Hartle-Hawking state
Encyclopedia
The Hartle-Hawking state is a proposal concerning the state of the universe prior to the Planck epoch
. Hartle-Hawking is essentially a no-boundary proposal that the universe is infinitely finite: that there was no time before the Big Bang
because time did not exist before the formation of spacetime
associated with the Big Bang and subsequent expansion of the universe in space and time.
James Hartle and Stephen 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.
, the Hartle–Hawking state, named after James Hartle
and Stephen Hawking
, 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 functional
.
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 Universum was at the age of the Planck time
.
Such a wave function of the Universe can be shown to satisfy the Wheeler–DeWitt equation.
Planck epoch
In physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which, it is believed, quantum effects of gravity were significant...
. Hartle-Hawking is essentially a no-boundary proposal that the universe is infinitely finite: that there was no time before the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
because time did not exist before the formation of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
associated with the Big Bang and subsequent expansion of the universe in space and time.
James Hartle and Stephen 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
Gravitational singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...
in both space and time, pre-Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
. Thus, the Hartle-Hawking state universe has no beginning, but it is not the steady state universe
Steady State theory
In cosmology, the Steady State theory is a model developed in 1948 by Fred Hoyle, Thomas Gold, Hermann Bondi and others as an alternative to the Big Bang theory...
of Hoyle
Fred Hoyle
Sir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...
; it simply has no initial boundaries in time nor space.
Technical Explanation
In theoretical physicsTheoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, the Hartle–Hawking state, named after James Hartle
James Hartle
James Burkett Hartle is an American physicist. He has been a professor of physics at the University of California, Santa Barbara since 1966, and he is currently a member of the external faculty of the Santa Fe Institute...
and Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
, is the wave function of the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
–a notion meant to figure out how the Universe started–that is calculated from Feynman's path integral
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
.
More precisely, it is a hypothetical vector in the Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
of a theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
that describes this wave functional
Functional (mathematics)
In mathematics, and particularly in functional analysis, a functional is a map from a vector space into its underlying scalar field. In other words, it is a function that takes a vector as its input argument, and returns a scalar...
.
It is a functional of the metric tensor
Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...
defined at a (D-1)-dimensional compact surface, the Universe, where D is the spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
dimension. The precise form of the Hartle–Hawking state is the path integral over all D-dimensional geometries that have the required induced metric
Induced metric
In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold which is calculated from the metric tensor on a larger manifold into which the submanifold is embedded...
on their boundary. According to the theory time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
diverged from three state dimension - as we know the time now - after the Universum was at the age of the Planck time
Planck time
In physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
.
Such a wave function of the Universe can be shown to satisfy the Wheeler–DeWitt equation.