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In relativity theory, proper acceleration [1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall , or inertial , observer who is momentarily at rest relative to the object being measured.
Even if we pick units where =, the magnitude of the proper acceleration will depend on our choice of units: for example, if we use units of light-years for distance, (or ) and years for time, (or ), this would mean = light year/year 2, equal to about 9.5 meters/second 2, while if we use units of light-seconds for distance, (or ), and seconds ...
In order to find out the transformation of three-acceleration, one has to differentiate the spatial coordinates and ′ of the Lorentz transformation with respect to and ′, from which the transformation of three-velocity (also called velocity-addition formula) between and ′ follows, and eventually by another differentiation with respect to and ′ the transformation of three-acceleration ...
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame.
Born rigidity is satisfied if the orthogonal spacetime distance between infinitesimally separated curves or worldlines is constant, [7] or equivalently, if the length of the rigid body in momentary co-moving inertial frames measured by standard measuring rods (i.e. the proper length) is constant and is therefore subjected to Lorentz contraction in relatively moving frames. [8]
Proper acceleration, ... The special theory of relativity describes the behavior of objects traveling relative to other objects at speeds approaching that of light in ...
So, calculations made in both frames show that the thread will break; in S′ due to the non-simultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread. In the following, the rest length [3] or proper length [4] of an object
This is illustrated in the figure at right, which shows radar time/position isocontours for events in flat spacetime as experienced by a traveler (red trajectory) taking a constant proper-acceleration roundtrip. One caveat of this approach is that the time and place of remote events are not fully defined until light from such an event is able ...