量子引力动力学因果结构中的关联测度等价性
Correlation Measure Equivalence in Dynamic Causal Structures of Quantum Gravity
摘要：
证明了因果无偏量子引力空间与因果有偏标准空间的关联测度函数之间的等价变换。量子引力理论融合了广义相对论的动态（非固定）因果结构和量子力学的量子不确定性。在量子引力空间中，事件是因果不可分的，所有的时间偏差都为零，这使得标准的因果偏差熵和相关测度函数无法使用。由于校正的因果无偏熵函数导致一个未定义的，模糊的数学结构，在我们的方法中，校正是在因果无偏空间的数据表示。在这里，我们证明了标准的因果偏差熵函数与数据校正可以用来识别动态因果结构中的相关性。作为推论，因果有偏相关测度函数的所有数学性质都保持在因果无偏空间中。等价变换使我们能够测量量子引力空间中的相关性，具有量子香农理论的因果偏置函数的稳定的、定义明确的数学背景和装置。
英文摘要：
We prove an equivalence transformation between the correlation measure functions of the causally-unbiased quantum gravity space and the causally-biased standard space. The theory of quantum gravity fuses the dynamic (nonfixed) causal structure of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity space, the events are causally nonseparable and all time bias vanishes, which makes it no possible to use the standard causally-biased entropy and the correlation measure functions. Since a corrected causally-unbiased entropy function leads to an undefined, obscure mathematical structure, in our approach the correction is made in the data representation of the causally-unbiased space. Here we prove that the standard causally-biased entropy function with a data correction can be used to identify correlations in dynamic causal structures. As a corollary, all mathematical properties of the causally-biased correlation measure functions are preserved in the causally-unbiased space. The equivalence transformation allows us to measure correlations in a quantum gravity space with the stable, well-defined mathematical background and apparatus of the causally-biased functions of quantum Shannon theory.
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