Niels Bohr has often pointed out that already the simplest quantum rule, ΔE = hν, is irrational insofar as ΔE stands for a timeless energy jump, whereas a frequency ν is defined only over a long time span. However, when this irrational relation is accepted as a mainstay of the quantum theory, one cannot reject a corresponding irrationality for momentum jumps Δp connected with periodicities in space, the less so as it yields a unitary mechanical explanation of all wavelike‐looking phenomena of matter, in particular those of the diffraction of electrons, without resorting to any wave interference in space. (This has nothing to do with the complex–imaginary wave function ψ, which has a purely statistical significance.) We therefore propose to regard matter particles as real physical entities as always, in contrast to the matter waves with λ = h/p as a suggestive yet expendable fiction, permitting a return from dualism to unity, a simplification of the customary interpretation of standard quantum effects, also suggesting a long overdue reform in the teaching of the elements of quantum mechanics.Editor’s note: This is the fourth and last in a series of articles begun ten years ago in this Journal. Earlier parts in the series may be found in American Journal of Physics 33, 123 (1965); 34, 1160 (1966); and 37, 541 (1969).