Winding Solutions for the two Particle System in 2+1 Gravity

Using a PASCAL program to follow the evolution of two gravitating particles in 2+1 dimensions we find solutions in which the particles wind around one another indefinitely. As their center of mass moves `tachyonic' they form a Gott-pair. To avoid unphysical boundary conditions we consider a large but closed universe. After the particles have evolved for some time their momenta have grown very large. In this limit we quantize the model and find that both the relevant configuration variable and its conjugate momentum become discrete.Comment: 15 pages Latex, 4 eps figure

The effect of shear and bulk viscosities on elliptic flow

In this work, we examine the effect of shear and bulk viscosities on elliptic flow by taking a realistic parameterization of the shear and bulk viscous coefficients, $\eta$ and $\zeta$, and their respective relaxation times, $\tau_{\pi}$ and $\tau_{\Pi}$. We argue that the behaviors close to ideal fluid observed at RHIC energies may be related to non-trivial temperature dependence of these transport coefficients.Comment: 6 pages, 4 figures, to appear in the proceedings of Strange Quark Matter 2009 (SQM09

TransPlanckian Particles and the Quantization of Time

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.Comment: 12 pages plain tex, 1 figur

Quantum Gravity as a Dissipative Deterministic System

It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.Comment: 20 pages plain TeX, 2 figures PostScript. Added some further explanations, and the definitions of `beable' and `changeable'. A minor error correcte

The mathematical basis for deterministic quantum mechanics

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations adde

Two generalizations of the Boltzmann equation

We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities or equivalently by using nontrivial energy composition rules in the energy conservation constraint. Direct transformation formulas between key functions of the two approaches are given.Comment: Talk given at the 3rd NEXT-Sigma-Phi Conference, Crete, Aug.2005, revtex, 10 page, 2 fig