Quantum coherence down the wormhole

It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.     

Instability of flat spacetime in semiclassical gravity

The semiclassical theory of gravity is considered in which an asymptotically flat background metric is coupled to quantized matter. We show that, in general, there are modes with spacelike wave vectors for small metric fluctuations around flat spacetime. Besides the usual axioms of quantum field theory in flat spacetime, the proof rests on the existence of a hard trace anomaly in the energy-momentum tensor due to matter self-couplings. Two possible interpretations of the result are discussed.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Nonperturbative solutions for canonical quantum gravity: An overview

In this paper we will make a survey of solutions to the Wheeler-De Witt equation which have been found up to now in Ashtekar's formulation for canonical quantum gravity. Roughly speaking they are classified into two categories, namely, Wilson-loop solutions and topological solutions. While the program of finding solutions which are composed of Wilson loops is still in its infancy, it is expected to be developed in the near future. Topological solutions are the only solutions at present which can be interpreted in terms of spacetime geometry. While the analysis made here is formal in the sense that we do not deal with rigorously regularized constraint equations, these topological solutions are expected to exist even in the fully regularized theory and they are considered to yield vacuum states of quantum gravity. We also make an attempt to review the spin network states as intuitively as possible. In particular, the explicit formulae for two kinds of measures on the space of spin network states are given.     

Axiomatic Quantum Field Theory in Curved Spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.     

A Proof of Haag-Swieca's Compactness Property for Elastic Scattering States

 It is proved that in any massive relativistic quantum field theory satisfying two-particle asymptotic completeness, all the bounded energy components in the elastic two-particle range of all subsets of states which are excitations of the vacuum state by uniformly bounded observables localized in a given finite region of spacetime are compact in the Hilbert space of states. This result, which is in agreement with Haag-Swieca's conjecture, is also given a more precise form in terms of the rate of decrease of the ``N–dimensional thickness' (or approximation number) of such sets of states when N tends to infinity. A similar computation, valid at arbitrarily high energies, is also given for the massive free-field case. Received: 7 February 2003 / Accepted: 5 April 2003 Published online: 13 May 2003 Communicated by H. Araki, D. Buchholz and K. Fredenhagen     

Finite field-dependent symmetries in perturbative quantum gravity

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.     

Wavefront Sets in Algebraic Quantum Field Theory

The investigation of wavefront sets of n-point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the help of concepts from microlocal analysis in quantum field theory in curved spacetime. In the present paper, the notion of wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of the translation group in arbitrary dimension. In the case where one is given a quantum field theory in the operator algebraic framework, this generalized notion of wavefront set, called “asymptotic correlation spectrum”, is further investigated and several of its properties for physical states are derived. We also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding Wightman distributions if there is a Wightman field affiliated to the local operator algebras. Finally we present a new result (generalizing known facts) which shows that certain spacetime points must be contained in the singular supports of the 2n-point distributions of a non-trivial Wightman field. Received: 27 July 1998 / Accepted: 3 March 1999     

Glafka 2004: Generalizing Quantum Mechanics for Quantum Gravity

Familiar quantum mechanics assumes a fixed spacetime geometry. Quantummechanics must therefore be generalized for quantum gravity where spacetime geometry is not fixed but rather a quantum variable. This extended abstract sketches a fully fourdimensional generalized quantum mechnics of cosmological spacetime geometries that is one such generalization.This contribution to the proceedings of the Glafka Conference is an extended abstract of the author's talk there. More details can be found in the references cited at the end of the abstract expecially (Hartle, 1995).     

Existence of a Consistent Quantum Gravity Model from Minimum Microscopic Information

It is shown that a quantum gravity formulation exists on the basis of quantum number conservation, the laws of thermodynamics, unspecific interactions, and locally maximizing the ratio of resulting degrees of freedom per imposed degree of freedom of the theory. The First Law of thermodynamics is evaluated by imposing boundary conditions to the theory. These boundary conditions determine the details of the complex world structure. No explicite microscopic quantum structure is required, and thus no ambiguity arises on how to construct the model. Although no dynamical computations of quantum systems are possible on this basis, all well established physics may be recovered, and all measurable quantities may be computed. The recovery of physical laws is shown by extremizing the entropy, which means varying the action on the bulk and boundary of small volumes of curved space-time. It is sketched how Quantum Field Theory (QFT) and General Relativity (GR) are recovered with no further assumptions except for imposing the dimension of a second derivative of the metric on the gravitational field equations. The new concepts are 1. the abstract organization of statistical quantum states, allowing for the possibility of absent quantum microstructure, 2. the optimization of the locally resulting degrees of freedom per imposed degree of freedom of the theory, allowing for the reconstruction of the spacetime dimensions, 3. the reconstruction of physical and geometric quantities by means of stringent mathematical or physical justifications, 4. the fully general recovery of GR by quasi-local variation methods applied on small portions of spacetime.     

Exactly soluble diffeomorphism invariant theories

A class of diffeomorphism invariant theories is described for which the Hilbert space of quantum states can be explicitly constructed. These theories can be formulated in any dimension and include Witten's solution to 2+1 dimensional gravity as a special case. Higher dimensional generalizations exist which start with an action similar to the Einstein action inn dimensions. Many of these theories do not involve a spacetime metric and provide examples of topological quantum field theories. One is a version of Yang-Mills theory in which the only quantum states onS ³×R are the vacua. Finally it is shown that the three dimensional Chern-Simons theory (which Witten has shown is intimately connected with knot theory) arises naturally from a four dimensional topological gauge theory.On leave from the Department of Physics, University of California, Santa Barbara, CA, USA     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Building a Quantum Spacetime

A quantum spacetime is constructed from the freedata given at past null infinity. One starts with afield equation for a scalar function Z on the initialsurface and then shows that the solution depends on four constants of integration. Theseconstants become the spacetime points and the levelsurfaces of the scalar function, i.e., Z = const, becomenull hypersurfaces on the derived spacetime. A phase space together with a complex structure areconstructed on past null infinity. This Hilbert space ofincoming gravitons possesses a natural foliation whichdefines superselection sectors on the space of asymptotic quantum states. The dynamics of nullsurface quantization provides spacetime-valued quantumoperators on the superselection sectors. It is shownthat the spacetime points themselves become operators with nonvanishing commutationrelations.     

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.     

Categorical Smoothness of 4-Manifolds from Quantum Symmetries and the Information Loss Paradox

In this paper, we focus on some aspects of the relation of spacetime and quantum mechanics and the study counterparts (in Set) of the categorical local symmetries of smooth 4-manifolds. In the set-theoretic limit, there emerge some exotic smoothness structures on R4 (hence the Riemannian nonvanishing curvature), which fit well with the quantum mechanical lattice of projections on infinite-dimensional Hilbert spaces. The method we follow is formalization localized on the open covers of the spacetime manifold. We discuss our findings in the context of the information paradox assigned to evaporating black holes. A black hole can evaporate entirely, but the smoothness structure of spacetime will be altered and, in this way, the missing information about the initial states of matter forming the black hole will be encoded. Thus, the possible global geometric remnant of black holes in spacetime is recognized as exotic 4-smoothness. The full-fledged verification of this proposal will presumably be possible within the scope of future quantum gravity theory research.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Quantum Gravity If Non-Locality Is Fundamental

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.     

A Spin-Statistics Theorem for Quantum Fields¶on Curved Spacetime Manifolds¶in a Generally Covariant Framework

A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of a causal dynamical law, fixed spinor- or tensor type for all quantum fields of the theory, and that the quantum field on Minkowski spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem holds: If for some of the spacetimes the corresponding quantum field obeys the “wrong” connection between spin and statistics, then all quantum fields of the theory, on each spacetime, are trivial. Received: 1 March 2001 / Accepted: 28 May 2001     

On causality violation on a Kerr-de Sitter spacetime

The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. First, an inextendible Kerr-de Sitter spacetime is obtained by joining together Carter’s blocks, i.e. suitable four dimensional spacetime regions contained within Killing horizons or within a Killing horizon and an asymptotic de Sitter region. Based on this property, and leaving aside topological identifications, we show that the causal properties of a Kerr-de Sitter spacetime are determined by the causal properties of the individual Carter’s blocks viewed as spacetimes in their own right. We show that any Carter’s block is stably causal except for the blocks that contain the ring singularity. The latter are vicious sets, i.e. any two events within such block can be connected by a future (respectively past) directed timelike curve. This behavior is identical to the causal behavior of the Boyer–Lindquist blocks that contain the Kerr ring singularity. These blocks are also vicious as demonstrated long ago by Carter. On the other hand, while for the case of a naked Kerr singularity the entire spacetime is vicious and thus closed timelike curves pass through any event including events in the asymptotic region, for the case of a Kerr-de Sitter spacetime the cosmological horizons protect the asymptotic de Sitter region from a-causal influences. In that regard, a positive cosmological constant appears to improve the causal behavior of the underlying spacetime.