A Study in Parallel Universes: the Diproton “Catastrophe”

Advocates of “fine-tuned universe” claim that if the physical laws of our universe were just slightly different, life would not be able to exist. Some of my colleagues and I previously looked at these claims with the “Weakless Universe,” where the weak nuclear force doesn’t exist at all. (We later also looked at varying the strength of the weak force.)

Another fine tuning argument is that if the strong nuclear force were just a little bit stronger, two protons could stick together and form a helium-2 nucleus (also known as a diproton). They say that this would break the universe by converting all of the hydrogen into helium in the Big Bang.

Spoiler: it wouldn’t.

I have co-authored another paper with Fred Adams, Evan Grohs, and George Fuller, which is now publicly available on the arXiv, studying what would happen if the universe would look like if this did happen—if diprotons (and dineutons) were bound states. And there were some definite surprises, but none that would make life as we know it impossible.

First off, there’s an important distinction here that even a lot of scientific writing seems to gloss over between a stable nucleus and a bound nucleus. A stable nucleus is one that doesn’t decay at all. But you’ll often hear people talking about the diproton being “unstable” when that’s not really what they mean. A bound nucleus doesn’t have to be stable; it just has to be more stable than the individual particles separately.

If you stick a proton and a neutron together to make deuterium, they release energy. This is because the bound deuterium nucleus has less energy than the proton and neutron separately, so it would require an energy input to separate them. This difference is called the binding energy.

On the other hand, if you have two protons, you have to add energy to get them to stick together. The combined state has more energy than the individual particles, so they’ll fly apart again as soon as they can, like balls rolling down a hill. We call this an unbound nucleus. Because all the protons have to do is fly apart again, this nucleus doesn’t last very long—probably less than 10-21 seconds.

We’re proposing an alternate universe where protons will stick together and release energy. This mean that a diproton is a bound nucleus and won’t just fly apart, but that doesn’t mean it’s stable. This helium-2 nucleus could and probably would still beta decay into deuterium because a proton and a neutron will naturally have lower energy than two identical particles. (There are spin statistics involved.)

So bound diprotons do not mean that all of the protons would be locked up in helium. They would just decay to deuterium. Actually, stable diprotons that don’t decay probably wouldn’t do that either. The reasons are complicated, but in simple terms, the high entropy state of Big Bang nucleosynthesis (BBN) favors lighter nuclei forming, including free protons, because they are a more disordered state. This is one of the reasons why so little deuterium is produced in BBN, and it’s likely that diprotons would form even less efficiently because of the electrical repulsion between protons. The upshot here is that the “diproton universe” would still have plenty of hydrogen.

Now, what about stars? Fusing hydrogen into diprotons is a strong reaction, while the pp-chain that powers our Sun is weak reaction, which is much slower. Advocates of the fine-tuning hypothesis say this would cause stars to burn through their hydrogen much too fast for life to form. But as we already saw with the weakless universe, if you change the nuclear reaction rates, even by huge amounts, stars just find a new gravitational equilibrium, one that is cooler and redder, but depends only logarithmically on the reaction rates.

The interesting thing is that stars would undergo two stages of what we might call “main sequence” fusion: one to turn hydrogen into deuterium and then helium-3 via diprotons, and one to turn that helium-3 into helium-4. Depending on the mass of the star, the second stage may be brighter, dimmer, or about the same as the first.

The other surprising thing we found was a new class of theoretical objects called “frozen stars.” These are technically stars, in that they undergo steady-state fusion reactions in their cores, but they’re so cold that water ice clouds could form in their atmospheres—maybe even life.

These objects don’t look at all like normal stars. They’re much smaller; in fact, they can be as small as Jupiter, and their core temperatures are only 100,000 K, much less than the 1 million K normally assumed to be needed for strong (diproton or deuterium) fusion. The reason this still works is that we normally talk about fusion “switching on” in stars, but that’s not really what happens. Instead, fusion rates are exponentially dependent on temperature.[1] So, even at much lower than normal temperatures, fusion still happens at very low rates.[2]

These reactions are so slow that the heat they produce is not enough to support the star against gravity, like in a normal star. Instead, just like Jupiter and super-Jupiter planets of similar mass, their mass would be partially supported by degeneracy pressure, the same force that holds up white dwarfs and neutron stars. The actual nuclear reactions are just enough to keep that degenerate core warm, and they’re so slow that these stars could live for an enormous amount of time—hundreds of trillions of years compared with ten trillion for the longest-lived stars in our universe.

Bizarrely, this “frozen star” structure isn’t unique to diproton reactions. It applies equally to deuterium reactions. These frozen stars would probably occur in a weakless universe where stars are mostly made of deuterium, only we didn’t think of that at the time. And in fact, if you had an object the size of Jupiter in our own universe that was made of pure deuterium, it would also become a frozen star![3] (Though deuterium is rare enough that such an object could not actually exist.)

As far as we know, we cannot test theories of alternate universes. But doing thought experiments about these kinds of universes can teach us new insights about our own universe. It teaches us that, far from being a delicate balance, stars are incredibly robust objects that can work in a wide range of possible scenarios. It teaches us that nuclear burning is a more complex beast than we usually assume. And most importantly, it helps us to correct our misconceptions about how unique or unusual our own universe is, and that there could be many other ways of doing things.

[1] We normally say it’s a power law with some high power, but that’s an approximation. Over a wide enough temperature range, it’s exponential.

[2] Some amount of fusion can even happen at zero temperature through quantum tunneling in what are called pycnonuclear reactions. However, these reactions are slower than the age of the universe.

[3] Note that this is not true of the actual Jupiter itself. What happens when a Jupiter-mass object forms is that its core is compressed and becomes hot and dense. In a pure deuterium object, a trickle of fusion starts up that produces more heat, and that keeps it warm even after the core settles and stops contracting. In Jupiter, that trickle of fusion is still there, but it’s many orders of magnitude smaller. It’s not enough to keep the core warm, so as its contraction slows, the core cools, and those fusion reactions are exponentially suppressed.

About Alex R. Howe

I'm a full-time astrophysicist and a part-time science fiction writer.
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1 Response to A Study in Parallel Universes: the Diproton “Catastrophe”

  1. Wyrd Smythe says:

    So stars would work over a large range of possible universes. How about the complex biology of life processes?

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