Projection of relativistically moving objects on a two-dimensional plane, the `train' paradox and the visibility of the Lorentz contraction

Although many papers have appeared on the theory of photographing relativistically moving objects, pioneered by the classic work of Penrose and Terrell, three problems remain outstanding. (1) There does not seem to exist a general formula which gives the projection of a relativistically moving object, applicable to any object no matter how complicated, on a two-dimensional plane in conformity with Terrell's observation. (2) No resolution seems to have been provided for the associated so-called `train' paradox. (3) No analytical demonstration seems to have been offered on how the Lorentz contraction may be actually detected on a photograph. This paper addresses all of these three problems. The analysis does not require any more than trigonometry and elementary differentiation.Comment: LaTeX, 14 pages, 6 figures, misprint correcte

Functional treatment of quantum scattering via the dynamical principle

A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range interactions, such as for the Coulomb one, it is shown that this expression may be used to obtain explicitly the asymptotic "free" modified Green function near the energy shell.Comment: 7 page

Polarization Correlations in Pair Production from Charged and Neutral Strings

Polarization correlations of $e^{+}e^{-}$ pair productions from charged and neutral Nambu strings are investigated, via photon and graviton emissions, respectively and explicit expressions for their corresponding probabilities are derived and found to be \textit{speed} dependent. The strings are taken to be circularly oscillating closed strings, as perhaps the simplest solution of the Nambu action. In the extreme relativistic case, these probabilities coincide, but, in general, are different, and such inquiries, in principle, indicate whether the string is charged or uncharged. It is remarkable that these dynamical relativistic quantum field theory calculations lead to a clear violation of Local Hidden Variables theories.Comment: 6 pages, no figure, LaTeX with ws-mpla.cl