I think the idea of the supernatural interacting with the natural world is a contradiction in terms. If something can interact with the natural world, then it is, by my definition, natural.
There is only the natural world, but it is clouded with mystery. We know only glimpses of it. When it comes to universal truths, instead of the power to prove, contemporary science provides only the powers to support and to disprove. If there is anything like the supernatural capable of affecting the natural world, then it is simply a part of the natural world still as yet unscouted by science. A supernatural world incapable of interacting with the natural world, by any practical definition, does not, and indeed cannot,
You know I don't believe in any form of the supernatural, but there could be a natural analog for this thing called essence, and it would live on after death: All the ways in which a person impacted the universe around them. Every person will have interactions completely unique to them. On the micro scale, no photon will ever bounce off my skin and head off on a new trajectory the exact same way one is bouncing off your skin right now, there paths forever altered for having come in contact with us. On the macro scale, just the fact that we were born altered the universe and will continue to alter it in its own tiny, meaningless way. And on the humanitarian scale, every one of us alters everyone else.
My essence is what I produce interacting with my universe. All the little traces I leave behind by altering the paths of some photons here, and the behaviors of some children there, and leaving myself in the memories of my friends. And that is incorporeal and in its way, eternal. But it is not supernatural.
, I had considered posting something remarkably similar to this, but held back, because I didn't want to get bogged down in a scientific discussion of cause and effect.
In considering that, I was reminded of a very unusual science fiction book I read recently, called The Big Time by Fritz Leiber
. This novel is by no means for everybody; I need to read at least one more time to get a better idea of what's going on. But what's intriguing about it on topic is that it seems that some of the main characters can remain conscious outside the confines of their spatiotemporal existence. It's depicted as very weird and disorienting, and it sorta plays like a bad acid trip.
I do think your notion, of the lasting effects that a person has being a part of their essence, is definitely on the right track.
However, I do not think that science is in a position yet to comment reliably on whether there are any other aspects of the human experience that surpass bodily existence, as we currently understand bodily existence to be,
although there is presently no scientific reason to suppose that any such aspects exist. One reason I think that is because I am not remotely satisfied that science can account for consciousness, which is perhaps the preeminent aspect of each person's personal experience. Even though I have acknowledged the brain as the probable seat of consciousness, and I believe that all mental activity has a physical counterpart, the exact nature of the conscious I
has not yet been scientifically explained. In other words, the jury on the exact nature of consciousness is still out, and I think it likely will be for all our lifetimes. Supposing something to be an "emergent property" while lacking many of the crucial specifics is really an awfully big handwave (although I agree it is at least a plausible hypothesis), and it raises the question of whether the whole is in fact greater than the sum of its parts. Especially when it comes to psychology, there are pertinent natural aspects of our common experience that science is completely in the dark about. It would be a dull world, if that weren't so. Still, I have every reason to believe that, in time, progress will be made towards settling these issues scientifically.
Does such uncertainty in the meantime mean that one should resort to myth, conjecture, or superstitious mumbo jumbo to fill the gap? Not at all, the exception of there being some pressing need to produce an answer, when none is indicated by science, notwithstanding. As I indicated already, mystery as to the nature of the universe is simply the rule.
As to whether I think that there is anything for me to experience, beyond my corporeal existence? I honestly don't know. If there were, I wouldn't expect it to be anything like what my normal experience is now. It might be all weird and different.