The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet’s interaction with its own ripples, which form what’s known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles. From Quanta via Wired. article 
In theoretical physics, the pilot wave theory was the first known example of a hidden variable theory, presented by Louis de Broglie in 1927. wikipedia
YOUTUBE W9yWv5dqSKk Morgan Freeman's "Through the Wormhole" on the Science Channel. Season II Episode VI. How Does The Universe Work?
YOUTUBE nmC0ygr08tE Published on Dec 19, 2012 By Daniel M. Harris & John W. M. Bush Department of Mathematics, MIT
See more hydrodynamic quantum analogs collected by Bush and others. webpage
See Splitting the Photon for original experiments at the familiar quantum scale.