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Bell's Spaceship Paradox





THOUGHT EXPERIMENT


On a space platform two identical spaceships are positioned one behind the other, pointing in the same direction and separated by a distance L. They are linked by a flimsy rope also of length L, which is too weak to sustain any significant
tension. They are launched simultaneously and have identical propulsion schemes.

As the spaceships accelerate, ''will the rope break?''


SPECIAL RELATIVITY'S PREDICTION


Bell's view was in accord with that published by Dewan & Beran that although in Newtonian terms the rope would remain intact, if sufficiently high velocities were attained, then the theory of special relativity would predict that the rope would break.

The reasoning often given is that from the launch-platform the rope will appear Lorentz Contracted , but the distance between the spaceships will not exhibit similar contraction. This latter assertion is the weak point of the argument that has generated considerable counter-opinion, not least among Bell's CERN colleagues, who contradicted his conclusion.

The situation for an inertial observer already moving in the same direction, for whom the rope would "un-contract" and increase its apparent length to more than the spaceship distance, relies on a lack of simultaneity that makes the foremost spaceship appear to launch first.



CONTROVERSIES


This problem has raised controversy virtually every time it has emerged in print since its inception. In 1962 the American Journal of Physics printed a letter by P.J.Nawrocki, which opposed Dewan & Beran's previous argument that the distance between the spaceships would not "know how much" to Lorentz contract.

The first detailed analysis of the problem was published by J.E.Romain in 1963 using Minkowski diagrams to define the acceleration phase. More recently, a presentation in a Japanese physics journal that abridged the acceleration to a "before" and "after" argument aroused considerable counter opinion. But also in 2004, the physicist J.H.Field wrote a paper partly echoing Nawrocki's point that special relativity makes no distinction between extended bodies and the spaces between such bodies, so that the distance between the spaceships as well as the rope and the spaceships themselves should appear to Lorentz contract.

The most recent publication to tackle the problem is by two Japanese theoretical physicists (Hsu & Suzuki) who use generalised Moller and Wu transformations to resolve the problem in favour of the Nawrocki and Field view that the spaceship distance does contract and the rope does not therefore break.


LITERATURE


  • E. Dewan & M. Beran, ''Note on stress effects due to relativistic contraction'', Am. J. Phys. 27, 517/8 (1959)

  • P. J: Nawrocki, Am. J. Phys. 30, 771 (1962)

  • E.Dewan, (reply to P.J.Nawrocki), Am. J. Phys. 31, 383 (1963)

  • J.E. Romain, ''A Geometric approach to Relativistic paradoxes'', Am. J. Phys. 31, 576/9 (1963)

  • J. S. Bell, ''How to teach special relativity'', Progress in Scientific Culture, Vol 1, No 2, 1976

  • J. S. Bell, ''Speakable and unspeakable in quantum mechanics'', Cambridge University Press, 1987, ISBN 0521523389 (includes the above reference)

  • J. H. Field, ''On the Real and Apparent Positions of Moving Objects in Special Relativity: The Rockets-and-String and Pole-and-Barn Paradoxes Revisited and a New Paradox'', preprint online as physics/0403094



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