A wormhole is a speculative structure linking separate points in spacetime and is based on a solution of the Einstein field equations.

## A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime.

More precisely it is a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in Anti-de Sitter space.

Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.

A wormhole could connect extremely long distances such as a billion light-years or more, short distances such as a few meters, different universes, or different points in time.

### Visualization

For a simplified notion of a wormhole, space can be visualized as a two-dimensional (2D) 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), 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, the entry and exit points could be visualized as spheres in 3D space.

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, and the two points represent a distance to be traveled, however theoretically a wormhole could connect these two points by folding that plane so the points are touching. In this way, it would be much easier to traverse the distance since the two points are now touching.

### Schwarzschild wormholes

The equations of the theory of general relativity have valid solutions that contain wormholes.

The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the Schwarzschild metric 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, would only be possible if exotic matter with negative energy density could be used to stabilize them.

### Traversable wormholes

This Casimir effect shows that quantum field theory allows the energy density in certain regions of space to be negative relative to the ordinary matter vacuum energy, 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, and others, therefore argue that such effects might make it possible to stabilize a traversable wormhole.

Physicists have not found any natural process that would be predicted to form a wormhole naturally in the context of general relativity, although the quantum foam 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 candidates.

It has also been proposed that, if a tiny wormhole held open by a negative mass cosmic string had appeared around the time of the Big Bang, it could have been inflated to macroscopic size by cosmic inflation.

### Raychaudhuri’s theorem and exotic matter

To see why exotic matter is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side.

The expansion 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, this requires a violation of the averaged null energy condition.

Quantum effects such as the Casimir effect cannot violate the averaged null energy condition in any neighborhood of space with zero curvature, but calculations in semiclassical gravity 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.

### Time travel

If traversable wormholes exist, they could allow time travel.

A proposed time-travel machine using a traversable wormhole would 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, 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 of these methods, time dilation 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“.

More technically, the wormhole spacetime requires a distribution of energy that violates various energy conditions, 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 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.

### Interuniversal travel

A possible resolution to the paradoxes resulting from wormhole-enabled time travel rests on the many-worlds interpretation of quantum mechanics.

In 1991 David Deutsch showed that quantum theory is fully consistent (in the sense that the so-called density matrix can be made free of discontinuities) in spacetimes with closed timelike curves.

However, later it was shown that such a model of the closed timelike curve 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’s proposal of an Everett phone (named after Hugh Everett) in Steven Weinberg’s formulation of nonlinear quantum mechanics.

The possibility of communication between parallel universes has been dubbed interuniversal travel.

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