The Problem of Time in Quantum Gravity (1009.2157v3)

Abstract: The problem of time in quantum gravity occurs because time' is taken to have a different meaning in each of general relativity and ordinary quantum theory. This incompatibility creates serious problems with trying to replace these two branches of physics with a single framework in regimes in which neither quantum theory nor general relativity can be neglected, such as in black holes or in the very early universe. Strategies for resolving the Problem of Time have evolved somewhat since Kuchar and Isham's well-known reviews from the early 90's. These come in the following divisions I) time before quantization, such as hidden time or matter time. II) Time after quantization, such as emergent semiclassical time. III) Timeless strategies of Type 1: naive Schrodinger interpretation, conditional probabilities interpretation and various forms of records theories, and Type 2Rovelli': in terms of evolving constants of the motion, complete observables and partial observables. IV) I argue for histories theories to be a separate class of strategy. Additionally, various combinations of these strategies have begun to appear in the literature; I discuss a number of such. Finally, I comment on loop quantum gravity, supergravity and string/M-theory from the problem of time perspective.

• The paper highlights that reconciling the timeless Wheeler–DeWitt approach with experiential time is a central challenge in quantum gravity.
• It systematically compares strategies including Tempus Ante Quantum, Tempus Post Quantum, and timeless and histories-based approaches to address the problem.
• The analysis implies that integrating multiple frameworks may pave the way toward a consistent theory uniting General Relativity and Quantum Theory.

The Problem of Time in Quantum Gravity

The paper "The Problem of Time in Quantum Gravity" by Edward Anderson addresses a fundamental challenge in theoretical physics: reconciling the concept of time as understood in General Relativity (GR) with its role in Quantum Theory (QT). This issue, often termed the "Problem of Time," arises because each theory assigns a different ontology and functional role to time, complicating efforts to unify them under a single, consistent framework, especially in high-energy regimes such as black holes and the early universe.

Core Issues and Proposed Resolutions

The paper begins by detailing the confrontation between the timelessness implied by the Wheeler-DeWitt equation in canonical quantum gravity, known as the "Frozen Formalism," and our everyday experience of time. Anderson categorizes the Problem of Time into several facets, highlighting different strategies that have been proposed to address it:

1. Tempus Ante Quantum (Time Before Quantization): This approach attempts to define a classical notion of time before quantizing the theory. Several proposals exist, including using intrinsic or extrinsic time variables in GR or introducing matter clocks. However, these often encounter significant challenges, such as global obstructions or complex canonical transformations.
2. Tempus Post Quantum (Time After Quantization): This strategy accepts that time might not be fundamental and seeks its emergence through quantization. The Semiclassical Approach is a prominent member of this category, using the Born-Oppenheimer approximation to derive an approximate Schrödinger equation for "fast" degrees of freedom with respect to a "slow" semiclassical background. However, this relies on assumptions that may not always hold, such as the existence of a well-defined WKB state.
3. Tempus Nihil Est (Timeless Strategies): These suggest that time might not be a fundamental concept at all. Types include the Naïve Schrödinger Interpretation and Conditional Probabilities Interpretation, which attempt to replace the standard notion of time with relational or conditional temporal concepts. Additionally, Records Theory, which examines the universe's "records," or information-laden correlations, has been posited as a foundation for addressing time's emergent properties.
4. Non Tempus Sed Historia (Histories-based Approaches): Histories Theory considers entire histories as fundamental, with consistent sets of histories decohering to form our observed universe. This approach is often aligned with decoherence theories that suggest a semiclassical world emerges from a quantum superposition through environmental interactions.

Implications and Future Directions

The implications of resolving the Problem of Time are significant for both the theoretical and practical development of quantum cosmology and quantum gravity. Anderson's paper emphasizes the intricacy of each proposed strategy, noting that while significant progress has been made, a universally accepted solution remains elusive.

The paper suggests that a successful resolution may require synthesizing multiple approaches, such as combining aspects of Histories and Records Theories with Semiclassical Mechanics. Future research could involve exploring these combinations and potentially uncovering novel approaches within emerging frameworks such as Loop Quantum Gravity or string/M-theory. These theories inherently describe the universe in radically different terms, perhaps offering fresh insights into old problems, such as the nature and role of time.

In conclusion, while the Problem of Time remains one of the most profound open questions in theoretical physics, continued research into each of these strategies holds the potential to unlock new insights not only into the fundamental nature of time but also into the structure of reality itself.