Problem of time: facets and Machian strategy

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Cosmology

Background:

• Theories of quantum mechanics and general relativity possess incompatible notions of time.
• This incompatibility presents a significant obstacle in developing a unified theory of quantum gravity.
• The 'problem of time' manifests in various facets within canonical approaches.

Purpose of the Study:

• To clarify and reconceptualize the facets of the problem of time in canonical quantum gravity.
• To propose a novel, Machian resolution applicable at classical, semiclassical, and combined levels.
• To delineate pathways toward resolving the problem of time in full general relativity and cosmology.

Main Methods:

• Reconceptualization and renaming of eight facets of the problem of time.
• Introduction of 'temporal relationalism' and 'configurational relationalism' via 'best matching'.
• Development of a three-level Machian resolution (classical, semiclassical, semiclassical-histories-timeless records).

Main Results:

• Seven of the eight facets of the problem of time are shown to exist at the classical level.
• The 'frozen formalism' is reframed as 'temporal relationalism'.
• The 'thin sandwich' problem is reframed as 'configurational relationalism'.
• A local, conceptual resolution to the problem of time is achieved for relational triangle and minisuperspace models.

Conclusions:

• The proposed Machian resolution offers a viable path for addressing the problem of time.
• Further research is needed to extend this resolution to full general relativity and inhomogeneous cosmology.
• This work provides a conceptual framework and practical models for advancing quantum gravity research.