The Doubochinski Pendulum – A Paradigm for Quantization Through Nonlinear Interactions

The Doubochinski pendulum is a simply-constructed nonlinear oscillator having a discrete series of stable amplitudes, which can be seen to mimic the quantum behavior of microphysical objects in several respects. Apart from this system’s intrinsic interest, the specific form of phase-modulated interaction (so-called argumental interaction) which gives rise to amplitude “quantization” in the Doubochinski pendulum, might prove relevant to developing a more realistic and more intelligible form of quantum physics in the future. In this paper I describe the experimentally-observed behavior of the Doubochinski pendulum in some detail, and sketch some elements of the theory of the pendulum, focusing on insights into the mechanism of amplitude quantization and related phenomena in this system. I shall also briefly touch on a related model system, consisting of a low-frequency mechanical oscillator interacting with a high-frequency wave, which likewise displays a discrete set of stable amplitudes. Finally, I shall discuss some results of A. I. Shumaev and Z. A. Maizelis concerning the statistical distribution of quantized amplitudes of the Doubochinski pendulum as a function of initial conditions, which bears some analogy to probability densities in quantum mechanics.