Session U10: Quantum Gravity

The First Law for Acceleration Horizons

There are many reasons to believe that the notion of black hole entropy extends to all causal horizons. The first law should presumably therefore apply as well. However, the area change of an asymptotic Rindler horizon is infinite when energy falls freely across it. It will be argued that the resolution of this puzzle is that the process is out of equilibrium.   

Macroscopic Effects of the Trace Anomaly at Event Horizons

Although the trace anomaly was first obtained by a one-loop quantum calculation, it has macroscopic effects at low energies. These effects can be studied in a local auxiliary field description of the effective action for the anomaly, which requires two new scalar potentials, not contained in classical general relativity. These additional scalar degrees of freedom and the stress-energy they generate depend upon boundary conditions for their complete specification. The stress tensor is generally non-vanishing in spacetimes with boundaries or event horizons, with different choices of boundary conditions corresponding to different choices of the macroscopic quantum state of the system. The scalar potentials provide a coordinate invariant description of divergences in the stress tensor components as the event horizon is approached, and signal the breakdown of the semi-classical approximation in the vicinity of horizons. The consequences for the final state of gravitational collapse leading to a non-singular compact object quite different than a classical black hole will be discussed.   

Quantum Stress-Energy Tensor From ``Classical'' Trace Anomaly

We analytically computed the stress-energy tensor for generic quantum fields from the fourth order trace anomaly effective action in several fixed backgrounds including Rindler, de Sitter and Schwarschild spacetimes. The results were compared to analytical or numerical calculations done by the standard methods of quantum field theory. The exact agreement was found in the case of conformally flat spacetimes whereas in the geometrically less trivial Schwarschild space the success of the trace anomaly approach was only partial.   

Quantum Field Theory on a Growing Lattice

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth, at least if only a small number of points is born at each time step.   

Acceleration of the Universe by renormalization-invariant effects of a free quantized scalar field

We show how a non-interacting scalar field of very low mass can lead to a transition in vacuum energy and pressure that accelerates the recent expansion of the universe. This effect is invariant under renormalization, in the sense that it does not come from any of the renormalization constants, such as the cosmological constant, which we set to 0. [See L. Parker and D. A. T. Vanzella, Phys. Rev. D69, 104009 (2004), and references given there.]   

The Relativity of Entropy

This research begins to forward John A. Wheeler's ``It from Bit'' research paradigm. We ask, ``can the concepts of dimensionality and causal (spacetime) geometry emerge from information theory in some semi-classical limit?'' We describe the beginnings of an information-theoretic structure for sweeping out spacetime based on an network and an information metric. Following Leibnizian point of view that we live in a world of relationships, not of machinery, and recognizing that every physical quantity (every ``it'') derives its ultimate significance from bits, binary yes-no indications, we forward this information-based information pregeometry. We have shown one thing:given three random variables a, b and c, with each of them having a very large number of possible values, it is possible to make b half way between a and b in the sense of information distance. That is we can satisfy the triangle inequality. This is possible only if the variables take a large number of values, a fact which suggests that a spacetime point should be thought of as a variable having many possible values. One model is this: a spacetime event is a conglomeration of many binary variables.   

Elementary Model of Constraint Quantization with an Anomaly

Quantum gravity is made more difficult in part by its constraint structure. The constraints are classically first class; however, upon quantization they become partially second class. To study such behavior, we focus on a simple problem with finitely many degrees of freedom and demonstrate how the projection operator formalism for dealing with quantum constraints is well suited to this type of example.   

Testing Projection Operator Quantization on Linearized Gravity

The Klauder-Shabanov projection operator method of quantizing constrained Hamiltonian systems is applied to the cases of linearized gravity and source-free electromagnetism. Our results are in agreement with past results, but have been obtained with less computational effort.   

Consistent Quantum Cosmology: Decohering Histories of Recollapsing FRW Universes

Quantum mechanics normally requires that a history of a system be measured before the probability of that history can be meaningfully discussed. In quantum cosmology, measurement is not an available option and other strategies must be sought. ``Decoherent histories'' formulations of quantum theory take the hint from ordinary quantum mechanics that measurement serves to destroy interference between alternative histories and formalizes this observation into a scheme for making internally consistent quantum predictions for closed systems even in the absence of anything that resembles a classical measurement situation. These ideas have already been applied by Hartle and the author to the construction of a consistent quantum theory of recollapsing homogeneous universes -- the so-called ``Bianchi IX'' cosmological models. In this contribution I discuss the application of this quantum theory to the example of the recollapsing Friedmann-Robertson- Walker cosmology. In particular, coarse grainings suitable to characterize quasiclassical behavior are described, and the branch wave functions for quasiclassical FRW cosmologies are exhibited.