Quantum Mechanics, Discretization and Local Determinism

Ingemar Nordin

W. Michael Dickson

Léopold Halpern

Quantum mechanics is contemplated in closed Riemannian spaces where the momentum spectrum is discrete. The theory formulated in this case is equivalent to an exclusively discrete scheme; continuity occurs only statistically. The operators corresponding to the dynamical variables are determined and the uncertainity relation is examined. Agreement is obtained in the local limit with quantum mechanics as formulated in flat space within the experimental accuracy.

Robert W. Carroll

Paul P. Budnik

Franson showed that Aspect's experiment to test Bell's inequality did not rule out local realistic theories with delayed determinism. A class of local, deterministic discrete mathematical models with delayed determinism is described that may be consistent with existing experiments. These are not hidden variables theories in the sense that they are not theories of particles plus hidden variables. They are theories of `hidden' distributed information stored holographic like throughout a space time region. This information cannot be uniquely associated with individual particles although it determines the results observed in particle interactions. The classical parameters of an interaction are determined as {\it focal points} of continuous nonlinear changes in the wave function and not as discrete events. In addition to not violating Bell's inequality this class of theories can in principle be distinguished from standard quantum mechanics by other experiments. These differences and the experimental constraints on a test of Bell's inequality to discriminate between the existing theory and this class of models are discussed.

Roland Riek

The Einstein-Podolski-Rosen paradox highlights several strange properties of quantum mechanics including the super position of states, the non locality and its limitation to determine an experiment only statistically. Here, this well known paradox is revisited theoretically for a pair of spin systems in a singlet state under the assumption that in classical physics time evolves in discrete time steps t while in quantum mechanics the individual spin system(s) evolve(s) between the eigenstates harmonically with a period of 4 t . It is further assumed that time is a single variable, that the quantum mechanics time evolution and the classical physics discrete time evolution are coherent to each other, and that the precision of the start of the experiment and of the measurement time point are much less than t . Under these conditions, it is demonstrated for a spin system that the fast oscillation between the eigen states spin up | ↑> and spin down | ↓> reproduce the expected outcome of a single measurement as well as ensemble measurements without the need of postulating a simultaneous superposition of the spin system in its quantum state. When this concept is applied to a spin system pair in a singlet state it is shown that no entanglement between the two spins is necessary to describe the system resolving the Einstein-Podolski-Rosen paradox.