Hartle–Hawking state

Hartle–Hawking state The Hartle–Hawking state is a proposal in theoretical physics and cosmology that describes the quantum state of the universe at the beginning of time. It was proposed by James Hartle and Stephen Hawking in the 1980s as a way to describe the initial conditions of the universe in a quantum mechanical framework. The Hartle–Hawking state is an attempt to provide a no-boundary proposal for the universe, which posits that the universe had no boundaries or edges in the imaginary time direction. This proposal has been influential in the development of cosmology and black hole physics.

## Introduction The Hartle–Hawking state is a quantum mechanical description of the universe at the beginning of time, which is based on the path integral formulation of quantum mechanics. The path integral formulation, developed by Richard Feynman, is a mathematical approach to describe the quantum mechanics of a system by summing over all possible trajectories of the system. In the context of the universe, the path integral formulation is used to describe the evolution of the universe from an initial state to a final state.

## Definition and Mathematical Formulation The Hartle–Hawking state is defined as a wave function of the universe, which encodes the quantum mechanical information about the universe at the beginning of time. The wave function is a solution to the Wheeler–DeWitt equation, which is a partial differential equation that describes the evolution of the universe in minisuperspace. The minisuperspace is a mathematical space that describes the geometry of the universe in a simplified way. The Hartle–Hawking state is given by a path integral over all possible metrics and matter fields of the universe, subject to certain boundary conditions.

## Implications and Interpretations The Hartle–Hawking state has several implications and interpretations. One of the implications is that the universe had no singularity at the beginning of time, but instead had a smooth and finite geometry. This proposal has been influential in the development of eternal inflation, which is a theory that describes the multiverse as an eternally inflating brane. The Hartle–Hawking state also provides a framework for understanding the origin of the universe and the arrow of time.

## Derivation and Justification The Hartle–Hawking state can be derived using various methods, including the path integral formulation and the Wheeler–DeWitt equation. The derivation involves making certain assumptions about the initial conditions of the universe and the matter content of the universe. The Hartle–Hawking state has been justified using various arguments, including the no-boundary proposal and the principle of quantum mechanics. However, the derivation and justification of the Hartle–Hawking state are still active areas of research.

## Role in Cosmology and Black Hole Physics The Hartle–Hawking state plays a crucial role in cosmology and black hole physics. In cosmology, the Hartle–Hawking state provides a framework for understanding the origin and evolution of the universe. In black hole physics, the Hartle–Hawking state is used to describe the quantum mechanics of black holes and the information paradox. The Hartle–Hawking state has also been influential in the development of holographic principle, which is a theoretical framework that describes the information content of a region of spacetime.

## Criticisms and Controversies The Hartle–Hawking state has been subject to various criticisms and controversies. One of the criticisms is that the Hartle–Hawking state is not a well-defined mathematical object, and that the derivation of the state involves various assumptions and approximations. Another criticism is that the Hartle–Hawking state does not provide a complete description of the universe, and that it is incomplete in certain aspects. Despite these criticisms, the Hartle–Hawking state remains an influential proposal in theoretical physics and cosmology. Category:Theoretical physics Category:Cosmology Category:Quantum mechanics