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See also: Riemann cut, Schwarzschild solution, Eintein-Rosen bridge, Kerr ring singularity, Traversable wormhole with negative energy, Wave function of the universe.
This page contains some segments that were taken directly from my "time travel" section...
A wormhole would be a structure that connects two separate points in spacetime. Perhaps, this construct could be visualized as a tunnel with two end-points. Each of these end-points lies in a different location in spacetime. These hypothetical wormholes could connect points over very long distances, or short ones. It could connect different points in time, or even, different universes.
It is not known whether or not wormholes exist, however, they are consistent with Albert Einstein’s equations.
A way to visualize a wormhole...
Wormholes could be tunnels that reduce the time and distance of a long journey. This is a demonstration that the shortest path between two points, is not necessarily a straight line, however, it could be a wormhole. If these constructions are possible, it raises further questions, such as: if clocks tick at different rates, depending on where you are (a consequence of relativity), then could someone hypothetically enter one of these tunnels and come out the other end back in time? Could this be molded into a workable time machine? Could this be used to travel, even to other universes, if they exist? Perhaps, a wormhole could connect a universe with itself. This could be a means of interstellar travel. Wormholes, could also, hypothetically, provide the means necessary for time travel, connecting two different eras of time. Could wormholes connect an infinite series of parallel universes?
Our universe could be one, in an infinite series of parallel universes, that are each connected by an infinite series of wormholes. Travel between these wormholes could be possible. However, it is extremely unlikely.
Perhaps, until we have a full theory of quantum gravity, we can’t know the answers to these questions.
It should be stressed that the idea of “wormholes” are highly speculative. As we will see, wormholes and multiply connected spaces push the very limits of Einstein’s theory of space and time: general relativity. However, physicists are seriously interested in their properties. Every solution to Einstein’s equations should allow for at least some form of time travel, as we will see. These wormholes are tunnels that link distant points in space and time. We call them wormholes, because they demonstrate that the shortest path that a worm could take between points on the skin of an apple, is not necessarily a short line, however, he can eat his way through the apple by means of carving out a tunnel. This reduces the time of his travel tremendously. A wormhole, hypothetically, could connect a universe with itself. This could be a means of interstellar travel or even time travel. They could even (if they exist) connect a series of parallel universes. Hopefully, when a full theory of higher dimensions or a theory of everything like string theory is finished, it can prove whether wormholes are possible or the stuff of science fiction. The advantage to having a unified field theory like this is that we can calculate the energy necessary to form a wormhole of space and time.
Bernhard Riemann
The study of “multiply connected space” actually goes back to Bernhard Riemann. This is when different regions of space and time are “spliced” together. Riemann anticipated the concept of wormholes. Indeed, Riemann was the first to discuss multiply connected space or wormholes. A construction, known as a Riemann cut, connects two sheets of paper together by a line. You make a shortcut on each piece of paper with a pair of scissors. If we walk around the cut, nothing happens, however, if we walk through it, we can move from one plane to the other. It’s a multiply connected surface! This is a wormhole with a neck of length zero: Riemann’s cut.
The story brings us to Albert Einstein and Nathan Rosen, who, in 1935 constructed a model of a wormhole and published their result, the so-called: Einstein-Rosen bridge. These kinds of wormholes are also known as Schwarzschild wormholes. These are valid solutions of general relativity that allow wormholes. This was the first kind of wormhole to be discovered. However, this kind of wormhole would probably collapse too soon for anything significant to travel through it. This kind of wormhole would appear in a version of the Schwarzschild metric, that is maximally extended (or spacetime has no edges), working to describe an eternal black hole. This black hole would have no rotation and no charge.
Indeed, Einstein and Rosen's work was actually the origin on ideas on black holes. John Archibald Wheeler will later popularize the idea. What Einstein and Rosen speculated was that a black hole interior could connect to a distant place. This is the device that Wheeler later called a wormhole. Two black holes of arbitrary cosmic distance from each other could be connected at their horizons.
Karl Schwarzschild
Albert Einstein
Nathan Rosen
Karl Schwarzschild, in 1916, gives us the very first description of a black hole in general relativity. Schwarzschild published this result just months after Einstein published his theory of general relativity. Schwarzschild solved Einstein’s equations for the gravitational field of a massive (stationary) star. This black hole has some features, for example, the point of no return known as the event horizon, or simply, horizon. Any physical information that goes beyond this horizon will be sucked into the black hole with no chance of escape. This region beyond the horizon is known as the Schwarzschild radius and once you enter you will be crushed to death. However, there was another interesting property of this black hole. If one could pass the event horizon they would become aware of a kind of “mirror universe”. Einstein figured that communication with this mirror universe was not possible. Any kind of physical information that fell into this black hole would be crushed to death at infinite spacetime curvature at a nasty singularity. This is where the strength of the gravitational field becomes infinite. This is sufficient strength to crush any kind of matter. Atoms would literally be ripped apart. It also should be noted that if one wanted to penetrate to the other side to the mirror universe, one would have to move faster than the speed of light. This is of course forbidden by the theory of relativity. Thus, we could never observe this mirror universe physically, despite the fact that its existence is necessary for the consistency of the Schwarzschild solution mathematics.
The Einstein-Rosen bridge connects two different universes. However, according to Einstein, communication between these two universes would be impossible since any rocket ship that tried to travel through it would be crushed. However, this kind of travel may be possible with some new physics. However, it would be quite difficult.
Indeed, to understand the Einstein-Rosen bridge, we must go back and look at the work of Karl Schwarzschild in 1916. Schwarzschild, not long after Einstein published his general theory of relativity, proposed a solution to Einstein's equations for a stationary star of high mass. There was a point of no return, around this black hole. Objects that pass this horizon, will have no chance of escaping, as they are sucked into the black hole. The distance from the horizon to the black hole singularity is known as the Schwarzschild radius. It should also be noted that, if anyone fell into the Schwarzschild radius, they would become aware of another universe. This is a kind of mirror universe, on the other side of the horizon. However, Einstein proposed that communication with this mirror universe is not possible. Any object sent to the center of a black hole would encounter infinite spacetime curvature and be crushed. To get to the other mirror universe, one would have to travel faster than the speed of light. This is also impossible. This mirror universe can never be observed physically. However, it's existence is necessary for the Schwarzschild solution to work.
At any rate, the point that connects these two universes is known as the Einstein-Rosen bridge. This point was considered merely, a mathematical device to keep a consistent theory of black holes. However, we could never reach the mirror universe by traveling through the Einstein-Rosen bridge. Einstein-Rosen bridges, were, however, found in other solutions of gravitational equations. For example, they appeared in the Reissner-Nordstrom solution. This is the solution that describes a black hole with electric charge. Nevertheless, the notion of the Einstein-Rosen bridge fell into obscurity.
We must understand the topology of wormholes and visualize multiply connected spaces to figure out what happens to those that fall into the Einstein-Rosen bridge. There are various distortions of space and time that can be made with these multiply connected spaces. However, neither general relativity nor quantum mechanics, are powerful enough to answer these questions. We will likely have to wait for the higher theory: the theory of everything.
This geometry would contain:
A black hole.
A white hole, which is a black hole running backward in time. It is essentially, the opposite of a black hole. It cannot be entered from the outside, however, matter and radiation can escape from it. However, these violate the 2nd law of thermodynamics.
Two universes connected at their horizons by a wormhole. This is the Einstein-Rosen Bridge.
However, we do not observe these in nature, because, when stars collapse, they do not form a wormhole, they form a black hole. Even if one were found, it would be unstable and it would fly apart.
The solution actually has two parts:
the black hole part in one universe where matter flows in...
the white hole part in another universe where matter flows out...
The connection between our universe and this “mirror universe” is known as an Einstein-Rosen bridge. It is named after Albert Einstein and Nathan Rosen. The Einstein-Rosen bridge connects two different universes. However, Einstein believed that anyone would entered the bridge would be crushed and that there could be no communication between these two universes.
As mentioned previously, not only would there have to be a black hole with an event horizon, however, there would also necessitate the existence of a white hole (cannot be entered from the outside, however, matter and light can move out from it) interior. However, white holes violate the 2nd law of thermodynamics. Hypothetically, however, the presence of these two interior regions, would give way to two different exterior regions. These two exterior regions would be the different universes.
An illustration of the evolution of a Schwarzschild wormhole...
To sum it up: the idea of the wormhole came from Albert Einstein and his collaborator Nathan Rosen (and will be later popularized by John Archibald Wheeler). What Einstein and Rosen speculated was that the interior of a black hole, could connect to some very far away point in spacetime. The wormhole would be a shortcut through spacetime, connecting two black holes that are billions of light years away from each other, at their horizons.
Roy Kerr
Roy Kerr, in 1963, found another solution to Einstein’s equations. Kerr’s idea is that any collapsing star should rotate. Rotating stars would accelerate as they begin to collapse. Kerr’s idea was that a rotating massive star, when it collapses, does not form a point. However, it forms a ring. The distinction lies in whether you approach the ring from the side or from the top or bottom. If one were shot to the ring’s side, you would be crushed at infinite spacetime curvature. However, if one approached this Kerr ring singularity from the top or bottom, you would experience strong gravity, however, not infinite. This means that one could, in principle, survive gravitational field at black hole’s center and tunnel right through to the mirror universe. The Kerr black hole could be a gateway to another universe!
Schwarzschild wormhole - embedding diagram
Schwarzschild wormhold - artist's depiction
The other kind of wormhole, would be, one that can be crossed through in both directions. This kind of wormhole, is known as a traversable wormhole. However, a traversable wormhole, would only be possible, if, they were stabilized by a kind of exotic matter, with a negative energy density. There have been theoretical demonstrations, via quantum field theory, that, the energy density of certain regions of space can be negative. The Casimir effect, shows precisely this: that quantum field theory, can allow the energy density in certain regions of space, to be negative, relative to the energy of the vacuum. The Casimir effect represents a region of negative pressure density. This is the closest real physical representation of what this kind of exotic matter would look like. These effects could potentially provide stability for a traversable wormhole. It could be possible, at least, in theory. In the context of general relativity, physicists are at a loss, to find a natural mechanism that may produce a traversable wormhole. However, quantum mechanics gives us an interesting possibility: the quantum foam. Quantum foam is a term made by John Archibald Wheeler in the 1950s. This was the proposal that, spacetime, at it’s most fundamental level, is not necessarily smooth. However, instead, at the scale of quantum gravity, spacetime could be fluctuating, in an ever-changing kind of foam. This hypothesis could suggest that very small wormholes could be appearing and disappearing (perhaps frequently) at the Planck scale (10^-35 meters).
A simulation of a traversable wormhole...
Kip Thorne
In 1988, Kip Thorne, Michael Morris and Ulvi Yurtsever showed that it could be possible to build a time machine if someone could obtain some exotic negative matter (which has never been seen to exist) or energy (which only exists in small quantities). The idea behind negative matter and energy is that they can make a wormhole traversable. This means you can make a mild two-way trip through it. However, the problem with this kind of matter is that it is repelled by ordinary matter. It possesses antigravity. This makes it extremely difficult to find (if it even exists at all). That is not to say that there may not be some negative matter floating in deep space, that is possible. Negative energy, on the other hand, is possible, however, it is extremely rare.
Could a wormhole be used to build a working time machine? Kip Thorne from the California Institute of Technology, in 1988 asked that very question. Thorne proposed that time travel is possible by means of a wormhole under some specific conditions. There were several conditions that Thorne had to address when proposing his wormhole. These are the reasons that physicists didn’t take wormholes serious at the time:
1. The gravitational force at the center of a black hole is so strong that any time traveler would be ripped to shreds at the singularity.
2. Small disturbances could cause the Einstein-Rosen bridge to collapse, since these wormholes are in principle, unstable. Even the presence of the smallest of space crafts could be enough to close the mouth of this unstable wormhole.
3. To get to the other side of the wormhole, one would have to travel faster than the speed of light. This is impossible.
4. The large quantum effects may cause the wormhole to close in on itself. Intense radiation emitted by the black holes entrance would be sufficient to kill anyone who tries to enter or to even close the entrance.
5. Since time slows down as you approach a source of intense gravitational attraction, time would stop as one approached the center of the black hole.
The idea was that a wormhole could connect two distant points in time. A wormhole could connect to the present to the past. However, unlike in science fiction, this wormhole would require vast amounts of energy. This is perhaps reserved for advanced extraterrestrial civilizations. This is beyond what is technologically possible for centuries to come.
At any rate, this kind of wormhole is known as a transversable wormhole. This is too distinguish it from the non-transversable Schwarzschild wormhole or Einstein-Rosen bridge. Kip Thorne’s wormhole would not close up on itself and the traveler would experience the same amount of gravitational attraction that they feel on Earth. The trip would take about 200 days or less and would be about as comfortable as an airplane ride.
An example of a Thorne wormhole requires two chambers. These chambers were created, by means of two pairs of metal plates that run parallel to each other. There would be an intense electric force produced by these plates (larger than anything we are capable of by today’s technology). This force would be so strong that it produces a hole in the very fabric of spacetime that would connect the two chambers:
1. One chamber stays stationary on Earth.
2. The other chamber is accelerated by means of a high powered rocket to some near-light speed (relativistic) velocity and is
The chamber that has been accelerated (because of time dilation in special relativity: the faster you move the slower your clock ticks) ticks slower, thus, you can travel in time!
This kind of wormhole solution was titled, a "traversable wormhole." This is because, the one traveling through would not have to worry about being ripped apart by a collapsed star.
Hendrik Casimir
However, the reason we don’t have these transversable wormhole time machines for sale today has to do with the very nature of the matter/energy necessary to construct them. What is required is a kind of exotic matter. This matter has some unusual properties, however, does not violate any of the laws of physics. If this kind of exotic matter exists, which it may, then it could be harnessed by some sufficiently advanced civilization. In physics, all of the objects that we are aware of have a positive energy. However, if objects with negative energy can be produced, or energy less than the vacuum, then perhaps we can bend space in the kind of ways that we are talking about here. We could bend spacetime into a circle. What must be violated is known as the AWEC (averaged weak energy condition). For these kinds of time machines to be constructed, energy must become negative for some period of time. Although relativity theorists scoff at the idea of negative energy, as it would produce anti-gravity, which has never been observed, quantum mechanics can give us a glimmer of hope. Hendrik Casimir, in 1948, gave a quantum mechanical argument for negative energy. This demonstration involves two uncharged parallel metal plates. When we apply the Heisenberg Uncertainty principle to the vacuum or the “empty space” in between these plates we see that it is not so empty. In fact, there is a lot of activity. These are trillions of virtual particles: particle and antiparticle pairs that come in and out of existence. They are unobservable, however, do not violate the laws of physics. These virtual particles create a kind of negative attractive force between the two plates. Hendrik Casimir predicted that this force could be measured. This has been deemed the “Casimir effect”. Thus, perhaps we can place two parallel plates at the entrance and exit of the wormhole. This would produce negative energy at each end. We still do not know how plausible this idea is, as even Thorne admits. We will not know until we have a full theory of quantum gravity.
One must obtain large quantities of negative energy, which is rare indeed. Stephen Hawking has showed that, for all wormhole solutions, negative energy is required. To keep the mouth of the wormhole open and stable, large amounts of negative energy are necessary. Negative energy created using the Casimir effect would result in a wormhole too small to travel through. There are other places, besides using the Casimir effect, that we may find negative energy:
A rapidly moving mirror
High powered laser beams
Black hole event horizons
Stephen Hawking
Stephen Hawking, also has proposed an idea of wormholes that treats the entire universe as a quantum particle. As a wavefunction in quantum mechanics describes the different potential states of a particle, this wave function would describe a set of all possible universes. This wavefunction would be most highly concentrated around our own universe. We live in this universe because it has the largest probability in the wave function. That being said, there could be transition between these universes, via wormhole tunneling, since there is a small probability that the wave function prefers a neighboring universe. Thus, Hawking’s wormholes would begin with an infinite set of parallel universes. These infinite number of parallel universes would coexist with one another. The universe is no longer “all that exists” it is “all that can exist”. Hawking’s idea is that these universes can collide and there can even be wormholes that develop and link these parallel universes. The size of the Hawking wormhole that connects these parallel universe by means of a wave function is very small. They will be about the size of the Planck length (10^-35 meters). This is far too small for human travel. It would also take longer than life of the universe for this kind of quantum transition to occur. However, it is still possible, just unlikely.
Our universe could exist in an infinite series of parallel universes. These universes could be connected by a web of wormholes. Theoretically, it could be possible to travel between these wormholes. However, it is very unlikely.
Hawking said: “Wormholes, if they exist, would be ideal for rapid space travel. You might go through a wormhole to the other side of the galaxy and be back in time for dinner.”
Sidney Coleman
Sidney Coleman, a theoretical physicist, is optimistic that wormhole theories could be verified in the somewhat near future.
In general relativity, the matter-energy content of an object, will determine the curvature of the surrounding spacetime. Einstein asked the question: can the vacuum of empty space contain energy? This vacuum energy is known as the cosmological constant. Einstein, who found it unappealing, tried to find ways to work around including it in his equations, however, he couldn't. In fact, Einstein, found that his equations worked for an expanding universe. However, the accepted view at the time was for a static universe. Thus, Einstein introduced a small cosmological constant to balance it out.
We know today, that the cosmological constant is very close to zero. However, this problem came onto the scene again, this time, in particle physics. In the Standard Model, when symmetries are broken, the vacuum should gain some significant amount of energy. This amount of energy should be about 10^100 times the amount that we observe in experiment. This is the prediction of a large vacuum energy when symmetry is broken. This is the biggest divergence from experiment to theory in physics. It is a massive discrepancy.
The idea behind Sidney Coleman's wormholes, is that they can cancel these unwanted contributions to the vacuum energy. Coleman calculated that if we truly live in one of any infinite number of universes, connected by an interconnected web of Planck length-sized wormholes, then, the wavefunction of the universe would prefer to have a cosmological constant of zero. He found that the reason that the cosmological constant was zero, is because, that is the most probable outcome. This prediction would also help to determine the values of fundamental constants in the universe.
Alan Guth
Another speculation coming out of the speculative physics of wormholes comes from Alan Guth from MIT. What Guth proposed is that we could create “baby universes” in the laboratory. Intense heat and energy would be concentrated in a chamber, giving the potential of a wormhole opening up. This wormhole would act as a gateway to a much smaller universe. If this proves to be possible, cosmologists, in the laboratory, could be given insight into how a universe could be created.
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