Measuring the Fine-Structure Constant to the Best Precision Yet

As you might know if you've been following this blog, my PhD research focuses on the fine-structure constant, traditionally denoted by \(\alpha\). Specifically, I'm working on extending an astronomical method for searching for variation in the fine-structure constant's value to main-sequence (specifically Sun-like) stars for the first time. I'm more interested in searching for a change in \(\alpha\) than in that value per se, but I was still interested to see an article in Nature a few days ago reporting the most precise determination of \(\alpha\) yet.

The authors measured the value of \(\alpha\) to be 1/137.035999206(11) (the last two digits are uncertain), with an incredible precision of 81 parts per trillion. Interestingly, this value varies by more than \(5\sigma\) from the previous best measurement. This measurement used rubidium atoms, while the other measurement used caesium atoms, so it's possible it could be some systematic difference between the two different setups. But we don't know at this point, so we'll have to see as the respective teams go about improving their measurements even further. (Incidentally, this measurement helps rule out that the electron could be a compound particle, as such a state would conflict with the measured electron's anomalous magnetic moment at this level of precision.)

You'll notice there are no units on that value. That's because \(\alpha\) is a member of a small group of pure numbers which define the universe known as ‘dimensionless constants,’ whose values are independent of the units used to measure them. For comparison, if you measure the speed of light c in different systems, the numerical value will differ; for instance, approximately 186,000 miles per second or approximately 300,000,000 meters per second. The value of \(\alpha\), on the other hand, is always approximately 1/137, no matter what you measure it in. This lack of dimensionality is really quite remarkable when you think about it, and has fascinated physicists practically since \(\alpha\) was introduced by Arnold Sommerfeld in 1916.

Interestingly, it's looking like my PhD work will be able to put constraints on variation in \(\alpha\) at about the level of 10 parts per billion. That's two orders of magnitude better than the current best constraints from astronomical tests (~1 part per million), and only about another two orders of magnitude larger than the precision with which we can measure \(\alpha\), which is rather amazing to think about. Hopefully before too much longer I'll have my own published articles to share here on the subject. A hui hou!