Physicists have long treated space and time as the stage on which quantum particles perform, not as actors in the drama ...

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 ...

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 ...

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 ...

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 ...

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 ...

Oftentimes, we think of space as an endless, mostly empty vacuum, a silent backdrop where planets, stars, and galaxies play out their dance. We also think of time as something separate, a steady ...

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation ...

Contemporary physics has learned to describe the universe with unprecedented precision. Yet when it tries to say what time is, it stumbles again and ...

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 ...

There is a glaring gap in our knowledge of the physical world: none of our well-established theories describe gravity’s quantum nature. Yet physicists expect that this quantum nature is essential for ...