Problems on thin rods

Let us consider in detail the problem on 1-meter-long thin rod slipping over a thin plane having a 1-meter-wide hole [106] (see [33], exercise 54). It is rather strange, that any object should contract, turn or "deflect and slip down" in exactly the same manner, as it is required for SRT to be "saved" from contradictions at any cost (however, such an approach is an indirect recognition of principal indetectability of kinematic effects of SRT). What relation to the given problem can have a real rigidity of a rod? None! Let the rod be slipping between two planes (a sandwich), so that only a part of a rod freely hanging over a hole be participating in deflection (Fig. 1.17).

Figure 1.17: Slipping inside the sandwich.

If the 1-meter rod can "deflect and slip down" into the hole shortened down to 10 cm (or 10 times), then in exactly the same manner the 1-kilometer-long rod (which should not fall-through neither in the classical physics, nor even in SRT in the plane's frame of reference) could also "deflect and slip down" into the hole. The declarative mentioning of the velocity of acoustic oscillations (for the balance establishment mechanism) is the "plausible" hiding of the truth. Let there are two identical real horizontal rods at the same height (Fig. 1.18).

Figure 1.18: Rigidity and the deflect of a rod.

The first rod slips over the desktop (at the pressed position) and begins to hang downwards with one tip at instant $t=0$. At this instant ($t=0$) the second rod begins to fall freely downwards. Obviously, for any time instant $t > 0$ the second rod will be displaced downwards (or fall) to a much greater distance as compared to the deflection of first rod's tip (and, actually, SRT tries to replace the real body by a body with zero rigidity). For analyzed problems the relativistic velocities can only decrease the rigidity effect as compared to the case of low velocities, thus ever more approaching a real body to the model of absolutely solid body. Indeed, the rod is deflected in the direction perpendicular to the relativistic motion. Therefore, this problem is similar to the problem on massive body slipping over thin ice on a river: at low velocities the body can fall through (breaching of ice due to its deflection), and at rather high velocities the body can slip over ice without falling through (the ice deflection is small). The rate of acoustic oscillations is much lower, than the speed of light. Therefore, the molecules manage to efficiently participate in rod's deflection for shorter time as compared to the static case; that is, the deflection will be smaller. Let us take the width of the lower plane to be one molecule larger, than the displacement of rod's deflection (for some particular preselected material). At the second end of a hole we shall make a very shallow taper of the plane (Fig. 1.17), so that the given rod could continue slipping over the plane (smoothly). Obviously if the rod does not slip down into the real 10-cm hole at nonrelativistic speeds, the more so the rod could not slip down into the hole allegedly shortened down to 10 cm at relativistic speeds. What will happen to the 20-cm or 1-km rod for all former characteristics of the plane? And if we, for the former geometrical characteristics of the experiment, will take various materials for a rod (from zero to maximum rigidity)? Obviously, with precise adjustment of all parameters for one case it is impossible to eliminate the contradiction for all remaining cases. For "saving" SRT it is necessary either to postulate, that the rigidity in the experiment ceases to be an objective property of materials (but ad hoc depends on the observer, geometric size and velocity), or to postulate, that the second end of a hole jumps up ad hoc in the "necessary manner". Does the goal justify similar means?

A similar problem on passage of a rod, flying along axis $X$ (now the rod is no longer pressed against the plane) through the niche of the same size (slowly running over the rod along axis $Z$) has even entered the popular literature [6]. The relativists "eliminate" the contradiction in evidences of the observers by turning the rod in space (then the rod will pass through the niche in any case, as in the classical physics). However, the turning does not eliminate the Lorentzian contraction. Let us illuminate the niche from below along axis $Z$ by the parallel beam of rays (for example, from a remote source). Let now rapidly pass the photographic film high above the niche parallel to the plate, but perpendicular to the mutual motion of a rod and a plane, that is, along axis $Y$ (Fig. 1.19).

Figure 1.19: "Turning" the rod.

Then, in spite of rod passage, the result in SRT will all the same will be different for different observers. In the classical physics we would obtain the full darkening of the photographic film at the time of rod passage through the niche (this would be marked by a completely dark section on a light strip). A similar full darkening would take place in SRT from the viewpoint of the observer situated on a rod (since the niche will contract and turn). However, from the viewpoint of the observer situated on a plate (and on the photographic film) the rod will contract and turn. Therefore, the full darkening will never take place. In such a case, who is right? There is the more dramatic situation with an angle of turning of the rod, since it depends on the relation of velocities. Let other small rod slide on our rod at some arbitrary velocity. Observers at the both rods will claim that the clearance between the rods is absent. However, according to the SRT, these rods must be turned at different angles for an observer at the plate. There appears the evident logical contradiction.