Repeat ridge jumps associated with plume‐ridge interaction, melt transport, and ridge migration

Repeated shifts, or jumps, of mid-ocean ridge segments toward nearby hot spots can produce large, long-term changes to the geometry and location of the tectonic plate boundaries. Ridge jumps associated with hot spot–ridge interaction are likely caused by several processes including shear on the base of the plate due to expanding plume material as well as reheating of lithosphere as magma passes through it to feed off-axis volcanism. To study how these processes influence ridge jumps, we use numerical models to simulate 2-D (in cross section) viscous flow of the mantle, viscoplastic deformation of the lithosphere, and melt migration upward from the asthenospheric melting zone, laterally along the base of the lithosphere, and vertically through the lithosphere. The locations and rates that magma penetrates and heats the lithosphere are controlled by the time-varying accumulation of melt beneath the plate and the depth-averaged lithospheric porosity. We examine the effect of four key parameters: magmatic heating rate of the lithosphere, plate spreading rate, age of the seafloor overlying the plume, and the plume-ridge migration rate. Results indicate that the minimum value of the magmatic heating rate needed to initiate a ridge jump increases with plate age and spreading rate. The time required to complete a ridge jump decreases with larger values of magmatic heating rate, younger plate age, and faster spreading rate. For cases with migrating ridges, models predict a range of behaviors including repeating ridge jumps, much like those exhibited on Earth. Repeating ridge jumps occur at moderate magmatic heating rates and are the result of changes in the hot spot magma flux in response to magma migration along the base of an evolving lithosphere. The tendency of slow spreading to promote ridge jumps could help explain the observed clustering of hot spots near the Mid-Atlantic Ridge. Model results also suggest that magmatic heating may significantly thin the lithosphere, as has been suggested at Hawaii and other hot spots

The Definition of Mach's Principle

Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to Peter Mittelstaedt's 80th Birthday Festschrift. 30 page

There exist non orthogonal quantum measurements that are perfectly repeatable

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that when a non orthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.Comment: 4 pages, 1 figure, revtex4, minor change

Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalisation of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.Comment: 5 pages, 1 figure v2: more details in the proof of the main resul

Jacobi's Principle and the Disappearance of Time

Jacobi's action principle is known to lead to a problem of time. For example, the timelessness of the Wheeler-DeWitt equation can be seen as resulting from using Jacobi's principle to define the dynamics of 3-geometries through superspace. In addition, using Jacobi's principle for non-relativistic particles is equivalent classically to Newton's theory but leads to a time-independent Schrodinger equation upon Dirac quantization. In this paper, we study the mechanism for the disappearance of time as a result of using Jacobi's principle in these simple particle models. We find that the path integral quantization very clearly elucidates the physical mechanism for the timeless of the quantum theory as well as the emergence of duration at the classical level. Physically, this is the result of a superposition of clocks which occurs in the quantum theory due to a sum over all histories. Mathematically, the timelessness is related to how the gauge fixing functions impose the boundary conditions in the path integral.Comment: Published version. Significant amendments to presentation. 27 page

A quantum logical and geometrical approach to the study of improper mixtures

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that -alike the classical case- quantum interactions produce non trivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic

The development of path integration: combining estimations of distance and heading

Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well-understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the startpoint of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. 7-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing

Quantifying diffuse and discrete venting at the Tour Eiffel vent site, Lucky Strike hydrothermal field

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 13 (2012): Q04008, doi:10.1029/2011GC003991.The relative heat carried by diffuse versus discrete venting of hydrothermal fluids at mid-ocean ridges is poorly constrained and likely varies among vent sites. Estimates of the proportion of heat carried by diffuse flow range from 0% to 100% of the total axial heat flux. Here, we present an approach that integrates imagery, video, and temperature measurements to accurately estimate this partitioning at a single vent site, Tour Eiffel in the Lucky Strike hydrothermal field along the Mid-Atlantic Ridge. Fluid temperatures, photographic mosaics of the vent site, and video sequences of fluid flow were acquired during the Bathyluck'09 cruise (Fall, 2009) and the Momarsat'10 cruise (Summer, 2010) to the Lucky Strike hydrothermal field by the ROV Victor6000 aboard the French research vessel the “Pourquoi Pas”? (IFREMER, France). We use two optical methods to calculate the velocities of imaged hydrothermal fluids: (1) for diffuse venting, Diffuse Flow Velocimetry tracks the displacement of refractive index anomalies through time, and (2) for discrete jets, Particle Image Velocimetry tracks eddies by cross-correlation of pixel intensities between subsequent images. To circumvent video blurring associated with rapid velocities at vent orifices, exit velocities at discrete vents are calculated from the best fit of the observed velocity field to a model of a steady state turbulent plume where we vary the model vent radius and fluid exit velocity. Our results yield vertical velocities of diffuse effluent between 0.9 cm s−1 and 11.1 cm s−1 for fluid temperatures between 3°C and 33.5°C above that of ambient seawater, and exit velocities of discrete jets between 22 cm s−1 and 119 cm s−1 for fluid temperatures between 200°C and 301°C above ambient seawater. Using the calculated fluid velocities, temperature measurements, and photo mosaics of the actively venting areas, we calculate a heat flux due to diffuse venting from thin fractures of 3.15 ± 2.22 MW, discrete venting of 1.07 ± 0.66 MW, and, by incorporating previous estimates of diffuse heat flux density from Tour Eiffel, diffuse flux from the main sulfide mound of ∼15.6 MW. We estimate that the total integrated heat flux from the Tour Eiffel site is 19.82 ± 2.88 MW and that the ratio of diffuse to discrete heat flux is ∼18. We discuss the implication of these results for the characterization of different vent sites within Lucky Strike and in the context of a compilation of all available measurements of the ratio of diffuse to discrete heat flux.E. Mittelstaedt was supported by the International Research Fellowship Program of the U.S. National Science Foundation (OISE-0757920). Funding for the 2006, 2008, 2009, and 2010 cruises was provided by CNRS/ IFREMER through the MoMAR program (France), by ANR (France), the Mothseim Project NT05–3 42213 to J. Escartín and by grant CTM2010–15216/MAR from the Spanish Ministry of Science to R. Garcia and J. Escartín. T. Barreyre was supported by University Paris Diderot (Paris 7 – France) and Institut de Physique du Globe de Paris (IPGP, France).2012-10-1