基于自引力的Salecker-Wigner-Karolyhazy格丹肯实验
Salecker-Wigner-Karolyhazy Gedankenexperiment in light of the self-gravity
摘要：
在标题中提到的格丹肯实验中，时空测量的不精确性与钟的波函数随测量所需时间的推移而扩展有关。狭义相对论对测量时间提出了一个限制，它不能任意减少，因为用于测量的信号不能以大于光速的速度传播。根据这种推理，人们可以得出结论，时钟应该足够重，以减缓其波函数随时间的扩展。然而，广义相对论给钟的质量设定了一个上限，因为它的尺寸必须大于与之相关的史瓦西半径，这样就达到了长度测量的极限。然而，正如下面所讨论的，考虑到自引力效应，对这个问题的另一个见解就来了。因此，长度测量的不确定度降低到普朗克长度。
英文摘要：
In Gedankenexperiment mentioned in the title, the imprecision in space-time measurement is related to the spreading of clock's wave-function with the passage of time required for the measurement. Special relativity puts a bound on the measurement time, it cannot be reduced arbitrarily as the signal used for the measurement cannot propagate with speed greater than that of light. In view of this reasoning, one is led to conclude that the clock should be heavy enough to slow down its wave-function from spreading with time. However, the general relativity puts an upper bound on clock's mass, since its size must remain greater then the Schwarzschild radius associated to it. This way one reaches a limit in length measurement. However, as is discussed below, an additional insight into the question comes by taking into account self-gravitational effects. As a result, the uncertainty in length measurement is reduced to the Planck length.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
