For anyone that has ever mulled this over, I want to explain quantum “wave/particle duality.”
Imagine that you have a pool of water with a ball perched on the deck. The ball falls into the pool, causing waves. Ignoring for the moment the effects of the air and the loss of wave motion into heating of the water, the only way to stop the water waves is for the waves to combine to push the ball back up onto the deck.
In the quantum system, the “particle” is the ball. The “wave” is the water motion. Due to conservation of energy, you cannot bring the entire system back to rest unless both the particle (ball) and wave (water) are brought back to rest.
This understanding eludes quantum theorists because they subscribe to Einstein’s axiom that space is empty. This is necessary to his theory of gravity. In fact, however, we now know that space is filled with “dark energy.” Returning to our metaphor, dark energy is the “water.” An electron (for example) is the “particle.”
The mathematics are well known to the quantum theorists that study superconductivity. In that case, the particles are again electrons, and the waves are the vibrations in the metallic crystals (vibrations in the sense of a plucked guitar string).