Phrak said:
It doen't matter what I care about; the problem should stand on it's own, right?
As a reminder, I should say I didn't pose the problem as well as could be, and the improved problem statement is in post #7. Maybe Frederik could clean it up, so the misleading stuff, like "a gentle push" is gone.
This is my precise interpretion of the problem. Phrak, is my interpretation correct?
There is a flat two-dimensional surface S and a one-dimensional rod R.
Initially R is straight and parallel to S and R moves inertially relative to S in the direction of its own length.
Let I be the initial inertial rest frame of the rod. The rest-length of the rod, measured in I, is
L.
There is a linear slot cut in the surface S, parallel to R, wide enough for R to fit through, but its rest-length (measured in the S-frame) is less than
L. However its rest-length is greater than L/\gamma, where \gamma is the relative Lorentz factor between S and I. Thus, due to length contraction of the rod relative to S, the rod is short enough, in the S-frame, to parallel-slide through the hole, but in the I-frame it is not.
The rod now moves towards the hole in such a way that it it remains straight and parallel to the hole
according to the S-frame, and then passes through the hole.
Aside: The actual practicalities of how this is achieved are not relevant to the problem. You'd need to pre-arrange for a continuum of forces to be applied along the whole length of the rod, all pre-programmed to exert a specific force at a specific time to achieve the desired effect. It would be difficult to engineer in practice, but, as a thought experiment, no laws of physics need be broken to achieve this.
The question is then how does this appear in the I-frame, in view of the fact that the rod is longer than the hole is this frame?
The answer which has already been thrashed out in this thread is that the rod does not remain straight in this frame: it curves and passes through the hole at an angle.
(Note that rod curvature --relative to I -- is inevitable during acceleration, but afterwards it will straighten and so may well be straight by the time the rod meets the hole. But it will slide through at an angle, head first, so it doesn't matter that it's too long to fit. See diagrams below.)