Covariant Uniform Acceleration

Details Covariant Uniform Acceleration Covariant Uniform Acceleration

2011-05-03

arxiv.org/abs/1105.0492v2

Physics

General Physics

32 pages, 1 figure

Scientific paper

We introduce a new covariant defining equation for \emph{uniformly accelerated motion} in flat Minkowski space and obtain explicit trajectories for four separate types of uniformly accelerated motion, including both linear acceleration and rotation. Generalized Fermi-Walker transport is used to define a \emph{uniformly accelerated family} of comoving frames to a uniformly accelerated observer. Uniformly accelerated motion is characterized by an acceleration matrix, and we explain the physical meaning of its components. A uniformly accelerated family is used to define a uniformly accelerated \emph{system}. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations, as well as transformations of velocities and accelerations, from a uniformly accelerated system $K'$ to an inertial frame $K$. We derive the general formula for the time dilation between different clocks in $K'$, which depends on the state of the clock, that is, on its position and velocity. Every rest point is also uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. A uniformly accelerated system is rigid. The particular case of a rotating disk provides a resolution of the Ehrenfest Paradox. We obtain a formula for the angular velocity of a uniformly accelerated object.

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