## Hemeroteca del mes junio, 2012

Por Camilo Arcaya • 30 jun, 2012 • Category: Nacionales
La XLIII Cumbre de Jefes de Estado del Mercado Común del Sur (Mercosur) aprobó hoy el ingreso de Venezuela al bloque y ratificó la suspensión de Paraguay, ante la inaceptable ruptura del orden democrático en ese país

Tags: convenio, diplomacia, mercosur, Venezuela

Publicado en Nacionales | No hay comentarios »

Por Camilo Arcaya • 30 jun, 2012 • Category: Ciencia y tecnología
We critically examine the evidence available of the early ideas on the bending of light due to a gravitational attraction, which led to the concept of gravitational lenses, and attempt to present an undistorted historical perspective. Contrary to a widespread but baseless claim, Newton was not the precursor to the idea, and the first Query in his {\sl Opticks} is totally unrelated to this phenomenon. We briefly review the roles of Voltaire, Marat, Cavendish, Soldner and Einstein in their attempts to quantify the gravitational deflection of light. The first, but unpublished, calculations of the lensing effect produced by this deflection are found in Einstein’s 1912 notebooks, where he derived the lensing equation and the formation of images in a gravitational lens. The brief 1924 paper by Chwolson which presents, without calculations, the formation of double images and rings by a gravitational lens passed mostly unnoticed. The unjustly forgotten and true pioneer of the subject is F. Link, who not only published the first detailed lensing calculations in 1936, nine months prior to Einstein’s famous paper in {\sl Science}, but also extended the theory to include the effects of finite-size sources and lenses, binary sources, and limb darkening that same year. Link correctly predicted that the microlensing effect would be easier to observe in crowded fields or in galaxies, as observations confirmed five decades later.

Tags: Cosmology and Extragalactic Astrophysics (astro-ph.CO), General Relativity and Quantum Cosmology (gr-qc), History and Philosophy of Physics (physics.hist-ph)

Publicado en Ciencia y tecnología | No hay comentarios »

Por Camilo Arcaya • 30 jun, 2012 • Category: Ambiente
An integer $n$ is said to be \textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an application, in Section 2, we give an interesting characterization of Mersenne numbers.

Tags: investigación, matemáticas, Number Theory (math.NT), teoría de los números

Publicado en Ambiente | No hay comentarios »

Por Camilo Arcaya • 28 jun, 2012 • Category: Educacion
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms.

Tags: Category Theory (math.CT), física cuántica, matemáticas, Quantum Physics (quant-ph)

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Por Camilo Arcaya • 28 jun, 2012 • Category: sociologia
We recently measured the average distance of users in the Facebook graph, spurring comments in the scientific community as well as in the general press («Four Degrees of Separation»). A number of interesting criticisms have been made about the meaningfulness, methods and consequences of the experiment we performed. In this paper we want to discuss some methodological aspects that we deem important to underline in the form of answers to the questions we have read in newspapers, magazines, blogs, or heard from colleagues. We indulge in some reflections on the actual meaning of «average distance» and make a number of side observations showing that, yes, 3.74 «degrees of separation» are really few.

Tags: Física, Physics and Society (physics.soc-ph), Social and Information Networks (cs.SI), sociedad

Publicado en sociologia | No hay comentarios »

Por Camilo Arcaya • 28 jun, 2012 • Category: Ciencia y tecnología
The Finnish physicist Gunnar Nordstr\»om developed a competing theory of gravitation to Einstein’s 1912-1913 gravitation theory. The equivalence principle was valid in his theory and it also satisfied red shift of the spectral lines from the sun. However, it was unable to supply the Perihelion of Mercury, such as Einstein’s theory; it led to a Perihelion like the one predicted by Newton’s law, and, it could not explain the deflection of light near the sun, because in Nordstr\»om’s theory the velocity of light was constant. Einstein’s 1913-1914 theory, the field equations of which were not generally covariant, remained without empirical support. Thus a decision in favor of one or the other theory – Einstein’s or Nordstr\»om’s – was impossible on empirical grounds. Einstein began to study Nordstr\»om’s theory from the theoretical point of view and he developed his own Einstein-Nordstr\»om theory on the basis of his conception of the natural interval. Eventually, in a joint 1914 paper with Lorentz’s student Adrian Fokker, Einstein showed that a generally covariant formalism is presented from which Nordstr\»om’s theory follows if a single assumption is made that it is possible to choose preferred systems of reference in such a way that the velocity of light is constant; and this was done after Einstein had failed to develop a generally covariant formulation for his own theory.

Tags: Filosofía, Física, History and Philosophy of Physics (physics.hist-ph)

Publicado en Ciencia y tecnología | No hay comentarios »

Por Camilo Arcaya • 27 jun, 2012 • Category: Economía
In two previous papers the author developed a second-order price adjustment (t\^atonnement) process. This paper extends the approach to include both quantity and price adjustments. We demonstrate three results: a analogue to physical energy, called «activity» arises naturally in the model, and is not conserved in general; price and quantity trajectories must either end at a local minimum of a scalar potential or circulate endlessly; and disturbances into a subspace of substitutable commodities decay over time. From this we argue, although we do not prove, that the model features global stability, combined with local instability, a characteristic of many real markets. Following these observations and a brief survey of empirical results for price-setting and consumption behavior in markets for «real» goods (as opposed to financial markets), we conjecture that Stigler and Becker’s well-known theory of consumer preference opens the possibility of substantial degeneracy in commodity space, and therefore that price and quantity trajectories could lie on a relatively low-dimensional subspace within the full commodity space.

Tags: economía, General Finance (q-fin.GN);, investigación

Publicado en Economía | No hay comentarios »

Por Camilo Arcaya • 27 jun, 2012 • Category: Crítica
Statistical analysis is used throughout biomedical research and elsewhere to assess strength of evidence. We have previously argued that typical outcome statistics (including p-values and maximum likelihood ratios) have poor measure-theoretic properties: they can erroneously indicate decreasing evidence as data supporting an hypothesis accumulate; and they are not amenable to calibration, necessary for meaningful comparison of evidence across different study designs, data types, and levels of analysis. We have also previously proposed that thermodynamic theory, which allowed for the first time derivation of an absolute measurement scale for temperature (T), could be used to derive an absolute scale for evidence (E). Here we present a novel thermodynamically-based framework in which measurement of E on an absolute scale, for which «one degree» always means the same thing, becomes possible for the first time. The new framework invites us to think about statistical analyses in terms of the flow of (evidential) information, placing this work in the context of a growing literature on connections among physics, information theory, and statistics.

Tags: Data Analysis, Information Theory (cs.IT), Quantitative Methods (q-bio.QM), Statistics and Probability (physics.data-an), Statistics Theory (math.ST)

Publicado en Crítica | No hay comentarios »

Por Camilo Arcaya • 27 jun, 2012 • Category: Leyes
One of the great puzzles of modern science is that the laws that govern the universe on the largest scale are entirely different from the ones that govern on the smallest scale. That’s odd because all our intuition about the universe is that it ought to be internally consistent rather than at odds with itself. This is why physicists are inextricably wedded to the idea that relativity and quantum mechanics must be manifestations of a bigger and better idea that encompasses them both. The differences between general relativity and quantum mechanics are so great that every attempt to reconcile them has so far failed. However, these attempts have been entirely theoretical and that gives them limited utility.For example, physicists routinely measure the quantum phenomenon of entanglement by sending entangled pairs of photons from one location to another. In these experiments, the sender and receiver must both measure the polarisation of the photons, whether vertical or horizontal, for example. But that can only happen if both parties know which direction is up. That’s easy to specify when they are close together. But it becomes much harder if they are separated by distances over which the curvature of spacetime comes into play. The problem here is that the answer is ambiguous and depends on the path that each photon takes through spacetime. The experimenters can work this out by tracing the path of each photon back to their common source, if this is known. But then, how does each photon ‘know’ the path that the other has taken? Theorists can only guess. Another problem arises when these kinds of experiments are done with the sender and receiver travelling at relativistic speeds. This introduces the well known problem of determining the order of events, which Einstein famously showed depends on the observers’ points of view. That’s in stark contrast to the prediction of quantum mechanics. Here the measurement of one entangled photon instantly determines the result of a future measurement on the other, regardless of the distance between them. If special relativity ensures that the order of events is ambiguous, what gives? Once again, theorists are at a loss. Of course, the way to answer these questions is to test them and see.

Tags: experimentos, Física, física cuántica, física relativista, Velocidades y distancias relativistas

Publicado en Leyes | No hay comentarios »

Por Camilo Arcaya • 27 jun, 2012 • Category: Opinion
Great progresses have been made in exploring exciting physics of low dimensional materials in last few decades. Important examples include the discovering and synthesizing of fullerenes (zero dimensional, 0D), carbon nanotubes (1D) and graphene (2D). A fundamental question is whether we can create materials with dimensions higher than that of conventional 3D crystals, for example, a 4D crystal that has periodic structures in both space and time. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.

Tags: Atomic Physics (physics.atom-ph), espacio-tiempo, Filosofía, Física, frontera, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)

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