Singularity avoidance by collapsing shells in quantum gravity

We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A non-perturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.Comment: 5 pages, 1 figure, received honorable mention in the 2001 essay competititon, to appear in Int. J. Mod. Phys.

Gauge-invariant Hamiltonian dynamics of cylindrical gravitational waves

The model of cylindrical gravitational waves is employed to work out and check a recent proposal in Ref. [11] how a diffeomorphism-invariant Hamiltonian dynamics is to be constructed. The starting point is the action by Ashtekar and Pierri because it contains the boundary term that makes it differentiable for non-trivial variations at infinity. With the help of parametrization at infinity, the notion of gauge transformation is clearly separated from that of asymptotic symmetry. The symplectic geometry of asymptotic symmetries and asymptotic time is described and the role of the asymptotic structures in defining a zero-motion frame for the Hamiltonian dynamics of Dirac observables is explained. Complete sets of Dirac observables associated with the asymptotic fields are found and the action of the asymptotic symmetries on them is calculated. The construction of the corresponding quantum theory is sketched: the Fock space, operators of asymptotic fields, the Hamiltonian and the scattering matrix are determined.Comment: 16 pages, 1 figur

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).Comment: 15 pages, 3 figures, submitted to Phys. Rev.

Review Quantum Models of Classical World

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Implementace metodiky digitálního dvojčete

V souladu s Průmyslem 4.0 pokračuje proces digitalizace ve výrobních podnicích do fáze virtualizace, kdy konečným stavem by měla být plná virtualizace celého výrobního závodu, což však vyžaduje vysokou míru inovací. Tento článek shrnuje poznatky z implementace metodiky digitálního dvojčete v realitě výrobní společnosti. Hlavním tématem je virtualizace těžkých obráběcích strojů společnosti Škoda Machine Tool. Pro virtualizaci jsou použity moderní softwarové nástroje Siemens NX, Mechatronic Concept Designer, Simit a VNCK kernelAccording to Industry 4.0 the process of digitization in manufacturing companies has advanced to the virtualization phase. The final state should be a complete virtualization of the production plant. However, virtualization has a high demand for innovation. This article summarizes the findings of the implementation of the “Digital Twin” methodology in a real manufacturing company. The main topic is virtualization of heavy machine tools of Skoda Machine Tool Co. For the virtualization are used modern software tools Siemens NX, Mechatronic Concept Designer, Simit and VNCK kernel