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

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

Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we derive an expression for the conserved Pauli-Lubanski scalar in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point particles. We find that it is represented by an extra spatial shift $\Delta$ in addition to the usual identification rule (being a rotation over the cut). For two particles this invariant is expressed in terms of 't Hooft's phase-space variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are added. 6 pages Latex, 4 eps-figure

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

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

Lattice Regularization of Gauge Theories Without Loss of Chiral Symmetry

A lattice regularization procedure for gauge theories is proposed in which fermions are given a special treatment such that all chiral flavor symmetries that are free of Adler-Bell-Jackiw anomalies are kept intact. There is no doubling of fermionic degrees of freedom. A price paid for this feature is that the number of fermionic degrees of freedom per unit cell is still infinite, although finiteness of the complete functional integrals can be proven (details are outlined in an Appendix). Therefore, although perhaps of limited usefulness for numerical simulations, our scheme can be applied for studying aspects such as analytic convergence questions, spontaneous symmetry breakdown and baryon number violation in non-Abelian gauge theories.Comment: Correction of formula in Appendix, and extra references adde

The scattering matrix approach for the quantum black hole, an overview

If one assumes the validity of conventional quantum field theory in the vicinity of the horizon of a black hole, one does not find a quantum mechanical description of the entire black hole that even remotely resembles that of conventional forms of matter; in contrast with matter made out of ordinary particles one finds that, even if embedded in a finite volume, a black hole would be predicted to have a strictly continuous spectrum. Dissatisfied with such a result, which indeed hinges on assumptions concerning the horizon that may well be wrong, various investigators have now tried to formulate alternative approaches to the problem of ``quantizing" the black hole. We here review the approach based on the assumption of quantum mechanical purity and unitarity as a starting point, as has been advocated by the present author for some time, concentrating on the physics of the states that should live on a black hole horizon. The approach is shown to be powerful in not only producing promising models for the quantum black hole, but also new insights concerning the dynamics of physical degrees of freedom in ordinary flat space-time.Comment: Review paper, 71 pages plain TEX, 8 Figures (Postscript

When was Asymptotic Freedom discovered? or The Rehabilitation of Quantum Field Theory

We glance back at the short period of the great discoveries between 1970 and 1974 that led to the restablishment of Quantum Field Theory and the discovery of the Standard Model of Elementary Particles, in particular Quantum Chromodynamics, and ask ourselves where we stand now.Comment: small but important corrections were made as a response to several reactions. Minor typos corrected. 17 pages plain TeX, 4 figures PostScrip

The holographic mapping of the Standard Model onto the black hole horizon, Part I: Abelian vector field, scalar field and BEH Mechanism

Interactions between outgoing Hawking particles and ingoing matter are determined by gravitational forces and Standard Model interactions. In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon's dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components.Comment: 13 pages, no figure