An almost rigid rectangle with length D can rotate around its center. Assume that rectangle is horizontal and does not rotate before collision. According to observer S two balls collide at the same time at two ends points of rectangle R & L, in t=0 and before collision two balls have same speed u in y axis therefore there is no rotation for rectangle at all after clash. For these collisions we can assign two events in spacetime, that is E1=(−ct,r)=(0,−D/2,0,0) and E2=(0,+D/2,0,0). Note that S is at rest relative to rectangle.
Now let's consider another observer S′ who moves at speed −v relative to rectangle in x axis. By using Lorentz transformation we can see that E′1=(−γvD/2c,γ(−D/2+vt),0,0) and E′2=(γvD/2c,γ(+D/2+vt),0,0). Because two events E′1 and E′2 are not simultaneous in this frame (Δt′=γvD/c2) it's logical to deduce that the rectangle will rotate after first collision. While it's not possible for obvious reasons (one can put a bomb under rectangle for example). Where am i mistaken? Does system wait for a signal that is coming from two end points to the center?
PS: I am fully aware that 100% rigid bodies are not possible in SR, by almost rigid i meant that we have an elastic collision and rectangle tends to rotates than bends around it's center.
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