Hartle–Hawking state
The Hartle–Hawking state, also known as the no-boundary wave function, is a proposal in theoretical physics concerning the state of the universe prior to the Planck epoch.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> It is named after James Hartle and Stephen Hawking, who first proposed it in 1983. Template:Cn <math display="block"> \Psi[\gamma_{ij}]=N\int\delta g_{\mu\nu}(x)\exp(iS_\text{EH}[g_{\mu\nu}]) </math> Here <math>\gamma_{ij}</math> is the three metric (c.f. ADM formalism and Wheeler-DeWitt equation), <math>N</math> a normalization factor, <math>g_{\mu\nu}</math> the four metric and <math>S_\text{EH}[g_{\mu\nu}]=(2\kappa)^{-1}\int d^4 x R\sqrt{-g}</math> the Einstein-Hilbert action. The above integral is a functional integral.
History
According to the Hartle–Hawking state proposal, the universe has no origin as we would understand it: before the Big Bang, which happened about 13.8 billion years ago, the universe was a singularity in both space and time. Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the universe, we would note that quite near what might have been the beginning, time gives way to space so that there is only space and no time.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
Technical explanation
More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.
It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension. The precise form of the Hartle–Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary. According to the theory, time, as it is currently observed, diverged from a three-state dimension after the universe was in the age of the Planck time.<ref>Template:Cite book</ref>
Such a wave function of the universe can be shown to satisfy, approximately, the Wheeler–DeWitt equation.