An Invertible Linearization Map for the Quartic Oscillator

The set of world lines for the non-relativistic quartic oscillator satisfying Newton's equation of motion for all space and time in 1-1 dimensions with no constraints other than the "spring" restoring force is shown to be equivalent (1-1-onto) to the corresponding set for the harmonic oscillator. This is established via an energy preserving invertible linearization map which consists of an explicit nonlinear algebraic deformation of coordinates and a nonlinear deformation of time coordinates involving a quadrature. In the context stated, the map also explicitly solves Newton's equation for the quartic oscillator for arbitrary initial data on the real line. This map is extended to all attractive potentials given by even powers of the space coordinate. It thus provides classes of new solutions to the initial value problem for all these potentials

Comment on ``Consistent Sets Yield Contrary Inferences in Quantum Theory''

In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can be inferred with probability one, and such that the projectors representing these two propositions are mutually orthogonal. In this note we stress that, according to the rules of consistent history reasoning two such propositions are not contrary in the usual logical sense namely, that one can infer that if one is true then the other is false, and both could be false. No single consistent family contains both propositions, together with the initial and final states, and hence the propositions cannot be logically compared. Consistent histories quantum theory is logically consistent, consistent with experiment as far as is known, consistent with the usual quantum predictions for measurements, and applicable to the most general physical systems. It may not be the only theory with these properties, but in our opinion, it is the most promising among present possibilities.Comment: 2pages, uses REVTEX 3.

Ion Composition of Titan's Ionosphere Observed During T9 Magnetotail Crossing

In a recent paper, Sittler et al., (2010) presented new results on the T9 encounter by the Cassini spacecraft when it passed through Titan s induced magnetotail. Two crossings were observed, but the first crossing, event 1, is thought to be out flowing ionosphere plasma. T9 is ideal for CAPS IMS probing of the ionosphere, since the ion densities at the higher altitudes of the T9 flyby approx. 10,000 km, allows measurements to be made down to 1 eV without saturating its detectors. Sittler et al., (2010) reported possible detection of NH4+ ions, but favored the detection of CH5+ and C2H5+ ions. In this report we investigate both the medium mass resolution (straight through (ST)) and high mass resolution (linear electric field (LEF)) composition data from the Cassini Plasma Spectrometer (CAPS) Ion Mass Spectrometer (IMS). We present a more in depth analysis of the composition data and make comparisons with ionospheric models including nitrogen chemistry such as that by Vuitton et al. (2007). The LEF data does not support NH4+ identification, but favors a CH5+ and C2H5+ identification, but also molecular ions C2N+ and CH2NH2+ are chemically allowed possibilities

Hartle-Hawking state in supersymmetric minisuperspace

The Hartle-Hawking `no-boundary' state is constructed explicitly for the recently developed supersymmetric minisuperspace model with non-vanishing fermion number.Comment: 11 pages, revte

Many worlds and the emergence of probability in quantum mechanics

The interpretation of the squared norm as probability and the apparent stochastic nature of observation in quantum mechanics are derived from the strong law of large numbers and the algebraic properties of infinite sequences of simultaneous quantum observables. It is argued that this result validates the many-worlds view of quantum reality.Comment: 23 page

Wind-Induced Atmospheric Escape: Titan

Rapid thermospheric flows can significantly enhance the estimates of the atmospheric loss rate and the structure of the atmospheric corona of a planetary body. In particular, rapid horizontal flow at the exobase can increase the corresponding constituent escape rate. Here we show that such corrections, for both thermal and non-thermal escape, cannot be ignored when calculating the escape of methane from Titan, for which drastically different rates have been proposed. Such enhancements are also relevant to Pluto and exoplanets

Tunelling with a Negative Cosmological Constant

The point of this paper is see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the univeres. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the four manifold. We raise the questions of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its three volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.Comment: 36 pages, plain TE

An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom'', which states that whenever two particles of the same charge $e$ have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term'', in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.Comment: 37 pages, LaTeX with style package RevTeX 3.