Moving Mirrors and Thermodynamic Paradoxes

Quantum fields responding to "moving mirrors" have been predicted to give rise to thermodynamic paradoxes. I show that the assumption in such work that the mirror can be treated as an external field is invalid: the exotic energy-transfer effects necessary to the paradoxes are well below the scales at which the model is credible. For a first-quantized point-particle mirror, it appears that exotic energy-transfers are lost in the quantum uncertainty in the mirror's state. An accurate accounting of these energies will require a model which recognizes the mirror's finite reflectivity, and almost certainly a model which allows for the excitation of internal mirror modes, that is, a second-quantized model.Comment: 7 pages, Revtex with Latex2

`Operational' Energy Conditions

I show that a quantized Klein-Gordon field in Minkowski space obeys an `operational' weak energy condition: the energy of an isolated device constructed to measure or trap the energy in a region, plus the energy it measures or traps, cannot be negative. There are good reasons for thinking that similar results hold locally for linear quantum fields in curved space-times. A thought experiment to measure energy density is analyzed in some detail, and the operational positivity is clearly manifested. If operational energy conditions do hold for quantum fields, then the negative energy densities predicted by theory have a will-o'-the-wisp character: any local attempt to verify a total negative energy density will be self-defeating on account of quantum measurement difficulties. Similarly, attempts to drive exotic effects (wormholes, violations of the second law, etc.) by such densities may be defeated by quantum measurement problems. As an example, I show that certain attempts to violate the Cosmic Censorship principle by negative energy densities are defeated. These quantum measurement limitations are investigated in some detail, and are shown to indicate that space-time cannot be adequately modeled classically in negative energy density regimes.Comment: 18 pages, plain Tex, IOP macros. Expanded treatment of measurement problems for space-time, with implications for Cosmic Censorship as an example. Accepted by Classical and Quantum Gravit

Impacts of atmospheric stilling and climate warming on cyanobacterial blooms: An individual-based modelling approach

Harmful algal blooms of the freshwater cyanobacteria genus Microcystis are a global problem and are expected to intensify with climate change. In studies of climate change impacts on Microcystis blooms, atmospheric stilling has not been considered. Stilling is expected to occur in some regions of the world with climate warming, and it will affect lake stratification regimes. We tested if stilling could affect water column Microcystis distributions using a novel individual-based model (IBM). Using the IBM coupled to a three-dimensional hydrodynamic model, we assessed responses of colonial Microcystis biomass to wind speed decrease and air temperature increase projected under a future climate. The IBM altered Microcystis colony size using relationships with turbulence from the literature, and included light, temperature, and nutrient effects on Microcystis growth using input data from a shallow urban lake. The model results show that dynamic variations in colony size are critical for accurate prediction of cyanobacterial bloom development and decay. Colony size (mean and variability) increased more than six-fold for a 20% decrease in wind speed compared with a 2 °C increase in air temperature. Our results suggest that atmospheric stilling needs to be included in projections of changes in the frequency, distribution and magnitude of blooms of buoyant, colony-forming cyanobacteria under climate change

Individual-based modelling of cyanobacteria blooms: Physical and physiological processes

Lakes and reservoirs throughout the world are increasingly adversely affected by cyanobacterial harmful algal blooms (CyanoHABs). The development and spatiotemporal distributions of blooms are governed by complex physical mixing and transport processes that interact with physiological processes affecting the growth and loss of bloom-forming species. Individual-based models (IBMs) can provide a valuable tool for exploring and integrating some of these processes. Here we contend that the advantages of IBMs have not been fully exploited. The main reasons for the lack of progress in mainstreaming IBMs in numerical modelling are their complexity and high computational demand. In this review, we identify gaps and challenges in the use of IBMs for modelling CyanoHABs and provide an overview of the processes that should be considered for simulating the spatial and temporal distributions of cyanobacteria. Notably, important processes affecting cyanobacteria distributions, in particular their vertical passive movement, have not been considered in many existing lake ecosystem models. We identify the following research gaps that should be addressed in future studies that use IBMs: 1) effects of vertical movement and physiological processes relevant to cyanobacteria growth and accumulations, 2) effects and feedbacks of CyanoHABs on their environment; 3) inter and intra-specific competition of cyanobacteria species for nutrients and light; 4) use of high resolved temporal-spatial data for calibration and verification targets for IBMs; and 5) climate change impacts on the frequency, intensity and duration of CyanoHABs. IBMs are well adapted to incorporate these processes and should be considered as the next generation of models for simulating CyanoHABs

Kant's philosophy of the aesthetic and the philosophy of praxis

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2012 Association for Economic and Social Analysis.This essay seeks to reconstruct the terms for a more productive engagement with Kant than is typical within contemporary academic cultural Marxism, which sees him as the cornerstone of a bourgeois model of the aesthetic. The essay argues that, in the Critique of Judgment, the aesthetic stands in as a substitute for the missing realm of human praxis. This argument is developed in relation to Kant's concept of reflective judgment that is in turn related to a methodological shift toward inductive and analogical procedures that help Kant overcome the dualisms of the first two Critiques. This reassessment of Kant's aesthetic is further clarified by comparing it with and offering a critique of Terry Eagleton's assessment of the Kantian aesthetic as synonymous with ideology

Vacuum Polarization and Energy Conditions at a Planar Frequency Dependent Dielectric to Vacuum Interface

The form of the vacuum stress-tensor for the quantized scalar field at a dielectric to vacuum interface is studied. The dielectric is modeled to have an index of refraction that varies with frequency. We find that the stress-tensor components, derived from the mode function expansion of the Wightman function, are naturally regularized by the reflection and transmission coefficients of the mode at the boundary. Additionally, the divergence of the vacuum energy associated with a perfectly reflecting mirror is found to disappear for the dielectric mirror at the expense of introducing a new energy density near the surface which has the opposite sign. Thus the weak energy condition is always violated in some region of the spacetime. For the dielectric mirror, the mean vacuum energy density per unit plate area in a constant time hypersurface is always found to be positive (or zero) and the averaged weak energy condition is proven to hold for all observers with non-zero velocity along the normal direction to the boundary. Both results are found to be generic features of the vacuum stress-tensor and not necessarily dependent of the frequency dependence of the dielectric.Comment: 16 pages, 4 figures, Revtex style Minor typographic corrections to equations and tex

Detection of negative energy: 4-dimensional examples

We study the response of switched particle detectors to static negative energy densities and negative energy fluxes. It is demonstrated how the switching leads to excitation even in the vacuum and how negative energy can lead to a suppression of this excitation. We obtain quantum inequalities on the detection similar to those obtained for the energy density by Ford and co-workers and in an `operational' context by Helfer. We revisit the question `Is there a quantum equivalence principle?' in terms of our model. Finally, we briefly address the issue of negative energy and the second law of thermodynamics.Comment: 10 pages, 7 figure

Total angular momentum from Dirac eigenspinors

The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away be the gravitational radiation is also derived.Comment: 34 pages, typos corrected, four references added, appearing in Class. Quantum Gra

Bounds on negative energy densities in flat spacetime

We generalise results of Ford and Roman which place lower bounds -- known as quantum inequalities -- on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-negative sampling functions which are either compactly supported or decay rapidly at infinity. Our results hold in $d$-dimensional Minkowski space ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in 2-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference adde