The Koide Formula

This is my second ever post. Today I’ve decided to write about a fascinating and puzzling formula from the world of physics.

The Koide formula is a relatively simple formula which relates the masses of 3 of the fundamental particles of the standard model ($e$ for electron, $\mu$ for muon, $\tau$ for tauon):

$$\frac{m_e+m_{\mu }+m_{\tau }}{(\sqrt{m_e}+\sqrt{m_{\mu }}+\sqrt{m_{\tau }}{)}^2}\approx \frac{2}{3}$$

Since its inception by Yoshio Koide in 1981, the formula has been found to be more and more accurate with each subsequent measurement of the particle masses. This has left many people (including myself) both intrigued and puzzled, with no definitive answers.

It’s possible that the whole situation is just a mathematical fluke with no intrinsic meaning. On the other hand, it could point towards physics beyond the standard model. Some physicists have proposed specific extensions to the standard model in their attempts to explain the Koide relation.

In any case, I’m really not qualified to discuss this in much detail. I think it’s an intriguing formula that’s rarely talked about outside of physics. But the reason it’s so interesting is that, if it’s any more than just numerology, then it has profound implications for the very nature of existence.

I say this because, if there does turn out to be some principled reason why the Koide relation should hold exactly (or almost exactly), and if this reason can be supported experimentally, then it would allow us to predict one of the three particle masses in terms of the other two. That would be a big win for modern physics, because physical theories tend to have more predictive/explanatory power when they have fewer “moving parts” or free parameters.

That’s all from me today. I hope this was of interest for those who are scientifically inclined. Stay tuned for more physicsy stuff.

Take care!

Jamie