Well, you have the answer. Someone asked our company what we couldn't do one time. I said "we haven't figured out how to break the laws of physicis." Herman has already pointed out--that's what you're up against. We're about to publish a paper on sound isolation (hopefully I'll finish it this weekend). The basic problem in an apartment is that there are many structures in common. You pointed out one wall, but what about the ceiling? The concrete slab? The may all have the same structural components. You play loudly and the sound travels through this structure to the next room. Is it impossible to isolate these issues? Technically no--it can be done. Practically however is a different question. It would mean doing things pretty crazy like ripping out all carpet, putting up new walls, ceiling--well you can see it's just not at all possible in the real world sense.
Now I am going to digress to something I saw at CES this year. It was a headphone system that used Stax headphones and an infrared head tracking device--bear with me here. Basically the headphones were calibrated with a full 5.1 system. You put microphones in your ears and listened and did things like turned you head in certain directions. All the while the pink noise coming from the system was being recorded. Then you take the mics out and put on the headphones. You could move your head and got the same kind of enveloping feel as you did from the 5.1 system. For comparison you just took the headphone off, they would turn off and the real 5.1 system would come on. With matched volumes this was pretty incredible--I was amazed out how remarkable the processing was and they have only just begun--it will likely improve more. Anyway, if this comes to market it could solve some issues like this.
Now I am going to digress to something I saw at CES this year. It was a headphone system that used Stax headphones and an infrared head tracking device--bear with me here. Basically the headphones were calibrated with a full 5.1 system. You put microphones in your ears and listened and did things like turned you head in certain directions. All the while the pink noise coming from the system was being recorded. Then you take the mics out and put on the headphones. You could move your head and got the same kind of enveloping feel as you did from the 5.1 system. For comparison you just took the headphone off, they would turn off and the real 5.1 system would come on. With matched volumes this was pretty incredible--I was amazed out how remarkable the processing was and they have only just begun--it will likely improve more. Anyway, if this comes to market it could solve some issues like this.