Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute, host of “ask an astronaut” and “space radio” and author of “how to die in space.”
A seemingly innocuous, random, unitless, dimensionless number has appeared in so many places in physics and appears to control one of the most fundamental interactions in the universe.
His name is the fine structure constantand it is a measure of the strength of the interaction between the charged particles and the electromagnetic To obligate. The current estimate of the fine structure constant is 0.0072973525693, with an uncertainty of 11 in the last two digits. The number is easier to remember by its inverse, approximately 1/137.
If it had any other value, life as we know it would be impossible. And yet, we have no idea where it came from.
Watch: The most important number in the universe
A great discovery
Atoms have a curious property: they can emit or absorb radiation of very specific wavelengths, called spectral lines. These wavelengths are so specific because of quantum mechanics. An electron orbiting a nucleus in an atom cannot have any energy; it is limited to specific energy levels.
When electrons change level, they may emit or absorb radiation, but that radiation will have exactly the difference in energy between these two levels, and nothing else – hence the specific wavelengths and spectral lines.
But in the early 20th century, physicists started noticing that certain spectral lines were split or had “fine structure” (and now you can see where I’m coming from). Instead of a single line, there were sometimes two very closely separated lines.
The complete explanation of the “fine structure” of the spectral line relies on quantum field theory, a marriage of quantum mechanics and Relativity. And one of the first people to try to figure this out was physicist Arnold Sommerfeld. He discovered that to develop the physics to explain the splitting of spectral lines, he had to introduce a new constant into his equations – a fine structure constant.
Related: 10 mind-boggling things you should know about quantum physics
Introducing a constant wasn’t all that new or exciting back then. After all, physics equations throughout history have involved random constants that express the strength of various relationships. Isaac Newtonformula for universal gravitation had a constant, called G, which represents the fundamental force of gravitational interaction. The speed of light, c, tells us about the relationship between electric and magnetic fields. The spring constant, k, tells us how stiff a particular spring is. etc
But there was something different about Sommerfeld’s little constant: there were no units. There are no dimensions or system of units on which the value of the number depends. The other constants in physics are not like that. The real value of the speed of light, for example, doesn’t really matter, because this number depends on other numbers. Your choice of units (meters per second, miles per hour, or leagues per fortnight?) and the definitions of those units (how long exactly is a “meter” going to be?) matter; if you change any of these, the value of the constant changes with it.
But this is not true for the fine structure constant. You can have any system of units you want and any method of organizing the universe as you want, and that number will be exactly the same.
If you were to encounter an alien from a distant star system, you would have a hard time communicating the value of the speed of light. Once you have defined how we express our numbers, then you will need to define things like meters and seconds.
But the constant fine structure? You could just spit it out, and they would figure it out (as long as they count numbers the same way we do).
The limit of knowledge
Originally, Sommerfeld had not given much thought to the constant, but since our understanding of the quantum world grew, the fine structure constant began to appear in more and more places. It seemed to pop up whenever charged particles interacted with light. Over time, we have come to recognize it as the fundamental measure of the strength of the interaction of charged particles with electromagnetic radiation.
Change that number, change the universe. If the fine structure constant had a different value, then the atoms would have different sizes, the chemistry would change completely, and the nuclear reactions would be altered. Life as we know it would be downright impossible if the fine structure constant had even a slightly different value.
So why does it have the value it has? Don’t forget that this value itself is important and may even have meaning, because it exists outside of any system of units we have. It’s simply….
In the early 20th century, the constant was thought to have a precise value of 1/137. What was so important about 137? Why this number? Why not literally any other number? Some physicists have even gone so far as to attempt numerology to explain the origins of the constant; for example, the famous astronomer Sir Arthur Eddington “calculated” that the universe contained 137*2^256 protons, so “of course” 1/137 was also special.
Today, we have no explanation of the origins of this constant. Indeed, we have no theoretical explanation for its existence. We simply measure it in experiments and then plug the measured value into our equations to make further predictions.
one day one theory of everything – a complete and unified physical theory – could explain the existence of the fine structure constant and other similar constants. Unfortunately, we don’t have a theory of everything, so we have to shrug our shoulders.
But at least we know what to write on our alien greeting cards.
Learn more by listening to the “Ask a Spaceman” podcast, available on iTunes and askaspaceman.com. Ask your own question on Twitter using #AskASpaceman or following Paul @PaulMattSutter and facebook.com/PaulMattSutter.