Quantum Mechanics : Principles, New Perspectives, Extensions and Interpretation, Revised Edition

Interpretations of Quantum Mechanics galore. Since the pioneering works of Heisenberg, Bohr, Dirac, Schrodinger and others, when in 1927 the so called Copenhagen Interpretation was presented, there appeared interpretations using concepts like hidden variables, many worlds, coherent histories, and many others, some of them minor deviants of the Copenhagen Interpretation, others defying it. In almost all cases these interpretations are not fully coherent and consistent with each other.

One is then led to the question of which of them is to be accepted. This can be a tricky question; indeed, given the formal apparatus of a theory (its syntax), there may be a number of interpretations (its semantics) consistent with it, there being what can be called a hermeneutic indeterminacy. Of course, the syntactical apparatus shortens the semantic possibilities and one should expect only some interpretations to be acceptable. How many of such interpretations will find grounds in the underlying syntax is always unknown in advance. Quantum Mechanics, for instance, seems to accept a lot.

The issue to be learned here is that, sometimes, disputes occurring in the semantic level can be solved or dissolved at the syntactical level with a coercitive power. That is, the syntactical developments are so unambiguous that physicists, given their previous commitments with other criteria (as simplicity) for selecting physical theories, are compelled to accept the implications clearly posed by the syntactical framework.

However, the reader should not expect abstruse mathematical formalism. Indeed, we purposely chose to keep formal developments as simple as possible, since we believe that less involved formal developments restrict even more the set of possible interpretations consistent with them. Any graduate student is then completely prepared, from the formal point of view, to understand all the content of this book. This constraint also favoured the option of using an axiomatic approach, since in an axiomatized theory all its interpretation must be included in the axioms and must be inherited by results derived from them. As we will soon show, quantum mechanics can be completely described by only three postulates. Moreover, there will not be any semantic axiom, that is, axioms will be restricted to the syntactical structure, and its symbols, when interpreted in the usual way agreed upon by any physicist, will give rise to the semantics of quantum mechanics. In any way, whenever needed, philosophical thinking will not be stated without the underlying syntactical grounds to avoid empty physical discourse.