Related papers: Origin of Classical Singularities
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
Recent work has revealed intriguing connections between a Belinsky-Khalatnikov-Lifshitz-type analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the `maximally extended'…
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…
I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in…
We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…
After a brief review of the standard definition and analysis of classical singularities in general relativistic spacetimes, and of quantum singularities in static spacetimes with timelike classical singularities, an extension of quantum…
We study classical solutions of one dimensional rotating shallow water system which plays an important role in geophysical fluid dynamics. The main results contain two contrasting aspects. First, when the solution crosses certain threshold,…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
We conjecture that space-like singularities are simply regions in which all available degrees of freedom are excited, and the system cycles randomly through generic quantum states in its Hilbert space. There is no simple geometric…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
The transition from the quantum to the classical world is not yet understood. Here we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except in some specific basis. But we have no…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical…
We construct a class of analytic solutions with two free parameters to the five-dimensional Einstein field equations, which represents the collision of two timelike 3-branes. We study the local and global properties of the spacetime, and…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…