1 A ( geometrical ) Hilbert space based quantum gravity model (original) (raw)
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Quantum-theoretic considerations for the ground state of a black hole result in a change of its interior solution. lt is shown hat the interior of a Schwarzschild black hole can be modelled by an ur-theoretically described Robertson-Walker space-time. Thereby the Schwarzschild singularity is changed into a Friedman singularity. 1. INTRODUCTON One expects that an appropriate unification of quantum theory and gravitation theory should lead to an explanation of the observed smallness of the cosmological constant and to a better understanding of the space-time singularities of classical general relativity. We do not think that one should try to avoid or even remove space-time singularities in quantized gravity; we rather take singularities as precious hints to look for a new type of unification. The usual attempts to construct a union of quantum theory and gravity are applications of quantization procedures to gravitation theory retaining the space-time continuum even at very small distances. In this paper we do not presuppose a space-time continuum first but start with abstract quantum theory, i.e., the quantum theory of binary alternatives (Drieschner et al., 1987; Görnitz, 1988 a, b). Space-time is introduced via the invariance group of the "ur," the quantized binary alternative. This invariance group turns out to be U(2).
Quantum Gravity:the axiomatic approach, a possible interpretation
Twenty years ago, by extending the Wightman axiom framework, it has been found possible to quantize only a conformal factor of the gravitational field. Gravitons being excluded from this quantum scalar field theory, numerous attempts were done to give a valuable description of what could be quantum gravity. In this talk we present a familly of Lorentz manifolds which can be foliated by isotropic hypersurfaces and pose severe restrictions on the form of the energy-momentum tensor in Einstein's equations. They can be associated to gravitational waves "without gravitons" in a vacuum described by two cosmological functions, but not to a massless particle flow. From this cross-checking with the previous remark, a "very" primordial quantum cosmological scenario is proposed.
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A Quantum-Physical Theory of Gravitation
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Of the General Theory of Relativity it has been said that it is one of the most beautiful theories invented by man, in fact personally also at the time it impressed me a lot, which led me to study Tensor Analysis and to try to understand Riemannian Geometry, but the truth is that all that world seemed to me very complicated and therefore not very beautiful, and I understood why, when it was launched, it is said that only 12 people understood it. Enrique Loedel in his excellent book writes... “arriving at the same results obtained from the exact Schwarzchild solution... whose extremely simple structure does not agree with the extreme complication of the field equations, make us think of the possibility of obtaining such a solution in a simpler and more direct way”(7,pg318). It was this that motivated me, among others, to the present solution of the gravitational fields, after having applied the concept of Basic Systemic Unit in the derivation of the Pendulum Formula, of the Schrödinger wave equation and those of Special Relativity.
Abstract quantum theory and space-time structure. I. Ur theory and Bekenstein-Hawking entropy
International Journal of Theoretical Physics, 1988
We discuss the close connection between a quantum theory of binary alternatives and the local Lorentzian structure of space-time, and outline v. WeizsS.cker's concept of the "ur"-the quantized binary alternative. Then space-time is introduced mathematically as a symmetric space of the invariance group of the ur. It is physically interpreted as "the" cosmological space-time, the universe. In our model spacelike structures rest on the concept of "hypermembranes"-dynamical manifolds of codimension 1 in space-time. For a given number of urs a smallest length is introduced in this cosmic model by group-theoretic arguments. Already before introducing a dynamics the concept of isolated noncomposite objects can be given. They can be understood as simple models either for elementary particles or for black holes. Identifying the maximal localized states of many urs with a localized state of a particle, we get a good description of the large cosmological numbers and also a lower bound for a neutrino mass. A simple counting of the particle states given from the ur-theoretic ansatz allows an easy explanation of th e Bekenstein-Hawking entropy. One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seen to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory.-Albert Einstein, The Meaning of Relativity, 6th ed., Appendix liD.
Aspects of quantum gravity phenomenology
2015
Quantum gravity effects modify the Heisenberg's uncertainty principle to the generalized uncertainty principle (GUP). Earlier work showed that the GUP-induced corrections to the Schrödinger equation, when applied to a non-relativistic particle in a one-dimensional box, led to the quantization of length. Similarly, corrections to the Klein-Gordon and the Dirac equations, gave rise to length, area and volume quantizations. These results suggest a fundamental granular structure of space. This thesis investigates how spacetime curvature and gravity might influence this discreteness of space. In particular, by adding a weak background gravitational field to the above three quantum equations, it is shown that quantization of lengths, areas and volumes continue to hold. Although the nature of this new quantization is quite complex, under proper limits, it reduces to cases without gravity. These results indicate the universality of quantum gravity effects. I am thankful to my supervisor Dr. Saurya Das for his inspiring guidance, constructive criticism, friendly advice and academic as well as non-academic support throughout the research project. I would like to express my gratitude to my committee members Dr. Mark Walton and Dr. Kent Peacock for all the valuable suggestions and comments they provided. I would also like to thank my family and friends for their help and encouragement. v Contents List of Figures viii vi 3.6.1 Case 1 : Length quantization along x axis .