On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

Can Spacetime be a Condensate?

We explore further the proposal [Hu, B. L. (1996). General relativity as geometro-hydrodynamics. (Invited talk at the Second Sakharov Conference, Moscow, May 1996); gr-qc/9607070.] that general relativity is the hydrodynamic limit of some fundamental theories of the microscopic structure of spacetime and matter, i.e., spacetime described by a differentiable manifold is an emergent entity and the metric or connection forms are collective variables valid only at the low-energy, long-wavelength limit of such micro-theories. In this view it is more relevant to find ways to deduce the microscopic ingredients of spacetime and matter from their macroscopic attributes than to find ways to quantize general relativity because it would only give us the equivalent of phonon physics, not the equivalents of atoms or quantum electrodynamics.It may turn out that spacetime is merely a representation of certain collective state of matter in some limiting regime of interactions, which is the view expressed by Sakharov [Sakharov, A. D. (1968). Soviet Physics-Doklady 12, 1040–1041; Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Doklady Akad. Nauk S.S.R. 177, 70; Adler, S. L. (1982). Reviews of Modern Physics 54, 729]. In this talk, working within the conceptual framework of geometro-hydrodynamics, we suggest a new way to look at the nature of spacetime inspired by Bose–Einstein condensate (BEC) physics. We ask the question whether spacetime could be a condensate, even without the knowledge of what the‘atom of spacetime’ is. We begin with a summary of the main themes for this new interpretation of cosmology and spacetime physics, and the ‘bottom-up’ approach to quantum gravity. We then describe the ‘Bosenova’ experiment of controlled collapse of a BEC and our cosmology-inspired interpretation of its results. We discuss the meaning of a condensate in different context. We explore how far this idea can sustain, its advantages and pitfalls, and its implications on the basic tenets of physics and existing programs of quantum gravity.     

On the general covariance and strong equivalence principles in quantum general relativity

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

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.     

Return of the quantum cosmic censor

The influential theorems of Hawking and Penrose demonstrate that spacetime singularities are ubiquitous features of general relativity, Einstein's theory of gravity. The utility of classical general relativity in describing gravitational phenomena is maintained by the cosmic censorship principle. This conjecture, whose validity is still one of the most important open questions in general relativity, asserts that the undesirable spacetime singularities are always hidden inside of black holes. In this Letter we reanalyze extreme situations which have been considered as counterexamples to the cosmic censorship hypothesis. In particular, we consider the absorption of fermion particles by a spinning black hole. Ignoring quantum effects may lead one to conclude that an incident fermion wave may over spin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when quantum effects are properly taken into account, the integrity of the black-hole event horizon is irrefutable. This observation suggests that the cosmic censorship principle is intrinsically a quantum phenomena.     

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.     

Quantum construction of general relativistic spacetime

A construction of a model of general relativistic spacetime that arises naturally from within standard quantum theory is presented. In terms of this model all the usual structures of general relativity theory can be given a quantum-theoretic interpretation, so that the usual barriers between the two theories are absent.     

Born-Infeld Kinematics

We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is put to use in the discussion of particular point particle dynamics and the transition to a first quantized theory.     

Quantum spacetime

After a review and reformulation of previous results, further developments in the construction and interpretation of a quantum-theoretic model of general relativistic spacetime are presented. A theorem is proved that clarifies the nature of the boundaries separating the four-dimensional facets of the resulting piecewise linear model, and a simple example of such a spacetime is detailed. The precise way in which any such model unifies the essential features of both quantum theory and general relativity is discussed.     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime

The strong similarities between the light propagation in a curved spacetime and that in a medium with graded refractive index are found. It is pointed out that a curved spacetime is equivalent to an inhomogeneous vacuum for light propagation. The corresponding graded refractive index of the vacuum in a static spherically symmetrical gravitational field is derived. This result provides a simple and convenient way to analyse the gravitational lensing in astrophysics.     

The Classical Singularity Theorems and Their Quantum Loopholes

The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum violation of the classical energy conditions, and the presence of quantum fluctuations of the spacetime geometry. The possible significance of each is discussed.     

On the expansion of a quantum field theory around a topological sector

The idea of treating quantum general relativistic theories in a perturbative expansion around a topological theory has recently received attention, in the quantum gravity literature. We investigate the viability of this idea by applying it to conventional Yang–Mills theory on flat spacetime. This theory admits indeed a formulation as a modified topological theory, like general relativity. We find that the expansion around the topological theory coincides with the usual expansion around the free abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. On the other hand, we point out that the relation of this expansion with the actual quantum BF theory is far from being transparent. Some implications for gravity are discussed.     

Action and reaction in the theories of direct interparticle action

Newton's third law of motion is examined in the context of the theories of direct interparticle action. In such theories, interactions between particles travel backward and forward in time at speeds not exceeding the speed of light. It is shown that while in the flat spacetime the equality of action and reaction can be clearly demonstrated, the situation is considerably more complicated in the curved spacetime. The phenomenon of gravitational scattering intervenes to destroy the equality of action and reaction. Nevertheless, when gravitation is taken into account, there is no violation of the conservation law of energy and momentum. These results are discussed in the framework of general relativity for the case of the electromagnetic interaction.     

Quantum theory of fields and origin of gravity

The unification of the quantum theory of fields and general relativity is supposed possible on the basis of Sakharov's hypothesis that gravity results from variations in vacuum fluctuations. It is shown that under very general conditions this hypothesis leads to Riemannian geometry of the world-lines of free particle motion. The origin of causal spacetime relations is discussed as the problem complementary to that of the source of geometry. This involves an interpretation of the EPR experiment and supports the idea that spacetime relations in microphysics result from adjusting quantum processes to the causality of macroscopic participators.     

On the precision of a length measurement

We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime on lengths shorter than the Planck length. We then consider the fundamental limit coming from quantum mechanics, general relativity and causality on the precision of length measurement. PACS 04.20.-q; 03.65.-w     

1912: A turning point on Einstein's way to general relativity

On his way to general relativity, Einstein used the equivalence principle to formulate a theory of the static gravitational field. In this context he introduced an approximate coordinate transformation to an accelerated frame which turns out to be closely related to Rindler coordinates, widely used in modern general relativity. This work, published in the Annalen, led him directly to interpret gravitation in terms of spacetime curvature.