Hartle–Hawking state

In theoretical physics, the Hartle–Hawking state, named after James Hartle and Stephen Hawking, is a proposal concerning the state of the universe prior to the Planck epoch.

Hartle and Hawking suggest that if we could travel backward in time toward the beginning of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the universe is meaningless. According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: the universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle–Hawking state universe has no beginning, but it is not the steady state universe of Hoyle; it simply has no initial boundaries in time nor space.^[1]

Technical explanation

The Hartle–Hawking state is the wave function of the Universe—a notion meant to figure out how the Universe started—that is calculated from Feynman's path integral.

More precisely, it is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes this wave function.

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 diverged from three state dimension—as we know the time now—after the universe was at the age of the Planck time.^[2]

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

See also

• End of the Earth illusion
• End of the Rainbow illusion
• Imaginary time
• Multiple histories
• Signature change
• Universal wavefunction
• Vanishing point
• Wheeler–DeWitt equation

Notes

1. Hawking, Stephen. "The Beginning of Time". Retrieved 10 March 2014.
2. John D. Barrow, The Origin of the Universe: To the Edge of Space and Time, Basic Books, 1997.

References

• Hawking, S.; Hertog, T.; Reall, H. (2000). "Brane new world". Physical Review D 62 (4): 043501. arXiv:hep-th/0003052. Bibcode:2000PhRvD..62d3501H. doi:10.1103/PhysRevD.62.043501.
• 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.