5,388 research outputs found
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
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
Quantization of Space and Time in 3 and in 4 Space-time Dimensions
The fact that in Minkowski space, space and time are both quantized does not
have to be introduced as a new postulate in physics, but can actually be
derived by combining certain features of General Relativity and Quantum
Mechanics. This is demonstrated first in a model where particles behave as
point defects in 2 space dimensions and 1 time, and then in the real world
having 3+1 dimensions. The mechanisms in these two cases are quite different,
but the outcomes are similar: space and time form a (non-cummutative) lattice.
These notes are short since most of the material discussed in these lectures
is based on two earlier papers by the same author (gr-qc/9601014 and
gr-qc/9607022), but the exposition given in the end is new.Comment: Lectures held at the NATO Advanced Study Institute on ``Quantum
Fields and Quantum Space Time", Carg\`ese, July 22 -- August 3, 1996. 16
pages Plain TeX, 6 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
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 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
Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
By investigating the canonical commutation rules for gravitating quantized
particles in a 2+1 dimensional world it is found that these particles live on a
space-time lattice. The space-time lattice points can be characterized by three
integers. Various representations are possible, the details depending on the
topology chosen for energy-momentum space. We find that an
topology yields a physically most interesting lattice within which first
quantization of Dirac particles is possible. An topology also gives a
lattice, but does not allow first quantized particles.Comment: 23 pages Plain TeX, 3 Figure
Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates
We find that the momentum conjugate to the relative distance between two
gravitating particles in their center of mass frame is a hyperbolic angle. This
fact strongly suggests that momentum space should be taken to be a hyperboloid.
We investigate the effect of quantization on this curved momentum space. The
coordinates are represented by non commuting, Hermitian operators on this
hyperboloid. We also find that there is a smallest distance between the two
particles of one half times the Planck length.Comment: 18 pages Latex, 2 eps figure
Gedanken Experiments involving Black Holes
Analysis of several gedanken experiments indicates that black hole
complementarity cannot be ruled out on the basis of known physical principles.
Experiments designed by outside observers to disprove the existence of a
quantum-mechanical stretched horizon require knowledge of Planck-scale effects
for their analysis. Observers who fall through the event horizon after sampling
the Hawking radiation cannot discover duplicate information inside the black
hole before hitting the singularity. Experiments by outside observers to detect
baryon number violation will yield significant effects well outside the
stretched horizon.Comment: 22 pages (including 7 figures), SU-ITP-93-1
Effective Nonlocal Euclidean Gravity
A nonlocal form of the effective gravitational action could cure the
unboundedness of euclidean gravity with Einstein action. On sub-horizon length
scales the modified gravitational field equations seem compatible with all
present tests of general relativity and post-Newtonian gravity. They induce a
difference in the effective Newton's constant between regions of space with
vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they
may lead to a value for the critical density after inflation. The
simplest model considered here appears to be in conflict with nucleosynthesis,
but generalizations consistent with all cosmological observations seem
conceivable.Comment: 12 pages, LaTe
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