A new breakthrough may help scientists solve some of the mysteries of the quantum realm. For the first time, physicists have been able to measure the geometrical 'shape' a lone electron adopts as it ...

Noncommutative geometry offers a radical reformulation of traditional geometrical concepts by replacing the classical notion of a manifold with a noncommutative algebra of coordinates. This approach ...

The geometry of spacetime forms the very foundation of modern gravitational theory, where the elegant interplay between curvature and matter is described by Einstein’s field equations. In this ...

In October 2015, a young mathematician named Clemens Sämann was flying home to Austria from a conference in Turin, Italy, when he had a chance encounter. He found himself seated beside Michael ...

Exploring the BTZ black hole in (2+1)-dimensional gravity took me down a fascinating rabbit hole, connecting ideas I never expected—like black holes and topological phases in quantum matter! When I ...

For more than a century, physics has treated space and time as the smooth stage on which the universe unfolds, a flexible fabric that bends but never breaks. A new wave of theories is now challenging ...

Physicists of the 19th century assumed that space was distinct from time – and two researchers now suspect they were correct to do so. Their conclusion, which comes from considering the behaviour of ...

Chiral metasurfaces can strongly twist the polarization of light, but how this process unfolds in space and time has been unclear. Scientists in China have now used ultrafast electron microscopy and ...