Barrow entropy and spacetime foam

Quantum gravitational effects, on the one hand, lead to a limitation in the accuracy of measuring spatial and time intervals, and, on the other hand, they generate a discrete of spacetime structure (quantum foam). The common source of both measurement limitations and discreteness of spacetime is quantum fluctuations, so their characteristics must be related to each other. We study such a relationship using Barrow entropy as a source of fractal spacetime structure. The minimum inaccuracy in measuring spacetime intervals is expressed through the Barrow entropy parameter. The connection between the level of fractality and the speed of information processing is considered.