5 research outputs found
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