Multi-layer statistical gravity on the boundary

[摘要] Starting from an important research path, we consider gravity as a collective phenomenon governed by statistical mechanics. While previous studies have focussed on the thermodynamic heat flow across a 2d-horizon as perceived by a single, accelerated observer, we evaluate here the number of microscopic states arising for multiple observers perceiving multiple horizons within foliations of the boundary of a space-time region. This yields a temperature-independent, Boltzmann-type "entropy" which is equivalent to the boundary action and which we call m-entropy. According to its statistical interpretation, the m-entropy distribution as a function of the gravitational field is maximum when Einstein's Field Equations hold. However, if the number of "atoms of space" is small, Einstein's Equations do not hold and no sharp geometry can be defined. On the other hand, the transition probability of microstates can be computed and can be interpreted as processes of a (alternative) model of quantum space-time.

[发布机构] Department of Physics, University of Zurich, Winterthurerstrasse 190, Zürich; 8057, Switzerland^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Accelerated observers;Collective phenomena;Einstein's equations;Einstein's field equations;Entropy distribution;Statistical interpretation;Temperature independents;Transition probabilities