An effective approach to the problem of time

Abstract

A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial advantage of allowing the consistent use of local internal times in non-deparameterizable systems. Different local internal times are related merely by gauge transformations, thereby enabling relational evolution through turning points of non-global internal times. The main consequence of the local nature of internal time is the necessity of its complex-valuedness, reminiscent of but more general than non-unitarity of evolution defined for finite ranges of time. By several general arguments, the consistency of this setting is demonstrated. Finally, we attempt an outlook on the nature of time in highly quantum regimes. The focus of this note is on conceptual issues.

20 pages; v2: additional discussions mainly in Sec. 4

References in corpus (5)

• Effective approach to the problem of time: general features and examples
• Fundamental decoherence from quantum gravity: a pedagogical review
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Effective Constraints for Quantum Systems
• Relational physics with real rods and clocks and the measurement problem of quantum mechanics

Cited by in corpus (1)

• Effective approach to the problem of time: general features and examples