Problem of Interactions: Gravitational Interactions

Within the framework of a new approach to the problem of particles [1], gravitational interactions are considered. Interactions of this type are associated with the degeneracy of states of a relativistic bi-Hamiltonian system T _3,1 underlying the given approach. Within the framework of this approach, there is a clearly defined difference between the gravitation and the metric theory of space-time.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides, it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field. The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Unification of Electromagnetic Interactions and Gravitational Interactions

Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper.Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same mannerand are unified in a semi-direct product group of U(1) Abelian gauge group and gravitational gauge group.     

Gravitational and Electroweak Interactions

Schrodinger considered the variational principle , whereg is the determinant of the metricg, but noted that ifg is varied, the resultingEuler-Lagrange equations cannot serve as field equations. We writeg =g_ijh ⁱh ^j, where g_ij = diag(-1, 1,1, 1), and express the vectors of the tetradh ⁱ as derivatives ofnonintegrable functions xⁱ of the typecommonly used for phase factors in gauge theory, i.e.,h ⁱ =x_, ⁱ. We have previously shownthat if the xⁱ are varied, the resultingEuler–Lagrange equations serve as field equations which imply the validity of Einstein equationswith a stress-energy tensor for the electroweak fieldand associated currents. In this paper, we express theseEinstein equations into two new forms, and use these forms to derive Lorentz-force-likeequations of motion. The electroweak field appears as aconsequence of the field equations (rather than as acompensating field introduced to secure local gauge invariance). There is no need forsymmetry breaking to accommodate mass, because the gaugesymmetry is approximate from the outset.     

Twist-Deformed Gravitational Quantum Well

In this article we define the gravitational quantum well model on twist-deformed space with two spatial directions commuting to time-dependent function f_κ(t). Further, we find the corresponding energy spectrum and by its comparision with the GRANIT experiment predictions, we obtain bounds on the noncommutativity function in the case of two first energy levels.

     

Experimental Repeal of the Speed Limit for Gravitational, Electrodynamic, and Quantum Field Interactions

General relativity has a geometric and a field interpretation. If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. The field interpretation avoids this problem by allowing faster-than-light propagation of gravity in forward time. All existing experiments are in agreement with that interpretation. This implies the existence of real superluminal propagation and communication of particles and fields, free of causality problems. The introduction of real physical faster-than-light propagation into gravitation, electrodynamics and quantum theory has important consequences for physics.     

Gravitational Redshift Induces Quantum Interference

Quantum field theory in curved spacetime is used to show that gravitational redshift induces a unitary transformation on the quantum state of propagating photons. It is found that the transformation is a mode-mixing operation, and a protocol that exploits gravity to induce a Hong–Ou–Mandel-like interference effect on the state of two photons is devised. It is discussed how the results of this work can provide a demonstration of quantum field theory in curved spacetime.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian hasstrict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory.Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar fieldminimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian forscalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressedby gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Gravitational Gauge Interactions of Dirac Field

Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge field, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

Cosmological Density Perturbations from a Quantum Gravitational Model of Inflation

We derive the implications for anisotropies in the cosmic microwave background following from a model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. The model predicts that the amplitude of scalar perturbations is A_S = (2.0 ± 0.2) · 10^—5, that the tensor-to-scalar ratio is r ≈︂ 1.7 · 10^—3, and that the scalar and tensor spectral indices are n ≈︂ 0.97 and n_T ≈︂ —2.8 · 10^—4, respectively. By comparing the model's power spectrum with the COBE 4-year RMS quadrupole, the mass scale of inflation is determined to be M = (0.72 ± 0.03) · 10¹⁶ GeV. At this scale the model produces about 10⁸ e-foldings of inflation, so another prediction is Ω = 1. PACS numbers: 04.60.-m, 98.80.Cq     

Gravitational Collapse in Loop Quantum Gravity

In this paper we study the gravitational collapse applying methods of loop quantum gravity to a minisuperspace model. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust matter) is localized and the other (outside) where the metric is Kantowski–Sachs type. We study the Hamiltonian constraint obtaining a set of three difference equations that give a regular and natural evolution beyond the classical singularity point in “r=0” localized.     

Gravitational Collapse in Quantum Einstein Gravity

The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a “cosmic censor” which prevents any external observer from perceiving their existence. However, classical models describing the gravitational collapse usually results in strong curvature singularities, which can also remain “naked” for a finite amount of advanced time. This proceedings studies the modifications induced by asymptotically safe gravity on the gravitational collapse of generic Vaidya spacetimes. It will be shown that, for any possible choice of the mass function, quantum gravity makes the internal singularity gravitationally weak, thus allowing a continuous extension of the spacetime beyond the singularity.     

Gravitational Scattering of a Quantum Particle and the Privileged Coordinate System

In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschildmetrics in standard, harmonic, and other coordinate systems in linear and G²-approximations. In general, different coordinate systems lead to different scattering. This opens up the possibility to choose the privileged coordinate system which should lead to scattering in agreement with experiment.     

Quantum Nondemolition Measurements of a Particle in an Inhomogeneous Gravitational Field

In this work we obtain a family of quantum nondemolition variables for the case of a particle moving in an inhomogeneous gravitational field. Afterwards, we calculate the corresponding propagator, and deduce the probabilities associated with the possible measurement outputs. The comparison, with the case in which the position is being monitored, will allow us to find the differences with respect to the case of a quantum demolition measuring process.     

Toward a Finite-Dimensional Formulation of Quantum Field Theory

Rules of quantization and equations of motion for a finite-dimensional formulation of quantum field theory are proposed which fulfill the following properties: (a) Both the rules of quantization and the equations of motion are covariant; (b) the equations of evolution are second order in derivatives and first order in derivatives of the spacetime coordinates; and (c) these rules of quantization and equations of motion lead to the usual (canonical) rules of quantization and the (Schrödinger) equation of motion of quantum mechanics in the particular case of mechanical systems. We also comment briefly on further steps to fully develop a satisfactory quantum field theory and the difficuties which may be encountered when doing so.