Nuclear Fusion, Episode 1: Darwin and Kelvin

In 1859, Charles Darwin published “On the Origin of Species”, the book that first set out what has developed into the modern theory of evolution. As discoveries go — well, not for nothing have people called this the greatest idea that a person ever had. He was famously inspired by a trip to the Galapagos islands, where he observed a dozen different species of finches on each of the individual islands. Perhaps less famously, he was influenced by Malthus, as well. Loyal listeners will recall that we discussed the question of “overpopulation” and the “Malthusian catastrophe”, where human demands on the Earth outstrip the availability of resources, as part of our series of episodes on the apocalypse. The bleak, Malthusian view of the world — published over a decade before Darwin was born — was influential for Darwin when he was trying to figure out just why it was that so many different species seemed to exist, to appear and disappear, and to change. At this time, he already had an idea that “there is a force like a hundred thousand wedges, trying to force every kind of structure into gaps of nature… or thrusting out the weaker ones.”

It was then that he happened to read Malthus, and noted:

“In October 1838, that is, fifteen months after I had begun my systematic enquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species. Here, then, I had at last got a theory by which to work…”

The genius of this idea is probably that it’s so simple — if there’s a population that varies a lot — like animals and plants — and a selection process — the ability to survive and reproduce — then you’d expect those with favourable characteristics to be selected. Then if they pass on their characteristics to new generations, the population will gradually change to have these favourable characteristics. This doesn’t just apply to biology; even now, this process is being used by those in the evolutionary AI field to generate better algorithms by tweaking parameters and selecting the ones that work. It’s so simple as to almost seem obvious, yet so profound — it can explain a vast array of phenomena in the world that previously confounded thinkers. The way things were so adapted didn’t just need intelligent designers to explain it: it almost provided the main evidence that there was an intelligent creator.

But this profound idea had profound consequences. Darwin was reluctant to do more than hint at it in his first book, but the obvious implication was that humans had themselves evolved — and perhaps from animal ancestry. The timescales required for evolution meant that the Earth must be hundreds of millions of years old, at least. It was not impossible to reconcile the theory of evolution with the existence of a creator who set it all in motion — that was possibly the way that Darwin felt, although he described himself as agnostic. But it was certainly impossible to reconcile it with a literal reading of Genesis, where Earth is created in a week in 4004BC and God painstakingly designs every single species that exists… and, I guess, chucks some dinosaur skeletons in the ground to test our faith. More than the religious dogma that evolution contradicted, though, it was another great blow to our traditional view of ourselves. Copernicus and others had pointed out that the Earth wasn’t at the centre of the Universe; now, Darwin was saying that the human species wasn’t particularly special.

We’d gone in a few centuries from being created in the image of the divine God, the Universe revolving around us… to smart apes occupying an evolutionary niche on a not-particularly-special planet in an obscure corner of a vast Universe. It’s bound to be a blow to the ego when you look at it like that.

These consequences upset and disturbed Darwin too; he held off from publishing the work for years, and in his letters at the time of publication, he begged friends to see if there wasn’t merit in his theory and warned them that they might not like it. And, of course, because it’s science, people were immediately trying to take him down and pick apart his idea. And this is where the title of this episode comes in, because one of the scientists who tried to contradict Darwin presented a little paradox that seemed to make evolution impossible. It was the paradox that has occurred to every curious child: why does the Sun shine?

It wasn’t a child trying to take Darwin down, though, but Lord Kelvin. He was most famous for his contributions to thermodynamics, which is why they named the scale of absolute temperature after him, and I’m sure loyal listeners will recall we talked about him in the Second Law episode. So it’s natural that he took a thermodynamic approach to the problem of why the sun shone, for which you need to answer — where does the energy come from?

First Kelvin dismissed the possibility that the Sun might be burning some kind of fuel — no known fuel would provide you with that amount of energy for that long before burning out. If the Sun was made of something burning, its fuel must contain thousands of times more energy than anything known on Earth. Then he considered that perhaps the Sun’s fuel was continually replenished by meteorites, but this quickly became untenable, too; there just weren’t enough meterorites crashing into the Sun to refuel it.

So he was left with the conclusion that when the Sun had formed, it had a lot of energy; it was now radiating that energy away into space and cooling down. But where did that original energy come from? Kelvin thought that the energy that the Sun radiated came from a gravitational collapse. In many ways, you can see why he thought this– most of the astrophysical things we see are sculpted by gravity, and it seems to be the dominant force on those length-scales. So the idea was that all of the energy that was constantly radiating from the Sun came from gravity — from when the sun originally collapsed. As the stuff that formed the Sun collapsed into a star, gravitational potential energy was being converted into kinetic energy; and this was then radiated away from the Sun as heat. Since you can calculate how much gravitational potential energy is released when a sphere forms — it’s actually a really standard physics calculation — Kelvin could tell you how much energy the Sun should have from collapsing.

Since the Sun was clearly radiating away its energy at an astonishing rate, Kelvin reasoned that it must be cooling down. Based on distance measurements to the Sun and its brightness, Kelvin could obtain estimates for how hot the Sun had been when it first formed, and, using its current temperature, how long it had been cooling down for. He did so, and came up with an estimate for the Sun’s lifetime that was between ten and a hundred million years, with a best guess of 32 million years.

Let’s just take a second to appreciate that Kelvin’s theory is also rather doomy. The Sun is constantly cooling down, burning through its reserves of energy. In this model, all the matter in the Universe eventually clumps together into stars, which then radiate away that energy into the Universe, until everything is lukewarm soup and lukewarm stars.

But this theory spelled doom for Darwin. Kelvin reasoned that the Sun was probably the same age as the Earth — true — and even if they somehow didn’t form together, life is hardly going to flourish with no Sun. This meant that there had only been a few tens of millions of years during which evolution could possibly have taken place; simply not enough time for Darwin’s theory to be right.

You get a sense of the age-old animosity between physicists and biologists, here. There’s nothing worse than a physicist who’s just done a back-of-the-envelope calculation to try to disprove your theory. One can almost hear Kelvin saying: “Yes, Charles, that’s a very cute theory that you figured out by looking at the finches, and it’s a lovely story for your book, but it contradicts the Laws of Thermodynamics! You can’t break the Laws of Physics, so pipe down.” And the fact that geologists had also estimated the Earth to be hundreds of millions of years old, based on how quickly rocks were eroding, didn’t seem to faze Kelvin either. Darwin had considered this to be such an important aspect of his theory that he had done his own geological studies, demonstrating that the amount of time required to form a particular valley in England must have been at least 300 million years. But Kelvin thought that perhaps catastrophic floods could have caused much faster erosion. Besides, what would the people who actually studied the Earth know about the Earth?

Kelvin was even more smug when he was able to turn the thermodynamic arguments towards the Earth. It was known at the time that the Earth is filled with molten rock; well, by the same logic, presumably it was formed as a ball of molten rock that had gradually begun to cool down. By considering how long that cooling would take, he was able to get another estimate of the age of the Earth that was tens of millions, rather than hundreds of millions of years.

We now know that Kelvin’s calculations didn’t include everything. Those truly devoted listeners who remember the very first episodes of this show, about stellar formation, will remember this idea about gravitational potential energy from the collapse heating up a star. This is what happens in protostars — those newly-born stars that are really just masses of gas falling and spiralling inwards, getting hot and heavy! And we also know that many stars are just endlessly cooling, radiating energy away into space and getting dimmer: white dwarf stars, where fusion has already stopped. But we mark the moment when the star is truly born when it gets another source of energy, beyond just gravitational potential from infalling material. A star is born when that energy gets hot enough, and the gravitational pressures big enough, to ignite nuclear fusion in the heart of the star. This was the mysterious fuel that Kelvin couldn’t quite put his finger on. The energy came from the nuclear forces — the extraordinary amounts of energy that can be liberated when nuclei rearrange themselves.

We now know that the Earth is 4.54 billion years old — plenty of time for evolution to develop the vast array of species we see around us, and survive a few mass extinctions and a boring billion years along the way. Darwin and Kelvin are both dead, but they’re both famous in the annals of scientific history, so I suppose there’s no love lost there.

Yet now there was a new and tantalising prospect. Just imagine the field of radiation and nuclear physics developing today. Within [a few decades], you go from having no knowledge of radioactivity — no one having any conception that the atom had a nucleus, and the theory of atoms still controversial — to realising that the mysterious forces that bind the nucleus holds almost limitless energy, lights up the Universe. Imagine the dreams we’d have if such a discovery was made today! Shifting nuclei into that region of stability, where the binding energy increases when you fuse nuclei together. If there was enough energy to light up the stars and the night sky, across countless light years, sending twinkling signals into the void… could we perhaps harness this energy on Earth?

By the 1920s, it had become clear that Kelvin’s argument was wrong — the Sun must be drawing on some energy source, rather than gradually smouldering to nothing. Arthur Eddington — the man behind the experimental expedition that confirmed Einstein’s theory of general relativity — is generally credited with being the first one to declare that nuclear energy was powering the sun. It would fall to Bethe and other scientists to work out precisely how it worked, the exact nuclear fusion reactions that were occurring, and hence to estimate things like the stellar lifetime and talk about the various phases of nucleosynthesis — the creation of all the elements around us, as we’re built out of star-stuff. For more of this, of course, head way back to our first ever episodes, Hot and Heavy.

I’m going to quote Eddington, however. The whole speech is great — you can find it all online, I did at Andrew Hamilton’s homepage at the University of Colorado. The talk is called “The Internal Constitution of Stars”, and it’s a pretty amazing snapshot of the state of stellar physics in 1920.

First off, Eddington starts by summarising the state of stellar physics and observational science. Then he talks about Kelvin’s predictions and why they don’t make any sense:

This study of the radiation and internal conditions of a star brings forward very pressingly a problem often debated in this Section. What is the source of the heat which the Sun and stars are continually squandering? The answer given is almost unanimous-that it is obtained from the gravitational energy converted as the star steadily contracts. But almost as unanimously this answer is ignored in its practical consequences. Lord Kelvin showed that this hypothesis, due to Helmholtz, necessarily dates the birth of the Sun about 20,000,000 years ago; and he made strenuous efforts to induce geologists and biologists to accommodate their demands to this time-scale. I do not think they proved altogether tractable. But it is among his own colleagues, physicists and astronomers, that, the most outrageous violations of this limit have prevailed. I need only refer to Sir George Darwin’s theory of the earth-moon system, to the present Lord Rayleigh’s determination of the age of terrestrial rocks from occluded helium, and to all modern discussions of the statistical equilibrium of the stellar system. No one seems to have any hesitation, if it suits him, in carrying back the history of the earth long before the supposed date of formation of the solar system; and in some cases at least this appears to be justified by experimental evidence which it is difficult to dispute. Lord Kelvin’s date of the creation of the Sun is treated with no more respect than Archbishop Ussher’s.”

Eddington finally takes the side of other scientists, biologists and geologists by pointing out the hypocrisy of the physicists! They were happy to claim that stars were continually contracting, but also to contradict themselves by not really dealing with the age limit that this would imply. But you have to remember — this is 1920; Einstein has already published special relativity, and people accept that light has a finite speed. So this means that they know that, when they’re looking at faraway stars, they’re actually looking back in time. The reason is simple: if the light takes 20,000 years to get to you, the object being 20,000 light years away, then you’re seeing light that was emitted from the object 20,000 years ago. Whenever you look anywhere, you’re looking at the past: you can never see the world as it is now: the further you look, the further back into the past you see. In some ways, the present moment for you is defined by all the events in your “past light cone” — the region of spacetime that can influence you. But this is for the special relativity episodes.

Usually this effect is small, but with astronomical distances, it becomes important. Eddington pointed out that we can look at arrangements of stars called globular clusters at various different distances — and hence various different times. If stars are being fuelled by constantly contracting, you’d imagine further away clusters to have a stars that were bigger on average — they’ve had less time to contract! Yet there didn’t seem to be much difference in these clusters. There are also stars called Cepheid variables which are famous because they regularly pulsate — they get brighter and then darker again. Eddington pointed out that the period of this pulsation, the amount of time between pulsations, should change if the star was constantly contracting as it burned up all of its gravitational energy. But one particular star had been observed since 1785, and the period had barely decreased at all — by hundreds of times less than it should have done. Another nail in the coffin of this contraction theory.

So, finally, he comes on to discuss what the actual source of the stellar energy is. He knows about E = mc², the equivalence of mass and energy. It’s also known at this point that helium is slightly lighter than “4 hydrogen atoms” (which is what they thought helium was made of at that point.) This is how you can obtain energy from nuclear fusion — when the constituent parts combine, they’re lighter than the sum of the parts, and the difference in mass is the energy released. [We’ll talk about why in the next episode.] Eddington can then do a back-of-the-envelope calculation, working out how much energy might be released if the Sun is made of fusing hydrogen — and he gets a figure for the Sun’s lifetime that’s far longer, and far closer to what everyone suspects!

But I think it’s amazing that in this — perhaps the first public statement talking about fusion as the energy source that powers stars — we’re already discussing it as an ideal source of energy for the human species. Eddington realised straight away the immense potential of what this could mean.

A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known, exists abundantly in all matter; we sometimes dream that man will one day learn how to release it and use it for his service. The store is well-nigh inexhaustible, if only it could be tapped. There is sufficient in the Sun to maintain its output of heat for 15 billion years.

The nucleus of the helium atom, consists of 4 hydrogen atoms bound with 2 electrons. But Aston has further shown conclusively that the mass of the helium atom is less than the sum of the masses of the 4 hydrogen atoms which enter into it. There is a loss of mass in the synthesis amounting to about 1 part in 120, the atomic weight of hydrogen being 1.008 and that of helium just 4. …. We can therefore at once calculate the quantity of energy liberated when helium is made out of hydrogen. If 5 per cent of a star’s mass consists initially of hydrogen atoms, which are gradually being combined to form more complex elements, the total heat liberated will more than suffice for our demands, and we need look no further for the source of a star’s energy.

If, indeed, the sub-atomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race — or for its suicide.”

Amazingly prescient. The first time people talk about fusion as the power source for the Sun, he’s already seeing this dichotomy with nuclear energy — is it going to be the energy source that helps the human species ascend to new heights… or to destroy itself?

So present in this speech already is a dream that one day, we might be able to harness the miraculous, limitless-seeming source of energy from the fusion of light nuclei. It’s this idea that I really want to explore in the next series of episodes. Could it really be true? It’s going to take us through some incredible historical moments, some triumphs, some tragedies, and some scandals; from a century in the past to decades in the future.

Because there’s another famous quote about fusion.

“The idea is simple. You put the sun in a bottle. The only problem is building the bottle.”