Thoughts on Quantum Events, Quantizing Gravity and von Neumann Algebras

Abstract

This short document presents no new results. It is a collection of related ideas that may lead to a way of quantizing gravity. To achieve this it may be relevant to use my recent new approach to quantum theory, which is based on quantum events. Given that most standard quantum texts do not define a mathematical object which corresponds to a physical event, the definition of a quantum event is motivated and discussed in detail. This in turn leads to the idea that the mathematical object that contains enough quantum events for describing a quantum system is a von Neumann algebra. The next idea is that the kinematics of special relativity (as embodied in flat Minkowski space) should be quantized as a first step in the program of the quantization of general relativity, that is, quantizing Einstein's equation. It must be emphasized that the events of special relativity are viewed as part of the kinematics, rather than of the dynamics of that theory. The same holds for general relativity. Similarly, I am viewing quantum events as part of the kinematics of quantum theory, even though some find this to be counterintuitive. An Appendix shows how ``collapse'' is easily understood in this new approach to quantum theory.