76,783 research outputs found
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
On the necessity of complexity
Wolfram's Principle of Computational Equivalence (PCE) implies that universal
complexity abounds in nature. This paper comprises three sections. In the first
section we consider the question why there are so many universal phenomena
around. So, in a sense, we week a driving force behind the PCE if any. We
postulate a principle GNS that we call the Generalized Natural Selection
Principle that together with the Church-Turing Thesis is seen to be equivalent
to a weak version of PCE. In the second section we ask the question why we do
not observe any phenomena that are complex but not-universal. We choose a
cognitive setting to embark on this question and make some analogies with
formal logic. In the third and final section we report on a case study where we
see rich structures arise everywhere.Comment: 17 pages, 3 figure
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
Introduction to the Ontology of Knowledge iss. 20211125
We can only know what determines us as being and by the fact that it determines us as being.
Our knowledge is therefore logically limited to what determines us as being.
Since representation is defined as the act that makes knowledge dicible, our representation is logically limited to what dynamically determines us as being.
Our representation is included in our becoming.
Nothing that we represent, no infinite, can exceed the mere necessity of our becoming.
The world, my physical being and my consciousness are subsumed by the necessity of my becoming.
We know nothing but âwe becomeâÂ
To the question "Is there anything else to know?" we can give no logical answer
Summary:
Reality is pure logical interdependence, immanent, formless, unspeakable.
Logos is a principle of order in this interdependence.
Individuation is the necessary asymptote of any instance of the Logos.
Each knowing subject is Individuation, a mode of order among infinites of infinites of possible modes of order.
Everything that appears to the subject as Existing participates in his Individuation.
This convergence into Individuation defines a perspective that gives meaning.
The subject is representation.
It is in this representation that exist the subject, objects and laws of the world.
Without subject there are no objects, no laws, no framework.
The representation is not isomorphism but morphogenesis.
The physical world and the Spirit have the same logical nature: they are categories of representation.
The representation is animated because meaning is an Act.
Representation is limited by a horizon of meaning.
Below this horizon the subject represents the universe and itself.
Beyond this horizon there is no prevailing space, time or form.
The predicate expresses, below the horizon of meaning, a necessity whose source is beyond this horizon, unfathomable.
The OK is neither materialism nor idealism and frees itself from any psychological preconceptions.
The OK does not propose an "other reality" than that described by common sense or science, but another mode of representation.
The OK is compatible with the current state of science, while offering new interpretive avenues.
The OK differs from ontic structural realism (OSR) in various ways:
Just like being, the relationship is representation,
The knowing subject is present in any representation,
the real is non-founded
Pierre Duhemâs philosophy and history of science
LEITE (FĂĄbio Rodrigo) â STOFFEL (Jean-François), Introduction (pp. 3-6). BARRA (Eduardo Salles de O.) â SANTOS (Ricardo Batista dos), Duhemâs analysis of Newtonian method and the logical priority of physics over metaphysics (pp. 7-19). BORDONI (Stefano), The French roots of Duhemâs early historiography and epistemology (pp. 20-35). CHIAPPIN (JosĂ© R. N.) â LARANJEIRAS (CĂĄssio Costa), Duhemâs critical analysis of mechaÂniÂcism and his defense of a formal conception of theoretical phyÂsics (pp. 36-53). GUEGUEN (Marie) â PSILLOS (Stathis), Anti-Âscepticism and epistemic humility in Pierre Duhemâs philosophy of science (pp. 54-72). LISTON (Michael), Duhem : images of science, historical continuity, and the first crisis in physics (pp. 73-84). MAIOCCHI (Roberto), Duhem in pre-war Italian philosÂophy : the reasons of an absence (pp. 85-92). HERNĂNDEZ MĂRQUEZ (VĂctor Manuel), Was Pierre Duhem an «esprit de finesse» ? (pp. 93-107). NEEDHAM (Paul), Was Duhem justified in not distinguishing between physical and chemical atomism ? (pp. 108-111). OLGUIN (Roberto Estrada), «Bon sens» and «noĂ»s» (pp. 112-126). OLIVEIRA (Amelia J.), Duhemâs legacy for the change in the historiography of science : An analysis based on Kuhnâs writings (pp. 127-139). PRĂNCIPE (JoĂŁo), PoincarĂ© and Duhem : Resonances in their first epistemological reflecÂtions (pp. 140-156). MONDRAGON (DamiĂĄn Islas), Book review of «Pierre Duhem : entre fĂsica y metafĂsica» (pp. 157-159). STOFFEL (Jean-François), Book review of P. Duhem : «La thĂ©orie physique : son objet, sa structure» / edit. by S. Roux (pp. 160-162). STOFFEL (Jean-François), Book review of St. Bordoni : «When historiography met epistemology» (pp. 163-165)
Black holes, complexity and quantum chaos
We study aspects of black holes and quantum chaos through the behavior of
computational costs, which are distance notions in the manifold of unitaries of
the theory. To this end, we enlarge Nielsen geometric approach to quantum
computation and provide metrics for finite temperature/energy scenarios and
CFT's. From the framework, it is clear that costs can grow in two different
ways: operator vs `simple' growths. The first type mixes operators associated
to different penalties, while the second does not. Important examples of simple
growths are those related to symmetry transformations, and we describe the
costs of rotations, translations, and boosts. For black holes, this analysis
shows how infalling particle costs are controlled by the maximal Lyapunov
exponent, and motivates a further bound on the growth of chaos. The analysis
also suggests a correspondence between proper energies in the bulk and average
`local' scaling dimensions in the boundary. Finally, we describe these
complexity features from a dual perspective. Using recent results on SYK we
compute a lower bound to the computational cost growth in SYK at infinite
temperature. At intermediate times it is controlled by the Lyapunov exponent,
while at long times it saturates to a linear growth, as expected from the
gravity description.Comment: 30 page
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