This question raises that hoary old problem in Tolkien's Legendarium, how after many years he struggled to removed all references to what he felt were the cheap thrills of magic. He attempted to make any and all special effects the result of a highly developed, elevated elven art.
So, how does a "magic ring" make one invisible? How does"art" enable a body to cross over to the other side? (And why is that other side so dark?) Is this a form of mind/body imagery that the beauty of the ring inspires? Or is there some alchemical "stuff" in the metallurgy which causes the cells of the body to disperse beyond their usual density?
And as for the question, I frankly don't think the question is at all hypothetical. After all, this internets stuff makes us all invisible, although we each see each other's thoughts. I think we Downers have already put on the "magic ring". It's called the Internet. And many people think that is e-vil.