That could be an explanation using modern terminology.
sort of like transmission from this world to the other.
Perhaps communications via superstrings to use modern terminology. Communication via superstring might explain explain how God knows whenever a sparrow falls.
Perhaps we leave a trace (shadow, quantum representation, or entangled property) of what we are doing and thinking in this world in the other dimension and that this trace has an independent reality that can continue to exist after our physical body is destroyed.
Sort of like cosmic network storage and cosmic cloud computing via superstring networks to use modern terminology.
I would hesitate to argue that the Trinity of God is a physical property, if that is what you mean, since it would imply that God is part of the universe instead of its transcendent creator. Usually Christians believe that God is not part of the physical universe, but outside of it. He is the creator of the dimensions.
Certainly God transcends the universe. By physical property, I meant since God created the universe, he can become a part of it similarly to you or I building a structure and then entering it. Who knows, the entire universe may be a living part of God. Never-the-less, some means of God manifesting himself and interacting with Adam, Eve and their children existed. Similarly with Moses. Was it all done by remotely stimulating regions of their brain without there being any physical presence? We don't know.
What we do know is that the bible is a record of the relationship between an immensely powerful being and humans. At the time it was written, those humans were quite primitive by modern standards and the communication with those primitive people was in a manner suitable for them to understand.
In our modern world, I think we have to read scripture similarly to the way a parent communicates with a child. For example: When biblical hygiene laws were established, God didn't intend to go into any long discourse on biology, chemistry and medicine. He just said, "eat these type foods and avoid these other type foods and your life will generally be better as a result".
However, the idea of one person existing in two universes or dimensions could be taken as a metaphor for the trinity. Perhaps aspects of our reality is a creative reflection of Gods nature.
God did say let us create man in our image. So, yes, we are a creative reflection of God. As for the trinity, I generally say to those having some understanding of physics yet doubtful concerning the way the trinity has traditionally been presented to them that it may be little more than the personalities/descriptive characteristics of an immensely powerful being that can from time to time manifest itself to us in our dimensions. The most common manifestation being the Holy Spirit which possibly could be seen similarly to GPS navigational devices but on a cosmic/quantum scale whereby. With GPS navigation, most people haven't a clue as to how the units work. All they know is that they turn the devices on and obey driving instructions.
The Holy Spirit may be a communication path across the cosmos via superstrings that issues navigational signals to us.
The point is for me, it seems inadequate when people just assert: it's supernatural. Well, OK. But, what is actually happening. Seems like new physics might help us understand the ways of God and the nature of conscious beings.
You say that God interacts with our universe like the builder of a house may enter it. OK. But, I would still resist the idea that the universe could be “a living part” of God. The wholly other position seems a better fit for the God's interaction with the world (we don't want to worship the creation instead of the Creator). Otherwise it sounds more like the Hinduism
Really like your comment that the information in the soul lives on in heaven like: “cosmic network storage and cosmic cloud computing”