Mechanics of wormhole
Introduction-
The basic notion of an intra universe wormhole is that it is a compact region of space time whose boundary is topologically trivial but whose interior is not simply connected. A wormhole or Einstein–Rosen bridge is a hypothetical topological feature that would fundamentally be a shortcut connecting two separate points in space time.
Characterizing inter universe wormholes is more difficult. For example, one can imagine a ‘baby’ universe connected to its ‘parent’ by a narrow ‘umbilici. One might like to regard the umbilicus as the throat of a wormhole, but the space time is simply connected.
Albert Einstein and his colleague Nathan Rosen in 1953 discovered a solution that Schwarzschild wormholes are bridges between areas of space that can be modeled vacuum solution to the Einstein field equation by combining models of a black hole and a white hole. 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
While Schwarzschild wormholes are not traversable, their existence inspired kip throne to imagine traversable wormholes created by holding the ‘throat’ of Schwarzschild wormhole open with exotic matter (material that has negative mass/energy). Researchers have no observational evidence for wormholes, but the equations of the theory of general relativity have valid solutions that contain wormholes.
The American theoretical physicist John Archibald Wheeler coined the term wormhole in 1957; the German mathematician Hermann Weyl, however, had proposed the wormhole theory in 1921, in connection with mass analysis of electromagnetic field energy.[12]
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".
In above paragraphs you read that many researches happened on wormhole and many hypothesis were formed I also done research on wormholes that you study below. In this research we start from the beginning means what is wormhole and in the end I explain you how to use them for teleportation and time travel.
What is wormhole?
All of us know wormhole connect two parts of universe together and act like teleport able tunnel which create a shortcut between space times but this is not true (you will read more in another section). A wormhole is as like simple tunnel which connect two parts of universe through the inter galactic gap. A wormhole is much like a tunnel with two ends, each at separate points in space 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 rose 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.
To know about inter galactic gap see the diagram
Journey through it-
We think that wormhole make journey short between two universes short but this is not true it connect two parts at equal distance in which they are in universe. The impossibility of faster-than-light relative speed only applies locally. Wormholes might allow effective superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, superluminal (slower-than-light) speeds are used. If two points are connected by a wormhole whose length is equal to 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 wormhole would of course beat the traveler.
But we travel faster because it pass through inter galactic gap which is stable (not moving constantly like cosmos) so inside a wormhole we have no effect of time on us and also inside there is not a single force exerting on us means it is completely open not even a single force exerting on us so we travel ∞ time faster than light means we complete a journey (inside wormhole) in just a quantum second. When we come out wormhole we enter in a universe which is constantly moving and again connect to same time where we left the universe in simple see the diagram,
Note: wormhole cannot open in inter cosmos
The diagram shown is only of one universe
So inside a wormhole we see following effect-
No effect of time on us
No force exerting on us
No speed limitation
We travel ∞ times faster than light (based on power of our engine)
After getting outside a wormhole it is illusion that we think that we teleported but we travel the same distance.
See the diagram,
Also wormholes are not stable so they need continuous energy to stay open and if they close and the traveler is inside it so the traveler will never come back in the universe.
Wormhole tunnel-
A wormhole is not act like tunnel as like black hole or super massive tunnel because it cannot generate energy more than or equal to inter cosmic force. So when wormhole open it exert combine energy with cosmic plate means more the force on parallel plate and from the third law of Newton parallel cosmos also exert equal and opposite force to create equilibrium and as wormhole is a tunnel so it bend towards right. Don’t forget that wormhole tunnel is in inter galactic gap so inter galactic gap also exerts force on them
(which is a reason of collapsing a wormhole faster than light) which collapse them so wormhole need continuous energy supply of exotic matter which help wormhole to exert equal force to stay open. Also due to these extreme forces the space inside wormhole gets smaller. For simple explanation see the diagram below,
Or for 2D explanation see the diagram below,
How wormholes open naturally?
A wormhole cannot generate energy more than inter cosmic force but it generates energy not so far from inter cosmic constant means it generate energy between 1.74382×1021 but not equal to inter cosmic constant.
A wormhole open when energy of certain object at any place reaches to or above 1.74382×1021(if more than or equal to 6.3×1082it will become black hole). Take an example of a star (which explode) they are heavily massed so when they explode the energy level reach above1.74382×1021 so they turn into wormhole. These wormhole collapses quickly and not even allow light to successfully pass through them but they left electromagnetic radiation behind. These electromagnetic radiations start their journey to infinity. If we detect these radiation so we find weak areas in space time but we never reach to them when they are weak due some reasons-
The weak areas get cure a soon as light pass through them
Due to speed limitation we can’t reach to them because these area collapse faster than light.
So we came to conclusion that naturally formed wormhole is not for time traveling and teleportation.
How to supply energy to wormhole?
To prevent wormhole from collapsing and stay open it need continuous energy supply of exotic matter so we need help of Casmir effect see the diagrams below,
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. Wormholes are also a very powerful mathematical metaphor for teaching general relativity.
The Casimir effect shows that quantum field theory allows the energy density in certain regions of space to be negative relative to the ordinary 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.
So from this negative energy fields we travel through the wormhole completely and it cannot collapse in half.
Coordinate setting-
To find the coordinate of mouth of wormhole use the given formula below,
Ec+nm-nm+E△E
Here Ec= combine energy of a wormhole
nm= Inter cosmic force
△E= Energy applied by inter cosmic force
E= Energy of wormhole
So the answer is the light year value from the origin of opening.
Now some important points,
E=∆E
Here E is for energy of wormhole and ∆E is for the force applied by inter galactic gap
l=∆l
Here l is for length between two points in space time and ∆l is length between two points inside wormhole tunnel.
Time travel using wormhole-
(Theory of cosmic equivalence)
The viral method of time travel is to traveling from speed of light but there is also another method use of cosmic equivalence. In this method both the cosmos is inters locked together and move under our control to travel in past and future. This work is simply done by two wormholes. If two wormholes put in front of each other they apply force on each other which lock two cosmos together with force equal to inter cosmic force. Through this if one of the wormholes is move to any of the direction our cosmos also move with that wormhole thus the same effect like time traveling. (For detail information see below)
For simple explanation see the diagram:-
The whole energy by two wormholes is given by,
E=Ec+nm-nm+E△E+Ec+nm-nm+E△E
This energy is more than intercosmic force so the equilibrium of certain place gets affected. Another wormhole is act like negative density tunnel (a tunnel with negative energy wall) because of Casmir effect between the two wormhole and combine with parallel cosmos due to negative energy density and the 1st wormhole still connect with our cosmos create an equilibrium which cure the shape of inter galactic gap. Now if we move the wormhole which is connected to our cosmos (positive energy density) so change the cosmic time which affect our time so we travel in future. If we move the wormhole with negative energy density so it again affect the cosmic time but in opposite side so we travel in past or see the diagram below,
We can move one wormhole by attracting it by opposite energy density matter.
This time traveling event will last longer till the Casmir effect of both wormholes if we want to make it forever so we need to generate Casmir effect in both the wormhole continuously so they work perfectly (means stay connected with cosmic plates).
Challenge to today’s Physics-
Schwarzschild wormholes
An artist's impression of a wormhole from an observer's perspective, crossing the event horizon of a Schwarzschild wormhole that bridges two different universes. The observer originates from the right, and another universe becomes visible in the center of the wormhole’s shadow once the horizon is crossed, the observer seeing light that has fallen into the black hole interior region from the other universe; however, this other universe is unreachable in the case of a Schwarzschild wormhole, as the bridge always collapses before the observer has time to cross it, and everything that has fallen through the event horizon of either universe is inevitably crushed in the singularity.
Lorentzian wormholes known as Schwarzschild wormholes or Einstein–Rosen bridges are connections between areas of space that can be modeled as vacuum solutions to the Einstein field equations, and that are now understood to be intrinsic parts of the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation. Here, "maximally extended" refers to the idea that the space-time 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 the spacetime), unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. 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 from the outside, there must be a separate white hole 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 this spacetime, it is possible to come up with coordinate systems such that if you pick a hyper surface 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 separation, giving what is called a 'space-like surface') and draw an "embedding diagram" 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 history, 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.[13]
The Einstein–Rosen bridge was discovered by Ludwig Flamm[14] in 1916, a few months after Schwarzschild published his solution, and was rediscovered (although it is hard to imagine that Einstein had not seen Flamm's paper when it came out) by Albert Einstein and his colleague Nathan Rosen, who published their result in 1935. However, in 1962, John A. Wheeler and Robert W. Fuller 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 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 and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin) of matter. The minimal coupling between torsion and Dirac spinors 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.
Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.
Although Schwarzschild wormholes are not traversable in both directions, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the "throat" of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).
Traversable wormholes
Image of a simulated traversable wormhole that connects the square in front of the physical institutes of University of Tubingen with the sand dunes near Boulogne sur Mer in the north of France. The image is calculated with 4D ray tracing in a Morris–Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.[17]
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 by Kip Thorne and his graduate student Mike Morris in a 1988 paper. For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is referred to 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, 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 (a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology) 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 strings was put forth by Visser in collaboration with Cramer 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 explicitly how to convert a wormhole traversing space into one traversing time. 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 by accelerating one of its two mouths.
Time travel-
The theory of general relativity predicts that if traversable wormholes exist, can also alter the speed of time. They could allow time travel. This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.
For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2004 while the stationary mouth's clock read 2012. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2004, in the same region but now eight years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve. An object traveling through a wormhole could carry energy or charge from one time to another, but this would not violate conservation of energy or charge in each time, because the energy/charge of the wormhole mouth itself would change to compensate for the object that fell into it or emerged from it.
It is thought that it may not be possible to convert a wormhole into a time machine in this manner; the predictions are made in the context of general relativity, but general relativity does not include quantum effects. Analyses using the semiclassical approach to incorporating quantum effects into general relativity have sometimes indicated that a feedback loop of virtual particles would circulate through the wormhole and pile up on themselves, driving the energy density in the region very high and possibly destroying it before any information could be passed through it, in keeping with the chronology protection conjecture. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps, and a more technical discussion can be found in The quantum physics of chronology protection by Matt Visser.[27] There is also the Roman ring, which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.
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 model of 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 discovery of an "Everett phone" in Steven Weinberg’s formulation of nonlinear quantum mechanics. Such a possibility is depicted in the science-fiction 2014 movie Interstellar.
Summary-
A wormhole is as like simple tunnel which connect two parts of universe through the inter galactic gap.
Wormhole connects two parts at equal distance in which they are in universe it is not a teleport able tunnel.
Inside wormhole we travel ∞ time faster than light.
A wormhole cannot generate energy more than inter cosmic force.
A wormhole open when energy of certain object at any place reaches to or above 3.1×1041(if more than or equal to 6.3×1082it will become black hole).
Wormholes collapses quickly and not even allow light to successfully pass through them but they left electromagnetic radiation behind.
To prevent wormhole from collapsing and stay open it need continuous energy supply of exotic matter.
Some important equation,
E=∆E
Here E is for energy of wormhole and ∆E is for the force applied by inter galactic gap
l=∆l
Here l is for length between two points in space time and ∆l is length between two points inside wormhole tunnel.
