时空的局部线性是从概率的线性继承来的吗？
Is the local linearity of space-time inherited from the linearity of probabilities?
摘要：
从经典力学到现代的局部洛伦兹不变性概念，线性空间的出现，用矢量和张量描述物理量，在所有物理学中无处不在。然而，尽管这在物理学家看来很自然，但大多数计算机科学家会认为，类似于“局部线性切空间”的东西并不是非常典型的，实际上是任何可想象的世界或算法的一个相当令人惊讶的性质。在本文中，我们认真地看待计算机科学家的观点，并询问是否有任何内在的信息理论原因可以期待这种线性概念出现在物理学中。我们给出了一系列简单的论证，包括量子信息理论、群表示理论和量子引力中的重整化，这些论证支持了一个令人惊讶的论点：即时空的局域线性最终可能是概率线性的结果。虽然我们的论证包含了相当多的推测，但它们具有独立于任何关于量子引力的详细假设的优点，而且它们与高能物理学中涌现时空的几个独立的最新观点是一致的。
英文摘要：
The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the physicist, most computer scientists would argue that something like a "local linear tangent space" is not very typical and in fact a quite surprising property of any conceivable world or algorithm. In this paper, we take the perspective of the computer scientist seriously, and ask whether there could be any inherently information-theoretic reason to expect this notion of linearity to appear in physics. We give a series of simple arguments, spanning quantum information theory, group representation theory, and renormalization in quantum gravity, that supports a surprising thesis: namely, that the local linearity of space-time might ultimately be a consequence of the linearity of probabilities. While our arguments involve a fair amount of speculation, they have the virtue of being independent of any detailed assumptions on quantum gravity, and they are in harmony with several independent recent ideas on emergent space-time in high-energy physics.
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