Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time

The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the constraints as expectation-value equations over the true dynamical degrees of freedom of the gravitational field -- a representation of the underlying anisotropy of space. This self-consistent approach leads to qualitatively different predictions than the Dirac and the ADM quantizations, and in addition, our theory avoids the interpretational conundrums associated with the problem of time in quantum gravity. We briefly describe the structure of our functional equations, and apply our quantization technique to two examples so as to illustrate the basic ideas of our approach.Comment: 11, (No Figures), (Typeset using RevTeX

Gravitational Geons Revisited

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.Comment: 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been mad

Probing spacetime foam with extragalactic sources

Due to quantum fluctuations, spacetime is probably ``foamy'' on very small scales. We propose to detect this texture of spacetime foam by looking for core-halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy/matter, independent of the evidence from recent cosmological observations.Comment: LaTeX, 11 pages, 1 figure; version submitted to PRL; several references added; very useful comments and suggestions by Eric Perlman incorporate

On the Squeezed Number States and their Phase Space Representations

We compute the photon number distribution, the Q distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state using generating functions which allow to obtain any matrix element in the squeezed number state representation from the matrix elements in the squeezed coherent state representation. For highly squeezed number states we discuss the previously unnoted oscillations which appear in the Q function. We also note that these oscillations can be related to the photon-number distribution oscillations and to the momentum representation of the wave function.Comment: 16 pages, 9 figure

Husimi's Q(α)Q(\alpha) function and quantum interference in phase space

We discuss a phase space description of the photon number distribution of non classical states which is based on Husimi's $Q(\alpha)$ function and does not rely in the WKB approximation. We illustrate this approach using the examples of displaced number states and two photon coherent states and show it to provide an efficient method for computing and interpreting the photon number distribution . This result is interesting in particular for the two photon coherent states which, for high squeezing, have the probabilities of even and odd photon numbers oscillating independently.Comment: 15 pages, 12 figures, typos correcte

The Exceptionally Luminous Type Ia Supernova 2007If

SN 2007if was the third over-luminous Type Ia supernova (SN Ia) detected after 2003fg and 2006gz. We present the photometric and spectroscopic observations of the SN and its host by ROTSE-III, HET, and Keck. From the H a line identified in the host spectra, we determine a redshift of 0.0736. At this distance, the SN reached an absolute magnitude of -20.4, brighter than any other SNe Ia ever observed. If the source of luminosity is radioactive decay, a large amount of radioactive nickel (similar to 1.5 M(circle dot)) is required to power the peak luminosity, more than can be produced realistically in a Chandrasekhar mass progenitor. Low expansion velocity, similar to that of 2003fg, is also measured around the maximum light. The observations may suggest that SN 2007if was from a massive white dwarf progenitor, plausibly exploding with mass well beyond 1.4 M(circle dot). Alternatively, we investigate circumstellar interaction that may contribute to the excess luminosity.NASA NNX-08AN25G, NNX-08AV63GNSF AST-0707769, PHY-0801007Australian Research CouncilUniversity of New South WalesUniversity of TexasUniversity of MichiganAstronom

Shortcomings in the Understanding of Why Cosmological Perturbations Look Classical

There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. In fact, a recent article (C. Kiefer & D. Polarski, ArXiv: 0810.0087 [astro-ph]) addresses the question "Why do the Cosmological Perturbations look Classical?" and offers an answer based on unitary quantum mechanics (i.e., without reference to the projection postulate) relying on the decoherence type of analysis. The argument is, thus, implicitly assuming that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics. We will review here, why do we, together with various other researchers in the field, consider that this is not the case, in general, and particularly not at all in the situation at hand. In fact, as has been previously discussed (A. Perez, H. Sahlmann, and D. Sudarsky, CQG 23, 2317, (2006);[arXiv: gr-qc/0508100]), we will argue that the cosmological situation is one where the measurement problem of quantum mechanics appears in a particular exacerbated form, and that, it is this, even sharper conondrum, the one that should be addressed when dealing with the inflationary account of the origin of the seeds of cosmic structure in the early universe.Comment: New version: In press in International Journal of Modern Physics

Thermal properties of spacetime foam

Spacetime foam can be modeled in terms of nonlocal effective interactions in a classical nonfluctuating background. Then, the density matrix for the low-energy fields evolves, in the weak-coupling approximation, according to a master equation that contains a diffusion term. Furthermore, it is argued that spacetime foam behaves as a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables. These effects can be, at least in principle, experimentally tested.Comment: RevTeX 3.01, 11 pages, no figure

Pre-Existing Superbubbles as the Sites of Gamma-Ray Bursts

According to recent models, gamma-ray bursts apparently explode in a wide variety of ambient densities ranging from ~ 10^{-3} to 30 cm^{-3}. The lowest density environments seem, at first sight, to be incompatible with bursts in or near molecular clouds or with dense stellar winds and hence with the association of gamma-ray bursts with massive stars. We argue that low ambient density regions naturally exist in areas of active star formation as the interiors of superbubbles. The evolution of the interior bubble density as a function of time for different assumptions about the evaporative or hydrodynamical mass loading of the bubble interior is discussed. We present a number of reasons why there should exist a large range of inferred afterglow ambient densities whether gamma-ray bursts arise in massive stars or some version of compact star coalescence. We predict that many gamma-ray bursts will be identified with X-ray bright regions of galaxies, corresponding to superbubbles, rather than with blue localized regions of star formation. Massive star progenitors are expected to have their own circumstellar winds. The lack of evidence for individual stellar winds associated with the progenitor stars for the cases with afterglows in especially low density environments may imply low wind densities and hence low mass loss rates combined with high velocities. If gamma-ray bursts are associated with massive stars, this combination might be expected for compact progenitors with atmospheres dominated by carbon, oxygen or heavier elements, that is, progenitors resembling Type Ic supernovae.Comment: 14 pages, no figures, submitted to The Astrophysical Journa