Measurement Quantization and a Quantum Model of Gravity with Quantum Expressions For Special and General Relativity

Vasil Dinev Penchev

M. Bauer, Cesar Augusto Aguillon, Gustavo García

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

Stephen Bruce Sontz

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.

Pedro F. Gonzalez-Diaz

Lajos Diósi

We discuss the Hamiltonian hybrid coupling between a classical and a quantum subsystem. If applicable to classical gravity coupled to quantized matter, this hybrid theory might realize a captivating ``postquantum'' alternative to full quantum gravity. We summarize the nonrelativistic hybrid dynamics in improved formalism adequate to Hamiltonian systems. The mandatory decoherence and diffusion terms become divergent in special and general relativistic extensions. It is not yet known if any renormalization method might reconcile Markovian decoherence and diffusion with relativity. Postquantum gravity could previously only be realized in the Newtonian approximation. We argue that pending problems of the recently proposed general relativistic postquantum theory will not be solved if Markovian diffusion/decoherence are truly incompatible with relativity.

Norbert Wiener, Dirk Jan Struik