How important is hydrogen to you?
A quick survey of the world around us makes it pretty clear that we just can’t live without hydrogen. I live in Baltimore, and every Friday in the summer cars pack onto Interstate 95, headed to the beaches of Delaware or to Ocean City (Maryland or New Jersey). Yet, without hydrogen we wouldn’t have clear blue ocean waters or gasoline for our cars or steel or plastic to make cars—you get the picture. Not only does hydrogen enjoy a majority share in the makeup of water, i.e. H2O, but much of what we know about biochemistry is based on the fact that carbon and hydrogen like to bond to one another and form the organic molecules that result in life.
Hydrogen and the electric charges of the proton and electron out of which it’s built are not just important for a nice weekend at the beach. They are crucial to cosmic history.
How was hydrogen generated?
The universe didn’t always look the way it does today: big, open, and seemingly pretty empty. When the universe was just moments old it was a hot gas of elementary particles such as quarks, photons, electrons, and W bosons, and they had a lot of energy. Eventually, the “primordial fireball” cooled to the point where the quarks combined into a class of particles called hadrons. The proton is probably the most familiar of all the hadrons. After about 380,000 years of cooling and expansion, the protons could finally hold onto electrons without losing them in subsequent collisions. Recombination is the process where protons and electrons came together to form the first stable hydrogen atoms.
Recombination is fairly well understood. Various mechanisms affect the rate of formation of stable hydrogen atoms by either hindering or helping the process. On the “hydrogen-preventing” side are energetic collisions and the expansion of space-time. It takes a certain amount of energy to knock the electron out of the proton’s grasp. If a photon, for example, comes along and hits the electron with that much energy (or more) the electron will be freed, destroying the hydrogen atom. Additionally, space-time expansion works to dilute protons and electrons, making it more difficult for them to find one another. (Expansion also tends to cool the gas down, making hydrogen less likely to be ionized after formation, but the effect of dilution is much stronger than the effect of cooling.)
On the “hydrogen-forming” side is the electromagnetic force between the positive charge of a proton and the negative charge of an electron. Protons’ tendency to grab electrons and hold on tightly helps hydrogen “win” out against the factors that play against its formation. In fact, roughly only 1 out of every 1,000 electrons/protons is left over as a free particle.
How did hydrogen win?
Determining what fraction of electrons and protons end up as free particles versus how many are bound requires detailed numerical analysis on a computer. The competition between the rates described above is far too complicated for a closed-form analytical solution. However, a lot of insight can be gained by noting that the rate for protons to capture electrons into stable orbits is proportional to the sixth power of the electron charge. In other words, if you could turn a dial and give the electron three times as much charge, then the rate for hydrogen to form would increase by a factor of 36 = 729. Similarly, decreasing the fundamental unit of electric charge by only a factor of 1/3 would change the ratio of free electrons and protons to hydrogen atoms from about 1:1000 to roughly 1:1. In other words, hydrogen wins because the electron has the just-right charge.
Before recombination, the universe was a gas of charged particles known as a plasma. During this epoch the cosmos was opaque because light bounces off free charges and changes its course. Shortly after atoms formed, light traveled freely through the gas because few free charged particles remained to scatter it. This light—first let loose more than 13 billion years ago—makes up the cosmic microwave background radiation (CMBR).
Most people will probably go through life never hearing about the CMBR, so it may seem like the existence of human life is not dependent upon its formation. In reality, quite the opposite is true. All of the subsequent development of the cosmos—the formation of stars, galaxies, planets, and human beings—hinges upon having the right abundance of hydrogen in the early universe. The CMBR is a beacon, subtly telling us what we already know: the Creator got it right.
As mentioned above, hydrogen plays a vital role in the formation of the first stars. Free electrons and protons experience electromagnetic forces. In the early universe these forces acted as a pressure that prevented the plasma from collapsing under the influence of gravity. But the plasma needed to collapse in order to become dense enough and hot enough to start nuclear fusion and then turn into a star. Electrically neutral hydrogen atoms and hydrogen molecules (H2) do not experience such strong pressures. (In fact, the free electrons and protons act as catalysts for hydrogen gas to combine into H2.) H2 is much more efficient than ordinary hydrogen at radiating away its kinetic energy, which prevents star formation. Thus, the H2 molecules were able to slow down and condense, allowing the rest of the plasma to condense and eventually form the first stars. Following this event, hydrogen in the stellar furnaces produced heavier elements like carbon and oxygen.
The bottom line
If the charge of the electron had been a little bit smaller then hydrogen would not have formed in sufficient abundance to generate stars. If the charge of the electron had been a little bit bigger then hydrogen would have formed too efficiently, thus leaving behind insufficient numbers of free electrons and protons. If not for the existence of a small, but non-zero, fraction of free electrons and protons left over after recombination, H2 wouldn’t have formed in sufficient numbers.
Without H2, the clouds of gas in the early universe would likely never have been dense enough to become stars. And without stars we could not exist and neither could our beach destinations! What’s more, we couldn’t exist to appreciate and glory in how carefully our Creator fashioned the universe to support our existence.
For the mathematical details of recombination:
The Early Universe by E. Kolb and M. Turner.
Modern Cosmology by S. Dodelson.
Principles of Physical Cosmology by P.J.E. Peebles.
For the effects of residual ionization and the formation of structure:
Structure Formation in the Universe by T. Padmanabhan.