One of the driving forces behind the idea that the laws of physics should be considered as a framework to make probabilistic inferences about reality, rather than as a direct representation of reality, is the conjecture that the geometry of space can be explained as the information geometry of a statistical manifold. The following are two papers in which this idea has reached a certain level of completion.   

 

“The information geometry of space-time” 39th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Proc. MDPI 33, 15 (2019); arXiv:1909.09657.

 

“Geometry from Information Geometry” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. by A.Giffin and K. Knuth, AIP Conf. Proc. 1757, 030001 (2016); arXiv.org:1512.09076.

 

The following papers are earlier exploratory attempts. 

 

“The Information geometry of Space and Time” in Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2005), ed. by K. Knuth, A. Abbas, R. Morris, and J. Castle, AIP Conf. Proc. Vol. 803, 355 (2006); arXiv.org/abs/gr-qc/0508108. 

 

“Towards a Statistical Geometrodynamics” in Decoherence, Information, Complexity and Entropy, p. 103, ed. by H.-T. Elze, (Lecture Notes in Physics, Springer, 2003); arXiv.org/abs/gr-qc/0301061.