A playground for the ideas that run the universe

Lagrangian Playground is a collection of interactive physics: build Feynman diagrams, bend spacetime around black holes, and take a hands-on course in quantum mechanics. Everything you see is computed live from the real equations – the same mathematics physicists use, just with sliders attached.

Why I built this

Physics was my first love. I studied Maths and Theoretical Physics at university and, like many physics graduates, drifted into software engineering afterwards. The equations went quiet for years.

What brought them back, honestly, was the new generation of AI tools. Suddenly I could revisit the subject properly – relearn at my own pace, ask the questions I’d been too embarrassed to ask, and check my understanding the only way that really works: by building. You can’t fake a working simulation. If the orbit precesses wrongly or the interference fringes land in the wrong place, the mathematics tells on you. Getting these simulations right forced a depth of understanding that rereading a textbook never did.

Somewhere along the way, relearning became rebuilding, and rebuilding became this site. It is me rekindling a first love in public – and trying to share physics the way I always wished it had been taught: interactively, visually, with the equations moving.

What does “Lagrangian” mean?

It’s arguably the best idea physics has ever had. In the 18th century, Joseph-Louis Lagrange found a new way to do mechanics: instead of tracking forces push by push, write down a single quantity – now called the Lagrangian, written ℒ (the letter in our logo). For simple systems it’s just kinetic energy minus potential energy, L = T − V. Feed it into the principle of least action – nature takes the path that makes the total action stationary – and the equations of motion fall out.

The astonishing part is how far that one idea reaches. Planetary orbits come from a Lagrangian. Einstein’s general relativity comes from a Lagrangian – the black-hole geodesics in our Spacetime Visualizer are paths of extremal time. The entire Standard Model of particle physics is a Lagrangian – every Feynman diagram you can build here is a picture of one of its terms. And in quantum mechanics, Feynman showed that a particle in some sense takes every path, each weighted by its action – which is where the interference at the heart of our quantum course comes from.

One idea, running through every playground on this site. Hence the name.

No ads. No signups.

Everything here is open to everyone, and always will be: no account, no ads, no tracking you around the internet, no premium tier, no “unlock the rest of the course”. Curiosity about how the universe works shouldn’t have a toll booth in front of it.

If you want to support the project, the best way costs nothing: share it with one person who’d love it – a student, a teacher, the friend who always asks about black holes.

Follow along

Each new section of the course becomes a short film on Instagram – the same simulations, rendered frame by frame from the same equations.