Not only do curved spaces fascinate scientists and non-scientists, but they are also at the heart of general relativity and modern theories of quantum gravity. Optical systems can provide models for the wave and quantum behavior of curved spaces. Here we show how to construct optical systems that simulate triangulations of 3D curved spaces, for example, the curved 3D surface of a 4D hypersphere. Our work offers a new approach to the optical simulation of curved spaces, and has the potential to lead to new ways of thinking about physics in curved spaces and simulating otherwise inaccessible phenomena in non-Euclidean geometries.

中文翻译：

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弯曲空间的光学三角剖分

弯曲空间不仅使科学家和非科学家着迷，而且还是广义相对论和现代量子引力理论的核心。光学系统可以为弯曲空间的波和量子行为提供模型。在这里，我们展示了如何构建光学系统来模拟3D弯曲空间的三角剖分，例如4D超球面的弯曲3D表面。我们的工作为弯曲空间的光学模拟提供了一种新方法，并有可能带来新的方法来思考弯曲空间中的物理学，并模拟非欧几里得几何学中其他无法接近的现象。