Length contraction

Length contraction is time dilation seen from the other side. Take the cosmic-ray muon again: in our frame it survives the trip because its clock is stretched. In the muon's own frame its clock is perfectly normal and its lifetime is the usual short one — yet it still reaches the ground. The only way both accounts can describe the same events is if, in the muon's frame, the atmosphere it has to cross is thinner. It is.

The contraction happens only along the direction of motion. A cube moving along one of its edges is measured in the laboratory as a rectangular box, shortened in the direction of travel and completely unchanged across it. A sphere is measured as a flattened ellipsoid, not as a smaller sphere. This directionality is the practical test of whether someone has understood the effect or is picturing an object being crushed.

And nothing is being crushed. No force acts on the rod, its internal structure is untouched, and in its own rest frame it has exactly the length it always had — its proper length. Contraction is a statement about what a measurement in a relatively moving frame yields, not about damage done to the object. Ask "shorter according to whom?" and the apparent paradox disappears: to the crew riding along, it is the laboratory that is short.