We provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the Ghirardi-Rimini-Weber model. We anticipate that the collapse operators of our class of models may play a role in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states---a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model---supposed to be small.
In this study, a relativistic formulation of the
(q)-deformed Dunkl-Fokker-Planck equation in
(1+1)-dimensions is constructed within the reflection-deformed quantum framework. In this case, the formalism includes
(q)-deformed Dunkl operators and reflection symmetry to build a generalized dynamical structure for a relativistic quantum systems framework. Moreover, the corresponding
(q)-Wigner-Dunkl supersymmetric configuration is established via the construction of deformed ladder operators and supersymmetric algebraic relations, yielding a consistent spectral representation of the model within the algebraic framework. The analysis extends to the harmonic oscillator with centrifugal interaction, where exact algebraic solutions, similarity reduction techniques, and closed energy spectra are obtained analytically in detail. The role of the deformation parameter and reflection operator on spectral properties and wavefunction structure is examined systematically in detail. A generalized Foldy-Wouthuysen (FW) transformation is introduced within the deformed Dunkl framework to achieve relativistic decoupling of positive- and negative-energy sectors within the present theoretical formulation. In this case, this approach yields an effective reduced Hamiltonian, including higher-order relativistic and deformation-induced terms. Also, the associated Dunkl-Fokker-Planck dynamics generated through high-order FW reduction are examined in detail for reflection-deformed relativistic quantum systems. In this context, results obtained here yield a unified algebraic and relativistic description of
(q)-deformed Dunkl structures and construct a consistent framework for investigating supersymmetric and relativistic properties in reflection-symmetric quantum models in general.
This is the fifth update for the quantum gravity framework project. The research work has been split into two parts: Part A deals with unconscious matter, while Part B deals with conscious matter. Each has its own abstract. I introduce retrocausality in both. In Part A, based on the first five papers, I finalize a three-set of fundamental postulates for understanding time, quantum reduction, and consciousness from quantum general relativistic concepts. Then I introduce a new reduction theory that includes retrocausality and spontaneous reduction, and further concepts to include conscious and unconscious influence. Then I discuss three postulates in the quantum general relativistic framework. Toward the end, I discuss sample calculations and experimental verifications. I summarize various calculations done in the previous versions of the Quantum General Relativistic Framework. In Part B of this paper, I propose a set of ideas to explain the phenomena of life and consciousness in the universe and their relation to the interpretation of quantum mechanics using my past papers and other important work. Consciousness is described as a result of specific dynamical configurations of matter and fields aided by fundamental properties of nature proposed in this paper. First, I review the various theories of consciousness in current literature and come up with various hypotheses, definitions, and propositions to build a physical theory of consciousness. I propose three sets of postulates on the physical foundations of consciousness from a quantum general relativistic background, using the proposals in part A, to understand time and reduction. Various new concepts are introduced. The concept of classicum is introduced as an analog of quantum, and its relation to conscious being is discussed. Mathematical models for various ideas are discussed. I discuss theory and experiments to verify these.