Real Time Relativity: exploration learning of special relativity

Real Time Relativity is a computer program that lets students fly at relativistic speeds though a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year university students

Symplectic Gravity Models in Four, Three and Two Dimensions

A class of the $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n \times n$ matrix generalizations of the dilaton and Kalb-Ramond fields is considered. It is shown that the Pecci-Quinn axion matrix can be entered and the resulting equations of motion possess the $Sp(2n, R)$ symmetry in four dimensions. The stationary case is studied. It is established that the theory allows a $\sigma$-model representation with a target space which is invariant under the $Sp[2(n+1), R]$ group of isometry transformations. The chiral matrix of the coset $Sp[2(n+1), R]/U(n+1)$ is constructed. A K\"ahler formalism based on the use of the Ernst $(n+1) \times (n+1)$ complex symmetric matrix is developed. The stationary axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending on the original field variables is obtained. The Kramer-Neugebauer transformation, which algebraically maps the original variables into the target space ones, is presented.Comment: 21 pages, RevTex, no figurie

Policy responses to invasive native species: issues of social and private benefits and costs

Farm and catchment managers in Australia face decisions about controlling invasive native species (or scrub) which may infest agricultural land. The treatment of this land to remove the infestation and re-establish native pastures is likely to be expensive for landholders. Yet there are potential social benefits from such remediation and so a policy question arises of what to do to about facilitating such change. New South Wales state government legislation addresses this issue through regulations, and the Catchment Management Authorities are responsible for administering public funds to achieve associated natural resource improvements. However, the extent of the private costs and social benefits associated with such changes are not known, which precludes benefit-cost analyses using the traditional welfare economics framework. This paper reports results of a social and private economic analysis of the impacts of a typical infestation remediation decision. We show that for the landholder the private costs exceed the benefits achieved from increased livestock productivity. However, there are social benefits expressed by the willingness to pay by members of the local catchment community for improvements in native vegetation and biodiversity. When these social benefits are included, the economic analysis shows a positive social net benefit. This raises questions of how to reconcile the public and private accounting, and whether any changes to policies, regulations or procedures for natural resource management in New South Wales are warranted.Invasive native scrub, environmental values, choice modelling, financial, economic, Namoi catchment,

BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla \phi)^2$ is degenerate under the global invariance $\phi \to \phi + \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2\alpha V}}\bigl(\int_{S^4} dV \phi \bigr)^2$ where $\alpha$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under SO(5), the symmetry group of $S^4$, and the associated two-point functions have no infrared divergence. The well-known infrared divergence which appears by taking the massless limit of the massive scalar field propagator is therefore a gauge artifact. By contrast, the massless scalar field theory on de Sitter space $dS^4$ - the lorentzian version of $S^4$ - is not invariant under the symmetry group of that spacetime SO(1,4). Here, the infrared divergence is real. Therefore, the massless scalar quantum field theories on $S^4$ and $dS^4$ cannot be linked by analytic continuation. In this case, because of zero modes, the euclidean approach to quantum field theory does not work. Similar considerations also apply to massive scalar field theories for exceptional values of the mass parameter (corresponding to the discrete series of the de Sitter group).Comment: This paper has been published under the title "Zero modes, euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)

Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue on Dark Energ

The radiation environment near the lunar surface: CRaTER observations and Geant4 simulations

[1] At the start of the Lunar Reconnaissance Orbiter mission in 2009, its Cosmic Ray Telescope for the Effects of Radiation instrument measured the radiation environment near the Moon during the recent deep solar minimum, when galactic cosmic rays (GCRs) were at the highest level observed during the space age. We present observations that show the combined effects of GCR primaries, secondary particles (“albedo”) created by the interaction of GCRs with the lunar surface, and the interactions of these particles in the shielding material overlying the silicon solid-state detectors of the Cosmic Ray Telescope for the Effects of Radiation. We use Geant4 to model the energy and angular distribution of the albedo particles, and to model the response of the sensor to the various particle species reaching the 50 kilometer altitude of the Lunar Reconnaissance Orbiter. Using simulations to gain insight into the observations, we are able to present preliminary energy-deposit spectra for evaluation of the radiation environment\u27s effects on other sensitive materials, whether biological or electronic, that would be exposed to a similar near-lunar environment

GCR access to the Moon as measured by the CRaTER instrument on LRO

[1] Recent modeling efforts have yielded varying and conflicting results regarding the possibility that Earth\u27s magnetosphere is able to shield energetic particles of \u3e10 MeV at lunar distances. This population of particles consists of galactic cosmic rays as well as energetic particles that are accelerated by solar flares and coronal mass ejections. The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) onboard the Lunar Reconnaissance Orbiter is in orbit about the Moon and is thus able to directly test these modeling results. Over the course of a month, CRaTER samples the upstream solar wind as well as various regions of Earth\u27s magnetotail. CRaTER data from multiple lunations demonstrate that Earth\u27s magnetosphere at lunar distances produces no measurable influence on energetic particle flux, even at the lowest energies (\u3e14 MeV protons) where any effect should be maximized. For particles with energies of 14–30 MeV, we calculate an upper limit (determined by counting statistics) on the amount of shielding caused by the magnetosphere of 1.7%. The high energy channel (\u3e500 MeV) provides an upper limit of 3.2%

Update on Radiation Dose From Galactic and Solar Protons at the Moon Using the LRO/CRaTER Microdosimeter

The NASA Lunar Reconnaissance Orbiter (LRO) has been exploring the lunar surface and radiation environment since June 2009. In Mazur et al. [2011] we discussed the first 6 months of mission data from a microdosimeter that is housed within the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument onboard LRO. The CRaTER microdosimeter is an early version of what is now a commercially available hybrid that accurately measures total ionizing radiation dose in a silicon target (http://www.teledynemicro.com/product/radiation-dosimeter). This brief report updates the transition from a deep solar minimum radiation environment to the current weak solar maximum as witnessed with the microdosimeter

A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenvalue equation for the ADM mass of the hole, from the point of view of a distant observer at rest, is obtained. Our eigenvalue equation implies that the ADM mass and the electric charge spectra of the hole are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure