Does space stretch its contents as the universe expands? Usually, we say the answer is no—the stretching of space is not like the stretching of a rubber sheet that might drag things with it. In this paper, we explore a potential counterexample—namely, we show that it is impossible to make an arbitrarily long object in an expanding universe, because it is impossible to hold the distant end of the object ‘stationary’ with respect to us (as defined in the Friedmann–Lemaître–Robertson–Walker metric). We show that this does not mean that expanding space has a force associated with it, rather, some fictitious forces arise due to our choice of reference frame. By choosing our usual time slice (where all comoving observers agree on the age of the universe), we choose a global frame that does not correspond to the frame of any inertial observer. As a result, simple relativistic velocity transforms generate an apparent acceleration, even where no force exists. This effect is similar to the fictitious forces that arise in describing objects in rotating reference frames, as in the case of the Coriolis effect.

中文翻译：

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一个无限长的物体能适应膨胀的宇宙吗？

随着宇宙的膨胀，空间是否会拉伸其内容？通常，我们说答案是否定的——空间的拉伸不像橡皮布的拉伸，它可能会拖拽物体。在本文中，我们探讨了一个潜在的反例——即，我们证明不可能在膨胀的宇宙中制造任意长的物体，因为不可能将物体的远端相对于我们保持“静止”（如在 Friedmann-Lemaître-Robertson-Walker 度量中定义）。我们表明，这并不意味着膨胀的空间具有与之相关的力，而是由于我们选择参考系而产生了一些虚构的力。通过选择我们通常的时间片（所有共同运动的观察者都同意宇宙的年龄），我们选择了一个与任何惯性观察者的坐标系都不对应的全局坐标系。因此，简单的相对论速度变换会产生明显的加速度，即使在不存在力的情况下也是如此。这种效应类似于在旋转参考系中描述物体时产生的虚拟力，例如科里奥利效应。