A wormhole (
Einstein-Rosen bridge
A wormhole ( Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.
A wormhole can be visualized as a tunnel with two ends at separate p ...
) is a hypothetical structure connecting disparate points in
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 differen ...
, and is based on a special
solution of the Einstein field equations.
A wormhole can be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different points in time, or both).
Wormholes are consistent with the
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
, but whether wormholes actually exist remains to be seen. Many scientists postulate that wormholes are merely projections of a
fourth spatial dimension, analogous to how a two-dimensional (2D) being could experience only part of a three-dimensional (3D) object.
Theoretically, a wormhole might connect extremely long distances such as a billion
light year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
s, or short distances such as a few
meter
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
s, or different points in time, or even
different universes.
In 1995,
Matt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington, in New Zealand.
Work
Visser's research interests include general relativity, quantum field theory and cosmology.
Visser has produced a large number of research papers ...
suggested there may be many wormholes in the universe if
cosmic string
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simp ...
s with negative mass were generated in the early universe. Some physicists, such as
Frank Tipler
Frank Jennings Tipler (born February 1, 1947) is an American mathematical physicist and cosmologist, holding a joint appointment in the Departments of Mathematics and Physics at Tulane University. Tipler has written books and papers on the Omeg ...
and
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
, have suggested how to make wormholes artificially.
Visualization
For a simplified notion of a wormhole,
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
can be visualized as a two-dimensional surface. In this case, a wormhole would appear as a hole in that surface, lead into a
3D tube (the inside surface of a
cylinder
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
A cylinder may also be defined as an infin ...
), then re-emerge at another location on the 2D surface with a hole similar to the entrance. An actual wormhole would be analogous to this, but with the spatial dimensions raised by one. For example, instead of circular holes on a
2D plane
In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as su ...
, the entry and exit points could be visualized as spherical holes in
3D space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
leading into a four-dimensional "tube" similar to a
spherinder
In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3-ball (or solid 2-sphere) of radius ''r''1 and a line segment of length 2''r''2:
:D = \
Like th ...
.
Another way to imagine wormholes is to take a sheet of paper and draw two somewhat distant points on one side of the paper. The sheet of paper represents a plane in the
spacetime continuum
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 diffe ...
, and the two points represent a distance to be traveled, but theoretically a wormhole could connect these two points by folding that plane (''i.e.'' the paper) so the points are touching. In this way it would be much easier to traverse the distance since the two points are now touching.
Terminology
In 1928, German mathematician, philosopher and theoretical physicist
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...
proposed a wormhole hypothesis of matter in connection with mass analysis of
electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
energy; however, he did not use the term "wormhole" (he spoke of "one-dimensional tubes" instead).
["Hermann Weyl"]
entry in the ''Stanford Encyclopedia of Philosophy
The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...
''.
American
theoretical physicist
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 experimen ...
John Archibald Wheeler
John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in e ...
(inspired by Weyl's work)
[ coined the term "wormhole" in a 1957 paper co-authored by ]Charles Misner
Charles W. Misner (; born June 13, 1932) is an American physicist and one of the authors of '' Gravitation''. His specialties include general relativity and cosmology. His work has also provided early foundations for studies of quantum gravity ...
:
Modern definitions
Wormholes have been defined both ''geometrically'' and ''topologically''. From a topological point of view, an intra-universe wormhole (a wormhole between two points in the same universe) is a compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
region of spacetime whose boundary is topologically trivial, but whose interior is not simply connected
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the spac ...
. Formalizing this idea leads to definitions such as the following, taken from Matt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington, in New Zealand.
Work
Visser's research interests include general relativity, quantum field theory and cosmology.
Visser has produced a large number of research papers ...
's ''Lorentzian Wormholes'' (1996).
Geometrically, wormholes can be described as regions of spacetime that constrain the incremental deformation of closed surfaces. For example, in Enrico Rodrigo's ''The Physics of Stargates, ''a wormhole is defined informally as:
Development
Schwarzschild wormholes
The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
describing an ''eternal black hole'', but it was found that it would collapse too quickly for anything to cross from one end to the other. Wormholes that could be crossed in both directions, known as traversable wormholes, were thought to be possible only if exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical particl ...
with negative energy
Negative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects.
Gravitational potential energy
Gravitational potential energy can be defined as being ne ...
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
could be used to stabilize them. However, physicists later reported that microscopic traversable wormholes may be possible and not require any exotic matter, instead requiring only electrically charged
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
ic matter with small enough mass that it cannot collapse into a charged black hole
A charged black hole is a black hole that possesses electric charge. Since the electromagnetic repulsion in compressing an electrically charged mass is dramatically greater than the gravitational attraction (by about 40 orders of magnitude), it is ...
. While such wormholes, if possible, may be limited to transfers of information, humanly traversable wormholes may exist if reality can broadly be described by the Randall–Sundrum model 2, a brane
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime accordin ...
-based theory consistent with string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
.
Einstein–Rosen bridges
Schwarzschild wormholes, also known as ''Einstein–Rosen bridges''[Vladimir Dobrev (ed.), ''Lie Theory and Its Applications in Physics: Varna, Bulgaria, June 2015'', Springer, 2016, p. 246.] (named after Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
and Nathan Rosen
Nathan Rosen (Hebrew: נתן רוזן; March 22, 1909 – December 18, 1995) was an American-Israeli physicist noted for his study on the structure of the hydrogen atom and his work with Albert Einstein and Boris Podolsky on entangled wave functio ...
),[ are connections between areas of space that can be modeled as ]vacuum solution
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non ...
s to the Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
, and that are now understood to be intrinsic parts of the maximally extended version of the Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that 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 differen ...
should not have any "edges": it should be possible to continue this path arbitrarily far into the particle's future or past for any possible trajectory of a free-falling particle (following a geodesic
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
in the spacetime).
In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
from the outside, there must be a separate white hole
In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy-matter, light and information can escape from it. In this sense, it is the reverse of a black ho ...
interior region that allows us to extrapolate the trajectories of particles that an outside observer sees rising up ''away'' from the event horizon. And just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates
In general relativity, Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetim ...
.
In this spacetime, it is possible to come up with coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
s such that if a hypersurface
In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidean ...
of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like
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 differen ...
separation, giving what is called a 'space-like surface') is picked and an "embedding diagram" drawn depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein–Rosen bridge". Note that the Schwarzschild metric describes an idealized black hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's geography, it removes the part of the diagram corresponding to the white hole interior region, along with the part of the diagram corresponding to the other universe.
The Einstein–Rosen bridge was discovered by Ludwig Flamm
Ludwig Flamm (29 January 1885 - 4 December 1964) was an Austrian physicist.
Biography
Ludwig Flamm, who came from a family of watchmakers, studied physics at the University of Vienna. In 1916 he was awarded the ''pro venia legendi'' at the T ...
in 1916, a few months after Schwarzschild published his solution, and was rediscovered by Albert Einstein and his colleague Nathan Rosen, who published their result in 1935.[A. Einstein and N. Rosen, "The Particle Problem in the General Theory of Relativity," ''Phys. Rev.'' 48(73) (1935).] However, in 1962, John Archibald Wheeler
John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in e ...
and Robert W. Fuller
Robert Works Fuller (born 1936) is an American physicist, author, social reformer, and former president of Oberlin College.
Biography
Robert Fuller attended Oberlin College, leaving without graduating in order to earn his Ph.D. in physics at ...
published a paper showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region.
According to general relativity, the gravitational collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formatio ...
of a sufficiently compact mass forms a singular Schwarzschild black hole. In the Einstein–Cartan–Sciama–Kibble theory of gravity, however, it forms a regular Einstein–Rosen bridge. This theory extends general relativity by removing a constraint of the symmetry of the affine connection
In differential geometry, an affine connection is a geometric object on a smooth manifold which ''connects'' nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values i ...
and regarding its antisymmetric part, the torsion tensor
In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet–Serret formulas, for instance, quantifies the twist of a curve ...
, as a dynamic variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
) of matter. The minimal coupling between torsion and Dirac spinor
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solution to the Dirac equation, and is a certain combin ...
s generates a repulsive spin–spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity. Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.
Although Schwarzschild wormholes are not traversable in both directions, their existence inspired Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
to imagine traversable wormholes created by holding the "throat" of a Schwarzschild wormhole open with exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical particl ...
(material that has negative mass/energy).
Other non-traversable wormholes include ''Lorentzian wormholes'' (first proposed by John Archibald Wheeler in 1957), wormholes creating a spacetime foam
Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroye ...
in a general relativistic spacetime manifold depicted by a Lorentzian manifold
In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the r ...
, and ''Euclidean wormholes'' (named after Euclidean manifold, a structure of Riemannian manifold
In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real manifold, real, smooth manifold ''M'' equipped with a positive-definite Inner product space, inner product ...
).
Traversable wormholes
The Casimir effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pr ...
shows that quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
allows the energy density in certain regions of space to be negative relative to the ordinary matter vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experimental ...
, and it has been shown theoretically that quantum field theory allows states where energy can be ''arbitrarily'' negative at a given point. Many physicists, such as Stephen Hawking, Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
, and others, argued that such effects might make it possible to stabilize a traversable wormhole.The only known natural process that is theoretically predicted to form a wormhole in the context of general relativity and quantum mechanics was put forth by Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...
in his ER = EPR
ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole (or Einstein–Rosen bridge) and is thought by some to be a basis for unifying general rela ...
conjecture. The quantum foam
Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroye ...
hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the Planck scale, and stable versions of such wormholes have been suggested as dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...
candidates. It has also been proposed that, if a tiny wormhole held open by a negative mass
In theoretical physics, negative mass is a type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg. Such matter would violate one or more energy conditions and show some strange properties such as the ...
cosmic string
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simp ...
had appeared around the time of the 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 ...
, it could have been inflated to macroscopic
The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic.
Overview
When applied to physical phenomena an ...
size by cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
.
Lorentzian traversable wormholes would allow travel in both directions from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. The possibility of traversable wormholes in general relativity was first demonstrated in a 1973 paper by Homer Ellis[
] and independently in a 1973 paper by K. A. Bronnikov.[
] Ellis analyzed the topology and the geodesic
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
s of the Ellis drainhole
The Ellis drainhole is the earliest-known complete mathematical model of a traversable wormhole. It is a static, spherically symmetric solution of the Einstein vacuum field equations augmented by inclusion of a scalar field \phi minimally coupled ...
, showing it to be geodesically complete, horizonless, singularity-free, and fully traversable in both directions. The drainhole is a solution manifold of Einstein's field equations for a vacuum spacetime, modified by inclusion of a scalar field minimally coupled to the Ricci tensor
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure ...
with antiorthodox polarity (negative instead of positive). (Ellis specifically rejected referring to the scalar field as 'exotic' because of the antiorthodox coupling, finding arguments for doing so unpersuasive.) The solution depends on two parameters: , which fixes the strength of its gravitational field, and , which determines the curvature of its spatial cross sections. When is set equal to 0, the drainhole's gravitational field vanishes. What is left is the Ellis wormhole
The Ellis wormhole is the special case of the Ellis drainhole in which the 'ether' is not flowing and there is no gravity. What remains is a pure traversable wormhole comprising a pair of identical twin, nonflat, three-dimensional regions joined ...
, a nongravitating, purely geometric, traversable wormhole.
Kip Thorne
Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Fey ...
and his graduate student Mike Morris, unaware of the 1973 papers by Ellis and Bronnikov, manufactured, and in 1988 published, a duplicate of the Ellis wormhole for use as a tool for teaching general relativity. For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical particl ...
, was from 1988 to 2015 referred to in the literature as a ''Morris–Thorne wormhole''.
Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington, in New Zealand.
Work
Visser's research interests include general relativity, quantum field theory and cosmology.
Visser has produced a large number of research papers ...
, in which a path through the wormhole can be made where the traversing path does not pass through a region of exotic matter. However, in the pure Gauss–Bonnet gravity
In general relativity, Gauss–Bonnet gravity, also referred to as Einstein–Gauss–Bonnet gravity, is a modification of the Einstein–Hilbert action to include the Gauss–Bonnet term (named after Carl Friedrich Gauss and Pierre Ossian Bonne ...
(a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology
Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory.
Brane and bulk
The central idea is that the visible, three-dimensional universe is restricted to a brane i ...
) exotic matter is not needed in order for wormholes to exist—they can exist even with no matter. A type held open by negative mass cosmic string
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simp ...
s was put forth by Visser in collaboration with Cramer Cramer may refer to:
Businesses
* Cramer brothers, 18th century publishers
* Cramer Systems, a software company
* Cramer & Co., a former musical-related business in London
Other uses
* Cramer (surname), including a list of people and fictional ...
''et al.'', in which it was proposed that such wormholes could have been naturally created in the early universe.
Wormholes connect two points in spacetime, which means that they would in principle allow travel in time, as well as in space. In 1988, Morris, Thorne and Yurtsever worked out how to convert a wormhole traversing space into one traversing time by accelerating one of its two mouths. However, according to general relativity, it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time "machine". Until this time it could not have been noticed or have been used.
Raychaudhuri's theorem and exotic matter
To see why exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical particl ...
is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side. The expansion
Expansion may refer to:
Arts, entertainment and media
* ''L'Expansion'', a French monthly business magazine
* ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004
* ''Expansions'' (McCoy Tyner album), 1970
* ''Expansio ...
goes from negative to positive. As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck. According to the optical Raychaudhuri's theorem
In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter.
The equation is important as a fundamental lemma for the Penrose–Hawking singularity the ...
, this requires a violation of the averaged null energy condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathema ...
. Quantum effects such as the Casimir effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pr ...
cannot violate the averaged null energy condition in any neighborhood of space with zero curvature, but calculations in semiclassical gravity
Semiclassical gravity is the approximation to the theory of quantum gravity in which one treats matter fields as being quantum and the gravitational field as being classical.
In semiclassical gravity, matter is represented by quantum matter field ...
suggest that quantum effects may be able to violate this condition in curved spacetime. Although it was hoped recently that quantum effects could not violate an achronal version of the averaged null energy condition, violations have nevertheless been found, so it remains an open possibility that quantum effects might be used to support a wormhole.
Modified general relativity
In some hypotheses where general relativity is modified, it is possible to have a wormhole that does not collapse without having to resort to exotic matter. For example, this is possible with R gravity, a form of () gravity.
Faster-than-light travel
The impossibility of faster-than-light relative speed applies only locally. Wormholes might allow effective superluminal (faster-than-light
Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with zero ...
) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole whose length is shorter than the distance between them ''outside'' the wormhole, the time taken to traverse it could be less than the time it would take a light beam to make the journey if it took a path through the space ''outside'' the wormhole. However, a light beam traveling through the same wormhole would beat the traveler.
Time travel
If traversable wormholes exist, they might allow time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
. A proposed time-travel machine using a traversable wormhole might hypothetically work in the following way: One end of the wormhole is accelerated to some significant fraction of the speed of light, perhaps with some advanced propulsion system
Propulsion is the generation of force by any combination of pushing or pulling to modify the translational motion of an object, which is typically a rigid body (or an articulated rigid body) but may also concern a fluid. The term is derived fro ...
, and then brought back to the point of origin. Alternatively, another way is to take one entrance of the wormhole and move it to within the gravitational field of an object that has higher gravity than the other entrance, and then return it to a position near the other entrance. For both these methods, time dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
causes the end of the wormhole that has been moved to have aged less, or become "younger", than the stationary end as seen by an external observer; however, time connects differently ''through'' the wormhole than ''outside'' it, so that synchronized clocks at either end of the wormhole will always remain synchronized as seen by an observer passing through the wormhole, no matter how the two ends move around. This means that an observer entering the "younger" end would exit the "older" end at a time when it was the same age as the "younger" end, effectively going back in time as seen by an observer from the outside. One significant limitation of such a time machine is that it is only possible to go as far back in time as the initial creation of the machine; it is more of a path through time rather than it is a device that itself moves through time, and it would not allow the technology itself to be moved backward in time.
According to current theories on the nature of wormholes, construction of a traversable wormhole would require the existence of a substance with negative energy, often referred to as "exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical particl ...
". More technically, the wormhole spacetime requires a distribution of energy that violates various energy condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathe ...
s, such as the null energy condition along with the weak, strong, and dominant energy conditions. However, it is known that quantum effects can lead to small measurable violations of the null energy condition, and many physicists believe that the required negative energy may actually be possible due to the Casimir effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pr ...
in quantum physics. Although early calculations suggested a very large amount of negative energy would be required, later calculations showed that the amount of negative energy can be made arbitrarily small.
In 1993, Matt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington, in New Zealand.
Work
Visser's research interests include general relativity, quantum field theory and cosmology.
Visser has produced a large number of research papers ...
argued that the two mouths of a wormhole with such an induced clock difference could not be brought together without inducing quantum field and gravitational effects that would either make the wormhole collapse or the two mouths repel each other, or otherwise prevent information from passing through the wormhole. Because of this, the two mouths could not be brought close enough for causality
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
violation to take place. However, in a 1997 paper, Visser hypothesized that a complex "Roman ring
In general relativity, a Roman ring (proposed by Matt Visser in 1997 and named after the Roman arch, a concept proposed by Mike Morris and Kip Thorne in 1988 and named after physicist Tom Roman) is a configuration of wormholes where no subset of ...
" (named after Tom Roman) configuration of an N number of wormholes arranged in a symmetric polygon could still act as a time machine, although he concludes that this is more likely a flaw in classical quantum gravity theory rather than proof that causality violation is possible.
Interuniversal travel
A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the many-worlds interpretation
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum me ...
of quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
.
In 1991 David Deutsch
David Elieser Deutsch ( ; born 18 May 1953) is a British physicist at the University of Oxford. He is a Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation (CQC) in the Clarendon Laboratory of ...
showed that quantum theory is fully consistent (in the sense that the so-called density matrix
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using ...
can be made free of discontinuities) in spacetimes with closed timelike curves. However, later it was shown that such a model of closed timelike curves can have internal inconsistencies as it will lead to strange phenomena like distinguishing non-orthogonal quantum states and distinguishing proper and improper mixture. Accordingly, the destructive positive feedback loop of virtual particles circulating through a wormhole time machine, a result indicated by semi-classical calculations, is averted. A particle returning from the future does not return to its universe of origination but to a parallel universe. This suggests that a wormhole time machine with an exceedingly short time jump is a theoretical bridge between contemporaneous parallel universes.
Because a wormhole time-machine introduces a type of nonlinearity into quantum theory, this sort of communication between parallel universes is consistent with Joseph Polchinski
Joseph Gerard Polchinski Jr. (; May 16, 1954 – February 2, 2018) was an American theoretical physicist and string theorist.
Biography
Polchinski was born in White Plains, New York, the elder of two children to Joseph Gerard Polchinski Sr. (1929 ...
's proposal of an Everett phone (named after Hugh Everett
Hugh Everett III (; November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation. In contrast to the then-dominant Cope ...
) in Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
's formulation of nonlinear quantum mechanics.
The possibility of communication between parallel universes has been dubbed interuniversal travel.
Wormhole can also be depicted in Penrose diagram
In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity. It is an ext ...
of Schwarzschild black hole
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
. In the Penrose diagram, an object traveling faster than light will cross the black hole and will emerge from another end into a different space, time or universe. This will be an interuniversal wormhole.
Metrics
Theories of ''wormhole metrics'' describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathema ...
is the following:
first presented by Ellis (see Ellis wormhole
The Ellis wormhole is the special case of the Ellis drainhole in which the 'ether' is not flowing and there is no gravity. What remains is a pure traversable wormhole comprising a pair of identical twin, nonflat, three-dimensional regions joined ...
) as a special case of the Ellis drainhole
The Ellis drainhole is the earliest-known complete mathematical model of a traversable wormhole. It is a static, spherically symmetric solution of the Einstein vacuum field equations augmented by inclusion of a scalar field \phi minimally coupled ...
.
One type of non-traversable wormhole metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathema ...
is the Schwarzschild solution
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
(see the first diagram):
The original Einstein–Rosen bridge was described in an article published in July 1935.
For the Schwarzschild spherically symmetric static solution
where is the proper time and .
If one replaces with according to
For the combined field, gravity and electricity, Einstein and Rosen derived the following Schwarzschild static spherically symmetric solution
where is the electric charge.
The field equations without denominators in the case when can be written
In order to eliminate singularities, if one replaces by according to the equation:
and with one obtains
In fiction
Wormholes are a common element in science fiction
Science fiction (sometimes shortened to Sci-Fi or SF) is a genre of speculative fiction which typically deals with imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, parallel unive ...
because they allow interstellar, intergalactic, and sometimes even interuniversal travel within human lifetime scales. In fiction, wormholes have also served as a method for time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
.
See also
* Alcubierre drive
The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable ...
* ER=EPR
ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole (or Einstein–Rosen bridge) and is thought by some to be a basis for unifying general rela ...
* Gödel metric
The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous di ...
* Krasnikov tube
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive (and like them requires exotic ...
* Non-orientable wormhole
In wormhole theory, a non-orientable wormhole is a wormhole connection that appears to reverse the chirality of anything passed through it. It is related to the "twisted" connections normally used to construct a Möbius strip or Klein bottle.
In ...
* Self-consistency principle
* Polchinski's paradox
Joseph Gerard Polchinski Jr. (; May 16, 1954 – February 2, 2018) was an American theoretical physicist and string theorist.
Biography
Polchinski was born in White Plains, New York, the elder of two children to Joseph Gerard Polchinski Sr. (1929 ...
* Retrocausality
Retrocausality, or backwards causation, is a concept of cause and effect in which an effect precedes its cause in time and so a later event affects an earlier one. In quantum physics, the distinction between cause and effect is not made at the mos ...
* Ring singularity
A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring.
Description of a ring singularity
When a spherical non-rotating body of a critical radius collapses und ...
* Roman ring
In general relativity, a Roman ring (proposed by Matt Visser in 1997 and named after the Roman arch, a concept proposed by Mike Morris and Kip Thorne in 1988 and named after physicist Tom Roman) is a configuration of wormholes where no subset of ...
Notes
References
Citations
Sources
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* An excellent and more concise review.
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External links
"What exactly is a 'wormhole'? Have wormholes been proven to exist or are they still theoretical??"
answered by Richard F. Holman, William A. Hiscock and Matt Visser
"Why wormholes?"
by Matt Visser (October 1996)
*
A comprehensive wormhole FAQ by Enrico Rodrigo
heory on how the collider could create a small wormhole, possibly allowing time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
into the past
animation that simulates traversing a wormhole
Renderings and animations of a Morris-Thorne wormhole
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Albert Einstein
Astronomical hypotheses
Black holes
Conjectures
Connection (mathematics)
Exotic matter
Faster-than-light travel
General relativity
Gravity
Hypothetical astronomical objects
Lorentzian manifolds
Space
Theory of relativity
Time travel