Related papers: A Summary: Quantum Singularities in Static and Con…
The physical world is quantum. However, our description of the quantum physics still relies much on concepts in classical physics and in some cases with `quantized' interpretations. The most important case example is that of spacetime. We…
While Quantum Gravity remains elusive and Quantum Field Theory retains the interpretational difficulties of Quantum Mechanics, we have introduced an alternate approach to the unification of particles, fields, space and time, suggesting that…
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge…
We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation…
I argue that there are no physical singularities in space-time. Singular space-time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein's field equations. I…
Simple classical mechanical systems and solution spaces of classical field theories involve singularities. In certain situations these singularities can be understood in terms of stratified Kaehler spaces. We give an overview of a research…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
Challenging Mermin's perspective that ``correlations have physical reality; that which they correlate does not'' we argue that correlations and correlata are not fundamentally distinct. These are dual concepts depending on the tensor…
The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
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…
We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional,…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at…