You're talking the uncertainty principle here, right? My knowledge of quantum physics is very sparse. But what you're saying applies to individual photons, certainly, but as a group all of their characteristics can be measured. By taking enough such measurements you can make predictions for virtually all photons.
But there's the problem. If you allow yourself to accept hallucinations as coming from some non-physical realm, whether god or something else, then you would have to explain just how this non-physical realm interacts with ours. And such interactions, if they are real, should be able to be measured scientifically, which removes them from the supernatural. A far more likely explanation is that they are just hallucinations.
The question of "what existence is" is a philosophical question, for sure. I'm not equipped, either educationally or temperamentally, to discuss philosophy. I find it tedious and contradictory, with little or no evidence of having any real value, at least to me. However, "how does the universe work" is strictly a science question, one which mankind has been asking, and finding answers to, from the very beginning.
Ultimately, I'm not sure we can honestly conclude that there is anything beyond human understanding. If we apply our intelligence, I think we can eventually learn how everything works. And it is quite possible that, someday, we will learn that some of the things we've ignored as being supernatural are, indeed, natural. But that does not mean that we should accept every supernatural explanation for something we don't understand. Doing that will only restrict our ability to find out what's really happening.
There have been numerous studies done which show that:
1) People will see patterns in random data, such as faces in clouds.
2) What people claim to see can be influenced by environment, culture and expectations.
3) People can be made to see a specific pattern when influenced by another person.
Most mass hallucinations are caused by some combination of these three, and other influences. Sightings of the Loch Ness Monster are like this. People go there expecting to see it, so anything they see which is different and unexplainable automatically becomes Nessie. But when you go there and try to find her scientifically, there's nothing to see.
I'm not saying we should discard an idea just because it doesn't seem probable. But when you propose such an idea you have to have some way of showing that it is even possible. You can't throw something out there and say, "Now go and prove me wrong." You have to provide evidence for it first, otherwise it's purely speculation, and hardly worth the time of someone else to investigate.
When Alfred Wegener first proposed the idea that the continents drifted, spreading apart and colliding like bumper cars, he was laughed at, his idea ridiculed. After all, what could be more solid than the ground beneath your feet? But he had the evidence, the observations, the tests. Everything that was needed to convince the scientific establishment to look deeper. If he had simply come out with a statement that the continents moved, with no evidence or data, the ridicule would have been justly deserved.
When astronomers look out into the universe and detect distant galaxies, and stars, and planets, even, they have solid science to back up their conclusions. Their data are checked, double checked and triple checked. Their conclusions are torn down and rebuilt, to insure that the science is right. Only then are they able to say with any confidence that they are PROBABLY correct. All scientists know that future observations, future advances in measurements, may turn their theories upside down. But everything we know tells us that, as far as we can determine, THIS is how the universe works!