Hartle–Hawking state

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Big Bang and Hartle–Hawking State diagram.

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.[1][2][3] It is named after James Hartle and Stephen Hawking.

According to the Hartle–Hawking 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.[4]

Technical explanation[edit]

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.[5]

Such a wave function of the universe can be shown to satisfy, approximately, the Wheeler–DeWitt equation.

See also[edit]


  1. ^ Hartle, J.; Hawking, S. (1983). "Wave function of the Universe". Physical Review D. 28 (12): 2960. Bibcode:1983PhRvD..28.2960H. doi:10.1103/PhysRevD.28.2960. S2CID 121947045.
  2. ^ Lehners, Jean-Luc (June 2023). "Review of the no-boundary wave function". Physics Reports. 1022: 1–82. arXiv:2303.08802. doi:10.1016/j.physrep.2023.06.002.
  3. ^ Weinberg, Steven (1989-01-01). "The cosmological constant problem". Reviews of Modern Physics. 61 (1): 1–23. doi:10.1103/RevModPhys.61.1. hdl:2152/61094. ISSN 0034-6861.
  4. ^ Hawking, Stephen. "The Beginning of Time". Archived from the original on 6 October 2014. Retrieved 10 March 2014.
  5. ^ John D. Barrow, The Origin of the universe: To the Edge of Space and Time, Basic Books, 1997.