3,163 research outputs found
Review of Nelson's analysis of Bell's theorem
This article contains a review of Nelson's analysis of Bell's theorem. It
shows that Bell's inequalities can be violated with a theory of local random
variables if one accepts that the outcomes of these variables are not
predetermined prior to measurement. The article describes the relation between
Bell's theorem and the Strong Free Will theorem of Conway and Kochen. Then, the
original articles of Bell are analyzed in detail. Following an article of
Faris, it is explained that Bell's work on the hidden variable question in fact
describes two separate theorems. Bell's first theorem says that there can be no
model for the singlet state where an outcome does not depend locally on the
settings of the detector where the outcome was measured. Bell's second theorem
shows that Bell's inequalities can be violated by a theory that is either not
deterministic, or violates causality in the sense of relativity or the free
will assumption of the experimenters. It is shown in detail where Bell
implicitly makes the various locality assumptions that Nelson has shown to be
necessary for deriving Bell's inequality. The article closes by relating the
various assumptions needed to derive Bell's theorem with the reality criterion
of EPRComment: 19 pages, section added where Bell's original articles are analyzed
and compared in detail with Nelson's wor
On the physical implications of Hawking's spacetime foam
Hawking's spacetime foam model predicts that due to quantum fluctuations,
spacetime is filled with black hole like objects. We argue that Hawking's model
implies a cosmological constant of the observed order and that it can also be
used to solve the problem of time in quantum gravity.Comment: 12 page
Self tolerance in a minimal model of the idiotypic network
We consider the problem of self tolerance in the frame of a minimalistic
model of the idiotypic network. A node of this network represents a population
of B lymphocytes of the same idiotype which is encoded by a bit string. The
links of the network connect nodes with (nearly) complementary strings. The
population of a node survives if the number of occupied neighbours is not too
small and not too large. There is an influx of lymphocytes with random idiotype
from the bone marrow. Previous investigations have shown that this system
evolves toward highly organized architectures, where the nodes can be
classified into groups according to their statistical properties. The building
principles of these architectures can be analytically described and the
statistical results of simulations agree very well with results of a modular
mean field theory. In this paper we present simulation results for the case
that one or several nodes, playing the role of self, are permanently occupied.
We observe that the group structure of the architecture is very similar to the
case without self antigen, but organized such that the neighbours of the self
are only weakly occupied, thus providing self tolerance. We also treat this
situation in mean field theory which give results in good agreement with data
from simulation.Comment: 7 pages, 6 figures, 1 tabl
Quantum gravity and space-time foam
This thesis argues that Hawking's model on space-time foam predicts, after several modifications, a cosmological constant of the observed order. Inconsistencies of Hawking's model that were pointed out by Christensen and Duff are removed. A mechanism is given that can be used to remove the Ostrogradski instability of the effective matter action.
The modified space-time foam model of Hawking describes a space-time filled with a gas of microscopic black- and wormholes. It is noted that particles which fly through such a space-time are governed by different equations of motion than in vacuum, since they scatter with the Hawking radiation of the microscopic black-holes and they are additionally under a collective influence of the gravitational field on long time scales. Under the assumption that Hawking radiation restores any information that was removed by the black-holes, one can derive the Schrödinger equation at low energies if one puts a classical particle into the space-time foam.
The space-time foam model implies topology changes of the space-time during the expansion of the universe. It is argued that ordinary quantum field theory on Lorentzian space-times is incompatible with such changes since they give rise to singularities. It is proposed that if a stochastic model with non-differentiable paths underlies quantum mechanics at small scales (the usual path integral formulation is restricted to differentiable paths) then this could be used near the singularities during a topology change of the space-time
On topology changes in quantum field theory and quantum gravity
Two singularity theorems can be proven if one attempts to let a Lorentzian
cobordism interpolate between two topologically distinct manifolds. On the
other hand, Cartier and DeWitt-Morette have given a rigorous definition for
quantum field theories (qfts) by means of path integrals. This article uses
their results to study whether qfts can be made compatible with topology
changes. We show that path integrals over metrics need a finite norm for the
latter and for degenerate metrics, this problem can sometimes be resolved with
tetrads. We prove that already in the neighborhood of some cuspidal
singularities, difficulties can arise to define certain qfts. On the other
hand, we show that simple qfts can be defined around conical singularities that
result from a topology change in a simple setup. We argue that the ground state
of many theories of quantum gravity will imply a small cosmological constant
and, during the expansion of the universe, will cause frequent topology
changes. Unfortunately, it is difficult to describe the transition amplitudes
consistently due to the aforementioned problems. We argue that one needs to
describe qfts by stochastic differential equations, and in the case of gravity,
by Regge calculus in order to resolve this problem.Comment: 85 pages, to appear in rmp. The article is now in the production
stag
- …