Do vacuum fluctuations prevent the creation of closed timelike curves?
Do vacuum fluctuations prevent the creation of closed timelike curves?
复制标题
真空波动是否会阻止闭合类时曲线的创建？
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
K. Thorne
中科院分区：
文献类型：
--
作者：
Sung;K. Thorne
在其他地方已经证明，在具有多个连通空间切片的经典时空（虫洞时空）中，可以一般地形成闭合的类时曲线。没有封闭类时曲线的初始时空区域和具有封闭类时曲线的后续区域之间的边界是柯西视界，柯西视界可以对小的经典扰动保持稳定。本文通过计算柯西视界附近量子化场的重整化应力-能量张量，研究量子化场对真空涨落的稳定性。计算仅限于一个无质量的共形耦合标量场，但有人认为，结果将是相同的顺序为其他非相互作用的量子场的统一因素内。对于任何具有闭合类时曲线的时空，计算都是按数量级给出的，然后对这样一个时空的一个具体例子给出详细的计算：一个具有可穿越虫洞的时空，虫洞的口通过它们的相对运动产生闭合的类时曲线。重整化的应力-能量张量被发现发散作为一个接近柯西视界。
然而，这种发散是非常微弱的：如此微弱，以至于在其中一个虫洞口的静止坐标系中可以看到，真空极化的引力只使口附近的时空度规扭曲了δ g μ ν VP（lP/D）（lP/Δ t），其中Δ t是到达柯西视界的适当时间，D是柯西视界形成时两个口之间的距离。对于一个D = 1 m的宏观虫洞，当一个虫洞在视界的普朗克长度内时，δ g μ ν VP仅增长到lP/D = 10 - 35。由于经典时空的概念本身通常被认为是失败的，并被Δ t lP尺度上的量子引力的量子泡沫所取代，作者们由此推测，真空极化发散在达到微小尺度lP/D时被量子引力切断，时空在宏观上保持光滑和经典，并毫无困难地发展出封闭的类时曲线。霍金对此做出了回应，他指出柯西视界附近的时空在D Δ t（在某种意义上是标架不变的）变得小到△ lP2之前仍然是经典的，相应地直到δ g μ ν VP △ lP2，结果，真空偏振发散将阻止闭合的类时曲线的形成。对这两种结构进行了讨论和对比。对它们进行测试的尝试可能会使人们对量子引力的候选理论有更深入的了解。
It has been shown elsewhere that in a classical spacetime with multiply connected space slices (wormhole spacetime), closed timelike curves can form generically. The boundary between an initial region of spacetime without closed timelike curves and a later region with them is a Cauchy horizon which can be stable against small classical perturbations. This paper investigates stability against vacuum fluctuations of a quantized field, by calculating the field’s renormalized stress-energy tensor near the Cauchy horizon. The calculation is restricted to a massless, conformally coupled scalar field, but it is argued that the results will be the same to within factors of order unity for other noninteracting quantum fields. The calculation is given in order of magnitude for any spacetime with closed timelike curves, and then a detailed calculation is given for a specific example of such a spacetime: one with a traversable wormhole whose mouths create closed timelike curves by their relative motions. The renormalized stress-energy tensor is found to diverge as one approaches the Cauchy horizon.
However, the divergence is extremely weak: so weak, that as seen in the rest frame of one of the wormhole mouths the vacuum polarization’s gravity distorts the spacetime metric near the mouth by only δgμνVP∼(lP/D)(lP/Δt), where Δt is the proper time until one reaches the Cauchy horizon and D is the distance between the two mouths when the Cauchy horizon forms. For a macroscopic wormhole with D∼1 m, δgμνVP has only grown to lP/D∼10-35 when one is within a Planck length of the horizon. Since the very concept of classical spacetime is normally thought to fail, and be replaced by the quantum foam of quantum gravity on scales Δt≲lP, the authors are led to conjecture that the vacuum-polarization divergence gets cut off by quantum gravity upon reaching the tiny size lP/D, and spacetime remains macroscopically smooth and classical and develops closed timelike curves without difficulty. Hawking, in response to this, has conjectured that the spacetime near the Cauchy horizon remains classical until DΔt (which in a certain sense is frame invariant) gets as small as ∼lP2, and correspondingly until δgμνVP∼1, and that, as a result, the vacuum-polarization divergence will prevent the formation of closed timelike curves. These two conjectures are discussed and contrasted. The attempt to test them might produce insight into candidate theories of quantum gravity.