Posted: Jan 17, 2022 11:56 am
by hackenslash
newolder wrote:Ralph Berger has a treatment:

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.


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.


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?

That's awesome, and gels completely.

So yes, it is the spaghettification principle, but massively (geddit) reduced. In the planetary scenario, the difference in elevation means that they're experiencing fundamentally different degrees of acceleration due to gravity, and that's why acceleration corrections are required to maintain equilibrium of acceleration between front and back so that their acceleration is equivalent in all the accelerated frames along the gradient. Free of a gravity well, these corrections are unnecessary and the string won't break.