Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• Lin-Lunin-Maldacena geometries are specific solutions in string theory.
• Classical coherent states typically possess trivial topology.
• Understanding spacetime topology in quantum gravity is a fundamental challenge.

Purpose of the Study:

• To investigate how superpositions of classical states affect spacetime topology.
• To explore the implications for the nature of spacetime geometry and topology.
• To reconcile findings with semiclassical effective field theory for gravity.

Main Methods:

• Analysis of superpositions of classical coherent states within Lin-Lunin-Maldacena geometries.
• Investigating the classical limits of these superpositions.
• Comparing results with standard semiclassical approximations in quantum gravity.

Main Results:

• Superpositions of trivial topology states lead to new classical limits with changed spacetime topology.
• This phenomenon implies spacetime topology and geometry are not operator measurement results.
• Identified a discrepancy with standard semiclassical analysis.

Conclusions:

• Spacetime topology can emerge dynamically from classical states.
• Operator measurements may not determine spacetime topology or geometry.
• Further work is needed to reconcile these findings with effective field theory for gravity.