Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock Hypothesis and using these solutions, we are able to describe the space-time transformations between two uniformly accelerated and rotating systems.Comment: 15 pages 1 figur

Commentary on Family-Directed Structural Therapy: Ten Years of Building on Family Strengths

This is an original and ground-breaking article because the authors have operationalized important concepts in family-centered thinking and practice, developed assessment tools that can be used for testing the validity of these concepts and then collected data from control and treatment groups of families in four very different service areas. Nevertheless, the use of \u27structural family therapy\u27 in the title and design of instruments without grounding this research in the non-linear systems assumptions that are the hallmark of the literature on structural family therapy, obscures some of the theoretical and practice problems that are faced in family treatment today

A new view on relativity: Part 2. Relativistic dynamics

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form

Present and Future Prospects for GRB Standard Candles

Following our previous work, we conclude that a GRB standard candle constructed from the Ghirlanda et al. power-law relation between the geometry-corrected energy (E_gamma) and the peak of the rest-frame prompt burst spectrum (E_p) is not yet cosmographically useful, despite holding some potential advantages over SNe Ia. This is due largely to the small sample of \~20 GRBs with the required measured redshifts, jet-breaks, and peak energies, and to the strong sensitivity of the goodness-of-fit of the power-law to input assumptions. The most important such finding concerns the sensitivity to the generally unknown density (and density profile), of the circumburst medium. Although the E_p-E_gamma relation is a highly significant correlation over many cosmologies, until the sample expands to include many low-z events, it will be most sensitive to Omega_M but essentially insensitive to Omega_Lambda and w, with some hope of constraining dw/dt with high-z GRB data alone. The relation clearly represents a significant improvement in the search for an empirical GRB standard candle, but is further hindered by an unknown physical basis for the relation, the lack of a low-z training set to calibrate the relation in a cosmology-independent way, and several major potential systematic uncertainties and selection effects. Until these concerns are addressed, a larger sample is acquired, and attempts are made to marginalize or perform Monte Carlo simulations over the unknown density distribution, we urge caution concerning claims of the utility of GRBs for cosmography and especially the attempts to combine GRBs with SNe Ia.Comment: 5 pages, 2 figures, "Proceedings, Gamma-Ray Bursts in the Afterglow Era: 4th Workshop, Rome, Italy, Oct 18-22, 2004". Accepted to Il Nuovo Cimento. For more details, see astro-ph/0408413 (ApJ accepted), and other work from the cosmicbooms.net Team at http://www.cosmicbooms.net