ON THE RESOLUTION OF TIME PROBLEM IN QUANTUM-GRAVITY INDUCED FROM UNCONSTRAINED MEMBRANES

The relativistic theory of unconstrained p-dimensional membranes (p-br anes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstra ined membrane evolving in an N-dimensional embedding space. The parame ter of evolution or the evolution time tau is a distinct concept from the coordinate time t = x(0), Quantization of the theory is also discu ssed. A covariant functional Schrodinger equation has a solution for t he wave functional such that it is sharply localized in a certain subs pace P of space-time, and much less sharply localized (though still lo calized) outside P. With the passage of evolution the region P moves f orward in space-time. Such a solution we interpret as incorporating tw o seemingly contradictory observations: (i) experiments clearly indica te that space-time is a continuum in which events are existing; (ii) n ot the whole 4-dimensional space-time, but only a 3-dimensional sectio n which moves forward in time, is accessible to our immediate experien ce. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained emb edding model.