Related papers: Discrete Hilbert Space, the Born Rule, and Quantum…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special…
Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In…
Quantum gravitational effects become significant at a cut-off species scale that can be much lower than the Planck scale whenever we get a parametrically large number of fields becoming light. This is expected to occur at any perturbative…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger-Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational…
The existence of a minimum length and a generalization of the Heisenberg uncertainty principle seem to be two fundamental ingredients required in any consistent theory of quantum gravity. In this letter we show that they would predict…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low…
This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity…
We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we…
The idea that gravity can act as a regulator of ultraviolet divergences is almost a century old and has inspired several approaches to quantum gravity. In fact, a minimum Planckian length can be shown to emerge from the nonlinear dynamics…
Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
We consider Hilbert's problem of the axioms of Physics at a qualitative or conceptual level. This issue is more pressing than ever as we seek to understand how both General Relativity and quantum theory could emerge from some deeper theory…