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The Hartle–Hawking state, also known as the no-boundary wave function is a proposal in
The Hartle–Hawking state, also known as the no-boundary wave function 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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
concerning the state of the universe
The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
prior to the Planck epoch. It is named after James Hartle and Stephen Hawking.
History
According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: before theBig Bang
The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, 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.
Technical explanation
More precisely, the Hartle-Hawking state is a hypothetical vector in theHilbert space
In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
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 v ...
that describes the wave function of the universe.
It is a functional 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 allows ...
defined at a (''D'' − 1)-dimensional compact surface, the universe, where ''D'' is the spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
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
Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...
, as it is currently observed, diverged from a three-state dimension after the universe was in the age of the Planck time.
Such a wave function of the universe can be shown to satisfy, approximately, the Wheeler–DeWitt equation.
See also
* Imaginary time * Multiple histories * Signature changeReferences
{{DEFAULTSORT:Hartle-Hawking state Physical cosmology Stephen Hawking