  It was known long ago that quantum theory and general relativity, two pillars
of modern physics, are in sharp conflict in their foundations. Their
fundamental inconsistencies render a consistent theory of quantum gravity the
most challenging problem in physics. Here we propose an information-complete
quantum field theory (ICQFT), which describes elementary fermions, their gauge
fields, and gravity (together, called the trinary fields) as an elementary
trinity without any conceptual inconsistency of existing theories. We then
argue that the ICQFT provides a coherent picture and conceptual framework of
unifying matter and spacetime (gravity) as information via spacetime-matter
entanglement and gives a compelling solution to the problem of time and time's
arrow. The trinary fields are characterized by dual entanglement and dual
dynamics. Spacetime-matter entanglement encodes complete physical predictions
of the theory and allows us to give a quantum information definition of dark
energy. We consider two particular forms of spacetime-matter entangled states
and their physical consequences. One of them\ is consistent with the
variational holographic relation and another results in an universal relation
between entanglement entropy and geometry (area and volume). This latter
relation allows us to determine the cosmological constant term in the classical
Einstein equation and implies that our Universe is not strictly holographic due
to dark energy (related to an universal negative pressure). We predict the
interior quantum state of a Schwarzschild black hole to be maximally
information-complete. As a concrete quantum formulation of gravity coupled with
matter, the ICQFT is about quantum information dynamics for spacetime and
matter and eliminates the conceptual obstacles of existing quantum gravity
theory.
