Abstract
The boundary conditions for the minimum elementary signal defined: f0 t0 = ΔfΔt= 1/2 (where f0 is signal midfrequency, t0 is signal midperiod. Δf is signal bandwidth, and Δt is signal duration) also describe the topologically defined condition known as either (i) a critical point, (ii) a singularity in mapping one manifold into another, (iii) a local potential fluctuation, or (iv) a flow on a cusp catastrophe. An elementary signal, or any quantum, is a limit cycle or oscillation hysteresis defined within an area of instability of a precisely defined mapping plane. The collection of unstable maps of the potential function, from which the elementary signal is derived, defines those instances in which quantum theory is applicable. Thus, a wave event cannot become infinitely small and still be meaningful, i.e., informationally relevant. This result provides an explanation for parametric excitation, as well as a tool for the study of cochlear fluid mechanics.
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