Quantum Probability without a Phase and a Topological Resolution of the Two-slit Experiment

摘要

As is well known, classical probability and statistical mechanics cannot account for the phenomenon of interference as exemplified by the famous two-slit experiment. Quantum probability on the other hand is unlike anything known in probability theory for being attached to a phase. Traditionally this is one of the least understood features of quantum mechanics. The present work by contrast asserts that there are two ways to resolve the paradox of the two-slit experiment. The first is the well known one leading to complex wave functions and probability with a phase. The second possibility which seems to have been overlooked for a considerable time, is an irrational probability related to the most irrational number φ = (5{sup}(1/2) - 1)/2. In other words, one can have quantum-like probability without a phase. This leads directly to a realistic and well defined resolution of the two-slit experiment.