Wormhole

A wormhole (or Einstein–Rosen bridge) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime (i.e., different locations or different points of time). 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.This analysis forces one to consider situations ... where there is a net flux of lines of force, through what topologists would call 'a handle' of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming a 'wormhole'.If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form ∂Σ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intrauniverse wormhole.a region of spacetime containing a 'world tube' (the time evolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line (the time evolution of a point).The four-dimensional space is described mathematically by two congruent parts or 'sheets', corresponding to u > 0 {displaystyle u>0} and u < 0 {displaystyle u<0} , which are joined by a hyperplane r = 2 m {displaystyle r=2m} or u = 0 {displaystyle u=0} in which g {displaystyle g} vanishes. We call such a connection between the two sheets a 'bridge'.The solution is free from singularities for all finite points in the space of the two sheets A wormhole (or Einstein–Rosen bridge) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime (i.e., different locations or different points of time). 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. Many scientists postulate wormholes are merely a projection of the 5th dimension, analogous to how a 2D being could only experience part of a 3D object. 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. 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. In 1928, Hermann Weyl proposed a wormhole hypothesis of matter in connection with mass analysis of electromagnetic field energy; however, he did not use the term 'wormhole' (he spoke of 'one-dimensional tubes' instead). American theoretical physicist John Archibald Wheeler (inspired by Weyl's work) coined the term 'wormhole' in a 1957 paper co-authored by Charles Misner: 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 region of spacetime whose boundary is topologically trivial, but whose interior is not simply connected. Formalizing this idea leads to definitions such as the following, taken from Matt Visser'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: