Time and a physical Hamiltonian for quantum gravity

Abstract: We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts in technical reach applications to cosmology, quantum gravitational collapse and Hawking radiation.

• The paper introduces a non-perturbative quantum gravity approach using dust as a time variable, enabling a non-square root physical Hamiltonian.
• Integrating with loop quantum gravity, this framework presents a complete, practically applicable quantum gravity theory.
• The theory simplifies loop quantum cosmology and offers potential for exploring cosmological singularities and gravitational collapse.

Time and a Physical Hamiltonian for Quantum Gravity

The paper "Time and a physical Hamiltonian for quantum gravity" by Viqar Husain and Tomasz Pawłowski addresses a pivotal issue in theoretical physics—the quest for a quantum theory of gravity. The authors present a non-perturbative quantization approach to general relativity, where—aided by coupling to dust and other matter fields—they introduce a natural time variable. This enables the formulation of a physical Hamiltonian retaining the symmetry of spatial diffeomorphism.

Key Insights and Contributions

1. Non-Square Root Hamiltonian: A noteworthy feature of the results is the non-square root form of the Hamiltonian. This is significant, avoiding unresolved complications typically associated with Hamiltonians that are quadratic in canonical variables.
2. Complete Quantum Gravity Theory: By integrating the kinematical structure of loop quantum gravity (LQG) with the proposed Hamiltonian, the work presents a complete quantum gravity theory. This is an advancement from previous endeavors, which generated only formal frameworks without practical applicability.
3. Dust as a Natural Time Variable: The modification of the Brown-Kuchar dust, where T serves as the time variable, resolves the problem of time. The time gauge fixing simplifies the canonical structure, facilitating a coherent theoretical model.

Implications

• Cosmological Applications: The model simplifies and extends traditional loop quantum cosmology (LQC), allowing for varied matter content and potential. This extension is crucial for examining cosmic phenomena like singularity avoidance and possible bounces.
• Gravitational Collapse and Hawking Radiation: The framework presented is poised to explore critical gravitational phenomena, potentially altering understandings of singularity avoidance, cosmic censorship, and the information loss paradox.
• Quantum Field Theory on Curved Spacetime: The paper proposes that quantum field theories can emerge on curved spacetimes using semiclassical states of geometry. This results in an effective Hamiltonian that simplifies the traditional semiclassical approximation, potentially revising approaches to standard Hawking radiation calculations.

Formal and Methodological Advances

• Kinematical and Physical Hilbert Space: Utilizing the unique LQG kinematical quantization, the physical Hamiltonian constraint becomes technically manageable. This is achieved without anomalies typically arising in prior formulations with arbitrary lapse functions.
• Algebraic Loop Quantum Gravity: The work leverages developments from algebraic LQG, choosing a more tractable formulation of acting the Hamiltonian on spin networks, thereby expanding LQG's applicability.

Speculation on Future Developments

This quantum gravity theory may catalyze significant shifts in the study of quantum cosmological models, potentially offering resolutions to long-standing problems such as singularities and cosmic censorship. Moreover, the approach could pave the way for more integrated models of QFT and gravitation, opening doors to novel predictions about the universe's quantum structure.

Overall, Husain and Pawłowski provide a substantive theoretical framework which markedly advances the study of quantum gravity by reducing the technical and conceptual barriers inherent to the field. Their work lays the groundwork for future explorations into the domains of cosmology, black hole physics, and quantum field theory in curved spacetimes.