2,932 research outputs found
Can the Arrow of Time be understood from Quantum Cosmology?
I address the question whether the origin of the observed arrow of time can
be derived from quantum cosmology. After a general discussion of entropy in
cosmology and some numerical estimates, I give a brief introduction into
quantum geometrodynamics and argue that this may provide a sufficient framework
for studying this question. I then show that a natural boundary condition of
low initial entropy can be imposed on the universal wave function. The arrow of
time is then correlated with the size of the Universe and emerges from an
increasing amount of decoherence due to entanglement with unobserved degrees of
freedom. Remarks are also made concerning the arrow of time in multiverse
pictures and scenarios motivated by dark energy.Comment: 14 pages, to appear in "The Arrow of Time", ed. by L.
Mersini-Houghton and R. Vaa
Classical and quantum LTB model for the non-marginal case
We extend the classical and quantum treatment of the Lemaitre-Tolman-Bondi
(LTB) model to the non-marginal case (defined by the fact that the shells of
the dust cloud start with a non-vanishing velocity at infinity). We present the
classical canonical formalism and address with particular care the boundary
terms in the action. We give the general relation between dust time and Killing
time. Employing a lattice regularization, we then derive and discuss for
particular factor orderings exact solutions to all quantum constraints.Comment: 23 pages, no figures, typos correcte
Time in Quantum Gravity
The Wheeler-DeWitt equation in quantum gravity is timeless in character. In
order to discuss quantum to classical transition of the universe, one uses a
time prescription in quantum gravity to obtain a time contained description
starting from Wheeler-DeWitt equation and WKB ansatz for the WD wavefunction.
The approach has some drawbacks. In this work, we obtain the time-contained
Schroedinger-Wheeler-DeWitt equation without using the WD equation and the WKB
ansatz for the wavefunction. We further show that a Gaussian ansatz for SWD
wavefunction is consistent with the Hartle-Hawking or wormhole dominance
proposal boundary condition. We thus find an answer to the small scale boundary
conditions.Comment: 12 Pages, LaTeX, no figur
The Born-Oppenheimer Approach to the Matter-Gravity System and Unitarity
The Born-Oppenheimer approach to the matter-gravity system is illustrated and
the unitary evolution for matter, in the absence of phenomena such as
tunnelling or other instabilities, verified. The Born-Oppenheimer approach to
the matter-gravity system is illustrated in a simple minisuperspace model and
the corrections to quantum field theory on a semiclassical background
exhibited. Within such a context the unitary evolution for matter, in the
absence of phenomena such as tunnelling or other instabilities, is verified and
compared with the results of other approaches. Lastly the simplifications
associated with the use of adiabatic invariants to obtain the solution of the
explicitly time dependent evolution equation for matter are evidenced.Comment: Latex, 12 pages. Revised version as accepted for publication by
Class. and Quant. Grav. Some points explained and misprints correcte
Consistency of Semiclassical Gravity
We discuss some subtleties which arise in the semiclassical approximation to
quantum gravity. We show that integrability conditions prevent the existence of
Tomonaga-Schwinger time functions on the space of three-metrics but admit them
on superspace. The concept of semiclassical time is carefully examined. We
point out that central charges in the matter sector spoil the consistency of
the semiclassical approximation unless the full quantum theory of gravity and
matter is anomaly-free. We finally discuss consequences of these considerations
for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2
Single trapped ion as a time-dependent harmonic oscillator
We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result
Gibbs' paradox and black-hole entropy
In statistical mechanics Gibbs' paradox is avoided if the particles of a gas
are assumed to be indistinguishable. The resulting entropy then agrees with the
empirically tested thermodynamic entropy up to a term proportional to the
logarithm of the particle number. We discuss here how analogous situations
arise in the statistical foundation of black-hole entropy. Depending on the
underlying approach to quantum gravity, the fundamental objects to be counted
have to be assumed indistinguishable or not in order to arrive at the
Bekenstein--Hawking entropy. We also show that the logarithmic corrections to
this entropy, including their signs, can be understood along the lines of
standard statistical mechanics. We illustrate the general concepts within the
area quantization model of Bekenstein and Mukhanov.Comment: Contribution to Mashhoon festschrift, 13 pages, 4 figure
The Coherence of Primordial Fluctuations Produced During Inflation
The behaviour of quantum metric perturbations produced during inflation is
considered at the stage after the second Hubble radius crossing. It is shown
that the classical correlation between amplitude and momentum of a perturbation
mode, previously shown to emerge in the course of an effective
quantum-to-classical transition, is maintained for a sufficiently long time,
and we present the explicit form in which it takes place using the Wigner
function. We further show with a simple diffraction experiment that quantum
interference, non-expressible in terms of a classical stochastic description of
the perturbations, is essentially suppressed. Rescattering of the perturbations
leads to a comparatively slow decay of this correlation and to a complete
stochastization of the system.Comment: LaTeX (7 pages
The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
We give an introduction to the canonical formalism of Einstein's theory of
general relativity. This then serves as the starting point for one approach to
quantum gravity called quantum geometrodynamics. The main features and
applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu
(editors): `Approaches To Fundamental Physics -- An Assessment Of Current
Theoretical Ideas' (Springer Verlag, to appear
Hawking radiation from the quantum Lemaitre-Tolman-Bondi model
In an earlier paper, we obtained exact solutions of the Wheeler-DeWitt
equation for the Lemaitre-Tolman-Bondi (LTB) model of gravitational collapse,
employing a lattice regularization. In this paper, we derive Hawking radiation
in non-marginally bound models from our exact solutions. We show that a
non-vanishing energy function does not spoil the (approximate) Planck spectrum
near the horizon. We can also reliably compute corrections to the Bogoliubov
coefficient because our solutions are exact. The corrections are obtained by
going beyond the near horizon region and are shown to introduce additional
greybody factors, which modify the black body spectrum of radiation from the
black hole.Comment: 14 page
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