I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to “save” the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role.

中文翻译：

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封闭的时间曲线，奇异性和因果关系：从哥德尔到时间保护的调查

我对K.Gödel在1949年的旋转宇宙模型中首次认识到的历史进行了历史考察，讨论了宇宙一般相对论模型中闭合的类似时间的曲线的存在，打开了过去时间旅行的物理可能性。强调过去的旅程与没有时空奇点的时空模型密切相关。由于在物理上合理的假设下，这种奇异性是广义相对论方程的必然结果，因此只有在违反这些假设中的一个或另一个时，过去的时间旅行才有可能。虫洞式解决方案就是这种情况。S.霍金和其他作者试图通过提倡按时间顺序进行保护的物理机制来“保存”过去时间旅行的悖论后果。然而，即使考虑到地平线附近的量子涨落，这种机制目前仍然未知。我在简短的行人讨论中对因果动态三角剖分进行了简短的讨论，因果三角剖分是一种因果关系起着重要作用的量子引力方法。