Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Quantum CTC's in General Relativity

We review different spacetimes that contain nonchronal regions separated from the causal regions by chronology horizons and investigate their connection with some important aspects one would expect to be present in a final theory of quantum gravity, including: stability to classical and quantum metric fluctuations, boundary conditions of the universe and gravitational topological defects corresponding to spacetime kinks.     

Quantum Structures in Einstein General Relativity

We introduce the notion of a quantum structure on an Einstein general relativistic classical spacetime M. It consists of a line bundle over M equipped with a connection fulfilling certain conditions. We give a necessary and sufficient condition for the existence of quantum structures and classify them. The existence and classification results are analogous to those of geometric quantisation (Kostant and Souriau), but they involve the topology of spacetime, rather than the topology of the configuration space. We provide physically relevant examples, such as the Dirac monopole, the Aharonov–Bohm effect and the Kerr–Newman spacetime. Our formulation is carried out by analogy with the geometric approach to quantum mechanics on a spacetime with absolute time, given by Jadczyk and Modugno.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

Conventions in Relativity Theory and Quantum Mechanics

The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.     

Unification of Quantum Theory and Relativity

A underlying dynamical structure for bothrelativity and quantum theory —superrelativity — has been proposedin order to overcome the well-known incompatibilitybetween these theories. The relationship between curvature of spacetime (gravity) andcurvature of the projective Hilbert space of purequantum states is established as well.     

Noncommutative Unification of General Relativity and Quantum Mechanics

We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct limitingcases of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a shadowof the noncommutative regime of the fundamental level.A toy model is computed predicting the value of thecosmological constant (in the quantum sector) which vanishes whengoing to the standard spacetime physics.     

Quantum General Relativity,Torsion and Uncertainty Relations

It is shown that in gravitational theories with torsion one is led to commutation rules corresponding to Landau-Peierls type uncertainty relations.     

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics: not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero-dimensional) serves as the base for the holographic image of the universe. In this way our theory is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a surprising informational interrelation between the fundamental constants, h, c, G, and their DH analogues, h(D), c(D), G(D). DH theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhances the role of the Bohm potential.     

Quantum Mechanics and the Metrics of General Relativity

A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical mechanics, will emerge naturally from the procedure. Finally, we will find that the methodology will enable us to introduce not only test charges but also test masses by means of gauges.     

On a Quantum Theory of Relativity

As expressed in terms of classical coordinates, the inertial spacetime metric that contains quantum corrections deriving from a quantum potential defined from the quantum probability amplitude is obtained to be given as an elliptic integral of the second kind that does not satisfy Lorentz transformations but a generalised invariance quantum group. Based on this result, we introduce a new, alternative procedure to quantise Einstein general relativity where the metric is also given in terms of elliptic integrals and is free from the customary problems of the current quantum models. We apply the procedure to Schwarzschild black holes and briefly analyse the results.     

Kantowski-Sachs Cosmological Model in General Theory of Relativity

The field equations for perfect fluid coupled with massless scalar field are solved with two conditions p=ρ and R=AS ⁿ for Kantowski-Sachs space time in general theory of relativity. Various physical and geometrical properties of the model have also been discussed.     

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.