Ladder paradox and transmission of force Ladder paradox

what if door (the door ladder exits out of) closed permanently , not open? suppose door solid ladder not penetrate when collides, must stop. then, in scenario described above, in frame of reference of garage, there moment when ladder within garage (i.e., of ladder inside front door), before collides door , stops. however, frame of reference of ladder, ladder big fit in garage, time collides door , stops, of ladder still has not reached front door. seems paradox. question is, of ladder cross front door or not?

the difficulty arises assumption ladder rigid (i.e., maintains same shape). ladders seem rigid in everyday life. being rigid requires can transfer force @ infinite speed (i.e., when push 1 end other end must react immediately, otherwise ladder deform). contradicts special relativity, states information can travel no faster speed of light (which fast notice in real life, significant in ladder scenario). objects cannot rigid under special relativity.

in case, time front of ladder collides door, of ladder not know yet, keeps moving forwards (and ladder compresses ). in both frame of garage , inertial frame of ladder, end keeps moving @ time of collision, until @ least point of ladder comes light cone of collision (i.e., point force moving backwards @ speed of light point of collision reach it). @ point ladder shorter original contracted length, end inside garage. calculations in both frames of reference show case.

what happens after force reaches of ladder (the green zone in diagram) not specified. depending on physics, ladder break; or, if sufficiently elastic, bend , re-expand original length. @ sufficiently high speeds, realistic material violently explode plasma.