How would you go about proving that something exists if it's not a physically observable phenomenon? And if it's not separate from anything else, but intrinsically involved in everything?

I just had a thought. I just had another! And another! ;-) How do we go about proving that those thoughts existed? We can't. But I know I just had them, and I have no doubt about that. And our thoughts are real...because we experience them, they affect us profoundly, and they often move us to action (or lack of action, in some cases).

There are many things which are absolutely real, but which cannot be "proven" (or observed by someone else) in any outward sense. They can only be directly experienced within by the person having the experience. Such things lie at the heart of life, give it meaning, and have produced great poetry, art, song, and religious concepts and experiences.

Some people don't wish to think about stuff like that. Fine with me. (shrug) It doesn't matter one way or the other if they do or not.