A string between two accelerating spaceships vs two falling spaceships

Question

According to Bell's spaceship paradox, a string between two uniformly accelerating spaceships will break. According to the equivalence principle, a string between two spaceships freely falling in a uniform gravitational field won't break.
The difference has already been explained with math. Can you also explain the mere fact of the string breaking or not in a concise, verbal way without resorting to very specialized terms, unless necessary?

stuffu · Accepted Answer

I assume an uniform gravity field. (Which only means that tidal forces are absent, do not assume some uniformity that a "uniform gravity field" does not have)
Gravitational time dilation causes the lower spaceship to fall at slower speed than the upper spaceship. That causes a length contraction of the distance between the spaceships. The distance gets contracted the same amount that a rope connecting the spaceships gets contracted.

Andrew Steane · Answer

The accelerating spaceships in the case where the string breaks have been programmed so as to have the same acceleration relative to the starting frame at any given time in that starting frame. The freely falling spaceships have different accelerations relative to their starting frame at any given time in that starting frame, so the two situations are not equivalent.
If the accelerating spaceships were instead programmed so as to maintain a constant proper distance between them (in their own instantaneous rest frame) then the string would not break. In this case the proper acceleration of the leading rocket is smaller than the proper acceleration of the trailing rocket. This case would be the right one to compare with the freely falling rockets in a certain type of gravitational field.
In the gravitational field of a spherical body such as a neutron star, a long string extended in the vertical direction between freely falling masses will be in tension and will eventually break when this tension exceeds the tensile strength of the string.

A string between two accelerating spaceships vs two falling spaceships

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