Logicoalgebraic approach to spacetime quantization
Abstract
In the last decades the logicoalgebraic approach to quantum mechanics turned to be a successful tool to render the quantum mechanical formalism on a steady operationalistic background. The algebraic approach to general relativity first proposed by Geroch is used to build a smearing procedure for events in the quantized theory of spacetime. It stems from the notion of basic algebra which possesses both the differential structure (as functional algebras) and noncommutativity (as algebras of observables in quantum theories). The main essence of this formalism is that it deprives the notion of spacetime as event support of its fundamental status making it relative to the measurement performed. Before the observation is executed, it is pointless to speak of events as points of spacetime: there is no underlying manifold. Only when an eigensubalgebra of the basic algebra is outlined as eigenstate of the observable, it gives rise to its functional representation on the appropriate set thought of as spacetime.
 Publication:

arXiv eprints
 Pub Date:
 March 1995
 arXiv:
 arXiv:grqc/9503033
 Bibcode:
 1995gr.qc.....3033Z
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 16 Kb, Latex, no figures, the text of the talk presented on the First Mtg. of AFOS (Ass. for Foundations of Science), Warsaw, August, 28  30, 1994.