Hartle–Hawking state

Hartle–Hawking state
Name	Hartle–Hawking state

Hartle–Hawking state is a proposal in quantum cosmology for a boundary condition on the universal wavefunction that aims to describe the initial state of the universe and the quantum state of black holes. Developed as a path-integral prescription, it connects ideas from Stephen Hawking, James Hartle, Richard Feynman, Paul Dirac, and the Wheeler–DeWitt equation to propose a no-boundary condition that removes classical singularities. The proposal has influenced research at institutions such as California Institute of Technology, Institute for Advanced Study, Harvard University, University of Cambridge, and Perimeter Institute.

Introduction

The Hartle–Hawking proposal links concepts from general relativity, quantum mechanics, quantum field theory, Euclidean quantum gravity, and the path integral formulation developed by Richard Feynman and formalized by Paul Dirac. It aims to provide a wavefunction for the entire universe in the spirit of the Wheeler–DeWitt equation and has been discussed by researchers at Princeton University, University of Oxford, Stanford University, Massachusetts Institute of Technology, and University of Chicago. The idea has been cited in work by Edward Witten, Roger Penrose, Arkani-Hamed, Juan Maldacena, Andrew Strominger, and influences approaches in string theory, loop quantum gravity, and causal dynamical triangulations.

Definition and mathematical formulation

Mathematically the proposal specifies a quantum state via a path integral over compact four-geometries subject to specified three-geometry and field configurations on a boundary, inspired by the Euclidean path integral methods of Richard Feynman and the canonical quantization attempts of John Wheeler and Bryce DeWitt. The formalism employs the Wheeler–DeWitt equation and uses semiclassical saddle points akin to instantons studied by G. 't Hooft, Alexander Polyakov, Steven Weinberg, and Gerard 't Hooft. Calculations often invoke techniques from differential geometry, Riemannian geometry, and the theory of elliptic operators developed by Atiyah–Singer, Michael Atiyah, and Isadore Singer. The formulation requires specifying boundary conditions similar to those in Hartle and Hawking original papers and has been analyzed using methods from quantum cosmology employed by Andrei Linde, Alan Guth, Andreas Albrecht, and Paul Steinhardt.

Physical interpretation and implications

Physically, the state implies a universe without a classical temporal boundary, connecting to concepts discussed by Stephen Hawking, Roger Penrose, Andrei Linde, Alexander Vilenkin, and Max Tegmark. It purports to regularize the classical singularity theorems of Stephen Hawking and Roger Penrose by replacing a singular origin with a smooth Euclidean geometry, resonating with instanton ideas from Sidney Coleman and Steven Weinberg. The proposal has implications for observable parameters studied by teams at European Space Agency, NASA, Planck Collaboration, Wilkinson Microwave Anisotropy Probe, and BICEP2 because it constrains primordial perturbation spectra relevant to cosmic microwave background observations analyzed by Pieter van Nieuwenhuizen and Kip Thorne. It also relates to discussions involving Alan Guth on inflation and to quantum initial condition debates involving Alexander Vilenkin and Andrei Linde.

Applications in quantum cosmology and black hole physics

In quantum cosmology, the Hartle–Hawking state has been used to compute probabilities for classical spacetimes and perturbations by researchers at California Institute of Technology, Institute for Advanced Study, and University of Cambridge, and in models influenced by string theory work of Edward Witten, Cumrun Vafa, Shamit Kachru, and Joseph Polchinski. It appears in black hole quantum state discussions connected to the Hawking radiation derivation of Stephen Hawking and to proposals about black hole entropy by Jacob Bekenstein, Gerard 't Hooft, Leonard Susskind, and Andrew Strominger. Analyses of quasi-normal modes and semiclassical backreaction involve researchers such as Gary Gibbons, James Hartle, and Stephen Hawking and intersect with studies at Niels Bohr Institute, Max Planck Institute for Gravitational Physics, and Kavli Institute. The state is also compared with canonical approaches pursued by Carlo Rovelli, Lee Smolin, and numerical methods used in causal set theory by Rafael Sorkin.

Criticisms and alternative proposals

Critics including Alexander Vilenkin, Andrei Linde, Roger Penrose, and others have argued alternatives like the tunneling proposal of Alexander Vilenkin, chaotic inflation advocated by Andrei Linde, and conformal cyclic cosmology proposed by Roger Penrose. Technical objections draw on issues raised by Gerard 't Hooft about path integral measures, by Edward Witten concerning contour choices, and by Herman Verlinde and Erik Verlinde about holographic interpretations. Alternative boundary conditions and proposals include the tunneling wavefunction, the Leiden group work involving Herman Verlinde, stringy constructions by Joseph Polchinski and Cumrun Vafa, and holographic no-boundary-like proposals discussed by Juan Maldacena and Edward Witten.

Historical development and key contributors

The proposal originated in work by James Hartle and Stephen Hawking in the early 1980s, building on foundations laid by Richard Feynman, Paul Dirac, John Wheeler, and Bryce DeWitt. Subsequent development involved contributions from Andrei Linde, Alexander Vilenkin, Gerard 't Hooft, Edward Witten, Roger Penrose, Alan Guth, Paul Steinhardt, Andrew Strominger, Gary Gibbons, Carlo Rovelli, Lee Smolin, Juan Maldacena, Joseph Polchinski, Cumrun Vafa, and many research groups at Caltech, MIT, Princeton University, Harvard University, University of Cambridge, Oxford University, Stanford University, Perimeter Institute, Max Planck Society, and the Institute for Advanced Study. The dialogue continues in conferences such as the Solvay Conference, International Conference on General Relativity and Gravitation, Strings Conference, and workshops at CERN and KITP.

Category:Quantum cosmology