On the Resolution of Time Problem in Quantum Gravity Induced from Unconstrained Membranes

Abstract

The relativistic theory of unconstrained $p$-dimensional membranes ($p$-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an $N$-dimensional embedding space. The parameter of evolution or the evolution time $\tau$ is a distinct concept from the coordinate time $t=x^0$. Quantization of the theory is also discussed. A covariant functional Schr\" odinger equations has a solution for the wave functional such that it is sharply localized in a certain subspace $P$ of space-time, and much less sharply localized (though still localized) outside $P$. With the passage of evolution the region $P$ moves forward in space-time. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that space-time is a continuum in which events are existing; (ii) not the whole 4-dimensional space-time, but only a 3-dimensional 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. Possible sources are unconstrained worldlines which are free from the well known problem concerning the Maxwell fields generated by charged unconstrained point particles.

22 Pages

References in corpus (4)

• On the quantisation of gravity by embedding spacetime in a higher dimensional space
• An Alternative to Matter Localization in the "Brane World": An Early Proposal and its Later Improvements
• Wiggly Relativistic Strings
• The Classical and Quantum Theory of Relativistic p-Branes without Constraints

Cited by in corpus (5)

• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Clifford Space as the Arena for Physics
• On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb-Ramond Fields
• The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory
• Fock-Schwinger proper time formalism for p-branes