Does Quantum Mechanics Have Nonlinear Terms?

One hears about testing quantum electrodynamics or relativity theory, but the theoretical basis of quantum mechanics is rarely questioned. Nevertheless, Steven Weinberg (University of Texas) has recently called for high‐precision tests of quantum mechanics that are independent of any particular quantum mechanical theory. To pave the way for an examination of quantum mechanics, he has suggested one possible way of generalizing quantum mechanics to make it nonlinear. As Eugene Wigner pointed out in a 1939 paper, the linearity of quantum mechanics is an important assumption and one that may not necessarily always prove true. Weinberg stressed to us that he does not really feel that quantum mechanics is in any immediate danger, but he does believe that we can learn by questioning it: If we find that quantum mechanics cannot be generalized any further, we may come to understand better why it works so well. If we find that the theory can be generalized in a plausible way, then we must ask why ordinary quantum mechanics is so nearly valid—and we may discover some hidden physics in the process.

This article is only available in PDF format