My understanding of how Bybees work is slightly different in terms of the underlying physics. I learned the following from Jena Labs, who purposely designs her cables to not need a bybee filter. Jack has told her that her design is the first cable he's heard that received no additional benefit from the bybee filters. She certainly knows a thing or two to get that kind of praise.
Jack Bybee calls the filters a "quantum purifier" because it removes a form of noise that is quantized in a strict physical sense. An analog electrical signal is anything BUT quantized, but there is a special circumstance in which "phonons" are created by the transmission of an electrical signal in a conductor. This phonon moves at the speed of sound, and is thus instantly out of phase with the electrical signal. The phonon is then re-converted to an electrical signal at an impedance junction, at which point it is pure noise. Other names for impedance junctions are: voice coils, transformers, inductors, etc...
The phonons are created whenever an electron encouters a so-called "Josephson Junction", which can be caused by a number of things. A non-copper atom in the crystal lattice forces electrons to "bend" around, creating phononic energy. Likewise any break in the crystal structure of the copper atoms, either from physical cracks or many multiple crystal boundaries has the same effect.
Cryogenics and Bybee filters are very similar in the underlying physics. Cryo treatment works because it "crams" the copper crystals together, smoothing out any jaggedness. When the copper warms up again and expands, the copper crystal boundaries retain the smoothness. The colder the cryo gets, the better the effect and the smoother the crystal boundaries become. Cryogenics essentially helps to eliminate the need for bybee filters, because less phononic energy is produced.
But back on topic. I have seen people describe the Bybees to work by bringing the voltage and current back into phase. I believe this is an incorrect simplification for those who are either not familiar or unwilling to accept the quantum mechanical explanation. Instead, the bybees work by removing out-of-phase current from the signal entirely. Until bybees came along, there simply was no way to remove phononic energy except for cryogenics, which is only partially effective.
