QUANTUM-GRAVITY INTERPRETATION OF BRANS-DICKE THEORY---THE BACK-REACTION OF THE VACUUM MATTER FIELD UPON THE EINSTEIN SPACE-TIME

A quantum gravity version is given to the Brans-Dicke theory. We find that the matter field quantum fluctuation induces the conformal quantum fluctuation of space-time, and that the latter backreacts to the classical space-time and transforms it from Einstein space-time into the Brans-Dicke one.