4,734 research outputs found

### 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

### 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

### Distinguishing causal time from Minkowski time and a model for the black hole quantum eigenstates

A discussion is presented of the principle of black hole com- plementarity.
It is argued that this principle could be viewed as a breakdown of general
relativity, or alternatively, as the introduction of a time variable with
multiple `sheets' or `branches'
A consequence of the theory is that the stress-energy tensor as viewed by an
outside observer is not simply the Lorentz-transform of the tensor viewed by an
ingoing observer. This can serve as a justification of a new model for the
black hole atmosphere, recently re-introduced. It is discussed how such a model
may lead to a dynamical description of the black hole quantum states.Comment: Plenary Lecture Notes ICMP97, Brisbane, Australia, July 1997. 12
pages LaTeX, 5 Figures Postscrip

### Quantum information and information loss in General Relativity

When it comes to performing thought experiments with black holes,
Einstein-Bohr like discussions have to be re-opened. For instance one can ask
what happens to the quantum state of a black hole when the wave function of a
single ingoing particle is replaced by an other one that is orthogonal to the
first, while keeping the total energy and momentum unaffected. Observers at
$t\rightarrow\infty$ will not notice any difference, or so it seems in certain
calculational schemes.
If one argues that this cannot be correct for the complete theory because a
black hole should behave in accordance with conventional quantum mechanics,
implying a unitary evolution, one is forced to believe that local quantum field
theory near the black hole horizon is very different from what had hitherto
been accepted. This would give us very valuable information concerning physics
in the Planck length region, notably a mathematical structure very close to
that of super string theory, but it does lead to conceptual difficulties.
An approach that is somewhat related to this is to suspect a breakdown of
General Relativity for quantum mechanical systems. It is to some extent
unavoidable that Hilbert space is not invariant under general coordinate
transformations because such transformations add and remove some states.
Finally the cosmological constant problem also suggests that flat space-time
has some special significance in a quantum theory. We suggest that a new
causality principle could lead to further clues on how to handle this problem.Comment: Elaborated lecture notes for ISQM-Tokyo'95. 15 pages Plain TeX, 3
Figure

- âŠ