spin foam

History

The idea grew out of John Wheeler's foam model in the 1950s, and the modern incarnation — spin foams — was developed in the 1990s by Carlo Rovelli, Lee Smolin, and others.

How it works

Just as molecules in a crystal form a lattice, spin 'cubes' connect, forming quantum geometry. At very high energies, this pattern might manifest, perhaps inside black holes or at the beginning of the Big Bang.

History

The idea grew out of John Wheeler's foam model in the 1950s, and the modern incarnation — spin foams — was developed in the 1990s by Carlo Rovelli, Lee Smolin, and others.

How it works

Just as molecules in a crystal form a lattice, spin 'cubes' connect, forming quantum geometry. At very high energies, this pattern might manifest, perhaps inside black holes or at the beginning of the Big Bang.

History

The roots of the idea go back to John Wheeler, who in 1955 suggested that at Planck scales, spacetime turns into a 'quantum foam' due to fluctuations. In the 1990s, Carlo Rovelli and Lee Smolin, developing loop quantum gravity, turned this into a precise mathematical structure of spin foams, where amplitudes are computed using representation theory. John Baez also made significant contributions, connecting foams with topological quantum field theory.

How it works

Spin foam is built from 4-simplices (four-dimensional analogs of tetrahedra), whose faces are colored by spins. Spacetime arises as the history of merging and splitting of these quantum cells. The transition amplitude is computed according to rules similar to Feynman's, but with discrete spatial quanta. It resembles a crystal lattice, where defects and vibrations are interpreted as particles. The formalism leads to a discrete spectrum of areas and volumes and eliminates singularities, for example, in black holes and the Big Bang.

Open problems & fun facts

How to incorporate matter fields into spin foams and obtain the Standard Model?; How to prove that the macroscopic limit of spin foam gives smooth spacetime with general relativity?; How to connect spin foam to observable effects, for example, in the cosmic microwave background?

💡 In some models, spin foam turns out to be dual to tensor networks, which gave rise to the hypothesis of the holographic nature of gravity: our three-dimensional sensations may be a projection of a two-dimensional quantum foam on the boundary.