"The Equation Breaks Down"
I remember hearing this statement in a physics documentary some time ago. I presume it to mean that an equation which gives valid or verifiable predictions within a certain range, once that range is exceeded, produces incorrect statements or values (for example Newtonian Physics cannot describe activity on a quantum level, therefore its mathematical predictions would "break down"). That an equation should "break down" on one level but remain true on another would seem to mean that the equation is not in fact true or absolute. I would like to know any other current mathematical examples in Physics where equations appear to collapse or produce seemingly nonsensical predictions. Surely the root of the collapse is in the model which cannot make sense of the equation's data, rather than the equation itself. Is this best solved empirically?
Thanks in advance.