We give a closed expression for the Minkowski (1 + 1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform experiments in spacetime without making reference to inertial frames. To clarify the relation between inertial and non-inertial observers the coordinate transformation between radar and inertial coordinates also is given. We show that every conformally flat coordinate system can be regarded as the radar coordinate system of a suitable observer for a suitable parametrization of the observer worldline. Therefore, the coordinate transformation between arbitrarily moving observers is a conformal transformation and conformally invariant (1 + 1)-dimensional theories lead to the same physics for all observers, independently of their relative motion.
The Minkowski metric in non-inertial observer radar coordinates / Minguzzi, Ettore. - In: AMERICAN JOURNAL OF PHYSICS. - ISSN 0002-9505. - STAMPA. - 73:(2005), pp. 1117-1121. [10.1119/1.2060716]
The Minkowski metric in non-inertial observer radar coordinates
MINGUZZI, ETTORE
2005
Abstract
We give a closed expression for the Minkowski (1 + 1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform experiments in spacetime without making reference to inertial frames. To clarify the relation between inertial and non-inertial observers the coordinate transformation between radar and inertial coordinates also is given. We show that every conformally flat coordinate system can be regarded as the radar coordinate system of a suitable observer for a suitable parametrization of the observer worldline. Therefore, the coordinate transformation between arbitrarily moving observers is a conformal transformation and conformally invariant (1 + 1)-dimensional theories lead to the same physics for all observers, independently of their relative motion.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.