Abstract :
We can prove the theorems that in the mathematical formulation of standard quantum mechanics by von Neumann there exist simultaneously an explicit statement, p, and the negation of that statement, not-p. That formulation thus contains a deep intrinsic contradiction (apart from the usual interpretational “paradoxes”), and so is logically inconsistent, an outcome which has the well-known immediate consequence that one can then ultimately prove any theorem, assert any statement whatsoever. Even so, an important subtle point exists: in logically inconsistent theories a substantial body of derivations and resultant theorems can be reliable and correct. A logically inconsistent theory can therefore exhibit true empirical adequacy in a well-defined domain, a finding apparently relevant to standard quantum mechanics. We next consider what the physicist appears to intend when he uses the terms “consistent” and “complete”, and the like, for a physical theory, and suggest how logical inconsistency can in fact strictly enforce what the physicist seems to assume constitutes inconsistency and/or incompleteness in a physical theory. Further, we note that we can remove, in several ways, the contradiction in standard quantum mechanics. The resultant variants of standard quantum mechanics can then be correlated with numerous proposals (which we sketch) for alternatives to the standard theory advanced, for diverse reasons, by a minority community. Effectively, the communityʹs proposals may be regarded as gedankenexperiments attesting to the need for changes in a provisional standard theory, in view of that theoryʹs logical inconsistency.
