Search Results (13)

The canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space time into a 3 + 1 formalism. Such a simplification appears to come at the cost of general covariance. This quantization procedure requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as “intrinsic coordinates” (or a dynamical reference frame) that depend only on the spatial metric ($g_{ab}$) and the conjugate momenta ($p^{cd}$), allows for an alternative approach to canonical quantization of gravity. In this paper, we present the tensorial solution of the set of Weyl scalars in terms of canonical phase-space variables. Full article

Starting from the realization that the theory of quantum gravity (QG) cannot be deterministic due to its intrinsic quantum nature, the requirement is posed that QG should fulfill a suitable Heisenberg Generalized Uncertainty Principle (GUP) to be expressed as a local relationship determined from first principles and expressed in covariant 4-tensor form. We prove that such a principle places also a physical realizability condition denoted as “quantum covariance criterion”, which provides a possible selection rule for physically-admissible spacetimes. Such a requirement is not met by most of current QG theories (e.g., string theory, Geometrodynamics, loop quantum gravity, GUP and minimum-length-theories), which are based on the so-called multiverse representation of space-time in which the variational tensor field coincides with the spacetime metric tensor. However, an alternative is provided by theories characterized by a universe representation, namely in which the variational tensor field differs from the unique “background” metric tensor. It is shown that the latter theories satisfy the said Heisenberg GUP and also fulfill the aforementioned physical realizability condition. Full article

The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein’s theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time Geometrodynamics advocates a paradigm shift from four covariance to just spatial diffeomorphism invariance. Consequently, causal time-ordering and quantum Schrödinger–Heisenberg evolution in cosmic time become meaningful. The natural addition of a Cotton–York term to the physical Hamiltonian changes the initial data problem radically. In the classical context, this is studied with the Lichnerowicz–York equation; quantum mechanically, it lends weight to the origin of the universe as an exact Chern–Simons Hartle–Hawking state, which features Euclidean–Lorentzian instanton tunneling. At the level of expectation values, this quantum state yields a low-entropy hot smooth Robertson–Walker beginning in accord with Penrose’s Weyl Curvature Hypothesis. The Chern–Simons Hartle–Hawking state also manifests transverse traceless quantum metric fluctuations, with, at the lowest approximation, scale-invariant two-point correlations as one of its defining characteristics. Full article

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein’s equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics” as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada’s work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler’s geometrodynamics. They were added to it in the 1960s by Geroch. Ranada’s solutions of source-free Maxwell’s equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole. Full article

A possible solution of the problem of time in the Wheeler–DeWitt quantum geometrodynamics is that time appears within a semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved spacetime with quantum-gravitational corrections. In the present paper, we study the semiclassical limit in the case of a closed isotropic model with a scalar field decomposed into modes. We analyse calculations made within frameworks of three approaches. The first approach was proposed by Kiefer and Singh. Since the Wheeler–DeWitt equation does not contain a time derivative, it is constructed by means of a special mathematical procedure, a time variable being a parameter along a classical trajectory of gravitational field. The second method was suggested in the paper of Maniccia and Montani, who introduced the Kuchař–Torre reference fluid as an origin of time. Furthermore, the third is the extended phase space approach to the quantisation of gravity. In this approach, the temporal Schrodinger equation is argued to be more fundamental than the Wheeler–DeWitt equation, and there is no problem of time. Time is introduced due to fixing a reference frame of a certain observer, who can register the macroscopic consequences of quantum gravitational phenomena in the Very Early Universe. To go to the semiclassical limit, the Born–Oppenheimer approximation for gravity is used. In each of the approaches, in the order of $\mathcal{O}(1/M)$, a temporal Schrödinger equation for matter fields in curved spacetime with quantum gravitational corrections is obtained. However, equations and corrections are different in various approaches, and the results depend on the additional assumptions made within the scopes of these approaches. Full article

We give a concise review of the properties of quantum geometrodynamics in the pilot-wave quantum cosmology, focusing on the issue of its nonlocal character. We also discuss the problem of the origin of quantum probabilities in this theory with a focus on the ergodic approach to its resolution. Full article

Time in quantum gravity is not a well-defined notion despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we briefly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology—the application of quantum gravity to the Universe as a whole. Full article

The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger’s type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model. Full article

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark-energy models that could describe the future evolution of our universe. When the universe evolves towards either of these future cosmic events, all bounded structures and, ultimately, space–time itself are ripped apart. Nevertheless, it is commonly believed that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric $f\left(R\right)$ theories of gravity. The quantum analysis is performed in the framework of $f\left(R\right)$ quantum geometrodynamics. In this context, we analyze the fulfilment of the DeWitt criterion for the avoidance of these singular fates. This review contains as well new unpublished work (the analysis of the equation of state for the phantom fluid and a new quantum treatment of the big rip and the little sibling of the big rip events). Full article

Some of the approaches to quantization in gravity theory concerning gravitationally bound systems are considered. Grades of quantization applicable to these systems have been classified in terms of quantum mechanics, quantum field theory, and quantum geometrodynamics. Energy levels for the graviatom, Lemaître’s atom, quantum gravitational collapse have been calculated, and relationships for the masses of bound system components, as well as Universe’s birth probabilities, are presented to exemplify the properties of gravitationally bound systems. Objects and processes in them have been analyzed to construct quantum models of compact astrophysical objects and the early Universe. Full article

We derive the functional Schrödinger equation for quantum fields in curved spacetime in the semiclassical limit of quantum geometrodynamics with a Gaussian incoherent dust acting as a clock field. We perform the semiclassical limit using a WKB-type expansion of the wave functional in powers of the squared Planck mass. The functional Schrödinger equation that we obtain exhibits a functional time derivative that completes the usual definition of WKB time for curved spacetime, and the usual Schrödinger-type evolution is recovered in Minkowski spacetime. Full article

We consider the conditioning of the timeless solution to the Wheeler–DeWitt equation by a predefined matter clock state in the simple scenario of an FLRW universe. The resulting evolution of the geometrodynamical degree of freedom with respect to clock time is characterized by the “Berry connection” of the reduced geometrodynamical space, which relies on the coupling of the clock with the geometry. When the connection vanishes, the standard Schrödinger equation is obtained for the geometry with respect to clock time. When one considers environment-induced decoherence in the semiclassical limit, this condition is satisfied, and clock time coincides with cosmic time. Explicit results for the conditioned wave functions for minimal clocks made up of two quantum harmonic oscillator eigenstates are shown. Full article

A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy). Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity), the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement). In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum affects geometry of multidimensional phase space and gravity changes in any point the torsion in the ordinary four-dimensional Lorenz space-time metric. Full article