Uses of non-commutative geometry in quantum gravity

广义相对论编码了我们对时空经典性质的理解。这包括引力，但它没有描述时空的基本量子性质。例如，接近大爆炸，接近黑洞的奇点，理论就不再有效，因为量子效应开始出现。量子引力理论的发展是当代理论物理所面临的最具挑战性的问题之一。非对易几何和圈量子引力是解决这个问题的两种方法。他们使用各种数学技术为量子时空的概念提出了有希望的候选者。

The theory of general relativity encodes our understanding of the classical nature of space-time. This includes gravity, but it does not describe the fundamental quantum nature of space-time. For example, close to the Big Bang, and close to the singularity in a black hole, the theory ceases to be valid because quantum effects set in. The development of a quantum gravity theory is one of the most challenging problems faced by contemporary theoretical physics. Non-commutative geometry and loop quantum gravity are two approaches to tackle this issue. They propose promising candidates for the notion of quantum spacetime using a variety of mathematical techniques.