Problem Of Quantum Gravity Research Articles

Spacetime-noncommutativity regime of loop quantum gravity

A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by Loop-Quantum-Gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the $\kappa$-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.

The Transition from Pre-Octonionic to Octonionic Gravity and How It May Be Pertinent to a Re-Do of the HUP for Metric Tensors

The quantum gravity problem that the notion of a quantum state, representing the structure of space-time at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having initial Octonionic geometry embedded in a larger, nonlinear “pilot model” (semi classical) embedding structure. The Penrose suggestion of recycled space time avoiding a “big crunch” is picked as the embedding structure, so as to avoid the “instants” of time issue. Getting Octionic gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the complication of then afterwards “Schrodinger equation” states of the universe, and the transformation of Octonionic gravity to existing space-time is explored via its possible linkage to a new version of the HUP involving metric tensors. We conclude with how specific properties of Octonion numbers algebra influence the structure and behavior of the early-cosmology model. This last point is raised in Section 14, and is akin to a phase transition from Pre-Octonionic geometry, in pre-Planckian space-time, to Octonionic geometry in Planckian space-time. A simple phase transition is alluded to; making this clear is as simple as realizing that Pre-Octonionic is for Pre-Planckian Space-time and Octonionic is for Planckian Space-time. We state that the Standard Model of physics occurs during Planckian Space-time. We also argue that the Standard Model does not apply to Pre Planckian Space-time. This is commensurate with the Octonion number system NOT applying in pre-Planckian space-time, but applying in Plankian space-time. And the last line of Equation (54) gives a minimum time step in pre-Planckian space-time when we do NOT have the Standard Model of physics, or Octonionic Geometry.

Planck-Scale Dual-Curvature Lensing and Spacetime Noncommutativity

It was recently realized that Planck-scale momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual-curvature lensing, a feature which mainly affects the direction of observation of particles emitted by very distant sources. Several gray areas remain in our understanding of dual-curvature lensing, including the possibility that it might be just a coordinate artifact and the possibility that it might be in some sense a by-product of the better studied dual-curvature redshift. We stress that data reported by the IceCube neutrino telescope should motivate a more vigorous effort of investigation of dual-curvature lensing, and we observe that studies of the recently proposed “ρ-Minkowski noncommutative spacetime” could be valuable from this perspective. Through a dedicated ρ-Minkowski analysis, we show that dual-curvature lensing is not merely a coordinate artifact and that it can be present even in theories without dual-curvature redshift.

Clustering Implies Geometry in Networks.

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity.

Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

In Crull (2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality.

Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

Alternative approaches to the study of the quantum gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics, suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

Editorial: New Perspectives in the Philosophy of Physics

This special issue reflects the ongoing close connection between the foundations of physics and philosophy. In the first part, CarstenHeld discusses a new argument for the incompleteness of quantummechanics that does not involve a separation principle, and Elise Crull defends the view that decoherence minimizes any contribution to solving problems in quantum gravity and quantum cosmology that the conflicting interpretations of quantummechanics may be thought to have. In the second part, JohannaWolff discusses the role of a priori epistemological principles in articulating and defending alternative metaphysical views about physics, while Elay Shech focuses on idealizations and their potential contribution to the explanation and understanding of certain physical effects. In the third part, RichardDawid argues that certain limitations of John Norton’s material theory of induction are revealed by Norton’s dome scenario itself, and Gabor Hofer-Szabo investigates the connection between Bell’s local causality and the causal Markov condition, with an emphasis on Bayesian networks. The idea for this special issue stems from the conference “New Directions in the Philosophy of Physics” and the workshop “Einstein’s Philosophy of Science” which took place at the University of Bucharest, Faculty of Philosophy, from 23–25 May 2013. Neither event would have been possible without the encouragement and advice I received from two of my former mentors, Don Howard and Ilie Pârvu, the kind support of the Rector of the University of Bucharest, Mircea Dumitru, as well as the enthusiasm ofmy diligent graduate students. Half of the articles included in the present issue are revised versions of papers presented in Bucharest. The other half comprises new papers, invited for this special issue. I would like to thank all authors and referees for their efforts, Angela Lahee at Springer, for editorial support, and the editors of this journal, particularly Fedde Benedictus, for inviting me to edit this collection.

Exploring special relative locality with de Sitter momentum-space

Relative Locality is a recent approach to the quantum-gravity problem which allows to tame nonlocality effects which may rise in some models which try to describe Planck-scale physics. I here explore the effect of Relative Locality on basic special-relativistic phenomena. In particular I study the deformations due to Relative Locality of special-relativistic transformation laws for momenta at all orders in the rapidity parameter $\xi$. I underline how those transformations also define the RL characteristic (momentum-dependent) invariant metric. I focus my analysis on the well studied deSitter momentum-space framework and I investigate the differences and similarities between this model and Special Relativity, from the definition of the boost parameter $\gamma$ to a first discussion of transverse-effects characteristic of Relative Locality on clocks observables.

Categorical generalization of spinfoam models

We give a brief review of the problem of quantum gravity. After the discussion of the nonrenormalizability of general relativity, we briefly mention the main research directions which aim to resolve this problem. Our attention then focuses on the approach of Loop Quantum Gravity, specifically spinfoam models. These models have some issues concerning the semiclassical limit and coupling of matter fields. The recent developments in category theory provide us with the necessary formalism to introduce a new action for general relativity and perform covariant quantization so that the issues of spinfoam models are successfully resolved.

Invariants of the heat equation for non-minimal operators

A special class of non-minimal operators which are relevant for quantum field theory is introduced. The general form of the heat kernel coefficients of these operators on manifolds without boundary is described. New results are presented for the traces of the first two heat kernel coefficients for vector, Yang–Mills and perturbative gravity. It is argued that non-minimal operators can be used to define gauge-fixing independent actions and solve the conformal mode problem in quantum gravity.

Entanglement entropy and gravity/condensed matter correspondence

The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity. Especially, for more than twenty years, this quantity has been studied by many people in order to obtain a quantum mechanical interpretation of the gravitational entropy such as the black hole entropy. We will introduce recent progresses toward this long-standing problem in quantum gravity by applying the idea of holography, especially the AdS/CFT correspondence found in string theory. We will explain the holographic formula which computes the entanglement entropy of quantum field theories in terms of the area of minimal surfaces in general relativity. We will also review the recent application of AdS/CFT correspondence to condensed matter physics from the viewpoint of entanglement entropy.

Aspects of Transplanckian Scattering

We attempt to address the well known problem of quantum gravity - the information paradox, through the study of transplanckian collisions, that may proceed with the production of intermediate black hole states. We apply the S-matrix approach to study 2 → 2 scattering of particles with the center of mass energy much greater than the Planck mass, and investigate the dependence of the scattering amplitude on the impact parameter. It is expected that the main properties of the S-matrix (unitarity, analyticity and crossing) may provide sufficiently strong constrain for the scattering amplitude to unravel non-trivial information about the underlying properties of quantum gravity. However, we argue that our present understanding is far from complete and additional novel ideas are required to resolve this puzzle.

Benefits of Objective Collapse Models for Cosmology and Quantum Gravity

We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal, which relates the spontaneous collapse events of objective collapse models to microscopic virtual black holes.

Grandfather Paradox in Non-Quantum and Quantum Gravitation Theories

In this paper we resolve the grandfather paradox in non-quantum and quantum gravitation theories for time travelling in a time wormhole. For macroscopic bodies, the main solution is alignment of the thermodynamic time arrows, resulting in the time traveller destroying. For microscopic bodies and for small probability cases of macroscopic bodies, the main solution is fracture of the time wormhole. As a result, multi-world system appears. These explanations are similar in non-quantum and quantum gravity. On the contrary, we can clarify some problems of quantum gravity by this consideration. “Indestructible finite gravitation interaction of an observer with an observable system (resulting in the time arrows alignment)” and “instability with respect to even infinitesimally small interaction in the gravitation theory” can resolve the wave function reduction paradox of quantum mechanics.

Dual redshift on Planck-scale-curved momentum spaces

Several approaches to the investigation of the quantum-gravity problem have provided ‘theoretical evidence’ of a role for the Planck scale in characterizing the geometry of momentum space. One of the main obstructions for a full exploitation of this scenario is the understanding of the role of the Planck-scale-curved geometry of momentum space in the correlations between emission and detection times, the ‘travel times’ for a particle to go from a given emitter to a given detector. These travel times appear to receive Planck-scale corrections for which no standard interpretation is applicable, and the associated implications for spacetime locality gave rise to the notion of ‘relative locality’ which is still in the early stages of investigation. We here show that these Planck-scale corrections to travel times can be described as ‘dual redshift’ (or ‘lateshift’): they are manifestations of momentum-space curvature of the same type already known for ordinary redshift produced by spacetime curvature. In turn, we can identify the novel notion of ‘relative momentum-space locality’ as a known but under-appreciated feature associated with ordinary redshift produced by spacetime curvature, and this can be described in complete analogy with the relative spacetime locality that became of interest in the recent quantum-gravity literature. We also briefly comment on how these findings may be relevant for an approach to the quantum-gravity problem proposed by Max Born in 1938 and centered on Born duality.

Unification of Quantum and Gravity by Non Classical Information Entropy Space

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.

Conceptual Problems in Quantum Gravity and Quantum Cosmology

The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status, and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.

Introduction to causal sets and their phenomenology

In this introduction to the causal set approach to the problem of quantum gravity, I emphasise that causal sets are both fundamentally discrete and Lorentz invariant, which makes them nonlocal. I focus on opportunities for phenomenology arising from and stimulated by causal sets.

TIME AND A TEMPORALLY STATISTICAL QUANTUM GEOMETRODYNAMICS

This paper is an exposition of the author's recent work on modeling M-theory vacua and quantum mechanical observers in the framework of a temporally statistical description of quantum geometrodynamics, including measurement processes based on the canonical theory of quantum gravity. In this paper, we deal with several fundamental issues of time: the timeless problem in canonical quantum gravity; the physical origin of state reductions; and time-reversal symmetry breaking. We first model the observers and consider the timeless problem by invoking the time reparametrization symmetry breaking in the quantum mechanical world as seen by the observers. We next construct the hidden time variable theory, using a model of the gauged and affinized S-duality symmetry in type IIB string theory, as the statistical theory of time and explain the physical origin of state reductions using it. Finally, by the extension of the time reparametrization symmetry to all of the temporal hidden variables, we treat the issue of time reversal symmetry breaking as the spontaneous breaking of this extended time reparametrization symmetry. The classification of unitary time-dependent processes and the geometrizations of unitary and nonunitary time evolutions using the language of the derived category are also investigated.

Predictive description of Planck-scale-induced spacetime fuzziness

Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been proposed on the basis of semi-heuristic arguments, and in particular involves an irreducible Planck-scale contribution to the uncertainty of the energy of a particle. These arguments also inspired a rather active phenomenological programme looking for blurring of images of distant astrophysical sources that would result from such energy uncertainties. We here report the first ever physical characterization of spacetime fuzziness derived constructively within a quantum picture of spacetime, the one provided by spacetime noncommutativity. Our results confirm earlier heuristic arguments suggesting that spacetime fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances. However, we find no Planck-scale-induced lower bound on the uncertainty of the energy of particles, and we observe that this changes how we should picture a quantum spacetime and also imposes a reanalysis of the associated phenomenology.