Gravitational Theory with a Dynamical Time

A gravitational theory involving a vector field $\chi^{\mu}$, whose zero component has the properties of a dynamical time, is studied. The variation of the action with respect to $\chi^{\mu}$ gives the covariant conservation of an energy momentum tensor $T^{\mu \nu}_{(\chi)}$. Studying the theory in a background which has killing vectors and killing tensors we find appropriate shift symmetries of the field $\chi^{\mu}$ which lead to conservation laws. The energy momentum that is the source of gravity $T^{\mu \nu}_{(G)}$ is different but related to $T^{\mu \nu}_{(\chi)}$ and the covariant conservation of $T^{\mu \nu}_{(G)}$ determines in general the vector field $\chi^{\mu}$. When $T^{\mu \nu}_{(\chi)}$ is chosen to be proportional to the metric, the theory coincides with the Two Measures Theory, which has been studied before in relation to the Cosmological Constant Problem. When the matter model consists of point particles, or strings, the form of $T^{\mu \nu}_{(G)}$, solutions for $\chi^{\mu}$ are found. For the case of a string gas cosmology, we find that the Milne Universe can be a solution, where the gas of strings does not curve the spacetime since although $T^{\mu \nu}_{(\chi)} \neq 0$, $T^{\mu \nu}_{(G)}= 0$, as a model for the early universe, this solution is also free of the horizon problem. There may be also an application to the "time problem" of quantum cosmology.Comment: 21 pages, discussions extended, some more explicit proofs included, more references include

Selected topics in Planck-scale physics

We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy-momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: 1. looking for energy-dependent spreads in the arrival time of photons of the same energy from GRBs; 2. examining spacetime fluctuation-induced phase incoherence of light from extragalactic sources; 3. detecting spacetime foam with laser-based interferometry techniques; 4. understanding the threshold anomalies in high energy cosmic ray and gamma ray events. Some other experiments are briefly discussed. We show how some physics behind black holes, simple clocks, simple computers, and the holographic principle is related to Planck-scale physics. We also discuss a formulation of the Dirac equation as a difference equation on a discrete Planck-scale spacetime lattice, and a possible interplay between Planck-scale and Hubble-scale physics encoded in the cosmological constant (dark energy).Comment: 31 pages, 1 figure; minor changes; to appear in Mod. Phys. Lett. A as a Brief Revie

Scalar field fluctuations in Schwarzschild-de Sitter space-time

We calculate quantum fluctuations of a free scalar field in the Schwarzschild-de Sitter space-time, adopting the planar coordinates that is pertinent to the presence of a black hole in an inflationary universe. In a perturbation approach, doing expansion in powers of a small black hole event horizon compared to the de Sitter cosmological horizon, we obtain time evolution of the quantum fluctuations and then derive the scalar power spectrum.Comment: 16 pages and 4 figures, accepted by Classical and Quantum Gravit

Steady-state entanglement in a double-well Bose-Einstein condensate through coupling to a superconducting resonator

We consider a two-component Bose-Einstein condensate in a double-well potential, where the atoms are magnetically coupled to a single-mode of the microwave field inside a superconducting resonator. We find that the system has the different dark-state subspaces in the strong- and weak-tunneling regimes, respectively. In the limit of weak tunnel coupling, steady-state entanglement between the two spatially separated condensates can be generated by evolving to a mixture of dark states via the dissipation of the photon field. We show that the entanglement can be faithfully indicated by an entanglement witness. Long-lived entangled states are useful for quantum information processing with atom-chip devices.Comment: 9 pages, 7 figures, minor revisio

Intergenerational income mobility in Singapore

B.E. Journal of Economic Analysis and Policy7

On Quantum Nature of Black-Hole Spacetime: A Possible New Source of Intense Radiation

Atoms and the planets acquire their stability from the quantum mechanical incompatibility of the position and momentum measurements. This incompatibility is expressed by the fundamental commutator [x, p_x]=i hbar, or equivalently, via the Heisenberg's uncertainty principle Delta x Delta p_x sim hbar. A further stability-related phenomenon where the quantum realm plays a dramatic role is the collapse of certain stars into white dwarfs and neutron stars. Here, an intervention of the Pauli exclusion principle, via the fermionic degenerate pressure, stops the gravitational collapse. However, by the neutron-star stage the standard quantum realm runs dry. One is left with the problematic collapse of a black hole. This essay is devoted to a concrete argument on why the black-hole spacetime itself should exhibit a quantum nature. The proposed quantum aspect of spacetime is shown to prevent the general-relativistic dictated problematic collapse. The quantum nature of black-hole spacetime is deciphered from a recent result on the universal equal-area spacing [=lambda_P^2 4 ln(3)] for black holes. In one interpretation of the emergent picture, an astrophysical black hole can fluctuate to sqrt{pi/ln(3)} approx 1.7 times its classical size, and thus allow radiation and matter to escape to the outside observers. These fluctuations I conjecture provide a new source, perhaps beyond Hawking radiation, of intense radiation from astrophysical black holes and may be the primary source of observed radiation from those galactic cores what carry black hole(s). The presented interpretation may be used as a criterion to choose black holes from black hole candidates.Comment: This essay received an "honorable mention" in the 1999 Essay Competition of the Gravity Research Foundation - Ed. Int. J. Mod. Phys. D (1999, in press). For Joseph Knech

Room-temperature operation of GaAs Bragg-mirror lasers

Room-temperature operation of GaAs distributed Bragg reflector lasers is reported. The diodes are fabricated from conventional double heterostructures involving only a single step of liquid-phase epitaxy. For gratings with a period of 3700 Å, the diodes lased at 8770 Å, which corresponds to the high-absorption side of the spontaneous emission spectrum. Thresholds as low as 6 kA/cm^2 have been realized