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在一个封闭的时间型曲线中，生活看来是很单调的。Life on a closed timelike curve seems pretty drab.

封闭的时间型曲线一定会导致矛盾吗？Do closed timelike curves necessarily lead to paradoxes?

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换句话说，封闭的时间型曲线让未来代表了过去。Closed timelike curves, in other words, make the future resemble the past.

而如果在拥有封闭的时间型曲线的时空里，和谐一致的情况就可能是存在的。Consistent stories are possible, even in space-times with closed timelike curves.

我们在宇宙中是以一些特定时刻来起始的，没有封闭的时间型曲线。Let’s say we start in a universe that, at some particular moment, has no closed timelike curves.

而当出现了封闭的时间型曲线时，一些事件既出现在过去，也正在未来出现。But in the presence of closed timelike curves, some events are in our past and also in our future.

在有人制造出时间机器，又创造出一个封闭的时间型曲线后，这种预测能力很快就消失了。This ability vanishes as soon as someone builds a time machine and creates a closed timelike curve.

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封闭的时间型曲线会让这样进行的程序不复存在，就如同一项简单的思维实验所揭示的那样。Closed timelike curves would make such a program impossible, as a simple thought experiment reveals.

我们可以坚持凭喜好认为，在封闭的时间型曲线中所出现的情况都是一致的。We can insist all we like that what happens in the presence of closed timelike curves be consistent.

事实上，封闭的时间型曲线能让“在某个特定的时刻中的宇宙”不能自圆其说。Indeed, closed timelike curves can make it impossible to de-fine “the universe at one moment in time.”

我们能将决定论的价值高估到要彻底拒绝承认封闭的时间型曲线存在吗？Do we value determinism so highly that we should reject the possibility of closed timelike curves entirely?

在封闭的时间型曲线存在的环境下，我们一般不能那样切割时空。In the presence of closed timelike curves, though, we generally will not be able to slice space-time that way.

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由封闭的时间型曲线引起的这些困惑，它们的最终答案也许是这些曲线不可能存在。The ultimate answer to the puzzles raised by closed timelike curves is probably that they simply cannot exist.

如果我们用一个封闭的时间型曲线来观察未来的行为，那么这些行为就成了预先注定的。If we use a closed timelike curve to observe something about our future actions, those actions become predestined.

问题的关键在于在封闭的时间型曲线中没有一个连续一致的“时间箭头”。The nub of the problem is that you cannot have a consistent “arrow of time” in the presence of closed timelike curves.

通常，沿着一个封闭的时间型曲线发生的事件不可能与沿着这个曲线不间断地增加的一致性相符合。In general, events along a closed timelike curve cannot be compatible with an uninterrupted increase of entropy along the curve.

对于这类冷天体的类光和类时测试粒子的偏转角公式存在一个依赖于破缺标度的因子。There is a factor which depends on the breaking scale in the formula of deflection angle of timelike and spacelike test particles in the D-stars.

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利用对偶速度的概念，定义了物质运动的类时表象和类空表象。On the basis of the concept of the dual velocity this paper also discusses the timelike and space- like representations of the timelike and spacelike motions.

对于这类冷天体的类光和类时测试粒子的偏转角公式存在一个依赖于破缺标度的因子。There is a factor which depends on the breaking scale in the formula of angle of deflection of timelike and spacelike test particles in this kind of cold stars.

与封闭的时间型曲线相关的这种扭曲会导致我们的切分转回原处，不可能把所有的时空分成各自不同的时刻。The warping associated with the closed timelike curve could cause our slice to twist back on itself, making it impossible to divide all of space-time into distinct moments.