What happens when you take general relativity’s central lesson seriously and quantise geometry itself — 30 interactive demonstrations of a theory with no background stage. Rewrite gravity in terms of what a vector does when carried around a loop, and space turns out to have a basis of labelled graphs. Area and volume become operators with discrete spectra, there is a smallest nonzero patch of surface, the Big Bang singularity becomes a bounce, and counting the ways a graph can pierce a horizon gives back the Bekenstein-Hawking entropy. Every idea is shown geometry-first, with the operator formalism one toggle away — including an honest final lesson on what is still broken.
See also: Relativity for the classical theory whose background independence starts all of this, Quantum Mechanics for the operators, spectra, and states being applied here, String Theory for the other main approach to quantum gravity and a very different set of bets, Lie Groups for the SU(2) representation theory that labels every link, and Differential Geometry for the connections and parallel transport the whole theory is built from.
Two theories that each work perfectly, and a scale where they demand incompatible things of the same event
General relativity has no stage: the gravitational field and the geometry of space are the same object
Rewrite gravity in terms of what a vector does when you carry it around a loop, and the infinities go away
A graph with spins on its edges is not a picture of space — it is a quantum state of space itself
Area and volume become operators with discrete spectra, and there is a smallest nonzero patch of surface
Read the graph the other way and each node is a polyhedron, each link a shared face — space as a packing of grains
Let a spin network evolve and its history sweeps out a foam: the sum over spacetimes, one vertex at a time
Quantum geometry adds one term to the Friedmann equation, and the Big Bang singularity turns into a bounce
Count the ways a spin network can pierce a horizon and the Bekenstein-Hawking entropy comes back out
What a granular spacetime could actually do to a photon, what the data already rules out, and what is still broken