Lindemann's paradox

Lindemann's paradox highlights a contradiction in understanding how materials melt. The paradox arises because, at the melting point, some atoms in a solid vibrate so intensely that they seem to be more than halfway to breaking free from their fixed positions, yet the entire solid still remains intact. In other words, the atoms are vibrating strongly enough that one might expect it to melt, but the material doesn’t do so immediately. This suggests that melting depends not only on atomic vibrations but also on collective behaviors and the ability of atoms to move freely, making the transition from solid to liquid more complex than just atomic vibrations alone.