The language of Nature

Every practitioner of physics knows that the laws of physics, in their mathematical form, do not enable to make predictions about the real world. Quite often, solving the equations of mathematical physics provides two solutions, of which one is rejected on the basis of non-mathematical arguments.

A first example is that of the retarded and advanced potentials of classical electromagnetism. Only the former are considered, the latter being in contradiction with causality. A second example is the common situation in which one finds two possible functions: one that diverges at infinity and another one that converges to zero. Only the latter is kept, the former being termed “unphysical”.

What is interesting in the two examples is that mathematics predicts one thing as well as the opposite: causality and anti-causality, divergence and convergence. We choose the solution on the basis of non-mathematical arguments.

Mathematics may be the language of Nature, but we take some liberty in its interpretation.