Fluctuations and Correlations in Causal Diamonds
arXiv:2311.18049
Abstract
We argue that the correlation between the modular Hamiltonians of two causal diamonds related by a finite time translation is equal to the uncertainty in the modular Hamiltonian of the diamond in their overlap. In a separate section we investigate the relation between entropy fluctuations in a diamond, and length fluctuations calculated from the 't Hooft commutation relations.
12 pages, 3 figures, LaTeX