The Hartle–Hawking state is a proposal in

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

concerning the state of the

Universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...

prior to the

Planck epoch The chronology of the universe describes the history and future of the universe according to Big Bang cosmology. Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, wit ...

. It is named after James Hartle and Stephen Hawking. 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 otherwise have been the beginning, time gives way to space such that at first there is only space and no time. 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 The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...

. However, Hawking does state "...the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago.", but that the Hartle-Hawking model is not the steady state Universe of Hoyle; it simply has no initial boundaries in time or space.

Technical explanation

The Hartle–Hawking state is the

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the

—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 Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

in the

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

of a theory of

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...

that describes this

. It is a

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...

of the

metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allow ...

defined at a (''D'' − 1)-dimensional

compact surface In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only ''non-compact'' components. Examples The only connected one-dimensional example i ...

, the Universe, where ''D'' is the

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...

dimension. The precise form of the Hartle–Hawking state is the path integral over all ''D''-dimensional geometries that have the required

induced metric In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback. It may be determined using t ...

on their boundary. According to the theory,

time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

, as it is currently observed, diverged from a three-state dimension after the Universe was in the age of the Planck time. John D. Barrow, ''The Origin of the Universe: To the Edge of Space and Time'', Basic Books, 1997. Such a wave function of the Universe can be shown to satisfy, approximately, the

Wheeler–DeWitt equation The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and gene ...

Notes

References

* * {{DEFAULTSORT:Hartle-Hawking state Physical cosmology Stephen Hawking

Technical explanation

See also

Notes

References