Designer spacetimes for FTL and profits
Posted: Fri Mar 15, 2013 12:02 pm
I notice that usually, whenever there's some spacetime doohickey in a science fiction universe, the actual technical details tend to be rather vague. Wormholes are usually just spheres (or spiralling discs) floating in a vacuum, or at best are inside a fancy stargate. FTL travel is even less clear in its workings. And I noticed that overall on this forum, people tended to find FTL distasteful and lazy, perhaps because of this. So I thought I would try to compile a list of things on the topic of interesting spacetime features that are used a lot in science fiction, which is for the most part FTL and time travel.
Most of it is from either "Lorentzian wormholes" by Matt Visser or "Frontiers of Propulsion Science", which are probably the two best books on it for respectively the theoretical and engineering aspects, as well as the works of Morris, Thorne, Yurtsever, Ford, Roman, Krasnikov, etc etc.
In physics, such devices follow a cycle where someone will provide some clue that they cannot exist or be built, and someone else will then provide a clue otherwise. It's a highly speculative field, all the moreso because we have no idea what's the actual theory we should be using (it's a field that has a lot of quantum mechanics involved, so what is really needed is quantum gravity in the end), the math tends to be rather vague or intractable and it is currently way outside experimental reach. But then again, for conworlding, it's always possible to sweep that under the rug by claiming your own physics.
So here's a few things on the topic of all that
First, a few general considerations on the difficulties for building such things :
- A lot of those (if not all) require some form of weird matter. Either requiring singularities, matter with negative energy (or some form of violations of what are called the energy conditions), infinite structures and so on.
- The simplest solutions require the universe itself to be the machine. For instance, in the Gödel universe, any object within it will eventually make a complete loop in time. It makes the math much simpler but that is not really a time machine or wormhole that can be built.
- Many of those solutions are of dubious stability. As they are computed in a mostly empty universe, it is often the case that they may not survive someone trying to use it (or for even worse reasons, see further).
And some general technical considerations :
- They tend to be very energy intensive for any reasonable size. It's around 20 times the mass of Earth in negative energy for a tiny wormhole (about 10 cm) for instance, which is a lot denser than a neutron star.
- With spacetime mistreated so much, it has a lot of tidal effects. In the worst cases, they might be enough to rip apart atomic nuclei.
- Those gigantic energy densities, you may have to travel next to them or right through it, which may not be a good idea.
- In order to be practical, you should be able to use them rapidly - both from your own perspective and from earth's perspective. Say, when you go into a wormhole, you should come out of it before you die, and when you come out, it shouldn't be after the sun exploded.
- There are weird quantum effects aplenty.
That's for the general considerations. Now for some particular cases :
WORMHOLES
Wormholes are probably the oldest such device, both in physics and in science fiction (possibly along with "hyperspace", which has much shakier physical ground, so I won't discuss it). They were originally just an attempt at black hole physics : one solution of black holes is such that the black hole has two openings, leading to two different "universes". Bad math led to the creation of a solution that had this feature but without a singularity, the Einstein-Rosen bridge. While the reasoning was faulty, it was the first instance of the concept of wormholes.
As a quick note : black holes themselves aren't very good wormhole material. They have gigantic tidal forces, you're almost guarantee to crash in the singularity, even if you get to the "other side" you are still stuck in the event horizon and if by some miracle you manage to get out, an infinite amount of time might have passed for the outside. Also black holes from stellar collapse are very different from abstract theoretical black holes, and may not have such structure at all.
There hasn't been a lot done with wormholes after that for a while. They were mostly a curiosity, popping up in black hole physics and quantum gravity. But in the 80's, according to the story, Carl Sagan asked two physicists some ideas for his fancy alien story, Contact. That's when Morris and Thorne came up with the idea of the traversible wormhole in physics. The idea was to take the black hole type wormhole, but remove the singularities and event horizons.
The basic idea of the MT (Morris Thorne) wormhole is to take two universes (or the same universe, equivalently), cut out a small volume out of it and identifying the edges of that volume. The simplest example, if you only take two spatial dimensions, is to take two planes, cut a circle out of both and sewing the edges together. Someone traveling along one of plane hitting the wormhole will just continue travelling along the other plane.
When it comes to building one, there are a lot of problems involves :
1) Creating the wormhole. This may be the most difficult part, as it involves changing the shape of space (that whole cutting and sewing thing), which may not be permitted at all (general relativity is about changing the curvature, not the overall shape). Which still leaves a few solutions : the wormhole can have always been there, created along with the universe itself [although then see the stability problems later on], in which case the problem will be finding them. There may be tons of them in all space, or they may be rare. I couldn't really find much on the topic, but I would think that if it was the case, the cosmological inflation would make the mouths of such wormholes very far apart, which would be nice, even if odds are high they would end up in completely empty regions of space.
There may be a classical way of creating them. It's not explicitly forbidden, but there are very strong clues that it's impossible. Usually they involve weird results like causality violations, loss of time orientability (the ability to distinguish the future from the past) or singularities. Not a lot of work has been done on that as far as I know.
The "most likely" proposal is what is referred to as the spacetime foam. At quantum level (extremely small quantum level), spacetime may have a very different structure, not smooth at all, and maybe going as far as creating wormholes spontaneously. In this case, the wormholes are extremely tiny, about the size of the Planck scale (~10^-32 meters). To be precise they are not really created, there is just a transition from a state of spacetime with wormholes in it (sort of like quantum tunneling). There's some theoretical motivation that points to it, but so far it's not too clear. I couldn't really find a lot about how far apart would the mouthes of the wormholes be (the papers tend to be more about the topology than practical applications), although some say that it could be arbitrarily far apart. It's also not entirely clear if they are really wormholes in a practical sense and if they can be inflated to usable size.
Those wormholes aren't necessarily to our own universe, either. Some of them also lead to other spacetimes, so called "baby universes".
If a blackhole does have a wormhole structure (which isn't at all certain), it may also be possible to convert it by blasting it with exotic matter (see next point).
2) Stabilizing the wormholes. Wormholes tend to collapse on their own, either completely (the two mouthes disconnect, forming two black holes) or at least to the point of being unusable. To stabilize them, they require some amount of negative energy. The basic reason is that in general relativity, positive energy focus matter (it attracts) and negative energy repels it. A wormhole will take a lot of converging rays and then send them on completely divergent paths.
There's no classical form of matter with such properties, but some quantum mechanical systems can do it. Not all of them are necessarily helpful. Some of them only violate particular energy conditions (I didn't go into the various types). A general rule of thumb might be the quantum inequalities, which are a possible theorem relating the duration of negative energy to its intensity. Roughly, long pulses of negative energy are weaker, negative energy must be followed by positive energy and the longer the time between the negative and positive energy, the bigger is the positive pulse. They are only proven for one case though, and the exact form for general cases tends to be a bit vague, especially if the spacetime is curved.
If they are roughly true, though, wormholes would be limited to extremely small sizes (about a thousand Planck sizes, according to one estimate).
There's a laundry list of those quantum effects, like :
- Squeezed quantum states. They are quantum states where one of the uncertainty is "squeezed" to be very small (like the position is very well known but the momentum much less so), and they have alternating positive and negative energy, but overall positive energy. Mostly done currently by using lasers on certain crystalline structures, though there may be the possibility of making them by superposing single photons together 'by hand', so to speak. It has the problem of only having negative energy for a limited time, followed by an even larger positive one. There's some ideas to get around that, but so far I haven't seen anything really worked out.
- Gravitational squeezing (aka gravitational vacuum polarization). Near high gravitational sources, there's a constant flux of negative energy inward and positive energy outward (it's the basis of Hawking radiation in black holes). It has the benefit of being a constant source, requiring no constant new energy, but it is pretty hard to generate the densities required for it. It may also be possible that the gravitational squeezing of the wormhole itself may help it to keep open.
- All kinds of Casimir-like effects. Whenever there's a boundary of any kind, negative energy can be generated from it. Examples include the basic Casimir effects (two perfect conductors close to each other), moving mirrors, or boundaries in spacetime itself. While pretty easy to do, they have the problems of being extremely weak, compensated by the matter inside the plates and possibly being unrelated to the problem (the analysis only works by assuming they are perfect conductors, in reality it is probably a different effect).
Other proposals involve negative density cosmic strings and various weird quantum fields.
Some of those, or a combination of those, along with other fields (electric and magnetic fields are usually included for some fine tuning), might be used to inflate a wormhole to decent size and keep it open. The energy scales are pretty big, although they drop off linearly with size. A wormhole of 10 meters will require about 10 times the mass of Jupiter, while a wormhole of 1 cm only about two times the mass of earth (still pretty big). The analysis is only for one type of wormhole, though, and some analysis suggest that the quantity of exotic matter can be minimized.
The energies involved are pretty big, but on the other hand, so is any interstellar venture, even without FTL. For instance, a reasonable antimatter ship would require about 10^17 kg of antimatter (without involving the energy required for production), while a light sail for the same kind of trip would require several petawatts to run for several years. Interstellar travel is a pretty costly business.
3) Some various properties of wormholes. Wormholes can have basically any shape, as defined by the "cut and paste" procedure. Most analysis is done on spherical wormholes, as they have the simplest computations. Two other very interesting shapes are polyhedral wormholes (for instance, cubic wormholes), and flat wormholes. Wormholes with flat faces have the benefit of requiring less (and up to none) exotic matter, which would be interesting for actually crossing it without getting cooked. In the case of a cubical wormhole, in the ideal case, all the exotic matter is concentrated on the edges and corners. In the case of a flat wormhole, it's all on a curve.
Visually, neglecting what the exotic matter will look like, wormholes will look like what is happening on the other side of it as well as some reflections of our own side of it (there are some light rays that go in the wormhole and come out on the same "side" of the universe), plus some distortions due to the shape of the wormhole and the gravitational lensing it might produce. There might also be some redshifting involved, although I don't expect it to be very important in a traversible wormhole. For some actual examples, here's a few renderings from various articles :
"Visual appearance of a Morris-Thorne wormhole" probably has the best one. Our own side is represented by a lattice with some labels indicating the four cardinal directions.
https://dl.dropbox.com/u/19940612/E1_wh ... Layout.png
There is then the addition of a wormhole of radius 0.3 (the lattice is of length 1).
https://dl.dropbox.com/u/19940612/E3b_w ... .3zoom.png
The lattice on the side is slightly distorted. The "Universe 1 - North" sign a bit more, but it is still readable. There is a mirror image of the "Universe 1 - North" sign in between as well (that's because the light rays of the same point can travel in several ways to reach the observer). Inside that mirror image is yet more of our own universe - a mirror image of the lattice structure all around (because of light rays coming in and turning around on the wormhole before coming out), and at the very center, the image of the other universe.
A slightly bigger wormhole helps to see the situation :
https://dl.dropbox.com/u/19940612/E4_wh ... .0.big.png
There is also an animation of the whole process :
ftp://ftp.aip.org/epaps/am_j_phys/E-AJP ... Flight.mpg
As well as another example in two 3D modeled rooms, as it appears in both universes :
https://dl.dropbox.com/u/19940612/E5a_room_upper.png
https://dl.dropbox.com/u/19940612/E5b_room_lower.png
"Astrometric image centroid displacements due to gravitational microlensing by the Ellis wormhole" has this representation of an object passing behind a wormhole, the real one in blue and the two images in purple :
https://dl.dropbox.com/u/19940612/Lense.jpg
And "Natural wormholes as gravitational lenses" provide this diagram of how light is deflected by it if it has an overall negative mass :
https://dl.dropbox.com/u/19940612/Lense2.jpg
Neglecting the light from the other universe, there is a large region of space where such rays cannot pass into (the umbra) as well as a region where that light will concentrate (the caustic). This will basically look like a black disk surrounded by a bright ring that will drop to the usual background light (that is assuming that all the light comes from one side, of course, and nothing comes out of the other universe).
All of this is for what is called a Bronnikov-Ellis wormhole : static, spherical, and the "flaring out" of the throat following a particular form. Wormholes of different shapes and other parameters will look different. Flat faces in wormholes may look rather undistorted except for around the edges. There is the possibility that time may run at different speeds on each side (although in the case of interstellar travel type wormholes, it probably won't be the case). Another thing is that while it may not be required, there's some hints that wormholes have to be orientable, at least if they are within the same universe : if you go into it by one end, you will come out in the other direction - the wormhole mouthes are "mirror images" of each others. The mouth can still be rotated afterwards,
Wormholes have an associated mass and charge. The mass can be negative, positive or zero, and it does not have to be the same mass and charge on both sides. A further rule is that if something enters the mouth A and comes out of the mouth B, then A gains the mass and charge of the object while B loses it, which can get out of hand : A might start becoming so heavy that it will attract more matter while B will repel it. It might then be a good idea to do the travel both way or at least have this traffic negligible compared to the wormhole mass.
Wormholes between two points of the same universe can be turned very easily into a time machine (which I will describe more later on). While this may be interesting, some analysis show that the closer a wormhole is to being a time machine, the more hotter it gets (the process causes the quantum vacuum to emit a whole lot of radiations). It happens whenever the mouthes of the wormhole have time going at a different rate, either because they are moving or in gravitational fields. I think it would be very difficult to avoid this, so this might mean that such wormholes might completely collapse eventually because of this. If this process completely forbids time travel, the total collapse will happen before the distance between the two mouthes is such that you are able to travel back at the moment you departed (for instance, if the wormholes are one light year apart, the time difference between them cannot be greater than a year).
This can also be a benefit : since you might have to send the wormhole away by regular means (slower than light ships), it might be a good idea to induce a time shift between them so that you are able to go through it before it has arrived as seen on earth. For instance, 3 years after you sent the ship to Alpha Centauri. There's no causality problem there, because you won't be able to contact yourself in the past. There's several ways to induce such a time shift, mostly by either moving the mouth around to induce some time dilatation or putting it in some gravitational potential different from the other side. The mouth that accelerates [the most, if both are moving] will run faster, the mouth in the highest gravitational potential will run faster.
Going through the wormhole will be equivalent to sending positive energy through it. Technically it will shrink slightly from it (before going back to normal), but considering the density of matter with the density of the exotic matter threading the throat, the effect should be negligible.
WARP DRIVE
The other big FTL devices from general relativity are globally referred to as warp drives, and as far as I know, they are all variations on the Alcubierre drive and the Krasnikov tube.
The Alcubierre drive basically contracts the space in front of it and expands the space behind, being carried on a wave of space without any speed limitation (also called a "warp bubble"). It has the benefit of requiring no particular assumption about spacetime but the problem of being way more energy intensive than wormholes. A rough calculation shows that the energy needed is proportional to the thickness of the warp bubble's "wall" and goes as the square of the speed and the radius of the bubble. Because of the quantum inequalities discussed, it may not be possible to make the wall of the warp bubble that big, making it a rather big problem.
Like wormholes, it requires negative energy in spades, but much worse, it requires that energy to move faster than light. If you are far enough from the warp bubble, there's very little tidal forces and time dilatation, making it a rather convenient mean to travel. But the big problem is that even for very slow speeds, the energy required is way too high (up to several millions of times the energy of the observable universe).
There has been some propositions to fix it : van den Broek proposed to make a very small bubble but expand the space inside the bubble (it reduces the energy somewhat but requires even higher densities), and Krasnikov proposed to build a tube of negative energy at speeds slower than light to use afterwards (it solves the problem of the matter going faster than light but not really the energy problems).
TIME MACHINES
Time machines also happen a lot in general relativity. While they are usually dismissed as unphysical (a lot of the examples are unphysical on some level), there is no hard evidence that they cannot happen. There's a general set of rules that try to forbid them known as the chronology protection conjecture, but no general proof of it exists so far, as all the rules proposed end up having counter examples.
The three big arguments to prevent the formations of time machines are stability issues (that even if a time machine is formed, any particle going inside would make it collapse), energy conditions (that almost all time machines require negative energy, infinite objects or singularities to work) and quantum backreaction (when a time machine is close to forming, the quantum vacuum starts radiating more and more, up to infinity or at least very high values, collapsing everything). All three of those have counter examples, and so far there is no proof forbidding or allowing them. Some versions of quantum gravity forbids them outright (like loop quantum gravity), some allow it and some are unknown (like string theory).
To make a time machine, there are two ways in general relativity : use topology (the shape of the universe) or geometry (the curvature). The topological route is mostly useless, as it requires the universe to already be like that. The simplest example would be to take any spacetime, and identify two points in time, so that it forms a circle. It is often used for computations because it's very easy to work with, but there isn't really a way to build it.
The geometrical route is more interesting, because it depends on the distribution of matter, which can be changed. What it does basically is that the direction of time changes gradually, tipping over until it goes backward.
A few examples of time machine spacetimes are :
- The Gödel universe. The very first one considered. Made of rotating dust and a cosmological constant, it's not particularly interesting because it is built into the universe : the universe itself is the time machine. Any object within it will eventually travel back in time by itself.
- The van Stockum time machine. An infinitely long rotating cylinder. By going close enough to the cylinder and going in circles around it, it is possible to go arbitrarily far into the past, every turn bringing you back by some amount. The fact that the cylinder is infinite, and that this is a static solution (the cylinder exists for an eternity) makes it rather suspisious as a realistic example, as further study indicates a finite cylinder will probably not have those properties. (There's a very similar model involving a rotating cosmic string, as well as another one with two cosmic strings in orbit around each other, with the same problems)
- Rotating black holes are known to have that behaviour as well. The problems being that the time machine part is behind the event horizon (unless it's a naked singularity, which brings its own problems), and the fact that real black holes (created by star collapse) are not quite that perfect model. It's also very unstable.
Something to note here is the type of symmetries : all geometrical time machines have some symmetry around an axis. As far as I know, it's not possible to have a time machine that has spherical symmetry. All time machines have this symmetry around an axis, or less than that. The other thing to note is that there is no jump back in time. All that happens is that, in a way, you travel time as if it were space (that's the effect of the tipping of the direction of time).
To build "realistic" time machines, we want something that is both finite in space and in time. A consequence of this is that we cannot go back in time further than the creation of the time machine (and any calculation must also include the travel time to, in and out of the time machine)
Using the trick to induce a time shift in wormholes, you can turn any wormhole into a time machine. Especially useful is that you can then bring the two wormhole mouthes in the same place but at different times, making a time machine that appears to be just "jumping" from one time to the other (actually you are just making a very short trip through the wormhole throat). This has the problem of the previously mentionned vacuum radiations. One of the solution proposed is the Roman ring : instead of using a wormhole, take one wormhole with a time shift that doesn't break causality (say, 3 light years away with a time shift of two years), and then another wormhole in the same location with another time shift of the kind. Separately, there is no break in causality, but going through both wormholes does. This reduces the quantity of vacuum radiation (especially if they are well separated) to some degree. And of course, it is possible to do it an arbitrary number of time.
There's other designs for finite time machines. Many of the ones I have seen involve singularities and event horizons, making them also a bit problematic, but there's no lack of tempting models. For instance, the Ori time machine involves a sphere of matter with no negative energy and an empty torus inside that sphere. As a rule of thumb, most means of FTL travel can be rigged into time machines with some modifications (it has been also shown in the case of warp drives).
Besides constructing the time machine, there is also the matter of what happens once going through. There's two theories on that : The Novikov consistency principle and the idea of branching spacetime.
In the case of the Novikov principle, you cannot change the past (it's the predestination paradox all over again). That approach has the benefit of being computable to some degree. On the other hand, it is very rough on whatever tries to cross it. There's a lot of weird quantum effects happening (particle states get mixed) and while I don't know any paper on the topic of someone trying to cross such a time machine, my guess is that he would be scrambled into a fine mist of particles. It might be possible to get a message across (keeping in mind that the timeline has to remain consistent), but I can't be certain. It is also very hard to determine anything happening in a time machine because knowing about what goes in isn't enough. There's the possibility that a particle will go several time around before leaving, or that a particle will only exist within the time machine (it forms a loop in time). In science fiction, that is the bootstrap paradox : if you got the plan from a time machine by a time travelling you from the future, then who invented it? (see also transparent aluminium in Star Trek IV) Of course, it might be possible to do a probability analysis of how this happens, and then decypher whatever comes out of the time machine to find out what went in. But I would not try crossing that time machine.
The theory of branching spacetime is much more vague. It hinges on the idea that, in the case of a time machine, spacetime may "split" in two (or more) spacetimes, making it possible to change the past. It may or may not be linked to such quantum things as the many world interpretation of quantum mechanics and the behavior of particles going through is unknown, as there isn't even a basic model for quantum behavior for it. But it may be possible for an individual to actually go back in time without too much risks.
In both cases, note that there's no such thing as a paradox : in the case of Novikov, you can never change the past, you were already there. In the case of branching spacetime, you cannot not change it : your very presence has already changed it. But this is a new timeline and killing your grandfather won't change anything. In neither theory is there a rippling effect or fading away because your mom hooked up with the wrong guy.
There may be other prescriptions for how to deal with it, but as far as I know, those are the only two that have been developped to some degree.
***
So with all that, here is for instance how some civilization might evolve some FTL technology :
- First, it might have a better time at it if it is after developping some decent theory of quantum gravity.
- The stage we are currently at is that of research. Once in a while, NASA or some other organization will give a tiny budget on topics like interstellar travel. While it may not give us interstellar travel necessarily, it may give us some leads for interesting technologies growing out of such research. Examples of such projects are Vision-21 in 1990, the Breakthrough Propulsion Physics Project (1996 to 2002), Project Greenglow by BAE systems (starting in 1986) and the ESA's Advanced Concept Team. Some good topics of research would be to find out the limits of exotic matter in more details, means of producing it (in large quantities) and for a long period of time, finding different geometries that use less of it, perhaps using dynamic shapes rather than static and so on. I also didn't go much into the studies made into wormholes and warpdrives in theories other than general relativity, as modifications to it also change a lot of theorems.
- The first wormholes would probably be microscopic ones. Their existence could be deduced from, say, elementary particles passing through them. This would require either wormholes that are not too tiny (in some exotic matter), particles of very high energy (as they have a smaller wavelength, which would help getting in those tiny things), or probably both. This was actually one hypothesis (among many) that was formulated for the whole FTL neutrino a few months ago. Or alternatively, it could be cosmological wormholes. As previously stated, there's exotic matter around very dense objects, making it possible for wormholes of a decent size to develop around them. The best celestial bodies for this are objets of small mass but high density, perhaps small black holes and neutron stars, as large enough wormholes would induce some gravitational lensing around. Other possibilities include remnants from the big bang or other civilizations. There has been some studies done, and no definitive traces of such wormholes exist, although so far the study was done on wormholes of throat size ~ 1 parsec.
- The next step would be to turn wormholes into usable objects, with the various methods described. What they can be used for depends on the distance between them - if those distances are tiny, you can then use them for practical purpose. If you can't blow them up to human sizes, FTL communication can be of use. Time machines also have very interesting properties in quantum computing. If the distance between them is arbitrarily large, they can be used for astronomical observation. Perhaps even sending out signals to alien civilizations.
If we can blow them up to interesting sizes, then more interesting things can happen. If the distance between them is very large, this may still not be useful, or at least not for colonizing - statistically, they would probably end up in the voids in between supergalactic clusters. Then you might have to "run through" a lot of wormholes before finding one that's interesting. You might still need to move the other side closer to another planet. If the distance is small, then you might need to move it (IN SPACE) by the usual means. The time shifting trick might be used to shorten the time before we can get there, by say rotating one mouth at high speed. A good thing to do to save up on energy would be to keep the wormhole at microscopic size for the duration of the trip and inflate it when reaching destination.
Well, that's about all the things I can think of on the topic. I hope that you are now full of love for FTL~
Most of it is from either "Lorentzian wormholes" by Matt Visser or "Frontiers of Propulsion Science", which are probably the two best books on it for respectively the theoretical and engineering aspects, as well as the works of Morris, Thorne, Yurtsever, Ford, Roman, Krasnikov, etc etc.
In physics, such devices follow a cycle where someone will provide some clue that they cannot exist or be built, and someone else will then provide a clue otherwise. It's a highly speculative field, all the moreso because we have no idea what's the actual theory we should be using (it's a field that has a lot of quantum mechanics involved, so what is really needed is quantum gravity in the end), the math tends to be rather vague or intractable and it is currently way outside experimental reach. But then again, for conworlding, it's always possible to sweep that under the rug by claiming your own physics.
So here's a few things on the topic of all that
First, a few general considerations on the difficulties for building such things :
- A lot of those (if not all) require some form of weird matter. Either requiring singularities, matter with negative energy (or some form of violations of what are called the energy conditions), infinite structures and so on.
- The simplest solutions require the universe itself to be the machine. For instance, in the Gödel universe, any object within it will eventually make a complete loop in time. It makes the math much simpler but that is not really a time machine or wormhole that can be built.
- Many of those solutions are of dubious stability. As they are computed in a mostly empty universe, it is often the case that they may not survive someone trying to use it (or for even worse reasons, see further).
And some general technical considerations :
- They tend to be very energy intensive for any reasonable size. It's around 20 times the mass of Earth in negative energy for a tiny wormhole (about 10 cm) for instance, which is a lot denser than a neutron star.
- With spacetime mistreated so much, it has a lot of tidal effects. In the worst cases, they might be enough to rip apart atomic nuclei.
- Those gigantic energy densities, you may have to travel next to them or right through it, which may not be a good idea.
- In order to be practical, you should be able to use them rapidly - both from your own perspective and from earth's perspective. Say, when you go into a wormhole, you should come out of it before you die, and when you come out, it shouldn't be after the sun exploded.
- There are weird quantum effects aplenty.
That's for the general considerations. Now for some particular cases :
WORMHOLES
Wormholes are probably the oldest such device, both in physics and in science fiction (possibly along with "hyperspace", which has much shakier physical ground, so I won't discuss it). They were originally just an attempt at black hole physics : one solution of black holes is such that the black hole has two openings, leading to two different "universes". Bad math led to the creation of a solution that had this feature but without a singularity, the Einstein-Rosen bridge. While the reasoning was faulty, it was the first instance of the concept of wormholes.
As a quick note : black holes themselves aren't very good wormhole material. They have gigantic tidal forces, you're almost guarantee to crash in the singularity, even if you get to the "other side" you are still stuck in the event horizon and if by some miracle you manage to get out, an infinite amount of time might have passed for the outside. Also black holes from stellar collapse are very different from abstract theoretical black holes, and may not have such structure at all.
There hasn't been a lot done with wormholes after that for a while. They were mostly a curiosity, popping up in black hole physics and quantum gravity. But in the 80's, according to the story, Carl Sagan asked two physicists some ideas for his fancy alien story, Contact. That's when Morris and Thorne came up with the idea of the traversible wormhole in physics. The idea was to take the black hole type wormhole, but remove the singularities and event horizons.
The basic idea of the MT (Morris Thorne) wormhole is to take two universes (or the same universe, equivalently), cut out a small volume out of it and identifying the edges of that volume. The simplest example, if you only take two spatial dimensions, is to take two planes, cut a circle out of both and sewing the edges together. Someone traveling along one of plane hitting the wormhole will just continue travelling along the other plane.
When it comes to building one, there are a lot of problems involves :
1) Creating the wormhole. This may be the most difficult part, as it involves changing the shape of space (that whole cutting and sewing thing), which may not be permitted at all (general relativity is about changing the curvature, not the overall shape). Which still leaves a few solutions : the wormhole can have always been there, created along with the universe itself [although then see the stability problems later on], in which case the problem will be finding them. There may be tons of them in all space, or they may be rare. I couldn't really find much on the topic, but I would think that if it was the case, the cosmological inflation would make the mouths of such wormholes very far apart, which would be nice, even if odds are high they would end up in completely empty regions of space.
There may be a classical way of creating them. It's not explicitly forbidden, but there are very strong clues that it's impossible. Usually they involve weird results like causality violations, loss of time orientability (the ability to distinguish the future from the past) or singularities. Not a lot of work has been done on that as far as I know.
The "most likely" proposal is what is referred to as the spacetime foam. At quantum level (extremely small quantum level), spacetime may have a very different structure, not smooth at all, and maybe going as far as creating wormholes spontaneously. In this case, the wormholes are extremely tiny, about the size of the Planck scale (~10^-32 meters). To be precise they are not really created, there is just a transition from a state of spacetime with wormholes in it (sort of like quantum tunneling). There's some theoretical motivation that points to it, but so far it's not too clear. I couldn't really find a lot about how far apart would the mouthes of the wormholes be (the papers tend to be more about the topology than practical applications), although some say that it could be arbitrarily far apart. It's also not entirely clear if they are really wormholes in a practical sense and if they can be inflated to usable size.
Those wormholes aren't necessarily to our own universe, either. Some of them also lead to other spacetimes, so called "baby universes".
If a blackhole does have a wormhole structure (which isn't at all certain), it may also be possible to convert it by blasting it with exotic matter (see next point).
2) Stabilizing the wormholes. Wormholes tend to collapse on their own, either completely (the two mouthes disconnect, forming two black holes) or at least to the point of being unusable. To stabilize them, they require some amount of negative energy. The basic reason is that in general relativity, positive energy focus matter (it attracts) and negative energy repels it. A wormhole will take a lot of converging rays and then send them on completely divergent paths.
There's no classical form of matter with such properties, but some quantum mechanical systems can do it. Not all of them are necessarily helpful. Some of them only violate particular energy conditions (I didn't go into the various types). A general rule of thumb might be the quantum inequalities, which are a possible theorem relating the duration of negative energy to its intensity. Roughly, long pulses of negative energy are weaker, negative energy must be followed by positive energy and the longer the time between the negative and positive energy, the bigger is the positive pulse. They are only proven for one case though, and the exact form for general cases tends to be a bit vague, especially if the spacetime is curved.
If they are roughly true, though, wormholes would be limited to extremely small sizes (about a thousand Planck sizes, according to one estimate).
There's a laundry list of those quantum effects, like :
- Squeezed quantum states. They are quantum states where one of the uncertainty is "squeezed" to be very small (like the position is very well known but the momentum much less so), and they have alternating positive and negative energy, but overall positive energy. Mostly done currently by using lasers on certain crystalline structures, though there may be the possibility of making them by superposing single photons together 'by hand', so to speak. It has the problem of only having negative energy for a limited time, followed by an even larger positive one. There's some ideas to get around that, but so far I haven't seen anything really worked out.
- Gravitational squeezing (aka gravitational vacuum polarization). Near high gravitational sources, there's a constant flux of negative energy inward and positive energy outward (it's the basis of Hawking radiation in black holes). It has the benefit of being a constant source, requiring no constant new energy, but it is pretty hard to generate the densities required for it. It may also be possible that the gravitational squeezing of the wormhole itself may help it to keep open.
- All kinds of Casimir-like effects. Whenever there's a boundary of any kind, negative energy can be generated from it. Examples include the basic Casimir effects (two perfect conductors close to each other), moving mirrors, or boundaries in spacetime itself. While pretty easy to do, they have the problems of being extremely weak, compensated by the matter inside the plates and possibly being unrelated to the problem (the analysis only works by assuming they are perfect conductors, in reality it is probably a different effect).
Other proposals involve negative density cosmic strings and various weird quantum fields.
Some of those, or a combination of those, along with other fields (electric and magnetic fields are usually included for some fine tuning), might be used to inflate a wormhole to decent size and keep it open. The energy scales are pretty big, although they drop off linearly with size. A wormhole of 10 meters will require about 10 times the mass of Jupiter, while a wormhole of 1 cm only about two times the mass of earth (still pretty big). The analysis is only for one type of wormhole, though, and some analysis suggest that the quantity of exotic matter can be minimized.
The energies involved are pretty big, but on the other hand, so is any interstellar venture, even without FTL. For instance, a reasonable antimatter ship would require about 10^17 kg of antimatter (without involving the energy required for production), while a light sail for the same kind of trip would require several petawatts to run for several years. Interstellar travel is a pretty costly business.
3) Some various properties of wormholes. Wormholes can have basically any shape, as defined by the "cut and paste" procedure. Most analysis is done on spherical wormholes, as they have the simplest computations. Two other very interesting shapes are polyhedral wormholes (for instance, cubic wormholes), and flat wormholes. Wormholes with flat faces have the benefit of requiring less (and up to none) exotic matter, which would be interesting for actually crossing it without getting cooked. In the case of a cubical wormhole, in the ideal case, all the exotic matter is concentrated on the edges and corners. In the case of a flat wormhole, it's all on a curve.
Visually, neglecting what the exotic matter will look like, wormholes will look like what is happening on the other side of it as well as some reflections of our own side of it (there are some light rays that go in the wormhole and come out on the same "side" of the universe), plus some distortions due to the shape of the wormhole and the gravitational lensing it might produce. There might also be some redshifting involved, although I don't expect it to be very important in a traversible wormhole. For some actual examples, here's a few renderings from various articles :
"Visual appearance of a Morris-Thorne wormhole" probably has the best one. Our own side is represented by a lattice with some labels indicating the four cardinal directions.
https://dl.dropbox.com/u/19940612/E1_wh ... Layout.png
There is then the addition of a wormhole of radius 0.3 (the lattice is of length 1).
https://dl.dropbox.com/u/19940612/E3b_w ... .3zoom.png
The lattice on the side is slightly distorted. The "Universe 1 - North" sign a bit more, but it is still readable. There is a mirror image of the "Universe 1 - North" sign in between as well (that's because the light rays of the same point can travel in several ways to reach the observer). Inside that mirror image is yet more of our own universe - a mirror image of the lattice structure all around (because of light rays coming in and turning around on the wormhole before coming out), and at the very center, the image of the other universe.
A slightly bigger wormhole helps to see the situation :
https://dl.dropbox.com/u/19940612/E4_wh ... .0.big.png
There is also an animation of the whole process :
ftp://ftp.aip.org/epaps/am_j_phys/E-AJP ... Flight.mpg
As well as another example in two 3D modeled rooms, as it appears in both universes :
https://dl.dropbox.com/u/19940612/E5a_room_upper.png
https://dl.dropbox.com/u/19940612/E5b_room_lower.png
"Astrometric image centroid displacements due to gravitational microlensing by the Ellis wormhole" has this representation of an object passing behind a wormhole, the real one in blue and the two images in purple :
https://dl.dropbox.com/u/19940612/Lense.jpg
And "Natural wormholes as gravitational lenses" provide this diagram of how light is deflected by it if it has an overall negative mass :
https://dl.dropbox.com/u/19940612/Lense2.jpg
Neglecting the light from the other universe, there is a large region of space where such rays cannot pass into (the umbra) as well as a region where that light will concentrate (the caustic). This will basically look like a black disk surrounded by a bright ring that will drop to the usual background light (that is assuming that all the light comes from one side, of course, and nothing comes out of the other universe).
All of this is for what is called a Bronnikov-Ellis wormhole : static, spherical, and the "flaring out" of the throat following a particular form. Wormholes of different shapes and other parameters will look different. Flat faces in wormholes may look rather undistorted except for around the edges. There is the possibility that time may run at different speeds on each side (although in the case of interstellar travel type wormholes, it probably won't be the case). Another thing is that while it may not be required, there's some hints that wormholes have to be orientable, at least if they are within the same universe : if you go into it by one end, you will come out in the other direction - the wormhole mouthes are "mirror images" of each others. The mouth can still be rotated afterwards,
Wormholes have an associated mass and charge. The mass can be negative, positive or zero, and it does not have to be the same mass and charge on both sides. A further rule is that if something enters the mouth A and comes out of the mouth B, then A gains the mass and charge of the object while B loses it, which can get out of hand : A might start becoming so heavy that it will attract more matter while B will repel it. It might then be a good idea to do the travel both way or at least have this traffic negligible compared to the wormhole mass.
Wormholes between two points of the same universe can be turned very easily into a time machine (which I will describe more later on). While this may be interesting, some analysis show that the closer a wormhole is to being a time machine, the more hotter it gets (the process causes the quantum vacuum to emit a whole lot of radiations). It happens whenever the mouthes of the wormhole have time going at a different rate, either because they are moving or in gravitational fields. I think it would be very difficult to avoid this, so this might mean that such wormholes might completely collapse eventually because of this. If this process completely forbids time travel, the total collapse will happen before the distance between the two mouthes is such that you are able to travel back at the moment you departed (for instance, if the wormholes are one light year apart, the time difference between them cannot be greater than a year).
This can also be a benefit : since you might have to send the wormhole away by regular means (slower than light ships), it might be a good idea to induce a time shift between them so that you are able to go through it before it has arrived as seen on earth. For instance, 3 years after you sent the ship to Alpha Centauri. There's no causality problem there, because you won't be able to contact yourself in the past. There's several ways to induce such a time shift, mostly by either moving the mouth around to induce some time dilatation or putting it in some gravitational potential different from the other side. The mouth that accelerates [the most, if both are moving] will run faster, the mouth in the highest gravitational potential will run faster.
Going through the wormhole will be equivalent to sending positive energy through it. Technically it will shrink slightly from it (before going back to normal), but considering the density of matter with the density of the exotic matter threading the throat, the effect should be negligible.
WARP DRIVE
The other big FTL devices from general relativity are globally referred to as warp drives, and as far as I know, they are all variations on the Alcubierre drive and the Krasnikov tube.
The Alcubierre drive basically contracts the space in front of it and expands the space behind, being carried on a wave of space without any speed limitation (also called a "warp bubble"). It has the benefit of requiring no particular assumption about spacetime but the problem of being way more energy intensive than wormholes. A rough calculation shows that the energy needed is proportional to the thickness of the warp bubble's "wall" and goes as the square of the speed and the radius of the bubble. Because of the quantum inequalities discussed, it may not be possible to make the wall of the warp bubble that big, making it a rather big problem.
Like wormholes, it requires negative energy in spades, but much worse, it requires that energy to move faster than light. If you are far enough from the warp bubble, there's very little tidal forces and time dilatation, making it a rather convenient mean to travel. But the big problem is that even for very slow speeds, the energy required is way too high (up to several millions of times the energy of the observable universe).
There has been some propositions to fix it : van den Broek proposed to make a very small bubble but expand the space inside the bubble (it reduces the energy somewhat but requires even higher densities), and Krasnikov proposed to build a tube of negative energy at speeds slower than light to use afterwards (it solves the problem of the matter going faster than light but not really the energy problems).
TIME MACHINES
Time machines also happen a lot in general relativity. While they are usually dismissed as unphysical (a lot of the examples are unphysical on some level), there is no hard evidence that they cannot happen. There's a general set of rules that try to forbid them known as the chronology protection conjecture, but no general proof of it exists so far, as all the rules proposed end up having counter examples.
The three big arguments to prevent the formations of time machines are stability issues (that even if a time machine is formed, any particle going inside would make it collapse), energy conditions (that almost all time machines require negative energy, infinite objects or singularities to work) and quantum backreaction (when a time machine is close to forming, the quantum vacuum starts radiating more and more, up to infinity or at least very high values, collapsing everything). All three of those have counter examples, and so far there is no proof forbidding or allowing them. Some versions of quantum gravity forbids them outright (like loop quantum gravity), some allow it and some are unknown (like string theory).
To make a time machine, there are two ways in general relativity : use topology (the shape of the universe) or geometry (the curvature). The topological route is mostly useless, as it requires the universe to already be like that. The simplest example would be to take any spacetime, and identify two points in time, so that it forms a circle. It is often used for computations because it's very easy to work with, but there isn't really a way to build it.
The geometrical route is more interesting, because it depends on the distribution of matter, which can be changed. What it does basically is that the direction of time changes gradually, tipping over until it goes backward.
A few examples of time machine spacetimes are :
- The Gödel universe. The very first one considered. Made of rotating dust and a cosmological constant, it's not particularly interesting because it is built into the universe : the universe itself is the time machine. Any object within it will eventually travel back in time by itself.
- The van Stockum time machine. An infinitely long rotating cylinder. By going close enough to the cylinder and going in circles around it, it is possible to go arbitrarily far into the past, every turn bringing you back by some amount. The fact that the cylinder is infinite, and that this is a static solution (the cylinder exists for an eternity) makes it rather suspisious as a realistic example, as further study indicates a finite cylinder will probably not have those properties. (There's a very similar model involving a rotating cosmic string, as well as another one with two cosmic strings in orbit around each other, with the same problems)
- Rotating black holes are known to have that behaviour as well. The problems being that the time machine part is behind the event horizon (unless it's a naked singularity, which brings its own problems), and the fact that real black holes (created by star collapse) are not quite that perfect model. It's also very unstable.
Something to note here is the type of symmetries : all geometrical time machines have some symmetry around an axis. As far as I know, it's not possible to have a time machine that has spherical symmetry. All time machines have this symmetry around an axis, or less than that. The other thing to note is that there is no jump back in time. All that happens is that, in a way, you travel time as if it were space (that's the effect of the tipping of the direction of time).
To build "realistic" time machines, we want something that is both finite in space and in time. A consequence of this is that we cannot go back in time further than the creation of the time machine (and any calculation must also include the travel time to, in and out of the time machine)
Using the trick to induce a time shift in wormholes, you can turn any wormhole into a time machine. Especially useful is that you can then bring the two wormhole mouthes in the same place but at different times, making a time machine that appears to be just "jumping" from one time to the other (actually you are just making a very short trip through the wormhole throat). This has the problem of the previously mentionned vacuum radiations. One of the solution proposed is the Roman ring : instead of using a wormhole, take one wormhole with a time shift that doesn't break causality (say, 3 light years away with a time shift of two years), and then another wormhole in the same location with another time shift of the kind. Separately, there is no break in causality, but going through both wormholes does. This reduces the quantity of vacuum radiation (especially if they are well separated) to some degree. And of course, it is possible to do it an arbitrary number of time.
There's other designs for finite time machines. Many of the ones I have seen involve singularities and event horizons, making them also a bit problematic, but there's no lack of tempting models. For instance, the Ori time machine involves a sphere of matter with no negative energy and an empty torus inside that sphere. As a rule of thumb, most means of FTL travel can be rigged into time machines with some modifications (it has been also shown in the case of warp drives).
Besides constructing the time machine, there is also the matter of what happens once going through. There's two theories on that : The Novikov consistency principle and the idea of branching spacetime.
In the case of the Novikov principle, you cannot change the past (it's the predestination paradox all over again). That approach has the benefit of being computable to some degree. On the other hand, it is very rough on whatever tries to cross it. There's a lot of weird quantum effects happening (particle states get mixed) and while I don't know any paper on the topic of someone trying to cross such a time machine, my guess is that he would be scrambled into a fine mist of particles. It might be possible to get a message across (keeping in mind that the timeline has to remain consistent), but I can't be certain. It is also very hard to determine anything happening in a time machine because knowing about what goes in isn't enough. There's the possibility that a particle will go several time around before leaving, or that a particle will only exist within the time machine (it forms a loop in time). In science fiction, that is the bootstrap paradox : if you got the plan from a time machine by a time travelling you from the future, then who invented it? (see also transparent aluminium in Star Trek IV) Of course, it might be possible to do a probability analysis of how this happens, and then decypher whatever comes out of the time machine to find out what went in. But I would not try crossing that time machine.
The theory of branching spacetime is much more vague. It hinges on the idea that, in the case of a time machine, spacetime may "split" in two (or more) spacetimes, making it possible to change the past. It may or may not be linked to such quantum things as the many world interpretation of quantum mechanics and the behavior of particles going through is unknown, as there isn't even a basic model for quantum behavior for it. But it may be possible for an individual to actually go back in time without too much risks.
In both cases, note that there's no such thing as a paradox : in the case of Novikov, you can never change the past, you were already there. In the case of branching spacetime, you cannot not change it : your very presence has already changed it. But this is a new timeline and killing your grandfather won't change anything. In neither theory is there a rippling effect or fading away because your mom hooked up with the wrong guy.
There may be other prescriptions for how to deal with it, but as far as I know, those are the only two that have been developped to some degree.
***
So with all that, here is for instance how some civilization might evolve some FTL technology :
- First, it might have a better time at it if it is after developping some decent theory of quantum gravity.
- The stage we are currently at is that of research. Once in a while, NASA or some other organization will give a tiny budget on topics like interstellar travel. While it may not give us interstellar travel necessarily, it may give us some leads for interesting technologies growing out of such research. Examples of such projects are Vision-21 in 1990, the Breakthrough Propulsion Physics Project (1996 to 2002), Project Greenglow by BAE systems (starting in 1986) and the ESA's Advanced Concept Team. Some good topics of research would be to find out the limits of exotic matter in more details, means of producing it (in large quantities) and for a long period of time, finding different geometries that use less of it, perhaps using dynamic shapes rather than static and so on. I also didn't go much into the studies made into wormholes and warpdrives in theories other than general relativity, as modifications to it also change a lot of theorems.
- The first wormholes would probably be microscopic ones. Their existence could be deduced from, say, elementary particles passing through them. This would require either wormholes that are not too tiny (in some exotic matter), particles of very high energy (as they have a smaller wavelength, which would help getting in those tiny things), or probably both. This was actually one hypothesis (among many) that was formulated for the whole FTL neutrino a few months ago. Or alternatively, it could be cosmological wormholes. As previously stated, there's exotic matter around very dense objects, making it possible for wormholes of a decent size to develop around them. The best celestial bodies for this are objets of small mass but high density, perhaps small black holes and neutron stars, as large enough wormholes would induce some gravitational lensing around. Other possibilities include remnants from the big bang or other civilizations. There has been some studies done, and no definitive traces of such wormholes exist, although so far the study was done on wormholes of throat size ~ 1 parsec.
- The next step would be to turn wormholes into usable objects, with the various methods described. What they can be used for depends on the distance between them - if those distances are tiny, you can then use them for practical purpose. If you can't blow them up to human sizes, FTL communication can be of use. Time machines also have very interesting properties in quantum computing. If the distance between them is arbitrarily large, they can be used for astronomical observation. Perhaps even sending out signals to alien civilizations.
If we can blow them up to interesting sizes, then more interesting things can happen. If the distance between them is very large, this may still not be useful, or at least not for colonizing - statistically, they would probably end up in the voids in between supergalactic clusters. Then you might have to "run through" a lot of wormholes before finding one that's interesting. You might still need to move the other side closer to another planet. If the distance is small, then you might need to move it (IN SPACE) by the usual means. The time shifting trick might be used to shorten the time before we can get there, by say rotating one mouth at high speed. A good thing to do to save up on energy would be to keep the wormhole at microscopic size for the duration of the trip and inflate it when reaching destination.
Well, that's about all the things I can think of on the topic. I hope that you are now full of love for FTL~