This is caused by inducted noise. In other words, electrical signals that are picked up from the environment by the guitar, amp tubes and other electronics (wires, pots, etc) on the guitar. Your rig is essentially a big electro magnetic antennae.
Single coil pickups are known for picking up 60Hz (and other) noise from the environment.
The humbucker was invented specifically to address the 60Hz hum issue, but they are not impervious to picking up environmental noise. This is especially true as you add more gain.
There are several things you can do to minimize inducted noise:
First determine if you guitar control cavity is shielded. If it is shielded check to ensure that all sections of the Shield have continuity to ground. You can do this yourself with a multi-meter. Shielding the control cavity can help a lot. Shielding of pickup cavities (when separate from the control cavity) provide a much smaller benefit.
Next get a noise suppressor. Not a noise gate, a suppressor. Suppressors have both a noise filter and a noise gate.
You want a unit that has four 1/4 inch jacks. These allow you to run the guitar input through the unit then to the amp then to also run your effect loop through the pedal. This allows the filter to remove noise that was added to the signal between the guitar input and the effect loop. Two units that I have used are the Boss NS-2 and the ISP Decimator G String.
The ISP is top of the list in my opinion. Very transparent and has really good filtering and the best gate I have ever played on.