Related papers: Quantum Space-times: Beyond the Continuum of Minko…
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an…
We emphasize that noncommutative (NC) spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as NC. In order to understand NC spacetime correctly, we need to deactivate the thought patterns that…
It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
Space-time intervals corresponding to different events on the worldline of any ponderable object (for example a clock) are time-like. In consequence, in the analysis of any space-time experiment involving clocks only the region for $c\Delta…
The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding…
Starting from a new understanding of the vacuum energy problem based on the combination of the phase space regularization and the holographic bound, we argue that quantum gravity should be understood as gravitized quantum theory, that is,…
Nature abhors an infinity. The limits of general relativity are often signaled by infinities: infinite curvature as in the center of a black hole, the infinite energy of the singular big bang. We might be inclined to add an infinite…
This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…
In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed supporting the acceptability of a point-like form of Big Bang.…
General relativity is incomplete because it cannot describe quantum effects of space-time. The complete theory of quantum gravity is not yet known and to date no observational evidence exists that space-time is quantized. However, in most…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on…
The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in…