Positive Cosmological Constant and Quantum Theory

We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS) algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs) of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli).Comment: 44 pages, Latex, no figures. A revised version published in Symmetry, Special Issue: Quantum Symmetr

Introduction to a Quantum Theory over a Galois Field

We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.Comment: 43 pages, Latex, 1 figur

Dual Theories: ‘Same But Different’ or ‘Different But Same’?

I argue that, under the glitz, dual theories are examples of theoretically equivalent descriptions of the same underlying physical content: I distinguish them from cases of genuine underdetermination on the grounds that there is no real incompatibility involved between the descriptions. The incompatibility is at the level of unphysical structure. I argue that dual pairs are in fact very strongly analogous to gauge- related solutions even for dual pairs that look the most radically distinct, such as AdS/CFT

Time in quantum gravity

Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum general relativity and string theory and related approaches. Of particular interest is the question of which of the intuitive aspects of time will turn out to be fundamental, and which 'emergent' in some sense.Comment: 18 pages, 1 figur

Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

Early stage visual-orthographic processes predict long-term retention of word form and meaning: A visual encoding training study

Adult learners of Chinese learned new characters through writing, visual chunking or reading-only. Following training, ERPs were recorded during character recognition tasks, first shortly after the training and then three months later. We hypothesized that the character training effects would be seen in ERP components associated with word recognition and episodic memory. Results confirmed a larger N170 for visual chunking training than other training and a larger P600 for learned characters than novel characters. Another result was a training effect on the amplitude of the P100, which was greater following writing training than other training, suggesting that writing training temporarily lead to increased visual attention to the orthographic forms. Furthermore, P100 amplitude at the first post-test was positively correlated with character recall 3 months later. Thus the marker of early visual attention (P100) was predictive of retention of orthographic knowledge acquired in training