This is the problem of explaining the discrete macro-level of experience that humans experience. It's not easy to appreciate the problem so I will try and put it as starkly as possible.
There are two physical theories of the universe and each is thought of as being correct. The first is quantum mechanical where everything is but the interplay of micro-physical phenomena and the second is general relativity where the universe is treated as one complete system of space-time geometry.
The problem is this: how does either conception of the very basis of reality give room for macro-level experience that humans have?
I think modern science is still limited in a way because it doesn't take into account subjectivity. It has focused so much on the outside world, that it has not studied the observer itself. The scientific theories don't try to explain experience, perception, consciousness, thoughts, feelings/emotions etc. which though being as real as the various objects like sun, moon, galaxies and various chemicals, still haven't been studied much.
I would simplify the problem you pose, and say that the boundary doesn't really exist; it is only the limits of our perception which make us feel that there is a boundary. What I am trying to say would be easier to get if you consider instruments of differing capacities. For each instrument, there would exist a boundary which would be arbitrary and limited by the capacity of the instrument.
Consider it this way: there is absolutely no difference in quantum terms between me and the couch I am sitting on. Both the couch and I are made up of ordinary matter undergoing ordinary qm reactions. Why is it that I have this boundary of experience seperating the atoms of my body from the atoms of the couch? There is nothing at a quantum level that can explain this boundary to my experience because surely if qm was a total description then the only experience it would allow is experience at a micro-physical level for particles alone - a macro body is just an abstraction of those micro reactions - so why does my experience exist at this macro level?
Limits of our perception. Macro and micro levels are defined by us humans.
The other theory fares no better. In general relative terms there is only one manifold of space-time and all matter and energy are changes in this manifold. It is a complete and unitary system. Surely if experience was to exist with just this theory in mind it would have to be experience at a cosmic level, just one subject of experience not the many different middle-level organisms of experience that actually do exist. Just like the qm example, there would be no difference between the couch and me as both the couch and I are just curves in space time - what's so special about the curve that is me?
The limits of our perception. There is nothing special about you except for the fact that all your sensory organs, including the mind, have limitations. Whatever we can conceive of cannot grasp the reality.