On the resolution of time problem in quantum gravity induced from unconstrained membranes
Abstract
The relativistic theory of unconstrained pdimensional membranes (pbranes) is further developed and then applied to the embedding model of induced gravity. Spacetime is considered as a 4dimensional unconstrained membrane evolving in an Ndimensional embedding space. The parameter of evolution or the evolution time τ is a distinct concept from the coordinate time t=x^{0}. Quantization of the theory is also discussed. A covariant functional Schrödinger equation has a solution for the wave functional such that it is sharply localized in a certain subspace P of spacetime, and much less sharply localized (though still localized) outside P. With the passage of evolution the region P moves forward in spacetime. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that spacetime is a continuum in which events are existing; (ii) not the whole 4dimensional spacetime, but only a 3dimensional section which moves forward in time, is accessible to our immediate experience. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained embedding model.
 Publication:

Foundations of Physics
 Pub Date:
 February 1996
 DOI:
 10.1007/BF02058084
 arXiv:
 arXiv:grqc/9506057
 Bibcode:
 1996FoPh...26..159P
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 22 Pages