

    [CZ: I hope the passage I quoted in the previous comment helps clear things up. It’s not just a matter of whether convection speeds up heat transfer. It’s that Kelvin assumed that the planet was solid, when it’s not. His calculations of heat flow fall apart as a result.]

  5. I just read your Google+ posting… Now I think I get it! Here’s my reading of what you just said: Kelvin realized the interior would stay hot for billions of years, but his calculations showed that the Earth’s skin would cool off much faster. His error was not realizing that the Earth had a circulatory system that was constantly pushing that huge store of internal heat up into the skin, keeping it warm just like our hearts keep our skin warm. Is that roughly right?

  6. Perry’s model was as “wrong” as Kelvin’s. The interior of the earth is not well mixed. Radioactivity affects Kelvin’s calculations in two ways. First, it adds another source of heat, but most of earth’s internal heat does not come from radioactivity so that is not the largest effect. Radioactivity is concentrated in the earth’s crust to a large extent, which means the measured heat flow at the surface does have a large component due to radioactivity–and that is the measurement that Kelvin was assuming was all heat radiating from earth’s interior.

  7. The reason Kelvin did not abandon his argument against the old age of the Earth crust after radioactivity was discovered is that the argument was really based on much more reliable upper limit on the age of the Sun. It is this argument – based on the idea of Helmholtz that Sun derived its luminous energy from slow gravitational contraction – that was truly elegant. Indeed, this estimate in its simple form is still taught to students in astronomy classes and can be found in astronomy textbooks. At the time of Kelvin, no other physical source of energy required to sustain Sun’s luminosity except for gravity was conceivable. Radioactivity did not change this argument, as it could not provide energy required to power the Sun.

    The Kelvin-Helmholtz upper limit on the Sun’s age was only put to rest with discovery of thermonuclear reactions and development of working model of nucleosynthesis in the central region of the Sun some 40 years after Kelvin’s death.

    From Kelvin’s perspective then, the quibbling about his cooling Earth model was of minor consequence because a much stronger argument of the Sun’s young age was still there. This point is discussed concisely in this paper: http://www.es.ucsc.edu/~rcoe/eart206/Stacey_Kelvin_JGR00.pdf

    In the broad sense, the elegant argument of Kelvin and Helmholtz about age of the Sun was not a failure. In combination with radioactive dating (developed after Kelvin’s death), it led physicists to search for a completely new, alternative source of solar energy, effort that culminated in development of general theory of stellar nucleosynthesis and stellar structure in 1940s and 1950s. In other words, the argument was so elegant and powerful that only a completely new physics could resolve the discrepancy with the geological record and radioactive dating.

  8. The essence of the confusion it seems : CZ referred to the ‘Earth’s current temperature’ and ‘a hot Earth’ etc etc, meaning the SURFACE temperature, but it was very easy (for this non-geologist) to read that as meaning the CORE temperature.

    Hope that’s helpful… very much enjoyed the post.

  9. Hi Carl,
    I read the excerpt you kindly provided, but I still have a question…
    A convective interior (with or without a solid core) would still transport heat more efficiently to the surface – and hence out into space. Whilst his calculations seem to match the near-surface temperature gradient that we observe and provide for an age of the Earth on the order of billions of years, it leaves a problematic (to my non-expert thinking anyway) variable – the initial heat content of the Earth immediately after it formed.
    For a convecting body to continue radiating (with much greater efficiency than a solid body) for this large period of time, would not the initial temperature have been incredibly high (In the absence of on-going heat generating processes like decay and gravitational collapse)?
    I must go and do some Googling! 🙂

  10. Interesting choice indeed.

    @ Terry:

    I think you got it.

    Also, you asked in #5 about Earth heat budget, and indeed it is still a bit loose, IIRC. Here is how measuring neutrino fluxes may, quite recently, have pinned down the heat contribution from radioactivity:

    “Previous research has shown that Earth’s total heat output is about 44 terawatts, or 44 trillion watts. The KamLAND researchers found roughly half of that — 29 terawatts — comes from radioactive decay of uranium, thorium and other materials, meaning that about 50 percent of the earth’s heat comes from geoneutrinos.

    The researchers estimate that the other half of the earth’s heat comes from primordial sources left over when the earth formed and from other sources of heat.”

    @ Jim:

    I don’t think the estimated heat content is a problem, since already Perry got close to the actual age.

    Mind that differentiation, mantle convection and plate tectonics takes geological time to get going. An astrobiology lecture I have estimated it like this:

    Differentiation ~ < 0.1 billion years after formation (af). First diapir (mantle convection bulge) ~ 0.1 billion years af. Transient period with rigid crust (lid) before onset of plate tectonics from ~ 0.1 to ~ 0.6 billion years af.

    Then, in these models, you have an increase of heat flow before it starts to go into a secular regime slowly decreasing over time. The max, if it factually exists, is IIRC not pinned down, but the models place it ~ 2 billion years af.

    Maybe you can use something like Perry's secular model after the maximum, in which case the estimated time agrees perfectly.

  11. This is a facinating subject!

    Perry’s age-results would, I believe, still involve a very large initial heat quantity if the ‘secular regime’ is dominant – but I note from your reply to Terry, that you acknowledge that fully half of the Earth’s heat is the result of radioactive decay. That is today’s figure. The half-life of Uranium 238 (>99% of all Uranium in the rocks) is 4.47 billion years, so in the Earth’s early years, the heat generated by radioactive decay would be close to twice that of today. This radioactivity, constantly ‘topping-up’ the interior heat of the Earth, eliminates the need for the very large initial heat content of the early Earth in Perry’s purely convective/primordial-heat model.

  12. While there is no need for a very large initial heat content, the early earth was very likely hot anyway, simply from the gravitational energy released by its accretion.

  13. 10. R Says:
    January 16th, 2012 at 4:32 am

    4.567 billion years ago – What a joke!!!!!!!!!!!!!!!!!!!!

    Umm, R, do you mean that it could be much older?

  14. R Says: “4.567 billion years ago – What a joke!!!!!!!!!!!!!!!!!!!!”

    What!? You were expecting the 6,000 years of the bible?

  15. I think we’re looking at ,but still overlooking the reason our planet has a very big and very hot interior. Travel back to primordial earth when so many exoplanets met their demise, and we see the mars sized planet theia hitting the earth at about a 45 degree angle. Best models show the earth and theia had thick crusts, but they were blown away as molten silicates after the impact. via accretion, the earth robbed theia’s core and heavy(er) elements, leaving the silicates to form our very large moon. The earth came out of the crash an absolute winner. We do have a thinner crust, a big hot core and lots of heavy elements, while the moon has a very small core and very few elements beyond Si. And the result provided 23 degree tilt on axis gives our planet four lovely seasons. Our very big moon has a great influence on plate tectonics. You may debate this, but most scientists don’t. Yes, radioactive decay is a major player in our hot and churning interior. But the ying and yang of the moon’s attraction also causes much frictional heat. And our now thinner crust allows plate tectonics, earthquakes and volcanic activity to be very active and ever evolving. Earth has the largest moon in relation to planet size in our solar system.
    We are losing our grip on the moon to the tune of about an inch per year. So in a couple of billion years when the radioactive storehouse is playing out and the moon has far less influence via friction, then this world will be much different. How different is debatable also. But that’s justapose OUR star continues to behave. So yes, the sun and even the other planets, especially jupiter play a friction role that influences the heat of our terra firma. Now it’s your turn debate or dispute all or part of what I have written. Kelvin got a lot wrong, but the second law of thermodynamics is a prize. Remember, until recent times there were those who were steadfast in their belief that the universe is filled with ether, and those beliefs are not ancient.

  16. The same influence that Jupiter has on Europa which allows a liquid ocean under the ice. Friction from gravitational attraction.

  17. Hindu Science, determined around 3102 BC, that the earth’s age is 4.32 billion years. Western Science, as it continuously refines its calculations, is slowly approaching the Hindu Science figure.

  18. “It turned out that Kelvin was wrong, but not because his equations were ugly or inelegant. They were flawless. The problem lay in the model of the Earth to which Kelvins applied his equations.”

    Ingenious! Wrong model, wrong conclusions! Perhaps we should at least examine the scientific evidence for a young earth (“creationist”). Rather than presumptuously throwing out that model as impossible, reconsider it as a possibility despite the cries of those opposed to the idea. After all, if science only listened to the opinions of current consensus rather than critically considering reasonable alternatives, we would not have modern science at all!

  19. I have a problem with everyones static presumptions. The fact of the matter is that all of the explainations presume that the heat source within our planet came from it’s original formation and that only cooling has taken place since then (and as suggested when these theories seemed inconsistent, perhaps radioactivity explained thr extended heat source, which it undoubtly does). Therefore, it would seem that determining the age of the earth would be as simple as applying Kelvin’s thermodynamic theories to a stable cooling mass in space. I would not presume to argue the age that has been placed upon our home, since carbon dating provides irrefutable evidence of the age of the oldest terrestrial material in existence at around the 4 billion mark (for this example I don’t think I need to be worried about absolute precision). The part I have a problem with is that the Earths temperature is presumed to have been stable and continually decreasing throughout all these billions of years. It would seem to me that the example of hot Turkey or even the glass bottle is based on this assumption and is completely misleading. I believe an enormous can of paint would be a far better example of the convective flow of heat escaping from our sphere. Here is my explanation of this example; when you take a can of paint of one colour and add a second contrasting colour, it seems to take forever for the swirl of the added colour to finally completely disappear in the helical spiral that appears as you are stirring the paints with a stick. When you enlarge this can of paint to make it the size of Earth then you must also enlarge (or increase) the amount of time it will take to complete the process. However, this model would still presume that the planets heat was at a maximum during its creation and steadily cooled since then. But the fact of the matter is that we are sitting on a gigantic ball of Iron (mainly), along with all the other less common elements churning around inside of an enormous ball of rock. We travel around the sun the whole while spinning on a tilting axes with a large agitator (the moon) providing a very large paddle to help keep stirring this broth constantly. The result (it would seem to me) is that you have an extremely large body of abrasive elements constantly grinding away at each other that provides a constant heating effect that will continue to produce more heat nearly indefinitely. Thus, any model of thermodynamics used to explain the age of the planet will be flawed unless it takes into account that the Earth is not just simply a big Turkey that has been set out to cool! It is an enormous friction generator that has been constantly grinding away (creating internal heat) since it’s beginning and will continue to do so until the moon flies off and the planet stops spinning or old Sol goes supernova, whichever comes first!

  20. The estimate I have seen for tidal heating of the earth’s interior (as opposed to tidal energy dissipated in oceans) is 200 GW. This is small compared to geothermal heat flow (47 TW).

  21. Kelvin, a religious Scottish Presbyterian, was a declared enemy of Charles Darwin’s theory of evolution. His friend and colleague engineer Fleeming Jenkin collaborated with Kelvin in having Earth and Sun papers read at British Society for the Advancement of Sciences meeting. Kelvin’s original Sun paper, if I remember correctly, came out about 1858 and as stated above, the earth paper was published in 1862. In 1867 Jenkin, who shared Kelvin’s views, published an anonymous negative review of Darwin’s Origin of Species that touched both on the difficulties with natural selection (using a disturbingly racist thought experiment of a type typical of the epoch) and presented Kelvin’s conclusions of the age of the earth, less than 500 million but perhaps as little as 20 million years. Darwin was apparently unaware of Kelvin’s calculations and in later editions of the Origin, while continuing to stress natural selection, placed greater emphasis on Lamarckian inheritance to speed up evolution. As time passed Kelvin and his close associates reduced the time available for life on earth, and toward the end of the 19th century were defending spans of 10 to 20 million years. These conservative estimates were widely broadcast and even Mark Twain mentioned them, and the authority of Kelvin, in a 1903 essay.

    Kelvin seemed particularly incensed with the idea of evolution by natural selection. He also defended panspermia, the idea that pieces of life (moss, for example) could have been knocked off some other world and transported to earth. In a provocative recent paper Leonard Wilson (2010. “Religious assumptions in Lord Kelvin’s estimates of the earth’s age.” Earth Sciences History, 29: 187-121) suggests that Kelvin knew almost from the beginning that the assumptions of his temperature model were wrong, that empirical data denied that the earth was solid through to its core (just looking at volcanic lava suggests that it isn’t). The unflattering suggestion is that Kelvin faked his model, either through self-delusion or as a willful hoax, to defend his faith from the unbelief that Darwinian evolution had inspired. As Wilson put it, “Kelvin’s primary aim was to destroy Charles Darwin’s theory of evolution by natural selection . . .”.

  22. A question : Venus is similar in size to earth; why no evidence of plate tectonics on venus?
    There is evidence for tectonics on mars ; is there any calculation as to when it stopped on mars?

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