Ask Ethan: How did atoms come to be?

At the core of everything we’ve ever touched, seen, or interacted with here on Earth is the same humble physical structure: the atom. Each human body possesses around 10²⁸ of them, and they come in just under 100 different species, or elements, through natural processes, and we’ve synthesized several dozen more in laboratory experiments. Combined, atoms bind together to make unfathomably intricate, complex structures on both microscopic and macroscopic scales, and compose every living and nonliving object presently known to humanity.

But atoms weren’t always around; they only formed in the aftermath of the hot, early stage of our Universe known as the hot Big Bang. How did they arise, and what made their existence possible? That’s the question of Dave Drews, who wants to know:

“Out [of] the primordial soup after the Big Bang, how did atoms come to be? How did protons and neutrons come to be to make atoms? Were there free-floating quarks combining in the right combinations to form protons and neutrons? How did quarks come to be? Were there free-floating gluons that came together to create them? Free-ranging electrons were flying about, but what caused them to bind with protons to create hydrogen atoms and so on?”

Let’s start by recounting our own cosmic history, which did indeed lead to the formation of atoms, and then take a look back at the key steps that made their ubiquitous existence possible.

At the start of the hot Big Bang, we didn’t have any atoms at all. We also didn’t have their core constituents: the atomic nuclei, nor did we even have protons or neutrons. Electrons were present, as were their antimatter counterparts, positrons, and all the fundamental particles and antiparticles of the Standard Model. Conditions, way back then, were far too hot, dense, and energetic for any bound structures to form at all; anytime any two particles even attempted to bind together, the extraordinary conditions at that time led to another quantum interacting with them and blasting them apart.

Over time, however, the Universe expanded, and as it did, it cooled as well. That cooling means that photons and other massless particles redshift, and their wavelengths lengthen, and they lose energy. For massive particles, they similarly lose energy: you can think of them as matter waves (de Broglie waves) whose wavelengths lengthen, or you can think of them as particles traveling through expanding space, and the more space there is to go through, the slower they travel through it, losing kinetic energy in the process.

When things expand and cool enough, unstable particles decay, heavier particle-antiparticle pairs annihilate into lower-energy ones but can’t re-form via the annihilation of lighter species (as enough energy is no longer available via E = mc²), and only the lowest-energy, most stable species of particle survive.

At some point — and we don’t know exactly when or how it happened — two equal-and-opposite asymmetries arose early on in our cosmic past. For about every 550 million antiquarks that were present, that same number of quarks plus one was present, and for about every 3.3 billion positrons that were present, that same number of electrons plus one was present. When the Universe cools sufficiently so that the quarks and antiquarks annihilated away, there were a small number of extra quarks left over. When the cosmos cooled sufficiently, those extra quarks bound together into hadrons, eventually leading to protons and neutrons. (No extra gluons were necessary; bound states of quarks provide their own!)

Similarly, albeit a little later on, the electrons and positrons annihilate away, and they leave an excess of electrons: one electron for roughly every six excess quarks. Because half of the hadrons were protons and the other half were neutrons, and protons and neutrons are made of six quarks each, this leaves an electrically neutral Universe. After that, protons and neutrons interact and interconvert through the weak interactions, transforming the proton/neutron balance from 50/50 to about 85/15 before the weak interactions freeze out (or become non-efficient) entirely. (This also changes the number of electrons, as each neutron that was converted to a proton loses one net neutrino and gains one net electron.) A fraction of the neutrons radioactively decay, and then, by the time the Universe is a little over three minutes old, the background radiation has cooled enough that the first atomic nuclei can be synthesized without being immediately blasted apart: a period of Big Bang nucleosynthesis.

Although we have a Universe with a whole lot of constituents, including neutrinos, antineutrinos, dark matter, and dark energy, there are only three things that matter for making atoms at this point: once the nucleosynthetic period has ended.

• The primitive atomic nuclei, which are about (by number) 92% single-proton hydrogen, 8% helium-4, about 0.01% deuterium, about 0.01% helium-3, and about 0.0000001% lithium-7.
• The electrons, which, being negatively charged, would love to bind to the atomic nuclei, which are all positively charged; the electrostatic (Coulomb) force is extremely powerful.
• And the photons, which even though the Universe has expanded and cooled precipitously since its hottest, are still hot enough to ionize any neutral atom that attempts to form.

It takes tens of thousands of years for the Universe to cool enough so that the first ion with even one electron bound to it can stably form: doubly-ionized lithium. Singly-ionized lithium and singly-ionized helium follow, and then neutral helium, when the Universe is just over 100,000 years old, becomes the first stable species of neutral atom. Hydrogen atoms become neutral at an average of 380,000 years after the Big Bang, and lithium is the last to arrive at the party, requiring over a million years before that third and final electron binds to it. At last, neutral atoms have formed, and the Universe can proceed to evolve stars, galaxies, planets, living beings, and even humans as well.

That’s a quick recap of the cosmic story of how atoms came to be. But our Universe didn’t have to have the properties that led to the existence of atoms, much less to the existence of stable, neutral, long-persisting atoms. Even with the exact same laws of physics in place, a tiny difference in the conditions that the Universe began with could have led to an atom-free Universe in a wide variety of ways. Let’s unpack how that could have gone.

A universe where expansion and energy density don’t balance

One of the most remarkable facts about our Universe ー although we don’t often think about it as remarkable ー is that if you sum up the total energy density of all the different species of energy that exist in the cosmos:

• dark matter,
• dark energy,
• normal matter,
• radiation,
• neutrinos,
• black holes,

and everything else that exists, you get an amount that exactly matches the critical density, which is a value for density set by the current expansion rate of the Universe.

Those values aren’t just equal today, but were equal at all moments throughout cosmic history, going all the way back to the Big Bang. Back in those early, primeval stages, if those two values weren’t exactly equal, but had just a tiny mismatch of say 1-part-in-a-trillion, or 0.0000000001%, no atoms would ever have formed. If the energy density was greater than the critical density set by the expansion rate, the Universe would have recollapsed well before a single atom could ever have formed. If the energy density was smaller than that critical density, the Universe would have expanded so quickly that no proton and no electron would ever have met, making atoms an impossibility in either case. Only in the case where the total energy density and the expansion rate are in perfect balance can atoms form within the Universe: a situation that happens to still be true even today, 13.8 billion years later.

A universe with too little (or no) baryogenesis

At some point in cosmic history, the Universe created a fundamental, overall asymmetry: where it wound up, somehow, producing more overall matter than antimatter. Many things were still conserved: electric charge, energy, linear and angular momentum, and several other fundamental quantum quantities. But the “conservation of baryon number” was violated, as was the “conservation of lepton number” in equal amounts, leading to a Universe where, for every extra net proton that was created, an extra electron was created, too. (In theory, for every extra net neutron that was created, an extra neutrino was created as well, but we have no way to test for this.)

The amount of baryogenesis that we had means that for every 1.6 billion photons we had in the early stages of the Big Bang, we wound up with one excess baryon. If there were no asymmetry, then almost every baryon would have annihilated away with almost every antibaryon. They would annihilate and annihilate and annihilate until there were so few baryons and antibaryons left in such a vast, expanding Universe, that they’d pretty much never find each other.

This would leave us with about 1 baryon and 1 antibaryon for every 1 sextillion photons: with such a tiny value for density that the random electrons or positrons that still existed would pretty much never find them. No baryogenesis means an extremely low density of protons (and antiprotons) persist, and with such a sparse Universe — with fewer than one proton per cubic kilometer of space — nuclei and electrons just couldn’t find one another, and hence, no atoms form.

A universe where the strong nuclear force was a bit weaker

One of the fundamental facts about our Universe is that the strongest force is the strong nuclear force, with the electromagnetic force just a little bit weaker than it. The weak nuclear force is much, much weaker (and also, of an incredibly short range) while the gravitational force is by far the weakest of them all. The fact that the strong nuclear force acts like a spring — providing zero force at the shortest distances but increasing force at greater distances — is what allows particles like the proton to exist, and to exist with a particular size and mass.

But if you turned down the strength of the strong nuclear force, things would get difficult, and quickly. If you turned the strength down by about 50%, you could only have hydrogen atoms with zero, one, or (temporarily) two neutrons in its nucleus; beyond that, the strength of electromagnetic repulsion would prevent even a second proton from existing within the same nucleus. Go a bit further, and turn the strength down to about 1% of its current value, and the “spring” nature of the strong force would be so weak that even protons themselves couldn’t form, with the repulsion between the like-charged quarks in the nucleus then being strong enough to prevent proton formation at all. Without protons, there are no atoms; there would be zero elements in the periodic table in a Universe with too weak of a strong nuclear force.

A universe that’s too radiation-rich

Similarly, a later step that’s key to forming neutral atoms is allowing the electrons to stably bind to protons and other atomic nuclei. However, it’s important to remember this: our Universe doesn’t form stable, neutral hydrogen atoms until the leftover background of radiation from the Big Bang — colloquially known as the cosmic microwave background — is around 3000 K in temperature. However, if you convert a temperature of 3000 K to energy (using Boltzmann’s constant), you don’t get the ionization energy of the hydrogen atom, which is 13.6 eV. Instead, you get a much smaller value: something more like 0.3 eV.

This is because, in our Universe, there are literally more than 1 billion photons for every atom, and photons follow a Maxwell-Boltzmann distribution in their energy. In simple terms, that means that even though they have an average temperature and an average energy, there are a few photons in that “bath” that have much greater than average energy, and as long as there are as many photons above the ionization energy of a species of atom as there are atoms of that species, ionization will always occur, and the formation of neutral atoms won’t happen.

Even today, when the temperature of the Universe has cooled to just around 3 K, if we had enough overall photons (the number would be large, but not infinite), there would be a sufficient number of high-energy photons at the high-temperature “edge” of the Maxwell-Boltzmann distribution flying around to ionize every single atom, making the formation of stable, neutral atoms an impossibility, even today.

A universe where the symmetries between baryons and leptons didn’t hold

According to the Standard Model of particle physics, there isn’t a strict symmetry that says “baryon number must be conserved.” There also isn’t a rule that mandates “lepton number must be conserved,” although in both cases, we’ve never observed a single reaction that violates either one.

However, there is a rule that says, at least in the Standard Model alone, that the combination of “B – L,” or baryon number minus lepton number, must be conserved. In other words, anytime you create or destroy a baryon, you have to create or destroy a lepton as well.

But what if you didn’t have that symmetry? What if you could create or destroy baryons without creating or destroying a lepton as well? That would lead to a scenario where you could have a net baryon number but not a net lepton number: like a large number of protons but not an equal-and-opposite number of electrons.

This is a challenging scenario to envision, as even if you made, say, negatively charged pions (to conserve electric charge) instead of electrons, negative pions decay to negative muons, and then negative muons decay to electrons; you would have to interfere with the entire decay chain as well, and have some particle other than the electron (or another lepton) be the lightest charged particle. Still, if you had a Universe filled with protons but not electrons, neutral atoms wouldn’t be able to arise.

There are plenty of other scenarios that one can concoct that would have made the existence of neutral atoms a pathological impossibility. Examples include:

• If dark energy were significantly stronger, accelerating quanta away from each other too early, then atomic nuclei and electrons would never have found each other.
• If the rules of quantum mechanics were different, or the Universe weren’t quantum at all, then atoms themselves might not be stable, and electrons would spiral into the atomic nucleus itself, just as Rutherford warned before the Bohr model of the atom came along.
• If the mass difference between the proton and the neutron was just a little bit smaller, atoms would again be unstable, and any atomic state would decay into just a wad of neutrons bound together: a state known as neutronium, or “element zero” on the periodic table.
• If there were so many baryons that nuclear fusion occurred immediately and to completion in the early Universe, leading to a neutron star (or black hole) catastrophe: where neutral atoms would never get a chance to arise.

The fact that neutral atoms do exist, that so many species of neutral atoms are stable, and that the conditions present in the Universe allow a wide variety of atomic species to be naturally synthesized in stars, stellar cataclysms, and in events involving stellar remnants, is what directly enabled the existence of complex molecules, rocky planets, biochemical reactions, and all forms of life.

If our Universe had been just a little bit different in any one of a variety of possible ways, atoms wouldn’t be possible, and neither would beings like us. And yet, here we are: the product of 13.8 billion years of cosmic evolution in a cosmos that did indeed allow for neutral atoms to exist, and for incredibly intricate and complex combinations of atoms that can make possible everything under the Sun and more. It compels us to wonder, given all the possible combinations that nature allows, just what else might be lurking in the great abyss of space.

Send in your Ask Ethan questions to startswithabang at gmail dot com!

This article is featured on Big Think.