The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler – De Witt equation. We describe the derivation of the ‘quantum Einstein equation ’ and discuss the new features of their solutions. It gives me great pleasure to contribute this article to the volume in honor of Professor Jerzy Lukierski. I clearly remember when, still being a student, I have met him for the first time during one of the winter Karpacz schools in late 1970s. Since then he was always close to me, first as an advisor and referee of my PhD thesis, and then as a close collaborator in many research projects and a very good friend. I cannot possibly fully pay my debt to him; let this article be at least an expression of acknowledgement of what I owe him. 2.