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Five-dimensional (5D) space-time symmetry greatly facilitates how a 4Dobserver perceives the propagation of a single spinless particle in a 5Dspace-time. In particular, if the 5D geometry is independent of the fifthcoordinate then the 5D physics may be interpreted as 4D quantum mechanics. Inthis work we address the case where symmetry is approximate, focusing on thecase where the 5D geometry depends weakly on the fifth coordinate. We show thatconcepts developed for the case of exact symmetry approximately hold when otherconcepts such as decaying quantum states, resonant quantum scattering andStokes drag are adopted, as well. We briefly comment on the optical model ofthe nuclear interactions and Millikan's oil drop experiment.

On spinless null propagation in five dimensional space-times with approximate space-like Killing symmetry