# Alpha: the Key to the Universe?

The Answer to Life, the Universe and Everything, contrary to popular belief, is approximately 1/137.036 or 0.00729735. This value is known as the Sommerfeld fine structure constant, and it governs virtually everything about the way that matter behaves in the Universe. The understanding of why this value is what it is is one of the great unsolved mysteries of theoretical physics.

### The Numbers Stack Up

Arnold Sommerfeld died in 1951, but before he did, he discovered what is possibly the most fundamental of all physical constants. There are a quite a few of these. The speed of light, c, is 299,792,458 metres per second1. Sir Isaac Newton's constant of gravitation, G, which governs the strength of attraction between two masses, is 6.673 x 10-11 Nm2kg-2. This is a small number by anybody's stretch of the imagination, and goes to explain why the Earth's gravity doesn't squash us into piles of amorphous organic goo: gravity is much weaker than the electromagnetic force holding the atoms of our body together.

The simple fact is that nobody understands why these constants hold the values they do. The fine structure constant (or α for short) is of particular interest because it is a dimensionless constant. G and c are expressed in terms of dimensions, that is, units: ask people what the speed of light is, and they may tell you that it is 186,000 miles per second, or they may reply with 300 million metres per second, depending on their background and their nationality. α, in contrast is always 1/137.03599976, regardless of what system of units is used to measure it2. As such, it makes it of particular value to experimental physicists who know that any measurements they make of it should be independent of the apparatus or system of units they use to measure it. It provides a totally fixed yardstick against which all other measurements of physical constants can be calibrated.

### How does α affect me?

So why is α so fundamentally important? Looking at how it is derived gives us some clues. α is a coupling constant – it denotes the relative strength of the electromagnetic interaction between two charged point particles, such as electrons, compared to the other three fundamental forces. In contrast, the coupling constants for the strong nuclear force, the weak nuclear force and gravity are 1, 10-6 and 10-39 respectively.

The equation that yields the value of α is:

α = e2/2ε0hc

where c is the speed of light, e the charge on the electron, h is Planck's constant and ε0 the permittivity of free space. In one constant, relativity, particles, the quantum world and free space are united, making α about as fundamental a theoretical lynchpin as it gets.

#### Fine Structure

So if it is so fundamental, what has 'fine structure' got to do with anything? The explanation lies in the fact that when you have a light emitted from a gas discharge and you pass it through a prism, you see a spectrum made up of lots of bright lines. Certain of these lines are split into pairs. The fine structure constant determines how far apart the pairs are. It also specifies the ratio of the effective speed of an electron in a hydrogen atom3 to the speed of light.

α also has some rather more immediate implications for our own existence. It characterises how strong the electromagnetic force actually is between subatomic particles: higher α implies a stronger force. If α were lower, then the density of solid matter (which is proportional to α3) would also fall. Molecules would be less stable, falling apart at lower temperatures; on the other hand, atoms would be more stable: the number of stable elements in the periodic table would increase in proportion to (1/α).

Increase α, and some really alarming things start to happen. The electrical repulsion between protons would blow atoms apart. If α increased to 1/10, nuclear fusion would become impossible and stars would cease to shine. In fact, a change in the value of α of only 4% would bring about an end to the synthesis of carbon in stars. We have enough carbon to be going on with, but if this had happened when the Earth was being formed, you could say goodbye to Life as We Know It.

### Don't Panic!

Alarmed yet? There isn't really any need to be. α, as far as we can tell, has been pretty stable since the Universe began. Scientists, however, don't take even such fundamentals as these at face value. They like to know if the eventual fate of the universe, albeit several billions years away, is going to be anything like they envisaged: whether the end is going to be a bang or a whimper. The best way of doing this is to look far into the past of the universe to see whether matter behaved in a different way to the way it currently does. We can begin the search for clues right at home, on Earth.

#### The Oklo Reactor

In Gabon, West Africa, there is a very big uranium mine at Oklo. The French had been digging uranium there for some years when they noticed that something was very wrong. The proportion of fissile uranium, 235U, compared to that of its rather more stable isotope, 238U, was diminished compared to virtually every other deposit everywhere in the world (and outside of it, in places like the Moon). Even more alarmingly, about 200 kg of the fissile stuff was missing when one looked at the total amount of uranium ore that had passed through the mine – enough to make a very large atomic bomb. Had somebody spirited away a huge amount of dangerous material and was now building atom bombs in their garden shed?

Panic subsided when someone pointed out that the conditions at this mine were ideal for the establishment of a natural nuclear reactor. Nuclear reactors run on enriched uranium, which requires special processing of the raw material. About two billion years ago, there was enough fissile 235U– about 3% of the total – to sustain the operation of such a reactor. This underground furnace had burned up the fissile uranium to the point where it was no longer able to function and then had shut down. However, conditions were such that this reactor could not have operated were α significantly different from its current value. So we know that α was much the same two billion years ago.

#### Looking Further Afield

The universe is a lot older than two billion years4, so what would be the chance of α being significantly different in its infancy, as opposed to its early adolescence? Since light takes time to travel, when we look into the distance we are looking into the past. The best way of looking back in time is to look at the very edge of observable space, and just about the only things that can be seen out there are quasars. These are incredibly bright, young galaxies that generate huge amounts of light when they collide with other such galaxies and their central black hole starts devouring clouds of interstellar gas, turning much of the mass into energy. Observing quasars allows us to see cataclysmic events occurring in the infancy of the universe. We can see how interstellar gases, such as hydrogen, absorbed light at that time and from their spectra make deductions about the value of α. Such studies in 1999 claimed that such observations indicated a slight increase in α of slightly less than one part in 100,000 over the past 10 - 12 billion years. However, subsequent studies appear to go against this and indicate that there has not been any significant change since the universe began.

### So why is α the value it is?

Nobody knows, to be honest. α doesn't appear to be related to any mathematical constant whatsoever. The closest correlation so far is with a complex trigonometric formula involving 29 and 137, the 10th and 33rd prime numbers:

α = 29 cos(π/137) tan(π/(137×29)) / π

This may be regarded as cheating, since it puts the rounded version of 1/α (137) into the formula in the first place.

Putting aside number theory, the anthropic principle claims that there are many parallel universes currently in existence, with wildly differing values of the physical constants, and that at some point a universe will exist which favours life, rather like Goldilocks's porridge being just the right temperature. Therefore the only reason that α is just the right value to support life is that we are around to observe it. If this is indeed the explanation, it must also explain why we just happen to live in a universe where α has been constant enough for long enough to allow intelligent, stargazing life like ours to evolve.

If, like this Researcher, you are still mystified (albeit now at a higher level) by this enigmatic number, you are in good company. Richard Feynman, arguably one of the greatest physicists that lived, remarked:

It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to π or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the 'hand of God' wrote that number, and 'we don't know how He pushed his pencil.' We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!
In other words, we know the answer very well, but the proper question has yet to be formulated, let alone asked. Does this sound at all familiar?
1In a vacuum: speeds through all other media are somewhat slower.2For obscure reasons, physicists prefer to write the constant in this way as 1 divided by something, rather than the apparently more straightforward 0.007297352533.3In the simplest model of the atom, electrons can be thought of as orbiting the nucleus.4Current theories put the universe at about 13 billion years old.