Visualizing Four Dimensions in Special and General Relativity

Gravitational waves black hole neutron star
(Image via Mark Myers/OzGrav, All Rights Reserved)

Modern physics unfolds on the stage of four-dimensional spacetime. Grappling with century-old ideas of space and time, Albert Einstein revolutionised our understanding of the cosmos by merging space and time into a four-dimensional entity that takes an active role in shaping the laws of physics.


While experiments have repeatedly confirmed Einstein’s theories, the abstract character of this physical knowledge contradicts the common sense of many. Based on the physics of relativity and the mathematics of differential geometry, scientists have developed visualisations and representations of spacetime to make Einstein’s ideas more intelligible.


My latest Springer Nature chapter explores the links between the mathematics of space and time and our historic struggle to visualise these concepts. Technology serves as the lens to unpack the fruitful interplay between mathematics, physics, and arts that has shaped our understanding of spacetime. Linking mathematical concepts with physical intuition and artistic vision, imaginative thinkers developed representations that led from simple spacetime diagrams and analogies to powerful numerical simulations and virtual environments that allow exploring the extreme physics of black holes and gravitational waves. Visualisations of spacetime continue to be an active field of research that is driven by interdisciplinary efforts to understand the cosmos.

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