Figure 1
Conventional 3D Minkowski spacetime (two space axes, x, and y, and one time axis, ct, depicted in the left panel) is hyperbolic. Events in the past and future at a fixed spacetime distance from the origin form two sheets of the hyperbola as shown. A new reformulation of special relativity by Gopalan, called the renormalized blended spacetime (RBS), transforms the Minkowski hyperbolic sheets into a Euclidean sphere (right panel). This topological transformation allows one to express the symmetries of the Minkowski spacetime, namely a combination of Euclidean and hyperbolic rotations, all as pure Euclidean rotations. The relativistic physics content in both formulations is equivalent. (Figure courtesy of Hari Padmanabhan, The Pennsylvania State University, USA.) |