Thread by @astroparticular

1/ The Einstein Energy-Momentum Relation can be straightforwardly turned into the `Klein-Gordon Equation.` ✍🏽

Why’s that important?

The KG-Equation describes spinless particles of any charge! †

2/ If you use natural units (author’s note: ❤️) where ℏ = c = 1, and replace `E` and `p` for their quantum operators... ➡️

3/ You’ll find that the equation reduces to below.

Very serendipitiously, the *d’Alembertian* pops up and we can get a Lorentz-Invariant relativistic equation...

4/ 🎉 The Klein-Gordon Equation! 🎉

5/ Why is this important? The KG-Equation describes spinless particles of any charge.

However, unlike other wavefunctions, the norm squared |φ|^2 won’t give you a probability amplitude here, but it will give you a *charge density.*

6/ † It’s important to note though: for common spinless particles, e.g. the pion, the KG-Equation doesn’t tell the whole story because quarks & gluons also experience the Strong Force.

Oh well! 🤷🏽‍♂️

7/ 🤔 But isn’t there another cool spinless particle, that’s maybe a little more famous? Yeah, the Higgs!

In fact, if the Higgs we’ve observed is a Standard Model Higgs and not some wild, exotic kind, it should obey the KG-Equation.

8/8 Keep in mind that there are other ways to extract the KG-Equation, namely: through the Lagrangian of a scalar field or by noticing that the Dirac Equation is the “square-root” of the KG-Equation.

I /might/ make threads on these in the future. Stay tuned! 🥳

Images Credits: Wikipedia, CERN
Thread Idea Credits: @InertialObservr

#physics #athreadbyangel

I also remember having a short discussion with @PrionicProtein about this too. So credit there as well!