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Bell considered two rocket ships connected by a string, with both having the same acceleration in the inertial "lab frame", with one ship trailing the other and both moving along one line. The ships start out at rest in the lab. Their accelerations in the lab frame are required always to be equal, but these accelerations can vary with time. Because the ships always maintain equal accelerations in the lab frame, their speeds will be equal at all times in the lab, and so they'll remain a constant distance apart in the lab. But after a time they will acquire a high speed, at which point we ask what has become of the idea of the distance between them being Lorentz contracted. The actual paradox posed by Dewan & Beran and by Bell was that the string should eventually snap. But why should it snap, if the ships are maintaining a constant separation?
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Abstract

The Bell Spaceship Paradox has promoted confusion and numerous resolutions since its first statement in 1959, including resolutions based on relativistic stress due to Lorentz contractions. The paradox is that two ships, starting from the same reference frame and subject to the same acceleration, would snap a string that connected them, even as their separation distance would not change as measured from the original reference frame. This paper uses a Simple Relativity approach to resolve the paradox and explain both why the string snaps, and how to adjust accelerations to avoid snapping the string. In doing so, an interesting parallel understanding of the Lorentz contraction is generated. The solution is applied to rotation to address the Ehrenfest paradox and orbital precession as well.

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This measured change in tilt is proof of a measured change in orbit length. If no acceleration is involved, a second GP-B satellite can be tethered by string with the first and the string will not break no matter how long in orbit. If, however, through some machination, we accelerated the two GP-B satellites up to a much higher velocity while at the same radius, the overshoot in orbits will be proportionally larger, and the distance between satellites will grow, and the string will snap. Just like the edge of an Ehrenfest disk, the points separate, with motive power being whatever caused the satellite velocities to increase.

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Evolving wrote:That is the core of the Herringfest Paradox.

Evolving wrote:The herring wouldn't snap either.

newolder wrote:Ralph Berger has a treatment:

Abstract

The Bell Spaceship Paradox has promoted confusion and numerous resolutions since its first statement in 1959, including resolutions based on relativistic stress due to Lorentz contractions. The paradox is that two ships, starting from the same reference frame and subject to the same acceleration, would snap a string that connected them, even as their separation distance would not change as measured from the original reference frame. This paper uses a Simple Relativity approach to resolve the paradox and explain both why the string snaps, and how to adjust accelerations to avoid snapping the string. In doing so, an interesting parallel understanding of the Lorentz contraction is generated. The solution is applied to rotation to address the Ehrenfest paradox and orbital precession as well.

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This measured change in tilt is proof of a measured change in orbit length. If no acceleration is involved, a second GP-B satellite can be tethered by string with the first and the string will not break no matter how long in orbit. If, however, through some machination, we accelerated the two GP-B satellites up to a much higher velocity while at the same radius, the overshoot in orbits will be proportionally larger, and the distance between satellites will grow, and the string will snap. Just like the edge of an Ehrenfest disk, the points separate, with motive power being whatever caused the satellite velocities to increase.

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Is this stuff the origin of the spaghettification experienced when falling towards a gravitational black hole or have I got my phenomena mixed up again?