You’ll probably receive a lot of information and advice.
Surely, a neighbouring wall plate will have its earth connected to every other wall plate in the room by parallel wiring between the plates.
I’ll start with this concept first. If you currently have no hum or noise, then you’re lucky.
Your audio system needs to have one common ground that is wired directly to your service panel. These wall receptacles connected together will not have a direct path to ground at the service panel. By plugging your system into this rat’s nest of wiring you are sharing your audio with all the appliances and lighting in your house. This adds noise to the AC line which is audible through your speakers. If these wires have different ground impedances when they meet at the circuit panel, a ground-loop is created. You’ll hear a 60Hz hum thru your speakers if this happens.