Chaotic deterministic quantization in a 5D general relativity

Abstract

How to quantize gravity is a major outstanding open question in quantum physics. While many approaches assume Einstein's theory is an effective low-energy theory, another possibility is that standard methods of quantization are the problem. In this paper, I analyze a quantization mechanism based on chaotic dynamics of 5D general relativity (with imaginary time) with BKL dynamics in the mixmaster universe as an example. I propose that the randomness of quantum mechanics as well as its other properties such as nonlocality derive from chaotic flow of 4D spacetime through a 5th dimension, with the metric tensor under Wick rotation to Euclidean space acting as a heat bath for other quantum fields. This is done by showing that the theory meets mixing conditions such that it is chaotically self-quantizing and quantizes other fields to which it is coupled, such that in the limit taking chaotic dynamics scale to zero the quantization is equivalent to a stochastic quantization. A classical stability analysis shows this dimension is likely spacelike.