Correlation measure equivalence in dynamic causal structures of quantum gravity. Issue 1 (7th January 2020) - Gyongyosi, Laszlo
Summary: 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 make 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.