Bohmian Mechanics, also known as Pilot Wave Theory, elegantly describes the interaction of quantum particles. You can imagine a particle bouncing on a sheet with waves emanating around it. Just describing it like that brings to mind a common description of gravity, but that is probably just an amazing coincidence.
One thing Bohmian Mechanics does not explain is what Einstein referred to as "spooky action at a distance," or non-locality.
Non-locality is the notion that two entangled particles can interact with each other at vast distances.
Entanglement can be (overly) simplified with this thought experiment:
Alice and Bob decide to take two pieces of fruit, one apple and one orange. They have an assistant randomize the two pieces of fruit and place them both in identical bags so that Alice and Bob don't know which one is which. Then Alice goes to her home and Bob goes to his.
Once they arrive home, they each look into the bag to see which piece of fruit they have. Alice sees that she has the apple, so she instantly knows that Bob has the orange.
This seems pretty ordinary. Nothing spooky.
But in quantum mechanics, the fruit would be in a superposition. Both bags would literally have both pieces of fruit until inspected. When they look into the bag, the superposition collapses and only one piece of fruit exists in each bag. The collapse happens instantly for both and that's why it's "spooky."
Bohmian Mechanics does not (currently) describe entanglement and non-locality. But it does describe things like quantum tunneling and much of the double slit experiment (except not quantum erasure).
So the neat thing is, Bohmian Mechanics explains a lot of quantum weirdness. But not all. Here are three videos that go into Bohmian Mechanics:
Also see: What If: Quantum Bell
