Let's say there are two inertial reference frames F0 and F1 with relative velocity V along the x-axis. At rest in frame F0 there is a spring of length L that is completely compressed. This spring is oriented along the x-axis. There are no gaps between any of the coils of this spring when it is in this compressed state. In F1 the length is L' and again there are no gaps between any of the coils as observed in F1. At time t0, observers in F1, simultaneously accelerate all points of the spring in the y direction.
From F0 observers point of view, per Einstein, one end of the spring started accelerating before the other end. Therefore, the length of the spring increased from its rest length of L in F0 to something longer. Since the spring stretched, gaps appeared between each coil of the spring. From the point of view of observers in F1, the length of the spring remained L', so why do these observers now say there are gaps between the coils?
Thanks,
David Seppala
Bastrop TX

On Tuesday, April 27, 2021 at 2:56:09 PM UTC-7, sep...@yahoo.com wrote:
> Since the spring stretched, gaps appeared between each coil of the spring..

You are mixing assumptions, per the standard sophistry, by saying that the coil windings are accelerated simultaneously in terms of F1, but tacitly not saying that each particle of each coil is accelerated simultaneously. If each particle of each coil is accelerated simultaneously, then obviously two touching particles will remain touching (both frames), and the distances between particles in each coil will increase. On the other hand, if the particles of the coil are not accelerated simultaneously in terms of F1, but the coils are, there will be gaps (both frames) between the coils.

On 4/27/21 4:56 PM, sepp623@yahoo.com wrote:
> [...]

The spring is not "stretched". Rather, a snapshot of it taken
simultaneously in F1 shows it to lie along a diagonal in the x-y plane.
As Al Coe pointed out, molecules that are touching in F0 remain touching
in F1 -- this is NOT any sort of "physical" effect, it is merely a
different geometrical projection of the spring onto the coordinates of F1.

As has been said many times before: your repeated confusions are all
related to your misunderstanding of the geometry of SR.

Tom Roberts

On Tuesday, April 27, 2021 at 8:25:53 PM UTC-7, tjrob137 wrote:
> The spring is not "stretched".

There is deformation (stretching), similar to the stretching of the string between rockets in Bell's spaceships. In fact, this scenario is just a sideways variant of that. The answer to the question about gaps is that it depends on whether the "stretching" is uniformly spread, even to stretching the material of the individual wounds of the coil, or if it is just pulling the windings apart without distending them. This depends on the pattern of imposed forces, which the sophist tries to gloss over.