Related papers: Stochastic Ricci Flow dynamics of the gravitationa…
The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory,…
The possibility that the collapse of the wave function in quantum mechanics is a real and ultimately connected to (classical) gravity has been debated for decades, with main contributions by Di\'osi and Penrose. In particular, Di\'osi…
The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical…
We investigate the Di\'osi-Penrose (DP) proposal for connecting the collapse of the wave function to gravity. The DP model needs a free parameter, acting as a cut-off to regularize the dynamics, and the predictions of the model highly…
We propose an effective non-relativistic framework in which wave-function collapse emerges as a deterministic dynamical instability induced by gravitational self-interaction and regulated by short-distance repulsion. The dynamics is…
Roger Penrose proposed that a spatial quantum superposition collapses as a back-reaction from spacetime, which is curved in different ways by each branch of the superposition. In this sense, one speaks of gravity-related wave function…
We follow a new pathway to the definition of the Stochastic Quantization (SQ), first proposed by Parisi and Wu, of the action functional yielding the Einstein equations. Hinging on the functional similarities between the Ricci-Flow equation…
Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on…
A simple and natural introduction to the concept and formalism of spontaneous wave function collapse can and should be based on textbook knowledge of standard quantum state collapse and monitoring. This approach explains the origin of noise…
Imposing non-integrable constraints on Ricci flows of (pseudo) Riemannian metrics we model mutual transforms to, and from, non-Riemannian spaces. Such evolutions of geometries and physical theories can be modelled for nonholonomic manifolds…
On the basis of a proposed model of wave function collapse, we investigate spontaneous localization of a quantum state. The model is similar to the Ghirardi-Rimini-Weber model, while we postulate the localization functions to depend on the…
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the…
The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential…
We find the regime of our recently constructed topological nonrelativistic quantum gravity, in which Perelman's Ricci flow equations on Riemannian manifolds appear precisely as the localization equations in the path integral. In this…
We elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse-grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation,…
Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum…
The paper proposes a statistical fields theory of quantum reference frame underlying the Perelman's analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a d=4-{\epsilon} quantum non-linear sigma…
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability…
Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement…