What is a wormhole?
A wormhole is a short passage in spacetime that directly connects two universes or two distant regions within the same universe.
Two universes? How can there be more than one?
Understand that the word “universe” in this context does not mean “all that exists”. Rather, it means “an independently existing spacetime and its contexts”. To imagine two universes, think of two toy balloons floating near each other. A traversable wormhole connecting them would be like a short drinking straw glued between them that would allow an ant to crawl from one balloon to the other.
Is there a more precise definition of a wormhole?
Yes. In normal space it is always possible to shrink any closed surface down to a point. A wormhole is a region of space containing a closed surface for which this is not the case. More correctly, a wormhole is 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.
What is a black hole?
A region of intense gravitation characterized by a central point or ring of infinite energy density called a “singularity” and an enveloping surface called an “event horizon” from which nothing – not even light – can escape.
How are wormholes related to black holes?
Unlike a wormhole, a naturally occurring black hole -- one created through stellar collapse -- is not a bridge between two universes (or distant regions within the same universe). There nevertheless exist certain solutions to the Einstein equations of general relativity in which a bridge between universes – a wormhole -- appears to have a black hole at either end. This is the sense in which certain theoretically possible black holes can be said to be wormholes.
Can a wormhole with a back hole at either end be traversed?
No. The bridge between universes remains open for too short a time for any traveler to cross it.
Is there another way in which wormholes are related to black holes?
Yes. They are also related through inter-conversion. Were a black hole to exist as an untraversable wormhole, it could be converted into a traversable wormhole by dropping enough negative mass-energy into it. It is similarly possible to convert a traversable wormhole into a black hole by showering it with enough positive mass-energy. Unlike static traversable wormholes, black holes always contain singularities – regions of infinite mass-energy density, where classical physics breaks down.
Could I traverse a wormhole with a black hole at either end, if I could somehow exceed the speed of light?
Yes. Assuming, of course, that the black hole is large enough to allow you to tolerate its gravitational tidal forces as you approach and pass through. [The more massive the black hole, the weaker its tidal forces in the vicinity of its event horizon.]
What is a white hole?
A time-reversed black hole. Nothing can escape a black hole, but nothing can enter a white hole. The event horizon of a black hole prevents objects from exiting; the event horizon of a white hole prevents objects from entering. The singularity of a black hole absorbs whatever has entered its event horizon; the singularity of a white hole has emitted whatever exits its event horizon. The event horizon of a black hole is highly stable; the event horizon of a white hole is highly unstable. Black holes are believed to exist in nature; white holes are believed to exist only as parts of certain solutions to the Einstein equations.
How are wormholes related to white holes?
There are classic solutions to the Einstein equations -- called maximally extended solutions -- that describe untraversable wormholes. The mouths of these wormholes may be described as white holes that become black holes. Any external observer who views a mouth will see the white hole that it was in the past. When she approaches the mouth, she will find the black hole that it is in the present.
What is an Einstein-Rosen bridge?
A solution to the Einstein equations published in 1935 by Albert Einstein and Nathan Rosen in an attempt to create a gravity-based model for an elementary particle. This solution is today called “the maximally extended Schwarzschild solution”. It describes a dynamic wormhole connecting two universes. In each universe the mouth of the wormhole appears to be a black hole that was previously a white hole. As John Wheeler and Robert Fuller showed in 1962, this wormhole cannot be traversed. Its throat constricts too rapidly.
What is an Einstein-Podolsky-Rosen bridge?
A misnomer. In 1935 Einstein, Podolsky, and Rosen proposed a famous thought experiment intended to expose what they believed to be a paradox in quantum theory. The Einstein-Podolsky-Rosen (EPR) paradox has nothing to do with wormholes and, incidentally, is no longer regarded as paradoxical.
What is the difference between classical physics and quantum physics? Which one do I need to understand wormholes?
You need both: classical physics for macroscopic wormholes, quantum physics for microscopic ones. Quantum physics is the most accurate description of physical reality known. It applies in both macroscopic and microscopic realms. Classical physics, by contrast, is merely a convenient approximation to quantum physics that is only accurate for systems of macroscopic objects (i.e. systems for which the products of measured momentum and relative position always well exceed a particular fundamental constant of nature -- Planck’s constant).
What is general relativity and what does it have to do with wormholes?
General relativity is the theory formulated by Einstein that describes gravitation as curvature in spacetime induced by the presence of matter or energy. It is used to understand physical systems in which gravity is too strong for the Newtonian theory to accurately describe. Such systems include wormholes.
What is a stargate?
In science fiction, a synthetically controlled wormhole. We shall also use the term to describe a wormhole whose throat is a planar surface in the sense that it does not appear to enclose a volume (e.g. a disk and a square are both planar, unlike the surfaces of a sphere or a cube).
What is the origin of the word “stargate”?
Arthur C. Clarke used the term “star gate” to describe the interstellar shortcut featured in his novel upon which the 1968 movie 2001: A Space Odyssey was based. Common use of the contracted form “stargate” followed the release of the 1994 movie of the same name and its subsequent extension to television.
What is a traversable wormhole?
A wormhole through which human beings can repeatedly travel unharmed in a time short compared to the human life span.
Do wormholes have event horizons?
In general, no. They only have an event horizon – a surface surrounding a region from within which nothing can escape -- if they are black holes. Two-way traversable wormholes cannot have event horizons.
Do traversable wormholes have singularities?
Static traversable wormholes do not. Some dynamic traversable wormholes do. The singularity doesn’t sit inside these dynamic wormholes. It’s what the wormhole will become in the future. If the wormhole is traversable, the only way its singularity will cause a problem for a traveler is if he parks his spaceship at the throat and waits (perhaps years) for the wormhole to collapse into a singularity.
What about untraversable wormholes, do they have singularities?
Yes. These are called maximally extended black hole solutions to the Einstein equations. Unlike naturally occurring black holes, which don’t connect to anything, these form untraversable bridges to other universes or distant regions within the same universe.
Have any naturally occurring wormholes been discovered?
No. If they do exist, they are likely to be the result of primordial microscopic wormholes being inflated to macroscopic size during the inflationary phase of the universe’s development.
If no wormholes have ever been discovered, why should we consider them?
The best way to test and extend our theories of nature, especially in the absence of experimental data, is to check their logical consistency in extreme hypothetical cases. This, after all, is how Einstein discovered relativity. Wormholes are examples of such cases. They are predicted by an extremely well tested physical theory, general relativity. If we believe this theory, then we believe that they can exist. If they can exist, and if circumstances conducive to their creation and maintenance have occurred, they do.
How could a macroscopic wormhole arise naturally?
The primordial universe might have spawned, through a process known as “quantum tunneling”, unstable cosmic wormholes that have been expanding along with the universe. If the accelerating expansion of the universe first detected in 1998 is due to cosmic exotic matter, such matter might somehow have expanded the submicroscopic wormholes believed to be contained in the vacuum state of spacetime.
What hazards are encountered in attempting to traverse a wormhole?
A traveler attempting to traverse a wormhole might be ripped to death by gravitational tidal forces, be incinerated by high radiation emitted near a singularity, be damaged by contact with exotic matter, or die of old age in transit. He might also become trapped within the wormhole or on the distant side of it, after he inadvertently induces its collapse by attempting to pass through it. It is in principle possible, however, to engineer a wormhole that alleviates each of these hazards arbitrarily well.
Could wormholes be used for interstellar communication?
Yes. It would in fact be much easier to create a wormhole that permits the passage of message-carrying light signals than it would be to create one that ensures the safe passage of human travelers.
How difficult would it be to create a wormhole?
The ability to create a traversable wormhole is well beyond current human technology. It would require the enlargement of one of the many submicroscopic quantum wormholes believed to exist within any volume of space. The process would likely require an intense, ultra-high frequency negative energy source -- something we have no idea how to produce.
What are “energy conditions” and what do they have to do with wormholes?
They are conditions once believed to be satisfied by all forms of matter. They can be expressed as inequalities that constrain the energy density of matter and its principle pressures, the pressures in each spatial direction. The matter required to hold open a traversable wormhole must violate certain energy conditions.
How many energy conditions are there?
There are five primary energy conditions that have been used over the last 50 years. Three of them are now regarded as obsolete, because there are now clear examples of their being violated by perfectly ordinary matter.
Which energy conditions matter in wormhole physics?
The two non-obsolete energy conditions are called the “Weak Energy Condition” (WEC) and the “Null Energy Condition” (NEC). [Their averaged versions are also in use.] The NEC requires that the sum of the density of matter with each of its principle pressures be non-negative. The WEC requires in addition that the matter density itself be non-negative. These conditions might some day become obsolete, as both of them are known to be violated by quantum effects. The matter required to hold open a traversable wormhole must at least violate the WEC.
What is exotic matter and what does it have to do with wormholes?
Exotic matter is matter that violates an energy condition. A traversable wormhole requires the anti-gravitating effect of exotic matter at its throat to counter the wormhole’s tendency to inwardly contract.
Is exotic matter the same as antimatter?
No. There exists a reference frame in which the energy density of exotic matter, unlike that of antimatter, is negative. Therefore exotic matter, unlike antimatter, gravitationally repels normal matter.
How realistic is it to suppose that exotic matter exists?
Its existence isn’t as far fetched as you might at first think. Four arguments for its likely existence are: 1) The ordinary electromagnetic field is infinitesimally close to being exotic. 2) Quantum effects are known to create negative-energy densities. 3) Something is causing the expansion of the universe to accelerate. Cosmologists have recently speculated that it might be cosmic exotic matter (which they call “phantom energy” or “superquintessence”). 4) Formerly sacrosanct energy conditions have been dying off for the last few decades. Why not a couple more?
I hear that there are two types of exotic matter. Is this true?
Sort of. Strictly speaking, there are precisely as many types of exotic matter as there are energy conditions. Because there are only two pointwise energy conditions that are still widely believed to apply to matter, their violations define the two types of exotic matter normally considered. There is exotic matter that violates the Null Energy Condition (NEC) and that that violates the Weak Energy Condition (WEC). The NEC requires that the sum of the density of matter with that of each of its principle pressures be non-negative. The WEC requires in addition that the matter density itself be non-negative. The WEC, then, despite its name, is stronger than the NEC. So all matter that violates the NEC also violates the WEC, though the reverse is not true.
What are "quantum inequalities" and what do they have to do with wormholes?
Quantum inequalities are a set of principles in quantum field theory that state that any observer's exposure to negative energy must be followed by a compensating exposure to positive energy, whose magnitude and duration exceed that of the negative energy exposure. This implies that the negative energy density at the throat of a traversable wormhole must be surrounded by a compensating region of positive energy density. Hence, quantum theory forbids wormholes whose matter is entirely negative.
What shape is a wormhole’s mouth most likely to take?
A naturally occurring wormhole’s mouth is likely to be spheroidal for the same reason that stars and black holes tend to be – the absence of stresses that introduce an asymmetry. In general, a wormhole’s mouth must be a closed two-dimensional surface that would seem to be surrounding a three-dimensional volume. Although it is also possible to engineer a flat mouth (that does not seem to enclose a volume), such a configuration seems unlikely to develop naturally.
What is a thick-shell wormhole?
A wormhole whose matter is distributed throughout a nonzero (thick) volume centered about its throat, as opposed to being concentrated into an infinitesimally thin surface at its throat.
What’s the difference between a wormhole’s mouth and its throat?
If you think of a thick-shell wormhole as the three-dimensional analog of a two-dimensional tube that narrows at its middle, the throat is the analog of the circle of minimum circumference at the waist of this tube. That is, it is the surface of minimum area of the analogous three-dimensional hypertube. Its mouths are vaguely defined as the regions corresponding to the entrance and exit of the hypertube. In a macroscopic, traversable, thick-shell wormhole, it is sometimes useful to define the mouth more precisely -- as the surface at which the acceleration of gravity is 1 g. For a thin-shell wormhole in flat spacetime, its mouth and throat are the same.
What is a thin-shell wormhole?
A wormhole whose matter is all concentrated at the infinitesimally thin surface that defines its throat. There, energy densities and spacetime curvatures are infinite. These wormholes, also known as Visser wormholes, simplify the analysis of dynamics and other aspects of wormhole physics. These contrived objects are not expected to be found in nature. [To imagine a thin shell wormhole, consider two sheets of paper. Each sheet represents a universe. Stack the sheets horizontally and use a hole-punch to create a hole through both of them. Use a thin strip of glue to attach the rim of the hole in the upper sheet to that of the hole in the lower sheet. The edge of these attached rims represents the wormhole’s throat. Now an ant can crawl from the top of the upper sheet (universe A), through the hole (the thin-shell wormhole), onto the bottom of the lower sheet of paper (universe B).]
Can a traversable wormhole be used as a time machine?
How can a traversable wormhole be turned into a time machine?
Keep one of the mouths stationary. Move the other mouth -- at speeds approaching that of light -- away from the stationary mouth for a distance of a few light years. Then return it to the vicinity of the stationary mouth. Anyone who now enters the stationary mouth will be transported years into the future. Those entering the other mouth will find themselves transported years into the past. For shorter time jumps, shorten the journey of the traveling mouth.
Is there another way to turn a traversable wormhole into a time machine?
Yes. Leave one mouth, Mouth A, in a weak (or virtually nonexistent) gravitational field. Move the other mouth, Mouth B, into a strong gravitational field, such as that near the event horizon of a black hole. Wait. Now move Mouth B from the strong gravitational field and return it to the vicinity of Mouth A. Anyone now entering Mouth A will emerge from Mouth B into the past. Anyone entering Mouth B will emerge from Mouth A into the future. For longer time jumps, wait a longer time before removing Mouth B from the strong gravitational field. Alternatively, initially move Mouth B into an even stronger gravitational field. To have an ever growing time jump, leave Mouth B in the strong gravitational field.
Isn’t time travel by wormhole or any other means impossible due to the paradoxes that it implies?
Not necessarily. Dealing with time travel paradoxes by conjecturing the impossibility of time travel is only one of three ways of resolving the issue. The other ways are:
1) Impose self consistency on classical physics: A time traveler cannot change the past because he was always part of it. When he attempts to change the past, his efforts will be thwarted by an apparent conspiracy of events. 2) Impose self consistency on quantum physics: A time traveler cannot change the past because all possible pasts have already occurred in parallel universes. When he attempts to change the past, his efforts will not seem to him to be thwarted. This is because he will have entered the past of a preexisting parallel universe in which he has already made the changes that he seeks to effect.
Don’t quantum effects prevent wormholes from being turned into time machines?
No. It’s true that calculations seem to show that a wormhole-destroying feedback loop of virtual particles appears whenever a wormhole is configured as a time machine. But these calculations don’t assume the existence of the parallel universes that would have prevented the feedback. Even without this assumption, it’s possible to make the feedback arbitrarily small by replacing the single wormhole with a Roman ring of wormholes.
What is a Roman ring?
An arrangement of several wormholes that functions collectively as a time machine, even though no subset of the wormholes functions as one.
Are wormholes the only means of creating a time machine?
No. Any method of creating time loops – called “closed timelike curves” – will produce a time machine. Other methods include those that involve the generation of exceedingly high angular momentum densities.
Is a wormhole always a shortcut?
In practice, yes. In principle, no. Consider a wormhole that connects two regions within the same universe – an intra-universe wormhole. It is possible for the path through the wormhole to be longer than the shortest path through normal space between the wormhole’s mouths (Figure 1.1). Intra-universe wormholes have in practice, perhaps due to the influence of science fiction, come to be synonymous with shortcuts. Inter-universe wormholes, by contrast, cannot be described as shortcuts. There is no path through normal space between distinct universes in comparison to which the path through an inter-universe wormhole appears shorter.
Figure 1.1. A wormhole that is not a shortcut.
Such wormholes are even less stable than those
Is there such a thing as a quantum wormhole?
Yes. A quantum wormhole is one whose complete description requires quantum theory. An example of a quantum wormhole is the ephemeral, submicroscopic wormhole of the sort that characterizes Wheeler’s spacetime foam. Physicist John Wheeler was the first to imagine the vacuum state of a quantized gravitational field. He believed that the corresponding spacetime would at tiny length scales be a roiling froth (analogous to sea foam) that momentarily permits every conceivable geometry -- including wormholes. Unfortunately, the effort to create a theory of quantum gravity has not yet advanced sufficiently to permit anything approaching a complete description of spacetime foam or of the quantum wormholes it is presumed to contain.
If quantum wormholes exist, why don't we see elementary particles disappearing from one place and appearing elsewhere or jumping backward and forward in time?
The mouths of quantum wormholes are many orders of magnitude smaller than the smallest elementary particle.
How does a wormhole differ from a space warp?
A wormhole is a special case of space warp.
Are wormholes accurately depicted in science fiction films and television programs?
Not usually. Wormholes are normally depicted as swirling drain holes in space. Sometimes they are shown to have luminous event horizons.
What would a wormhole look like?
A wormhole would likely appear to be a bubble or window through which unfamiliar stars are visible. If the wormhole is massive, dense, rotating, and in the proximity of luminous matter -- such as that found in stellar atmospheres -- it could be surrounded by a visible “accretion disk” much like those surrounding black holes.
Can a wormhole’s mouth be a flat disk instead of spheroidal surface?
Yes. Some people refer to such wormholes as “stargates”. Others call them “portals”.
Would a flat “stargate-style” wormhole require less exotic matter than a spherically symmetrical one?
What is a ringhole?
A ringhole is a wormhole whose mouth and throat have the topology (rough shape) of a torus.
Can a wormhole possess an electric charge?
Yes. The maximally extended Reissner-Nordstrom solution to Einstein’s gravitational field equations, which describes a charged black hole, contains a one-way wormhole. A charged, two-way wormhole – no longer surrounded by an event horizon -- could be created by dropping sufficient amounts of negative-energy matter into a charged black hole. Solutions to the Einstein equations for such charged traversable wormholes have been found.
Is there such a thing as a rotating wormhole?
Yes. The Kerr black hole solution to Einstein’s equations, which describes a rotating black hole, contains a one-way wormhole. By dropping a sufficiently large amount of negative-energy matter into a rotating black hole, one could produce a spinning, two-way wormhole that is no longer surrounded by an event horizon. Such a solution was found in 1998.
How stable are wormholes?
It depends on a feature of the exotic matter that supports it. Specifically, it depends on what’s called the “equation of state” of the exotic matter – how its pressure depends on its density. For exotic matter modeled more or less conservatively (as massless particles of negative energy), traversable wormholes are unstable. Although it is always possible to choose an equation of state that guarantees stability, this stability is not unlimited. Any wormhole will collapse to a black hole after a sufficiently large influx of positive energy. Conversely, any wormhole will expand ceaselessly after a suitably large influx of negative energy.
Could wormholes be stabilized artificially?
Yes. When a wormhole begins to contract, an artificial stabilizer would halt the contraction by injecting negative energy. The stabilizer would similarly halt expansions by injecting positive energy.
Can a wormhole have more than one throat?
Yes. The neck – the inter-universe/intra-universe passage -- of a spherically symmetrical wormhole can narrow and widen in several locations. The spheres of locally minimal area at which the neck is locally most narrow are throats. Such a wormhole is highly unstable, but it could be stabilized artificially to create a static wormhole. Dynamic wormholes, whose geometric throats are either expanding or contracting, acquire multiple throats in a different way. The wormhole’s functional throat, which coincides with its geometric throat in the static case, splits in the dynamic case into two throats -- one on either side of the geometric throat.
What is the difference between a wormhole’s geometric throat and its functional throat?
Imagine an incoming spherical wave front of light that converges (contracts) on a spherically symmetrical wormhole, enters it, and diverges (expands) as an outgoing spherical wave front in the other universe. The functional throat of the wormhole is the surface at which the area of this incoming-outgoing wave front is minimal. A wormhole’s geometric throat, by contrast, is its surface of minimum area -- irrespective of the behavior of light passing through it. The geometric and functional throats of a static wormhole are the same. This is not true for dynamic wormholes, however, because the motion of the traversing light is affected by the expansion or contraction of the wormhole. In this case there are two functional throats -- one for each of the two directions in which the wave front could have traversed the wormhole.
When a wormhole forms a connection to another universe is this other universe a “parallel” universe?
Yes, but only if we assume that reality admits a single system of fundamental physical laws. In that case, the set of all parallel universes is the set of all universes that are physically possible according to this single system. Because, by assumption, no universes external to this set exist, a wormhole necessarily connects to a parallel universe.
What is a Tolman wormhole?
A Tolman wormhole, while mathematically similar to a wormhole, is a not a true wormhole. It is a cosmological solution to the Einstein equations -- that is, it is a universe -- that contracts to a point of maximum finite density, and re-expands. This contraction followed by a re-expansion (as opposed to a big crunch) is called a “bounce”. Hence, a Tolman wormhole is also known as a universe with a bounce.
A wormhole solution was known in 1916. Why did a thorough investigation of wormhole physics not begin until the late 1980s?
Beyond the fact that wormhole and black hole solutions were universally regarded as physically uninteresting until about 1935, the development of wormhole physics was retarded by sociological factors. Physicists are not in general financially independent. To survive, they must be employed. To be employed, they must be credible. To be credible, they must eschew topics of great interest to crackpots. [Crackpots are those engaged in the promulgation of irrationally held ideas typically involving the occult, fantasy, or science fiction.] One indication of the stigma associated with the subject is that the first wormhole paper of the “modern era” when published in 1988 was not billed as a research paper (which it was) but as “a tool for teaching general relativity”. It was only because its lead author was an established physicist of unquestioned credibility that less established physicists subsequently felt it professionally safe to publish traversable wormhole papers as well. They were further reassured when in the same year other established physicists happened by sheer chance to be publishing important papers involving Euclidean wormholes, which – due to their irrelevance as interstellar shortcuts – never invoked the same stigma as their Lorentzian counterparts. Another reason for the delay in wormhole research was that most practitioners of general relativity did not appreciate the existence of viable methods for creating exotic matter. Many had undoubtedly plugged a wormhole or other interesting geometry into the Einstein equations, discovered that the geometry required exotic matter, and consequently dismissed the geometry as unphysical.
How much exotic matter is needed to hold open a traversable wormhole?
A Morris-Thorne wormhole with tolerable tidal forces -- due to having a mouth that is 600 times the earth-sun distance -- requires about 108 solar masses of exotic matter. A thin-shelled (Visser) wormhole with a 1-meter wide mouth requires about 1 Jupiter mass of exotic matter. While it has recently been shown that a wormhole traversable in principle can be held open with arbitrarily small quantities of exotic matter, it still appears that enormous quantities of exotic matter are required to hold open wormholes that are traversable by humans in a timely fashion.
Does the exotic matter in traversable wormholes have anything do to with dark matter or dark energy?
It has nothing to do with dark matter. Dark matter is non-exotic matter hypothesized to exist because the assumed primordial inflation of the universe requires its density to be many times greater than that due to observed luminous matter. Dark energy, by contrast, is an attempt to explain the apparent acceleration of the expansion of the universe that was first detected in 1998. A possible explanation for dark energy is the supposition that the universe is awash in dark exotic matter. This is precisely the sort of matter required to sustain traversable wormholes.
If a wormhole is created or destroyed, won’t that require a change in the topology of space? I thought that was impossible.
Wormhole creation and destruction need not involve topology change. When wormhole creation is discussed, it’s generally understood that it means enlargement of preexisting microscopic wormholes. Wormhole destruction connotes their conversion into black holes or their contraction and absorption into the spacetime foam of virtual geometries.
Can a wormhole be used as a weapon?
Yes. But then, what can’t be used as a weapon?
What’s the connection between wormholes and string theory?
Not much, although the brane world concept that has emerged from string theory might provide a framework through which we might begin to understand how wormholes connect to parallel universes. In the brane world scenario the universe is a 3+1-dimensional membrane, or “3-brane” for short, embedded in a higher-dimensional spacetime called the “bulk” – rather like a sheet of paper floating in space. Parallel universes can be imagined as a stack of slightly separated parallel sheets (3-branes) floating in space (the bulk). It’s clear, then, that a wormhole that links different regions in the bulk would necessarily link different parallel universes. Another connection is the slight possibility that the projection of a specific string theory of the bulk onto a 3-brane representing our universe might have an interesting effect. Specifically, it might contribute to the stress energy of the 3-brane in a way that simulates the presence of exotic matter. Or to state the matter in a Wheeleresque fashion, there is still a chance that wormholes in string theory might enjoy the benefit of exotic matter without exotic matter.
How could an advanced civilization ensure that the mouths of their intra-universe wormholes are in desired locations?
They would proceed as follows. Step 1: At the desired location of the first mouth, enlarge a virtual wormhole extracted from the spacetime foam. Step 2: Determine the location of the second mouth by traversing the newly enlarged wormhole and studying the sky from the vantage point of the second mouth. Step 3: If this location is undesirable, return through the wormhole, collapse it, and begin again at Step 1. Otherwise, continue to Step 4. Step 4: Charge the second mouth by showering it with charged particles. Step 5: Use electrostatic attraction to precisely position the second mouth by suitably dragging it.
Is a wormhole whose mouths are arranged vertically in a gravitational field a source of unlimited energy?
No. The argument in favor of such a wormhole being an energy source is this: An object falls from the upper mouth, gains kinetic energy as it falls, enters the lower mouth, reemerges from the upper mouth with this newly acquired kinetic energy, and repeats the cycle to gain even more kinetic energy ad infinitum. The problem with this is that general relativity does not permit discontinuities in the metric – the descriptor of the geometry of spacetime. This means that the gravitational potential of an object at the lower mouth must continuously rise within the wormhole to match the potential it had at the upper mouth. In other words, this traversal of the wormhole is “uphill” and therefore requires work. This work precisely cancels the gain in kinetic energy.
What happens if a wormhole connects the surfaces of two planets with different surface gravities?
If the the wormhole connects Planet A to Planet B, and the surface gravity of Planet A exceeds that of Planet B, then a wormhole traversal from A to B will be "uphill", requiring the traveler to expend energy. The traversal from B to A will be "downhill", imparting energy to the traveler. If the planets have the same surface gravity, no gravitational energy is transferred to or from the traveler.
Can a wormhole be used as a source of energy?
Generally not. It could, however, be a font of energy. If it is a bridge to a hotter universe or to a hotter region of our own universe, a wormhole could funnel energy to us. In the special case of certain rotating wormholes, it would be possible to extract energy from them through the Penrose process. This is a well known method through which matter suitably injected into a rotating black hole by an object increases the energy of the object, while the black hole loses an equal amount of mass.
What is a geon and what does it have to do with wormholes?
A geon or “gravitational-electromagnetic entity” was conceived by John Wheeler as a divergence free, quasi-stable solution to the Einstein-Maxwell equations that might serve as a model for a charged particle. The idea was to model a negatively charged particle as the mouth of a wormhole into which electric lines of force entered. The other mouth, from which the same lines of force emerged, was to model a corresponding positive charge. Wheeler’s 1955 paper entitled “Geons” contained the first freestyle drawing of a wormhole ever to appear in the physics literature.
If wormholes that are black holes are not traversable, in what sense do they form an inter-universe or intra-universe connection?
They do in the sense that people from different universes (or from distant parts of the same universe) can both enter the black hole and meet each other. The meeting will likely be interrupted, however, by the violent deaths of both parties in the black hole’s singularity.
I’ve heard that some wormhole solutions are called “self-consistent”. How can a solution not be?
The self-consistency of a solution does not pertain to its logical consistency. It means instead that a solution is complete or self-contained. Such a solution not only specifies the curvature of spacetime due to the wormhole, but also explicitly specifies all of its matter. For example, if the wormhole’s matter includes an electromagnetic field, a self-consistent solution includes a solution to the combined Einstein-Maxwell equations that govern both gravity and electromagnetism. Solutions to these interwoven equations describe 1) the geometry of spacetime that is produced by the stress energy of the electromagnetic field, and 2) the electromagnetic field that produces this stress energy and is affected by this geometry. Self-consistent solutions are difficult to find.
What would it be like to pass through an event horizon?
You wouldn’t notice. For a huge, ultra-massive black hole, you wouldn’t notice a thing. For a somewhat smaller black hole there would be significant tidal forces in the vicinity of its event horizon. Assuming that you could tolerate these, you would find that they wouldn’t have changed in any sudden way as you passed through the horizon. Human beings could not, however, survive the approach to the event horizon of a “typical” black hole, whose mass would only be a few times that of the sun. The tidal forces there would be too great.
Does a traveler passing through a traversable wormhole have to come into contact with exotic matter?
No. Two methods have been proposed to protect travelers. The first was simply to punch a hole in the exotic matter through which travelers could pass. This violates the spherical symmetry of the wormhole solution. But it was assumed that if the hole was small enough, the perturbed wormhole solution would be very close to the original symmetric one. The other proposal, due to physicist Matt Visser, was to abandon spherical symmetry and consider polyhedral thin-shell solutions. In Visser’s wormholes exotic matter is confined to the edges and vertices of a polyhedral throat. This allows travelers to pass through the faces of the polyhedron without being exposed to exotic matter.
If I stick my arm into an event horizon, can I pull it back out again?
What does an event horizon look like?
It is completely black.
If a wormhole connects distant regions A and B, can its mass measured in region A differ from its mass measured in region B?
Yes. Residents of these regions can determine the mass of their end of the wormhole by putting an object in orbit around the wormhole mouth in their region. For a given orbital radius, the orbital period determines the wormhole mass that they measure. This value depends on how the wormhole curves their local region of spacetime. There is nothing requiring this curvature to be the same at both ends of the wormhole. Hence the wormhole masses measured at it ends need not agree.
Can a wormhole’s total mass be negative?
Yes, assuming that some form of classical exotic matter exists. However, the wormhole would be gravitationally repulsive. This would require travelers to expend additional fuel to approach the wormhole, because doing so would be an “uphill” trip.
What other nonspherical wormhole topologies are possible?
Klein bottles, disks, and tori with any number of handles have been discussed in the literature. There are no restrictions on wormhole topology imposed by classical physics. However, quantum physics, in particular that governing the weak interactions, requires spacetime to be orientable. At every point it should be possible to distinguish left from right.
How would the presence of wormholes in the cosmos be detected?
If its total mass is negative, it could be detected through the unusual way in which it distorts light. Unlike objects with positive mass that act as “convex” gravitational lenses, a negative-mass wormhole would, by contrast, function as a sort of “concave” gravitational lens.
Does wormhole physics suggest a preference among the competing interpretations of quantum theory?
Perhaps. If wormholes exist, then we must either explain: a) why it is impossible to turn them into time machines, or b) how it is possible to resolve the paradoxes that result, when they are turned into time machines. The latter seems most naturally accomplished in the Many Worlds interpretation.
Do wormholes behave qualitatively the same in theories of gravity other than general relativity?
Yes, at least in theories that become general relativity in the low-energy limit. It was once hoped that such a theory might permit traversable wormholes to exist in the absence of supporting exotic matter. This turned out not to be the case in nearly all of the commonly considered alternative theories of gravity. A notable exception is "Gauss-Bonnet gravity", which only differs from general relativity if spacetime is assumed to have more than 4 dimensions. In higher-dimensional Gauss-Bonnet gravity, gravity itself can act effectively as wormhole-supporting exotic matter.
If I toss a spinning object into a wormhole, will that cause the wormhole to spin?
Yes. However, if it is a traversable wormhole, any additional angular momentum imparted to it will be lost, when the spinning object emerges from the other side.
How could I destroy a wormhole?
If it’s an artificially stabilized wormhole, turn off its stabilizer. The wormhole would then collapse and become a black hole. If it’s a naturally stable wormhole, dumping into it an amount of positive matter that well exceeds that of its intrinsic exotic matter will similarly destroy it. To destroy the wormhole without leaving a black hole remnant, you would have to neutralize the matter in its throat region. You would have to repeatedly inject normal or exotic matter in just the right amounts to ensure that an observer at the throat would measure an ever decreasing stress-energy there. This would effectively destroy the wormhole by shrinking it to a microscopic size.
Can a black hole be used as a wormhole that is traversable in only one direction?
Possibly, if it is charged or rotating. As I mentioned before, there are certain well known solutions to Einstein’s field equations describing charged and rotating wormholes that might be one-way traversable. A traveler could in principle enter the black hole sector of these solutions and emerge from its white hole sector in another universe. From there he could never return to his universe of origination. There are a few problems with this scenario, however. The real universe is full of light and other radiation. This energy accumulates on certain surfaces in the traveler’s path. Crossing these surfaces could kill him. Moreover, these energy accumulations would likely destroy the wormhole. In particular, the wormhole’s white hole sector, from which the traveler would emerge, would be destroyed by the accumulation of energy on its outer horizon. Lastly, there is no reason to believe that this sort of wormhole would work as a shortcut – as a path to a distant region within a traveler’s own universe. Even if it somehow did, it would only be a path to the distant past of that universe.
Is it possible for travelers to simultaneously move through a traversable wormhole in opposite directions?
Yes. The only restriction is that the throat needs to be large enough to simultaneously accommodate at least two travelers.
Is there any way in which a wormhole might require a source of power to hold it open?
Yes. A synthetic wormhole’s stabilizer unit, which would inject normal or exotic matter as needed, would require power. Holding a wormhole’s exotic matter in place might also require power. One could imagine exotic matter that is self-repulsive both gravitationally and electrically. A wormhole’s designers could have decided to use electromagnetic fields to confine this matter at the throat. Generating such fields, even using superconducting coils, requires power. Turning such a wormhole “off” would amount to deactivating these fields. This would allow the exotic matter to spread out from the throat. Upon doing so, the matter’s density and pressure would decline sufficiently to enable physical barriers to confine it. The wormhole’s throat diameter would constrict, its traversal time would increase, and it would cease temporarily to be a viable means of human transport.
Could I use a wormhole to escape from the inside of a black hole?
Yes. Classically, there appears be to nothing to prevent the existence of a wormhole that connects the inside of a black hole with the region exterior to its event horizon. However, to an observer within the horizon, the outward direction points to the past, i.e. backward in time. So escaping a black hole via a wormhole is only possible, if time travel by wormhole is possible.
Are elementary particles really just tiny classical wormholes?
No. This is an idea that dates back to the 1930s. No one has gotten it to work in the intervening time. One problem is that the wormholes would have to be held open by a ubiquitous negative-energy field. We don’t observe such a field. In the absence of this field, the wormholes would become tiny black holes. Because of the large charge-to-mass and spin-to-mass ratios typical of elementary particles, the corresponding black holes would have to expose their singularities. Naked singularities are bad. The laws of physics break down there. Predictability is lost. Anything could fly out of them or be absorbed by them. We don’t observe this.
Are elementary particles really just quantum wormholes?
Not very likely. The main problem appears to be the discrepancy between the mass of the quantum wormhole and that of elementary particles. A quantum wormhole can have a mass of zero, or it can have a mass that is at least 1019 times that of the proton. This makes it impossible to reproduce the observed mass spectrum of elementary particles.
Can a wormhole periodically disappear and reappear?
Yes. It can do so in two ways: through external manipulation or internal dynamics. To externally manipulate a wormhole for this purpose, we would carefully inject it with matter in such a way as to ensure that its throat becomes microscopic. We would then reverse the process, by changing the sign on the matter injected, until the wormhole returns to its original size. For a wormhole to be periodic by virtue of its internal dynamics, its exotic matter need only possess a suitable equation of state. This equation determines how the matter’s pressure depends on its density. For certain pressure-density relationships, the wormhole will oscillate between being microscopic and macroscopic and thus appear to periodically disappear and reappear. We don’t know whether the type of exotic matter required to accomplish this exists.
Will the mouths of a periodic wormhole always appear in the same place?
Yes. True topology change is impossible within general relativity, as it is conventionally formulated. So a periodic wormhole never actually ceases to exist. It merely shrinks until it is microscopic. Its mouths, irrespective of their sizes, retain their positions relative to co-moving observers.
What would happen if two wormhole mouths were to collide?
If one mouth were much larger than the other, the smaller mouth would simply pass through the wormhole with the larger mouth, as any other object would. If the colliding mouths and their associated wormholes were identical, there would be two possible outcomes: 1) If the effective mass of both mouths is negative, they will approach, possibly coalesce briefly (if their relative momentum is high enough), emit gravitational waves, and separate. 2) If the effective mass of both mouths is positive, they will approach, coalesce, emit gravitational waves, and remain joined. In neither case would the topology of space have changed. When the mouths of the two wormholes coalesce, they do not become a single wormhole. Rather, they become a three-mouthed system roughly resembling a stethoscope: A mouth in one universe branches internally to connect to two separate mouths in separate universes (or distant regions within the same universe). Unfortunately, no one has yet taken the trouble to perform calculations that would confirm or refute this speculation.
What would happen if two mouths of the same wormhole were to collide?
After the collision identical mouths would 1) coalesce, if their masses are positive, or 2) separate, if their masses are negative. Upon coalescing, the wormhole’s shape would be something like the three-dimensional generalization of the surface of an eye screw (Figure 1.2). A traveler could enter the single mouth of the wormhole, travel the length of its interior region, and exit the mouth only to discover that she is back where she started.
Figure 1.2. A wormhole Self Collision. Mouths will likely coalesce.
What would it be like to travel through a wormhole?
As you enter a deep spherical wormhole, you will see stars concentrated in a sphere directly ahead. After awhile you peer out of your spaceship’s port window. You will notice another ship on a parallel course off in the distance. Upon inspecting it with your telescope, you will notice that it looks exactly like the starboard side of your spaceship. That’s because it is. Looking through your starboard window similarly reveals a distant port view of your ship. The sky will show relatively few stars in directions at right angles to your inward trajectory. The more forward your angle of view, the more stars you will see, until you see the aforementioned spherical concentration straight ahead. As you approach this concentration -- the wormhole’s throat -- you will notice that the parallel image of your ship is much closer. You wave and, after a momentary delay, can (through your telescope) see yourself waving. As you pass through the throat, you will find yourself gazing upon a normal sky of unfamiliar stars. The parallel image of your ship will recede and soon vanish. In contrast to this experience, traveling through a maximally benign Visser (thin-shell) wormhole would be just like stepping through a doorway. You could even straddle this doorway and be at once in two universes or vastly separated regions of the same universe.
Do the mouths of a rotating wormhole have to rotate at the same rate?
No. The wormhole’s exotic matter would merely need to have an angular momentum density that is distributed asymmetrically about the wormhole’s throat.
Do the mouths of a charged wormhole have to be equally charged?
No. But the wormhole’s exotic matter would need an asymmetrical charge density distribution.
Can a wormhole look like a black hole at one mouth and a traversable wormhole at the other, i.e. can only one of its mouths have an event horizon?
Yes. This, however, would result in a one-way traversable wormhole. Travelers entering from the horizon (black hole) side could reach the other mouth. But they would have to leave in time to avoid being crushed in the singularity that forms within this wormhole, as it pinches off. Travelers who innocently enter from the horizon-free mouth would invariably meet their doom at this singularity.
Can the size of a wormhole’s throat oscillate?
Yes. This would just be a periodic wormhole whose minimum throat size remains macroscopic. All comments regarding periodic wormholes apply, especially those emphasizing the importance of a suitable exotic matter equation of state to the realization of this phenomenon.
Is it always obvious that a traversable wormhole is not a black hole?
No. It's possible for a traversable wormhole to be arbitrarily close to being a black hole. It's an actual black hole only if it has an event horizon. You might try to test for the presence of an event horizon by attempting to detect Hawking radiation. That won't work. For a wormhole that's large enough to traverse, the Hawking radiation will be imperceptibly weak and drowned out by background radiation. You might try lowering a probe into the wormhole and trying to pull it back out. Unfortunately, gravitational time dilation ensures that this experiment could take centuries. The easiest method to test for a horizon in a short subjective time is to pilot your spaceship into the wormhole and try to reverse out of it. If you can't, you've entered a black hole.
What is the black hole information paradox and what do wormholes have to do with it?
In 1974 Stephen Hawking discovered that quantum theory requires black holes to emit radiation, which causes them to eventually evaporate away leaving nothing behind. This means that any information that fell into the black hole will vanish along with it. That’s a problem, because quantum theory also insists that information cannot be destroyed. That quantum theory applied to black holes seems to require information to both be destroyed and not be destroyed is called the black hole information paradox. Most physicists suspect that the paradox will be resolved by understanding how Hawking radiation actually carries away information. For example, when an encyclopedia is dropped into a black hole, physicists hope that the Hawking radiation emitted by the black hole will be perturbed in a manner that encodes the information of the encyclopedia. This preserves its information after the black hole evaporates away. However, if traversable wormholes can exist, this idea won’t work. A traversable wormhole that connects regions interior and exterior to the black hole will allow some of its contents to escape. The encyclopedia could fall into the black hole, fall into the mouth of a small wormhole beneath the black hole’s event horizon, and thereby escape the black hole. If Hawking radiation now encodes the encyclopedia’s information, we now have perfect information cloning exterior to the black hole – i.e. the encyclopedia together with its information encoded in radiation are simultaneously accessible to a single external observer. This is unacceptable, however, because perfect information cloning is also forbidden by quantum theory.
Does the motion in space of one wormhole mouth affect that of the other?
No. Because there is no way to establish an absolute frame of reference within a universe (or between universes), the mouths of a wormhole normally are in motion relative to each other. This translational motion of the mouths is completely independent.
So I can station the mouths on separate planets and not worry about the relative motion of the planets interfering with the wormhole’s operation?
Is it possible to create a network of wormholes in which any wormhole mouth could be used to reach multiple destinations directly?
Yes. Assuming that it’s possible to create a single wormhole, the creation of a network of many is not particularly far fetched. You would proceed as follows: 1) Create a wormhole that connects locations A and B. 2) Create another wormhole connecting locations A and C. There are now two wormhole mouths at the location A – one that leads to B and another that leads to C. 3) Move the A mouth of the AC wormhole into the A mouth of the AB wormhole until the A mouth of AC is at the throat of the AB wormhole. 4) You now have a wormhole network in which there is a non-stop connection between any of A, B, and C. Repeat the procedure to add other destinations. 5) Ease congestion at the throat nexus by expanding it (with additional exotic matter) and by adding an automated system that properly routes spacecraft based on their transmitted destination codes.
What would happen if one of the mouths of a traversable wormhole fell into the sun?
The wormhole’s stabilizer (if present) would be overwhelmed, causing the wormhole to collapse and become a black hole. This black hole would make its way to the center of the sun, where it would feed on the sun’s mass. As the black hole grows, the time dilation effects near its horizon would effectively retard the rate of nuclear fusion there. I would speculate that the resulting loss of outward pressure would cause the sun to contract. If this contraction occurs too rapidly -- which I think unlikely -- it could cause an inward-going high-pressure wave that would temporarily boost the rate of fusion. The sun could then explode, or it might merely expand until it returned to a size somewhat smaller than its original radius. Assuming that the sun did not explode, its radius would then decrease for the same reason as before. A sudden shrinkage would continue the sporadic cycle just described. Or it might continue to contract smoothly. In either case, the sun, or its remnant, will continue to shrink until the black hole completely devours it. Depending on the size of the black hole, the process could take seconds or millions of years.
© 2005 Enrico Rodrigo
For more information see The Physics of Stargates: Parallel Universes, Time Travel, and the Enigma of Wormhole Physics by Enrico Rodrigo.