Psy-Kosh: Position-space is special because it has a notion of locality. Two particles can interact if they collide with each other traveling at different speeds, but they cannot interact if they are far from each other traveling at the same speed.

The field, defined everywhere on the 4-D spacetime manifold, is "reality" (up until the magical measurement happens, at least). You can construct different initial value problem (e.g. if the universe is such-and-such at a particular time, how will it evolve?) by taking different slices of the spacetime. Just because there are are many ways to pose an initial value problem for the same spacetime history doesn't mean there isn't one field which is reality.

Eliezer is obviously unable to address all these issues here, as they are well outside his intended scope.