Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

The "ethical anthropic principle" and the religious ethics of Levinas

Why did Levinas choose Isaiah 45:7 ("I make peace and create evil: I the Lord do all that") as a superscription of his essay on evil? This article explores the role of evil in Levinas's religious ethics. The author discusses the structure of evil as revealed phenomenologically and juxtaposes it to the structure of subjectivity found in the writings of Levinas. The idea of the "ethical anthropic principle," modeled upon the cosmic anthropic principle, is then used to link evil to the responsibility of the subject. The link is subsequently extended to God. This is proposed as one way of understanding the meaning of Isaiah 45:7. © 2001 Journal of Religious Ethics, Inc.

A test of the hypothesis of ecological equivalence in an Australian subtropical rain forest

We tested the hypothesis that tree species in a subtropical rain forest in south-east Queensland are ecologically equivalent and therefore have identical environmental requirements for their regeneration. We assessed the evidence that juveniles of species differed in their distributions in treefall gap microsites and along gradients of light availability, soil pH, soil PO4-P availability and soil NO3-N availability. Pairwise comparisons were made on a subset of the common species selected on the basis that they showed a relatively high level of positive association, and would therefore, a priori, be expected to have similar regeneration requirements. Detailed comparisons between the species failed to demonstrate evidence for species differentiation with respect to their tolerance of the disturbance associated with gap microsites or to the gradient of NO3-N availability. However, species differed markedly in their distributions along the soil pH gradient and along the gradients of light availability and soil PO4-P availability. The overall level of ecological differentiation between the species is high: seven out of the 10 possible species pairings showed evidence for ecological differentiation. Such niche differentiation amongst the juveniles of tree species may play an important role in maintaining the species richness of rain-forest communities.

A new principle for tight junction modulation based on occludin peptides

The aim of this study was to investigate whether peptides from the extracellular loops of the tight junction protein occludin could be used as a new principle for tight junction modulation. Peptides of 4 to 47 amino acids in length and covering the two extracellular loops of the tight junction protein occludin were synthesized, and their effect on the tight junction permeability in Caco-2 cells was investigated using [C-14] mannitol as a paracellular marker. Lipopeptide derivatives of one of the active occludin peptides (OPs), synthesized by adding a lipoamino acid containing 14 carbon atoms (C-14-) to the N terminus of the peptide, were also investigated. Peptides corresponding to the N terminus of the first extracellular loop of occludin increased the permeability of the tight junctions without causing short-term toxicity. However, the peptides had an effect only when added to the basolateral side of the cells, which could be partly explained by degradation by apical peptidases and aggregate formation. By contrast, the lipopeptide C-14-OP90-103, which protects the peptide from degradation and aggregation, displayed a rapid apical effect. The L- and D-diastereomers of C-14-OP90-103 had distinctly different effects. The D-isomer, which releases intact OP90-103 from the lipoamino acid, displayed a rapid and transient increase in tight junction permeability. The L- isomer, which releases OP90-103 more rapidly, gave a more sustained increase in tight junction permeability. In conclusion, C-14-OP90-103 represents a prototype of a new class of tight junction modulators that act on the extracellular domains of tight junction proteins.