118402616
Comment on Jerrold Franklin, Superluminal neutrinos, arXiv:1110.0234v1
A reasonably short antineutrino run using OPERA and/or MINOS may test J. Franklin's explanation of recently claimed $\nu_\mu$ superluminality.
16978878
What is the statistical significance of the solar neutrino flux problem
Uniform random numbers, not Gaussian random numbers, should have been used with Standard Solar Models to estimate the effect on the neutrino flux of uncertainties in input data. The observed discrepancy is therefore probably quite smaller than currently accepted.
123329421
Lorentz-Invariant Equations of Motion of Point Masses in the General Theory of Relativity
After a general discussion of the problem of motion in the general theory of relativity a simple derivation of the law of motion is given for single poles of the gravitational field, which is based on a method originally developed by Mathisson. This law follows from the covariant conservation law for the matter energy-momentum tensor alone, without reference to any field equations, and takes the form of a geodesic of the (unknown) metric. Expanding this metric in terms of a power series in a parameter gamma and using the Minkowski proper time to parametrize the world lines of the particles, the (Lorentz-invariant) form of the approximate laws of motion follows. A method is developed to obtain the equations of motion (including the explicit form of the metric in terms of the particle variables) from Einsiein's field equations. A systematic linearization procedure leads to a series of second-order differential equations for the metric; the nth order approximation of the equations of motion, as well as the explicit form of the matter tensor in (n + l)st order, is obtained as an integrability condition on the (n + l)st order opproximation for the metric. No coordinate conditions are required to obtain themore » general form of the equations of motion; they are needed only to reduce the approximation equations to wave equations and thus to allow their explicit integration in terms of retarded or symmetric potentials. In developing the approximation method it is shown that consistency requires that any set of approximate equations is solved up to'' rather than in'' nth order; this implies that the form of the lower-order metric be maintained, but the motion corresponding to the nth order solutions rather than to lower order ones. In particular, the equations for the first- order metric imply zero-order equations of motion which restrict the particles to zero acceleration; the equations for the second-order metric imply first-order equation of motion involving the first-order metric, but without the previous restriction. In the retarded case the equations of motion contain retarded interactions and radiation terms of the form familiar from electrodynamics; no such terms appear in the symmetric case. The equations of the symmetric case are derivable from a Fokker-type variational principle. The relation of the results obtained to work on Lorentz-invariant equations by other autnors is discussed. In Appendix I a discussion of alternative derivations is prescnted; Appendix II contains remarks on Wheeler-Feynman type considerations for general relativistic equations of motion. (auth)« less
120995906
Degeneracy in loop variables
The small algebra of loop functionals, defined by Rovelli and Smolin, on the Ashtekar phase space of general relativity is studied. Regarded as coordinates on the phase space, the loop functionals become degenerate at certain points. All the degenerate points are found and the corresponding degeneracy is discussed. The intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions. The evolution of the holonomy group of Ashtekar's connection is examined, and the complexification of the holonomy group is shown to be preserved under it. Thus, an observable of the gravitational field is constructed.
119537735
Newman‐Penrose Constants and Their Invariant Transformations
The origin and significance of the Newman‐Penrose (N‐P) constants of the motion are examined from the point of view that constants of the motion generate invariant transformations. Here the calculation makes use of a generalization of Green's theorem to a situation applicable to the coupled Einstein‐Maxwell fields in general relativity. One finds strictly electromagnetic constants generated by an incoming electromagnetic shock wave, with dipole symmetry, at future null infinity. The gravitational constants contain an admixture from the electromagnetic field. They are generated by an incident quadrupole gravitational shock wave at future null infinity (J+). Both the electromagnetic dipole field and the gravitational quadrupole field behave like linearized fields at J+. All higher‐multipole fields do not uncouple from the nonlinear corrections induced by the self‐coupling of the gravitational field and its coupling with the electromagnetic field. It is shown that the gravitational constants are related to t...
120204158
Developments and predictions