Regge calculus is a method in theoretical physics that approximates curved spacetime by using a lattice of flat, geometric elements. Developed by Italian physicist Tullio Regge in 1961, it provides a way to study general relativity in a discrete setting rather than relying on continuous mathematics.
Key ideas of Regge calculus:
- Spacetime is broken into a mesh of simplexes (the multidimensional equivalent of triangles and tetrahedra).
- Each simplex is flat inside, but when assembled, the overall structure approximates curvature.
- Curvature is not spread out smoothly but concentrated at the edges where the simplexes meet—specifically at “hinges” in the lattice.
This method is particularly useful for:
- Numerical simulations of Einstein’s field equations in curved spacetimes.
- Exploring quantum gravity models, especially those based on discrete structures like loop quantum gravity or causal dynamical triangulations.
- Providing a way to model gravitational systems without requiring continuous differential geometry.
Regge calculus has become a foundational tool for discrete approaches to spacetime, allowing physicists to approximate complex geometries and understand how spacetime curvature can emerge from simple, local interactions between flat pieces.