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FIZIKA A 18 (2009) 2 , 45-52
 
HYPERBOLIC MOTION TREATMENT FOR BELL'S SPACESHIP EXPERIMENT
ADRIAN SFARTI
387 Soda Hall, University of Berkeley, Berkeley CA, U. S. A.
Received 6 November 2008; Revised manuscript received 2 June 2009
Accepted 1 July 2009 Online 17 July 2009
In Bell's "spaceship" experiment, two spaceships that are
initially at rest in some common inertial reference frame, are connected by a
taut string. At time zero in the common inertial frame, both spaceships start
accelerating, with a constant proper acceleration a as measured by an
on-board accelerometer. Question: does the string break, i.e. does the distance
between the two spaceships increase? We will present two treatments, one that
uses only Minkowski spacetime diagrams and a second approach that uses the
equations of accelerated motion in special relativity. The latter approach
allows the calculation of the distance between rockets as well as the strain
force in the string as a function of proper time. For simplicity, throughout the
paper, all objects (string, rockets) are considered as being Born-rigid, thus
neglecting the very minor effects on the length of the objects during the
accelerated motion. The subject of the Bell paradox is encountered frequently in
relativity graduate courses, but a complete, realistic solution has not been
published to date.
PACS numbers: 03.30.+p
UDC 531.18:530.12
Keywords: Bell's spaceship paradox, Minkowski diagrams, hyperbolic motion
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