Hartle-Hawking No-Boundary Proposal: A Universe With No Edge in Time
The Hartle-Hawking state, proposed by James Hartle and Stephen Hawking in 1983, is a quantum-cosmological model in which the universe has no initial boundary in time. By treating time as effectively spatial near the Big Bang, the proposal removes the question of what came before.
The Hartle-Hawking state, also called the no-boundary proposal or no-boundary wave function, is a model in quantum cosmology put forward by James Hartle and Stephen Hawking in 1983. It supplies an initial condition for the universe in which there is no boundary or edge to spacetime in the past, and was later extended in collaboration with Neil Turok. The proposal combines three ingredients. It uses Richard Feynman's path integral formulation of quantum mechanics, in which possible histories contribute amplitudes. It applies a Euclidean transformation, a Wick rotation that converts ordinary time into an imaginary, spatial-like dimension near the Big Bang. And it imposes a boundary condition of no boundary at all: the resulting curved Euclidean spacetime is finite in extent yet has no edge, analogous to the surface of a sphere, which is finite but boundaryless. The key consequence is that near the Big Bang, time behaves like another spatial direction, so there is no first instant and no "before" to ask about, much as there is no point north of the North Pole. This dissolves the question of what caused or preceded the universe rather than answering it, addressing the same first-cause puzzle as a bootstrap paradox but without invoking closed timelike curves. It is a leading proposal in quantum cosmology, though it remains untested and debated. See Gott-Li Self-Creating Universe: A Cosmos That Is Its Own Mother and The Universe as a Bootstrap Loop: Origin Without a First Cause.