Aspects of Interference and Measurement in Quantum Theory.

This work deals with some new aspects of measurement and interference in quantum theory as they grew from the formalism itself. In other words, by "pushing the formalism" to answer some well-defined questions, we found interesting results. One of these questions was motivated by the work of Von Neumann (and the elaboration by Bohm) on the interpretation of measurement in quantum theory. The solution that they proposed was, except for some special cases, not realizable experimentally, not even in principle. This is perhaps not a trivial problem and it might have been one of the reasons that people working on this question searched for alternative solutions. We can say, in one sentence, that the problem (as we see it) boils down to the following question: Can non-realizable Hamiltonians be realized? Aharonov and Lerner {Phys. Rev. D, 20, 1877 (1979) } gave an answer to this specific question which we use in Chapter Two in order to give an experimental meaning to the Hamiltonian that describes the measurement process. Chapter Three is an outgrowth of another question that was posed to the formalism {see related references in Aharonov and Vardi, Phys. Rev. D, 21, 2235 (1980) }. It turns out that, when applying the rules of quantum mechanics to continuous observations (rapidly repeated measurements) which intend to check the exact moment in which a system makes a transition from some initial state to some other final state, it is found that because of these observations the transition never occurs. Many publications address themselves to the experimental implications of this formal result (which seems paradoxical) {see related references in Aharonov and Vardi, Phys. Rev. D, 21 2235 (1980)}, where we instead pushed this formal result further and found that not only can one "freeze" the system in its initial state but one can even "force" it to evolve along a trajectory of states (VBAR) (psi) (t) > (t is the parameter) by successive measurements that are made dense in some given period of time. We then note that a phase is systematically accumulated when the. system is "forced" along the trajectory (VBAR) (psi) (t) > . This phase turns out to. be, essentially, the classical action (divided by (H/2PI)) when the choice for the trajectory is a set of coherent-states parametrized by the values x(t) and. p(t) that belong to a "smooth" space-time path. For more general. trajectories in Hilbert space, we find that the acccumulated phase is the(, ). quantum action (INT)< (psi) (VBAR) i(H/2PI) (psi) - H (psi) > dt (divided by (H/2PI)). This procedure, then, can be taken as the operational definition of the building blocks of what is known to be the Feynman path integral formulation of quantum mechanics. Using the principle of superposition we then show, in a thought experiment, that the phases associated with those trajectories can be made to interfere which means that the action, as a global quantity, can have a measurable meaning. Finally, this formalism suggests a new type of E.P.R. correlation; correlation between the measuring device and the trajectories that it measures. Chapter Four deals with the dual aspects of interface (or superposition) in quantum theory. We elaborate the double Stern-Gerlach experiment, combining it with the Aharonov-Bohm effect (while always using a single particle). We show that the nonlocal aspects of quantum mechanics manifest themselves in a deterministic way or in a nondeterministic way, depending on the setup one chooses. The last chapter is devoted to some general remarks concerning the role of measurement and interference in quantum theory, stressing the importance of experimental arrangements that do not have a classical counterpart in the search for the "natural" language to describe quantum phenomena.