Yesterday, a team of physicists from France announced a breakthrough in nailing down a "magic number" by adding three decimals to the the fine-structure constant (news article; technical paper)
$$\alpha^{-1}\approx 137.035\,999\,206(11)$$
To the layman's eyes, 3 more decimals does not seem so spectacular. Why is this such a big deal when it is about the fine-structure constant?
Best Answer
The fine structure constant tells us the strength of the electromagnetic interaction.
There are some misleading statements in the news story. The big one is how to read the result,
\begin{align} \alpha_\text{new}^{-1} & = 137.035\,999\,206(11) \\ &= 137.035\,999\,206\pm0.000\,000\,011 \end{align}
The digits in parentheses give the uncertainty in the final digits; you can see that the traditional $\pm$ notation is both harder to write and harder to read for such a high-precision measurement. The new high-precision experiment is better than the average of all measurements as of 2018, which was
$$\alpha_\text{2018}^{-1} = 137.035\,999\,084(21)$$
You can see that the new uncertainty is smaller than the old uncertainty by a factor of about two. But even more interesting is that the two values do not agree: the new result $\cdots206\pm11$ is different from the previous average $\cdots086\pm 22$ by about five error bars. A "five sigma" effect is a big deal in physics, because it is overwhelmingly more likely to be a real physical difference (or a real mistake, ahem) than to be a random statistical fluctuation. This kind of result suggests very strongly that there is physics we misunderstand in the chain of analysis. This is where discoveries come from.
This level of detail becomes important as you try to decide whether the explanations for other puzzles in physics are mundane or exciting. The abstract of the technical paper refers to two puzzles which are impacted by this change: the possibility that a new interaction has been observed in beryllium decays, and the tension between predictions and measurements of the muon’s magnetic moment, which is sensitive to hypothetical new interactions in a sneakier way.