没有时间的世界
A World Without Time
Palle Yourgrau · 初版 2002 年
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爱因斯坦与库尔特·哥德尔在爱因斯坦生命的最后十五年里是挚友，这是一个广为人知却鲜少被深入探讨的事实。两人每天一同从普林斯顿高等研究院步行回家；他们交流关于物理学、哲学、政治的见解，以及他们成长过程中那个已然消逝的德奥科学世界。然而，这段友谊所催生的重大发现却鲜为人知。到了1949年，哥德尔提出了一项惊人的证明：在任何由相对论描述的宇宙中，时间都不可能存在。爱因斯坦勉强接受了这一结论
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关于不完备性定理，我见过最棒的解释出自 Palle Yourgrau 的《A World Without Time》一书。他在讲解前的开场白写得极好：“理解哥德尔定理是你的与生俱来的权利；任何人，包括数学界的正统卫道士，都无权剥夺你享受这一乐趣的资格。”
The greatest explanation I've ever seen for the Incompleteness Theorems comes from Palle Yourgrau in his book A World Without Time. He gives an excellent introduction to his explanation: "To appreciate Godel's theorem is your birthright; let no one, including the mathematical police, deprive you of what you have a right to enjoy."
还有一本叫《A World Without Time》的书，也是讲爱因斯坦和哥德尔的，同样出版于 2005 年：https://www.amazon.co.uk/World-without-Time-Forgotten-Einste... 2005 年那会儿爱因斯坦和哥德尔这个话题似乎很流行。（修改：……
There is also the book 'A world without Time', also about Einstein and Godel, published in 2005 as well: https://www.amazon.co.uk/World-without-Time-Forgotten-Einste... The topic of Einstein and Godel seems to have been in the air in 2005. (Edit:…
>> 认为时间只是第四维度的看法具有极大的误导性。在狭义相对论中，时间方向在结构上不同于空间方向。在《A World Without Time》中，Palle Yourgrau 明确指出库尔特·哥德尔并不这么认为，而作为哥德尔好友的爱因斯坦本人在这点上也基本赞同他的看法。在这件事上我宁愿相信爱因斯坦而不是 Maudlin……
>> This notion that time is just a fourth dimension is highly misleading. In special relativity, the time directions are structurally different from the space directions. In "A World without Time" Palle Yourgrau makes it clear that Kurt Gödel didn't think so, and that Einstein himself, who was good friends with Gödel, mostly agreed with him on this. I'll take Einstein's word above Maudlin's here...…