Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators

Spectral shifting strongly constrains molecular cloud disruption by radiation pressure on dust

${\bf Aim:}$ To test the hypothesis that radiation pressure from star clusters acting on dust is the dominant feedback agent disrupting the largest star-forming molecular clouds and thus regulating the star-formation process. ${\bf Methods:}$ We perform multi-frequency, 3D, RT calculations including scattering, absorption, and re-emission to longer wavelengths for clouds with masses of $10^4$-$10^7\,$M$_{\odot}$, with embedded clusters and a star formation efficiencies of 0.009%-91%, and varying maximum grain sizes up to 200$\,\mu$m. We calculate the ratio between radiative force and gravity to determine whether radiation pressure can disrupt clouds. ${\bf Results:}$ We find that radiation acting on dust almost never disrupts star-forming clouds. UV and optical photons to which the cloud is optically thick do not scatter much. Instead, they quickly get absorbed and re-emitted by at thermal wavelengths. As the cloud is typically optically thin to far-IR radiation, it promptly escapes, depositing little momentum. The resulting spectrum is more narrowly peaked than the corresponding Planck function with an extended tail at longer wavelengths. As the opacity drops significantly across the sub-mm and mm, the resulting radiative force is even smaller than for the corresponding single-temperature black body. The force from radiation pressure falls below the strength of gravitational attraction by an order of magnitude or more for either Milky Way or starbust conditions. For unrealistically large maximum grain sizes, and star formation efficiencies far exceeding 50% do we find that the strength of radiation pressure can exceed gravity. ${\bf Conclusions:}$ We conclude that radiation pressure acting on dust does not disrupt star-forming molecular clouds in any Local Group galaxies. Radiation pressure thus appears unlikely to regulate the star-formation process on either local or global scales.Comment: 20 pages, 17 figure

The speed of gravity in general relativity

The question is discussed of what is the speed of gravity (at the fundamental non-perturbative level). The question is important, if nowhere else, in discussing the problem of information "lost" in black holes. It turns out that the duly defined "gravitational signal" generally may be causal, superluminal and "semi-superluminal". In the class of globally hyperbolic spacetimes the two last varieties coincide. And if some (often imposed, but not always satisfied) conditions hold, the signals may be \emph{only} causal. In this sense the speed of gravity does not exceed the speed of light.Comment: typos corrected, et

The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function

Solenoidal versus compressive turbulence forcing

We analyze the statistics and star formation rate obtained in high-resolution numerical experiments of forced supersonic turbulence, and compare with observations. We concentrate on a systematic comparison of solenoidal (divergence-free) and compressive (curl-free) forcing, which are two limiting cases of turbulence driving. Our results show that for the same RMS Mach number, compressive forcing produces a three times larger standard deviation of the density probability distribution. When self-gravity is included in the models, the star formation rate is more than one order of magnitude higher for compressive forcing than for solenoidal forcing.Comment: 1 page, to appear in the proceedings of the IAU General Assembly Joint Discussion 14 "FIR2009: The ISM of Galaxies in the Far-Infrared and Sub-Millimetre", ed. M. Cunningha

Light Sheets and the Covariant Entropy Conjecture

We examine the holography bound suggested by Bousso in his covariant entropy conjecture, and argue that it is violated because his notion of light sheet is too generous. We suggest its replacement by a weaker bound.Comment: 5 pages, to appear in Classical and Quantum Gravit

The influence of composition, annealing treatment, and texture on the fracture toughness of Ti-5Al-2.5Sn plate at cryogenic temperatures

The plane strain fracture toughness K sub Ic and conventional tensile properties of two commercially produced one-inch thick Ti-5Al-2.5Sn plates were determined at cryogenic temperatures. One plate was extra-low interstitial (ELI) grade, the other normal interstitial. Portions of each plate were mill annealed at 1088 K (1500 F) followed by either air cooling or furnace cooling. The tensile properties, flow curves, and K sub Ic of these plates were determined at 295 K (room temperature), 77 K (liquid nitrogen temperature), and 20 K (liquid hydrogen temperature)

Precise nondivergent analytic formulas for the radiative corrections to the beta energy spectrum in hyperon semileptonic decays over the entire Dalitz plot

Very accurate analytical expressions for the radiative corrections of unpolarized hyperons semileptonic decays of charged and neutral baryons have been obtained in the recent past. Some of these formulas contain logarithmic singularities at the edges of the Dalitz plot for the three- and four-body decays. These singularities are analyzed and integrated analytically to obtain new divergentless formulas for the energy spectrum of the produced beta particle. The new equations contain terms of the order alpha times the momentum transfer, are applicable to any beta decay process and are suitable for a model-independent experimental analysis.Comment: 22 pages, 4 figure

Necessary and sufficient conditions for optimal flow control in multirate multicast networks

The authors consider the optimal flow control problem in multirate multicast networks where all receivers of the same multicast group can receive service at different rates with different QoS. The objective is to achieve the fairness transmission rates that maximise the total receiver utility under the capacity constraint of links. They first propose necessary and sufficient conditions for the optimal solution to the problem, and then derive a new optimal flow control strategy using the Lagrangian multiplier method. Like the unicast case, the basic algorithm consists of a link algorithm to update the link price, and a receiver algorithm to adapt the transmission rate according to the link prices along its path. In particular if some groups contain only one receiver and become unicast, the algorithm will degrade to their previously proposed unicast algorithm