Classical general relativity derived from quantum gravity

The existence of long range macroscopic attractive forces between masses implies the existence of a mediating helicity ± 2 particle in special relativistic quantum particle theory. It is shown that this fact alone, without assuming the existence of an underlying tensor field, uniquely determines the long wavelength structure of quantum gravitation to be that of Einstein's theory. This equivalence is shown by deriving, from the Ward identities associated with the graviton propagator, the tree graph structure of the graviton-graviton and graviton-matter interaction and establishing that the classical Einstein action is the generating functional. Some properties of closed loop effects are also exhibited.     

Violation of signal locality and unitarity in a merger of quantum mechanics and general relativity

It is shown that a violation of signal locality and unitarity occur in a particular merger of quantum mechanics and general relativity.     

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.     

Between general relativity and quantum theory

Some possibilities of reconciling general relativity with quantum theory are discussed. The procedure of quantization is certainly not unique, but depends upon the choice of the coordinate conditions. Most versions of quantization predict the existence of gravitons, but it is also possible to formulate a quantum theory with a classical gravity whereby the expectation values ofT _µv constitute the sources of the classical metric field.     

From massive gravity to modified general relativity

Massive gravity which has been constructed from a cohomological formulation of gauge invariance by means of the descent equations is here investigated in the classical limit. Gauge invariance requires a vector-graviton field v coupled to the massive tensor field h _μν . In the limit of vanishing graviton mass the v-field does not decouple. On the classical level this leads to a modification of general relativity. The contribution of the v-field to the energy-momentum tensor can be interpreted as dark matter density and pressure. We solve the modified field equations in the simplest spherically symmetric geometry.     

Classical and quantum two-body problem in general relativity

The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different Schwarzschild radii. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.Revised version of Trieste preprint IC/80/124 (August 1980).A similar approach is being developed by a number of authors (see, e.g., References [9] and [10]); the reader will find a comprehensive bibliography in References [11] and [8].     

Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length, l_p = ?{(^h/_2p) G}{l_p = \sqrt{\hbar G}}. The classical and quantum dynamics of a particle propagating in κ-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which (^h/_2p) = 0{\hbar =0} but l_p = ?{(^h/_2p) G} 1 0{l_p = \sqrt{\hbar G}\neq 0}. This may be relevant for phenomenology such as observations by FERMI, because at leading order in l _p × distance there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.     

From massive gravity to modified general relativity II

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy–momentum tensor. On the classical level this leads to a further modification of general relativity.     

On general and restricted covariance in general relativity

We reconsider the principle of general covariance and give a rigorous formulation of a principle ofrestricted covariance. We give a number of examples of preferred coordinate systems, considered in the literature, and in each case demonstrate the applicability of the notion of restricted covariance proposed.     

Testing general relativity at the quantum level

It is shown that the effect of a gravitational field on a hydrogen atom is to admix states of opposite parity such as 2S _1/2 and 2P _1/2 The phase of this admixture is such as to produce circular polarization of the radiation emitted in transltions such as 2S _1/21S _1/2+ which arises from the interference between the gravity-induced amplitude and mat due to the weak neutral current. The predicted magnitude of the circular polarization, which could be sufficiently large to be detected in white dwarfs or in certain binary systems, varies from theory to theory. It is thus possible that a study of this effect could provide a feasible means of testing general relativity at the quantum level.This essay received the fourth award from the Gravity Research Foundation for the year 1979-Ed.     

T4 gauge theory of gravity and new general relativity

We formulate a space-time translationT ₄ gauge theory of gravity on the Minkowski space-time with appropriate choice of the Lagrangian. By comparing the energy-momentum law of this theory with that of new general relativity constructed on the Weitzenböck space-time we find that in the classical limit the gauge potentials correspond to the parallel vector fields in the Weitzenböck space-time and the gauge field equation coincides with the field equation of gravity in new general relativity in the linearized version. Thus we conclude that in the classical limit theT ₄ gauge theory of gravity leads to the new general relativity.     

Minimum length from quantum mechanics and classical general relativity

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.     

Classical and quantum general relativity: A new paradigm

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework. Fifth Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

On Birkhoff's theorem in general relativity

Two generalisations of Birkhoff's theorem are proved for the cases where the three-parameter group of motions acts on two-dimensional time-like and null orbits. A complete list of possible extensions of the three-parameter group to one of four parameters and of the resulting metrics is given.Turner and Newall Research Fellow.     

On decoherence in quantum gravity

It was previously argued that the phenomenon of quantum gravitational decoherence described by the Wheeler‐DeWitt equation is responsible for the emergence of the arrow of time. Here we show that the characteristic spatio‐temporal scales of quantum gravitational decoherence are typically logarithmically larger than a characteristic curvature radius of the background space‐time. This largeness is a direct consequence of the fact that gravity is a non‐renormalizable theory, and the corresponding effective field theory is nearly decoupled from matter degrees of freedom in the physical limit . Therefore, as such, quantum gravitational decoherence is too ineffective to guarantee the emergence of the arrow of time and the “quantum‐to‐classical” transition to happen at scales of physical interest. We argue that the emergence of the arrow of time is directly related to the nature and properties of physical observer.