CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 3 JUNE 2002

General-Linear-Acceleration Transformations of Spacetime,
Jerks and Limiting 4-Dimensional Symmetry

Jong-Ping Hsu

Department of Physics, University of Massachusetts Dartmouth

North Dartmouth, MA 02747-2300, USA
(Received September 28, 2001)

Based on the limiting 4-dimensional symmetry of the Lorentz and Poincaré groups, new general spacetime transformations for frames with arbitrary linear acceleration in any direction are obtained in a fairly simple form. A new feature in the metric tensors is the presence of jerk, the time derivative of acceleration. The Riemann curvature tensor of spacetime in these non-inertial frames vanishes. For one-dimensional motion, the general spacetime transformations are shown to form a group. The transformations of Wu, M$\o$ller, Poincaré and Lorentz are special limiting cases of this general-linear-acceleration transformation. The Planck constant $\hbar$ and the speed of light c are not invariant universal constants under such general spacetime transformations. The theory suggests that the electromagnetic coupling strength $\alpha_e$ = 1/137.035989 and a new quantum constant $J=\text{3.5177293}\times 10^{-38} g\cdot cm,$ are truly universal constants in both inertial and non-inertial frames.

PACS. 11.30.Cp - Lorentz and Poincaré invariance.

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