1,438 research outputs found
The Schr\"odinger-Newton equation and its foundations
The necessity of quantising the gravitational field is still subject to an
open debate. In this paper we compare the approach of quantum gravity, with
that of a fundamentally semi-classical theory of gravity, in the weak-field
non-relativistic limit. We show that, while in the former case the
Schr\"odinger equation stays linear, in the latter case one ends up with the
so-called Schr\"odinger-Newton equation, which involves a nonlinear, non-local
gravitational contribution. We further discuss that the Schr\"odinger-Newton
equation does not describe the collapse of the wave-function, although it was
initially proposed for exactly this purpose. Together with the standard
collapse postulate, fundamentally semi-classical gravity gives rise to
superluminal signalling. A consistent fundamentally semi-classical theory of
gravity can therefore only be achieved together with a suitable prescription of
the wave-function collapse. We further discuss, how collapse models avoid such
superluminal signalling and compare the nonlinearities appearing in these
models with those in the Schr\"odinger-Newton equation.Comment: 17 pages, 3 figures, revised version (some minor changes
The quark-gluon plasma, turbulence, and quantum mechanics
Quark-gluon plasmas formed in heavy ion collisions at high energies are well
described by ideal classical fluid equations with nearly zero viscosity. It is
believed that a similar fluid permeated the entire universe at about three
microseconds after the big bang. The estimated Reynolds number for this
quark-gluon plasma at 3 microseconds is approximately 10^19. The possibility
that quantum mechanics may be an emergent property of a turbulent proto-fluid
is tentatively explored. A simple relativistic fluid equation which is
consistent with general relativity and is based on a cosmic dust model is
studied. A proper time transformation transforms it into an inviscid Burgers
equation. This is analyzed numerically using a spectral method. Soliton-like
solutions are demonstrated for this system, and these interact with the known
ergodic behavior of the fluid to yield a stochastic and chaotic system which is
time reversible. Various similarities to quantum mechanics are explored.Comment: 41 pages. Content changes in the azimuthal soliton sectio
Singularities and Quantum Gravity
Although there is general agreement that a removal of classical gravitational
singularities is not only a crucial conceptual test of any approach to quantum
gravity but also a prerequisite for any fundamental theory, the precise
criteria for non-singular behavior are often unclear or controversial. Often,
only special types of singularities such as the curvature singularities found
in isotropic cosmological models are discussed and it is far from clear what
this implies for the very general singularities that arise according to the
singularity theorems of general relativity. In these lectures we present an
overview of the current status of singularities in classical and quantum
gravity, starting with a review and interpretation of the classical singularity
theorems. This suggests possible routes for quantum gravity to evade the
devastating conclusion of the theorems by different means, including modified
dynamics or modified geometrical structures underlying quantum gravity. The
latter is most clearly present in canonical quantizations which are discussed
in more detail. Finally, the results are used to propose a general scheme of
singularity removal, quantum hyperbolicity, to show cases where it is realized
and to derive intuitive semiclassical pictures of cosmological bounces.Comment: 41 pages, lecture course at the XIIth Brazilian School on Cosmology
and Gravitation, September 200
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