Quantum Interference/Noninterference Interactions and their Statistics

     In classical statistical mechanics, although one has averages of a system, a single particle within the system has properties which are sharply defined at any x,t, even though these properties change stochastically, i.e. through interactions. A quantum free particle, on the other hand, has information based on the Lorentz invariant -Et+px, multiplied by i to create periodicity which indicates an inherent information, not one based on the outcome of trial runs or interactions. The probability is exp(-iEt+ipx). If E and p are considered as constant, then there are independent probabilistic fluctuations in x and t, which means there may be corresponding probabilistic interactions, both impulse ones (one dimensional reflection/refraction, n-slits) and temporal ones (Rabi frequency). In such a case, one has interference and the form exp(ipx) or exp(-iEt) governing the statistics, not a maximization of entropy linked to interaction/outcome results. Nevertheless, the quantum particle interacts with fields, it seems, which give rise to p or E changes. It seems the key idea is that one has stochastic uncertainty before an interaction occurs and hence interference.

   The alternative is that such stochastic uncertainty does not exist before a specific interaction, i.e. the inherent probability exp(-iEt) or exp(ipx) has no effect on the interaction. This is not to say that there cannot be probabilities before the interaction. In a Maxwell-Boltzmann gas, there are probabilities P(e1) and P(e2) for particles with e1 and e2, but a specific e1 and e2 have no uncertainty. The uncertainty is in the outcome of the reaction. 

  Another  example is a two state electron in an atom which absorbs and emits photons. The rules for time evolution are that the ground state is represented by exp(-iEot), but at some stochastic t value, it changes to exp(-iE1t) and vice versa. The ground state absorbs a photon and the excited emits. The two states are clearly defined by the differing interactions which govern their time dependence which is taken to be simply the changing of Eo to E1 and vice versa. This problem is then based on probabilities based on outcomes of an interaction and maximization of entropy subject to a constraint is employed. There is no initial interference.