Do wormholes really exist? we can see most of the science fiction stories, movies, and television serials use the concept of wormholes. Do wormholes really exist in this universe? I'm curious about it.
And also, what are the types of wormholes?
 A: There are considerable theoretical objections to the formation of a wormhole by any process of gravitational collapse. Such a process requires that the topology of the universe change, which is sort of like cutting or gluing spacetime. General relativity loses its predictive power in these situations. That doesn't mean that it can't happen, but it does mean that we would need some other theory of physics to describe it. Many such scenarios also require exotic matter of types that don't actually seem to exist in our universe. These issues are summarized in theorems on topology change by Geroch and Tipler.
Empirically, we do see objects that act like black holes in our universe, including very impressive agreement with theory for black hole mergers are observed in gravitational wave astronomy. This lends support to the theoretical arguments that runaway gravitational collapse produces black holes, not other exotic objects such as naked singularities or wormholes.
The theoretical arguments are classical, so they don't prevent topology change at the microscopic scale in the early universe, where quantum mechanics comes into play. We don't have a theory of quantum gravity, so we don't know. It's conceivable that there are relic microscopic wormholes in our universe right now.
A wormhole can't be traversible without exotic matter inside it. Therefore if there are wormholes in our universe, they probably aren't traversible.
A: Short answer: Nobody knows.
Longer one =>

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*Theoreticians have constructed a "traversable wormhole", a wormhole which does not need a negative energy for being stable. Wormhole sides are quantum mechanically connected, like in quantum teleportation. So at least, physicality of wormholes is now one step-closer for us.


*Scientists are actively inventing methods for wormhole detection. This wormhole detection method is based on the fact that wormhole could induce subtle star -near wormhole throat- orbit perturbations in some way. This method talks that a wormhole will induce a phase modulation in an electromagnetic field passing-by, which can be detected by laser interferometers. But this is of course a very challenging project, due to noise and elimination of unnecessary gravitational waves effect. Scope is bigger than a LIGO project. But it is viable.


*I'm not a theoretical physicist, but as I've heard, from theoretical physics perspective a wormhole is very hardly distinguishable from a black-hole. So IF wormhole(s) do exists, then we aren't sure anymore - Is there a black-hole or a wormhole in our Milky Way galaxy center?


*And finally, it depends on how we define what is "a wormhole". If, for example I would define a wormhole as "A quantum channel where quantum information can be teleported from one end to the other" (albeit no faster than light-speed transport is permitted here). Then, such quantum-mechanical wormholes are already proven to exist and tested. For example, here quantum information was teleported over 143 km distance.
A: General relativity asserts that certain configurations of spacetime, called wormholes, will satisfy the equations that govern spacetime and this is why they are part of mainstream physics. However, there are two qualifying observations:

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*If at some time there are no wormholes anywhere, then it seems that none can form by any physical process of a type which could in principle be described by classical as opposed to quantum physics. I say "seems" here because this has not been proved in complete generality but it is certainly true in all configurations that one can reasonably expect to come about by natural processes.


*The mere existence of a wormhole does not necessarily imply that travel through the wormhole is possible, because of stability considerations (and some kinds of wormhole are not timelike anyway). The stability problem is of two kinds: the impact on the traveler of other stuff such as light passing into the wormhole, and the fact that their very presence (their mass) may cause the spacetime to distort in such a way as to seal the wormhole.
At the moment it is hard, therefore, to assert with any confidence that there really could be a traversable wormhole somewhere.
However one should add that when we bring in quantum physics then the range of possibilities becomes a lot richer. It seems now that one ought not to discount the possibility of wormholes, at least at microscopic scales, which is another way of saying that the structure of spacetime may be very complicated at the Planck scale. However this is not the kind of thing that ordinary people mean when they think about wormholes in science fiction scenarios.
A: Wormholes presently is a theoretical hypothesis which arises from general relativity. To this date, there is no concrete observational data or experimental evidence in support for existence of wormholes. Wormhole is like bridge in fabric of spacetime which connects two distant regions.
There are different types of hypothetical and thought wormholes like:
Einstein-Rosen Bridge, which describes that blackhole in our universe is connected to a parallel universe in which there is white-hole which spews everything out which fell in blackhole
String-Theory based wormholes, which describe that if string theory is correct description of our universe, then there are already natural wormholes kept open bycosmic strings, waiting to be discovered.
Man-made/Artificial wormholes, which could be made by humans. One possible way could be by creating exotic matter, which has negative gravitational mass, so it could repel things, and keep wormholes open.
These theories and ideas are indeed very wild which however are still unproven or unaccpeted to this date.
There are very strong statements in against existence of wormholes. Many physicists say that opening and traversing a wormhole could break several physics laws.
First and foremost is that object traversing the wormhole in fact could travel faster than light which is not possible according to special theory of relativity. It could also create time travel paradoxes, or break casual structure of universe.  So, existence of wormhole looks bleak according to our current theories.
A: No, as far as we know there are no wormholes anywhere in the universe. In fact, we know of no realistic physical mechanism that would lead to the creation of a wormhole in nature.
A: Worm holes are the product of the fact that the differential equations for general relativity have (permit) closed loop solutions. This implies that at the very MOST, the very simple and neat equations allow, looped space and time. These things need a real interpretation which isn't easy. One is that, space gets so warped that it can loop as opposed to being flat, has to do with geometry, and Klein bottle type stuff. But I suppose this leads to unintuitive phenomena, like travelling one way, and ending up a larger distance away than what would seem possible via normal paths.
Similarly with time, I suppose, which is even harder to apply to reality, but would be forward temporal destination leading to past times. Some of these are paradoxical and some reject they could be possible.
On normal scales there is no way to get feedback to the issue. On small scales there are issues with difficulty in making observation again. So I would presume there is little actual evidence in either direction. Only correlation with common measurable phenomena with general relativity field equations. There is no reason necessarily to presume they follow such curves far beyond these regions. It could be that different phenomena emerge which if predictable require new formulations, which do not have such closed solutions.
It is interesting to note that NASA does research a warp drive. This drive would utilize warping space time, so that faster than light travel is achieved. But no holes are utilized, only the contraction of space. This requires the contraction of space, which brings the object closer then normal, allowing faster transit than what would normally be possible even at light speed travel. This method is much more realizable but not to a level that is actually useful for transporting anything yet. But no puncturing of space and time travel is done. No observable puncture has ever been discovered. Black holes could be an example if General Relativity stands, but if not it could be just an extremely massive planet/star thing.
If we think, to any one that did not know better, and thought the earth was flat, because everything locally is flat, it would be similarly odd, to see someone leave travelling one direction, and arrive from the other. So it is presumable that spatial punctures could exist, as well as finite closed space. Closed time seems a little more problematic. But I do not know of any evidence for punctured space. And it can not be known if such things which are solutions to the equations, follow reality.
A: A huge deal in physics going on now is the realization of "ER == EPR".
If this turns out to be true, then a wormhole can be created by taking two sets of entangled particles (every particle in A has an entangled partner in B) and collapsing both of them to black holes.
Leonard Suskind has given talks going over this in some detail, including the extent to which the interior can be probed.
By this mechanism, you can't make a sci-fi trope doorway to another part of the universe.  And it would be exceedingly difficult to make an actual macroscopic wormhole at all, with which you can do the exact analogy of quantum teleportation (as explained by Leonard), requiring classical communication as well in order to teleport the quantum state through the wormhole.
But, if true, the mechanism exists in a simmering sense, under the scenes and is responsible for the emergence of GR and maybe spacetime itself from more fundamental QM fields.  Think of it like "virtual particles" make electric and magnetic forces work, but don't require actual photons to materialize.
A: Whether or not wormholes exist is an empirical question. So far, the answer seems to be "No", because we simply have not observed any. However, the Universe is very, very big and there is no reason a wormhole might necessarily be easy to spot in all possible ways they could occur. So this is not a really strong "no".
It is sometimes claimed that wormholes are "predicted to exist" by general relativity. This is not actually what it says. It would be better to say that what it says is that they are permitted to exist, in that the existence of one would not in any way, shape, or form contradict or invalidate the theory of general relativity. However, general relativity alone also offers no physical process by which a wormhole could form starting only from things we know to exist, such as ordinary matter and radiation. This would mean that if any wormholes exist, they had to have either been primordial - formed with the creation of the Universe in the Big Bang - or they would have to arise through some other process on whose existence general relativity is silent.
Note that, again, in this last comment, that also doesn't mean general relativity forbids such processes. Only that, given what we know, their existence is not implied by the theory.
In the end, the real answer is "maybe". And it likely will be that way for a quite long time, until we gather the right empirical evidence either to observe an actual wormhole, to rule them and/or their physical processes out, or to gather the empirical evidence needed to substantiate a post-standard model theory from which we can then infer the possible (non)existence of wormholes. And in that regard, we likely will need a moment of serendipity, because the methods we know already to probe post-SM (which I define here as meaning "our existing understanding of the physics of our Universe") physics are stupendously out of reach technologically, such as particle accelerators of dimensions equal to interstellar distances, so that, without wormholes :) they would necessarily take thousands or millions of years to build.
A: As many answers point out, we don't know.
Yet, recently wormholes became a bit more likely. Indeed it has been discovered that wormholes can be built, as a solution of  Einstein-Dirac-Maxwell gravity, in 4D without requiring exotic matter. The key insight with respect to the past has been inserting Dirac fermions (e.g. electron, quarks, etc.).
What does this result teach us? It teach that solid no-go theorems are very hard to build, since there are many ways to add new game changing elements to an existing theory. Also many theorems work with simplified assumptions (e.g. a theory with no fermions), which are often too simple to describe our universe.
So yes, wormholes may very well exists, time will tell!
