Correlation Measure Equivalence in Dynamic Causal Structures of Quantum Gravity

TL;DR

This paper establishes an equivalence between correlation measures in causally-unbiased quantum gravity spaces and causally-biased standard spaces, enabling correlation analysis with well-defined mathematical tools.

Contribution

It introduces a transformation that allows correlation measures in quantum gravity to be analyzed using standard causally-biased entropy functions after data correction.

Findings

Correlation measures are equivalent in both spaces.

Standard causally-biased entropy functions can be applied after data correction.

Mathematical properties of correlation measures are preserved across spaces.

Abstract

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.