902,975 research outputs found
Choice, internal consistency, and rationality
The classical theory of rational choice is built on several important internal consistency conditions. In recent years, the reasonableness of those internal consistency conditions has been questioned and criticized, and several responses to accommodate such criticisms have been proposed in the literature. This paper develops a general framework to accommodate the issues raised by the criticisms of classical rational choice theory, and examines the broad impact of these criticisms from both normative and positive points of view.
Topological set theories and hyperuniverses
We give a new set theoretic system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK and the theory of hyperuniverses. On the other hand, it retains most of the expressiveness of these theories and has the same consistency strength as ZF. We single out the additional axiom of the universal set as the one that increases the consistency strength to that of GPK and explore several other axioms and interrelations between those theories.
Hyperuniverses are a natural class of models for theories with a universal set. The Aleph_0- and Aleph_1-dimensional Cantor cubes are examples of hyperuniverses with additivity Aleph_0, because they are homeomorphic to their hyperspace. We prove that in the realm of spaces with uncountable additivity, none of the generalized Cantor cubes has that property.
Finally, we give two complementary constructions of hyperuniverses which generalize many of the constructions found in the literature and produce initial and terminal hyperuniverses
Localization of Negative Energy and the Bekenstein Bound
A simple argument shows that negative energy cannot be isolated far away from
positive energy in a conformal field theory and strongly constrains its
possible dispersal. This is also required by consistency with the Bekenstein
bound written in terms of the positivity of relative entropy. We prove a new
form of the Bekenstein bound based on the monotonicity of the relative entropy,
involving a "free" entropy enclosed in a region which is highly insensitive to
space-time entanglement, and show that it further improves the negative energy
localization bound.Comment: 5 pages, 1 figur
A Kolmogorov Extension Theorem for POVMs
We prove a theorem about positive-operator-valued measures (POVMs) that is an
analog of the Kolmogorov extension theorem, a standard theorem of probability
theory. According to our theorem, if a sequence of POVMs G_n on
satisfies the consistency (or projectivity) condition then there is a POVM G on the space
of infinite sequences that has G_n as its marginal for
the first n entries of the sequence. We also describe an application in quantum
theory.Comment: 6 pages LaTeX, no figure
Quantum Breaking Bound on de Sitter and Swampland
Quantum consistency suggests that any de Sitter patch that lasts a number of
Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of
light particle species suffers an effect of quantum breaking. Inclusion of
other interactions makes the quantum break-time shorter. The requirement that
this must not happen puts severe constraints on scalar potentials, essentially
suppressing the self-reproduction regimes. In particular, it eliminates both
local and global minima with positive energy densities and imposes a general
upper bound on the number of e-foldings in any given Hubble patch.
Consequently, maxima and other tachyonic directions must be curved stronger
than the corresponding Hubble parameter. We show that the key relations of the
recently-proposed de Sitter swampland conjecture follow from the de Sitter
quantum breaking bound. We give a general derivation and also illustrate this
on a concrete example of -brane inflation. We can say that string theory as
a consistent theory of quantum gravity nullifies a positive vacuum energy in
self-defense against quantum breaking.Comment: 4 pages, matches published version; v2: added reference
Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
Recently modified gravitational theories which mimic the behaviour of dark
matter, the so-called "Mimetic Dark Matter", have been proposed. We study the
consistency of such theories with respect to the absence of ghost instability
and propose a new tensor-vector-scalar theory of gravity, which is a
generalization of the previous models of mimetic dark matter with additional
desirable features. The original model proposed by Chamseddine and Mukhanov
[JHEP 1311 (2013) 135, arXiv:1308.5410] is concluded to describe a regular
pressureless dust, presuming that we consider only those configurations where
the energy density of the mimetic dust remains positive under time evolution.
For certain type of configurations the theory can become unstable. Both
alternative modified theories of gravity, which are based on a vector field
(tensor-vector theory) or a vector field and a scalar field
(tensor-vector-scalar theory), are free of ghost instabilities.Comment: 23 pages, v4: clarifies and/or extends the discussion on the
positivity of total energy, the instability found in the original mimetic
model, and the number of physical degrees of freedom in each considered
theory. Presentation improved in section 3. To be published in J. High Energy
Phy
Holographic dual of a time machine
We apply the holography to the simplest possible eternal time
machine solution in based on two conical defects moving around their
center of mass along a circular orbit. Closed timelike curves in this
space-time extend all the way to the boundary of , violating causality
of the boundary field theory. By use of the geodesic approximation we address
the "grandfather paradox" in the dual dimensional field theory and
calculate the two-point retarded Green function. It has a non-trivial
analytical structure both at negative and positive times, providing us with an
intuition on how an interacting quantum field could behave once causality is
broken. In contrast with the previous considerations our calculations reveal
the possibility of a consistent and controllable evolution of a quantum system
without any need to impose additional consistency constraints.Comment: 37 pages, 26 figure
Construction of Field Algebras with Quantum Symmetry from Local Observables
It has been discussed earlier that ( weak quasi-) quantum groups allow for
conventional interpretation as internal symmetries in local quantum theory.
From general arguments and explicit examples their consistency with (braid-)
statistics and locality was established. This work addresses to the
reconstruction of quantum symmetries and algebras of field operators. For every
algebra \A of observables satisfying certain standard assumptions, an
appropriate quantum symmetry is found. Field operators are obtained which act
on a positive definite Hilbert space of states and transform covariantly under
the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation
relations, these fields are demonstrated to obey local braid relation.Comment: 50 pages, HUTMP 93-B33
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