Quantum Gravity Framework 1.0
Fifteen years ago Allen Janis conducted a discussion group at university Pittsburgh, physics department, on the conceptual problems in quantum mechanics, and launched me on a quest to solve problem of unifying quantum mechanics and general relativity. There are two problems to be solved -- extract the classical reality and time from the infinite quantum superposition of quantum gravity. One needs a concept of objective measurement, a process in which our classical reality with space and time can emerge from the quantum world of superposition. Today I finished writing a research paper that is pragmatically, heuristically, oriented to address the two problems. It is closely related to many of the existing proposals. The Title and abstract is as follows:
Abstract: The purpose of this article is to outline a framework of concepts and principles to combine quantum mechanics and general relativity so that time and measurement (reduction) are present as integral parts of the basic foundations. First, the problem of time in quantum gravity and the measurement problem in quantum mechanics are briefly reviewed and the popular proposals to tackle these two problems are briefly discussed. Next, on the already known foundations of quantum mechanics, a framework of principles of dynamics is built: 1) Self-Time Evolution - Newtons first law is reinterpreted to define time, 2) Local Measurement by Local Reduction - Quantum diffusion theory is adapted, and 3) Global Evolution by Global Reduction. Ideas on how to apply the framework to study quantum general relativistic physics are discussed. Further, more general and modified forms of some of these principles are also discussed. The theoretical elements in the framework to be made concrete by further theoretical and experimental investigations are listed.
The ideas in the paper are understandable for those who understand general relativity and quantum mechanics. The basic principles proposed are quite intuitive. Some of the ideas in the article relating to decoherence and quantum diffusion are not usually explored in graduate level courses. But with computer industry shrinking the size the circuit elements all the time towards the atomic scale, and emergence of quantum computing, influence of random processes associated with quantum measurement by the environment are important design criteria. Those who want to work in fundamental physics or applied physics really need to get a hold on decoherence theories. Quantum diffusion equation proposed in  is just an equivalent of density matrix evolution equations in decoherence theories. It just a modified form of the Schrödinger equation, to reproduce the probabilistic collapse, and is very natural and intuitive. But for some reasons it is not as popular as the density matrix equation in decoherence. I believe it has to be explored more.
For me I have been searching for a way to include measurement in quantum gravity in an objective manner, so the classical reality can be extracted out of quantum world. The density matrix equation form of measurement was really not fitting very well because it deals with the square of wavefunction, and so is non-linear. But, I was very happy to know the modified Schrödinger form used in quantum diffusion theory, which was kind of linear. But I got hit by the problem of selecting a proper space time split of the four dimensional space-time manifold. I tried to establish a deterministic way to determine the foliation, but couldn’t. I finally made up mind the space-time split has to be determined probabilistically because of quantum collapse of the superposed quantum histories.
Now the framework that I have proposed is a general theory, it can be applied to single point models, all the way to infinite point model like our 3+1 dimensional universe. I have simulated models with few points, but given the quantum nature of the theory, the quantum states are a function on a multidimensional internal space, and my laptop just couldn’t handle any thing of reasonable complexity. The next step may be testing on simple models numerically.
The article is good starting point for those who want to explore the quantum aspects of reality. Attention from those who have background in physics and also in mathematics, computing are required to tackle the debacle in the foundational concepts in physics. This blog is dedicated to research in the subject matter. More updates as the research advances will be posted here. Discussion, criticisms, suggestions, comments are welcome. There is a twitter page for this blog for communication.
Revision info: It is almost one year that version 1.0 of quantum gravity framework has been published. This work has not been advertised because the author has been busy with other projects that are not related to physics. On recent review of the paper, it has been observed that the paper has many problems. It is not complete; the paper reviews well known material too much so that it is hard to differentiate between new and old; some of the definitions are recursive. The arxiv link has an updated article with improvements.
A more advanced and slightly conceptually different revision of the article has been published. Please read the next article .
 Nicolas Gisin and Ian C. Percival, Quantum State Diffusion Models applied to quantum systems, J. Phys. A: Math.Gen.25 (1992) 5677-5671