14,757 research outputs found
Entropy and temperature of black holes in a gravity's rainbow
The linear relation between the entropy and area of a black hole can be
derived from the Heisenberg principle, the energy-momentum dispersion relation
of special relativity, and general considerations about black holes. There
exist results in quantum gravity and related contexts suggesting the
modification of the usual dispersion relation and uncertainty principle. One of
these contexts is the gravity's rainbow formalism. We analyze the consequences
of such a modification for black hole thermodynamics from the perspective of
two distinct rainbow realizations built from doubly special relativity. One is
the proposal of Magueijo and Smolin and the other is based on a canonical
implementation of doubly special relativity put forward recently by the
authors. In these scenarios, we obtain modified expressions for the entropy and
temperature of black holes. We show that, for a family of doubly special
relativity theories satisfying certain properties, the temperature can vanish
in the limit of zero black hole mass. For the Magueijo and Smolin proposal,
this is only possible for some restricted class of models with bounded energy
and unbounded momentum. With the proposal of a canonical implementation, on the
other hand, the temperature may vanish for more general theories; in
particular, the momentum may also be bounded, with bounded or unbounded energy.
This opens new possibilities for the outcome of black hole evaporation in the
framework of a gravity's rainbow.Comment: 11 pages, 2 new references added, version accepted for publication in
Physical Review
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
Building a case for a Planck-scale-deformed boost action: the Planck-scale particle-localization limit
"Doubly-special relativity" (DSR), the idea of a Planck-scale Minkowski limit
that is still a relativistic theory, but with both the Planck scale and the
speed-of-light scale as nontrivial relativistic invariants, was proposed
(gr-qc/0012051) as a physics intuition for several scenarios which may arise in
the study of the quantum-gravity problem, but most DSR studies focused
exclusively on the search of formalisms for the description of a specific
example of such a Minkowski limit. A novel contribution to the DSR physics
intuition came from a recent paper by Smolin (hep-th/0501091) suggesting that
the emergence of the Planck scale as a second nontrivial relativistic invariant
might be inevitable in quantum gravity, relying only on some rather robust
expectations concerning the semiclassical approximation of quantum gravity. I
here attempt to strengthen Smolin's argument by observing that an analysis of
some independently-proposed Planck-scale particle-localization limits, such as
the "Generalized Uncertainty Principle" often attributed to string theory in
the literature, also suggests that the emergence of a DSR Minkowski limit might
be inevitable. I discuss a possible link between this observation and recent
results on logarithmic corrections to the entropy-area black-hole formula, and
I observe that both the analysis here reported and Smolin's analysis appear to
suggest that the examples of DSR Minkowski limits for which a formalism has
been sought in the literature might not be sufficiently general. I also stress
that, as we now contemplate the hypothesis of a DSR Minkowski limit, there is
an additional challenge for those in the quantum-gravity community attributing
to the Planck length the role of "fundamental length scale".Comment: 12 pages, LaTe
The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values
A which-way measurement destroys the twin-slit interference pattern. Bohr
argued that distinguishing between two slits a distance s apart gives the
particle a random momentum transfer \wp of order h/s. This was accepted for
more than 60 years, until Scully, Englert and Walther (SEW) proposed a
which-way scheme that, they claimed, entailed no momentum transfer. Storey,
Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed,
showed that Bohr was right. This work reviews and extends a recent proposal
[Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a
weak-valued probability distribution for momentum transfer, P_wv(\wp). We show
that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero
because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is
measurable in a way understandable to a classical physicist. We introduce a new
measure of spread for P_wv(\wp): half of the unit-confidence interval, and
conjecture that it is never less than h/4s. For an idealized example with
infinitely narrow slits, the moments of P_wv(\wp) and of the momentum
distributions are undefined unless a process of apodization is used. We show
that by considering successively smoother initial wave functions, successively
more moments of both P_wv(\wp) and the momentum distributions become defined.
For this example the moments of P_wv(\wp) are zero, and these are equal to the
changes in the moments of the momentum distribution. We prove that this
relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but
only for the first two moments. We also compare these moments to those of two
other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find
agreement between all of these, but again only for the first two moments.Comment: 14 pages, 6 figures, submitted to J. Opt.
Effects due to a scalar coupling on the particle-antiparticle production in the Duffin-Kemmer-Petiau theory
The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used
to point out a few misconceptions diffused in the literature. It is explicitly
shown that the scalar coupling makes the DKP formalism not equivalent to the
Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of
the DKP theory looks formally like the spin-0 sector. With proper boundary
conditions, scattering of massive bosons in an arbitrary mixed vector-scalar
square step potential is explored in a simple way and effects due to the scalar
coupling on the particle-antiparticle production and localization of bosons are
analyzed in some detail
The theory and phenomenology of perturbative QCD based jet quenching
The study of the structure of strongly interacting dense matter via hard jets
is reviewed. High momentum partons produced in hard collisions produce a shower
of gluons prior to undergoing the non-perturbative process of hadronization. In
the presence of a dense medium this shower is modified due to scattering of the
various partons off the constituents in the medium. The modified pattern of the
final detected hadrons is then a probe of the structure of the medium as
perceived by the jet. Starting from the factorization paradigm developed for
the case of particle collisions, we review the basic underlying theory of
medium induced gluon radiation based on perturbative Quantum Chromo Dynamics
(pQCD) and current experimental results from Deep Inelastic Scattering on large
nuclei and high energy heavy-ion collisions, emphasizing how these results
constrain our understanding of energy loss. This review contains introductions
to the theory of radiative energy loss, elastic energy loss, and the
corresponding experimental observables and issues. We close with a discussion
of important calculations and measurements that need to be carried out to
complete the description of jet modification at high energies at future high
energy colliders.Comment: 78 pages, 24 figures, submitted to prog. part. nucl. phy
Bounded Rationality and Heuristics in Humans and in Artificial Cognitive Systems
In this paper I will present an analysis of the impact that the notion of “bounded rationality”,
introduced by Herbert Simon in his book “Administrative Behavior”, produced in the
field of Artificial Intelligence (AI). In particular, by focusing on the field of Automated
Decision Making (ADM), I will show how the introduction of the cognitive dimension into
the study of choice of a rational (natural) agent, indirectly determined - in the AI field - the
development of a line of research aiming at the realisation of artificial systems whose decisions
are based on the adoption of powerful shortcut strategies (known as heuristics) based
on “satisficing” - i.e. non optimal - solutions to problem solving. I will show how the
“heuristic approach” to problem solving allowed, in AI, to face problems of combinatorial
complexity in real-life situations and still represents an important strategy for the design
and implementation of intelligent systems
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