6,058 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
Measurement of Quantum Fluctuations in Geometry
A particular form for the quantum indeterminacy of relative spacetime
position of events is derived from the limits of measurement possible with
Planck wavelength radiation. The indeterminacy predicts fluctuations from a
classically defined geometry in the form of ``holographic noise'' whose spatial
character, absolute normalization, and spectrum are predicted with no
parameters. The noise has a distinctive transverse spatial shear signature, and
a flat power spectral density given by the Planck time. An interferometer
signal displays noise due to the uncertainty of relative positions of
reflection events. The noise corresponds to an accumulation of phase offset
with time that mimics a random walk of those optical elements that change the
orientation of a wavefront. It only appears in measurements that compare
transverse positions, and does not appear at all in purely radial position
measurements. A lower bound on holographic noise follows from a covariant upper
bound on gravitational entropy. The predicted holographic noise spectrum is
estimated to be comparable to measured noise in the currently operating
interferometer GEO600. Because of its transverse character, holographic noise
is reduced relative to gravitational wave effects in other interferometer
designs, such as LIGO, where beam power is much less in the beamsplitter than
in the arms.Comment: 7 pages, 2 figures, LaTeX. Extensive rewrite of original version,
including more detailed analysis. Main result is the same but the estimate of
noise in strain units for GEO600, showing 1/f behavior at low f and flat at
high f, is improved. To appear in Phys. Rev.
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
Indeterminacy of Holographic Quantum Geometry
An effective theory based on wave optics is used to describe indeterminacy of
position in holographic spacetime with a UV cutoff at the Planck scale.
Wavefunctions describing spacetime positions are modeled as complex
disturbances of quasi-monochromatic radiation. It is shown that the product of
standard deviations of two position wavefunctions in the plane of a holographic
light sheet is equal to the product of their normal separation and the Planck
length. For macroscopically separated positions the transverse uncertainty is
much larger than the Planck length, and is predicted to be observable as a
"holographic noise" in relative position with a distinctive shear spatial
character, and an absolutely normalized frequency spectrum with no parameters
once the fundamental wavelength is fixed from the theory of gravitational
thermodynamics. The spectrum of holographic noise is estimated for the GEO600
interferometric gravitational-wave detector, and is shown to approximately
account for currently unexplained noise between about 300 and 1400Hz. In a
holographic world, this result directly and precisely measures the fundamental
minimum interval of time.Comment: 4 pages, LaTeX. Considerably shortened from earlier version.
Conclusions are unchanged. Submitted to PR
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
Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
We study the phase space structure and the quantization of a pointlike
particle in 2+1 dimensional gravity. By adding boundary terms to the first
order Einstein Hilbert action, and removing all redundant gauge degrees of
freedom, we arrive at a reduced action for a gravitating particle in 2+1
dimensions, which is invariant under Lorentz transformations and a group of
generalized translations. The momentum space of the particle turns out to be
the group manifold SL(2). Its position coordinates have non-vanishing Poisson
brackets, resulting in a non-commutative quantum spacetime. We use the
representation theory of SL(2) to investigate its structure. We find a
discretization of time, and some semi-discrete structure of space. An
uncertainty relation forbids a fully localized particle. The quantum dynamics
is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory
improve
Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions
We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge
theories, by simulating lattice theories with a Wilson plaquette action. We
find that there is a strong-to-weak coupling cross-over in the lattice theory
that appears to become a third-order phase transition at N=oo, in a manner that
is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo)
lattice gauge theory. There is also evidence for a second order transition at
N=oo at approximately the same coupling, which is connected with centre
monopoles (instantons) and so analogues to the first order bulk transition that
occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice
spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a
sequence of (apparently) first-order ZN symmetry breaking transitions
associated with each of the tori (ordered by size). We discuss how these
transitions can be understood in terms of a sequence of deconfining transitions
on ever-more dimensionally reduced gauge theories.We investigate whether the
trace of the Wilson loop has a non-analyticity in the coupling at some critical
area, but find no evidence for this although, just as in D=1+1,the eigenvalue
density of a Wilson loop forms a gap at N=oo for a critical trace. The physical
implications of this are unclear.The gap formation is a special case of a
remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1
and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue
spectra are nearly identical.This holds for finite as well as infinite N;
irrespective of the Wilson loop size in lattice units; and for Polyakov as well
as Wilson loops.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new
results on non-analyticities and eigenvalue spectra of Wilson loops. This
version to be submitted for publicatio
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
The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we describe the matter-free toroidal spacetime in 't Hooft's
polygon approach to 2+1-dimensional gravity (i.e. we consider the case without
any particles present). Contrary to earlier results in the literature we find
that it is not possible to describe the torus by just one polygon but we need
at least two polygons. We also show that the constraint algebra of the polygons
closes.Comment: 18 pages Latex, 13 eps-figure
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