Tuesday, November 27, 2018

Wormhole Musings

I have questions about how wormhole portals in science fiction stories work.

Recently I started reading another science fiction novel where wormholes allow instantaneous travel between distant points. In books that use this mechanism, the author typically explores how the ability to travel easily and quickly between the stars shapes the course of history.

But I always get hung up thinking about all the other ways in which a portal might possibly be used, for good or evil, in ways much less grand but potentially more disruptive than distant travel. Of course, since the use of wormholes in these books does not rely on our currently generally accepted science, these questions do not have well-defined answers. That's why I muse.

In this article, I ask some questions about how some of our currently accepted principles of physics apply (or don't apply) to wormholes, and ponder the ways in which one might use (or misuse) a wormhole based on the answer to those questions.

Caveat lector: If you want to keep reading wormhole stories without being distracted by questions like these, you might want to stop reading now. Because once you read these questions, you won't be able to unread them.

My Questions

How big and expensive is the equipment required to create and maintain a wormhole?

Mainly what I want to know for this question is whether the equipment is small and inexpensive enough that an individual can own one. If they are within the reach of many people, that makes it much more likely that there will be some people who will use it for unexpected purposes.

I once read a story in which someone had invented a personal flying belt that anyone could get for five dollars. With such easy personal mobility, border control suddenly became much more difficult, which of course led to some interesting problems. If anyone could buy and control a wormhole for five dollars, that would be a very different situation than if there were only a few wormholes controlled by a few rich and powerful entities.

How much energy is required to create and maintain a wormhole?

Although science fiction wormholes don't rely on any currently known physics, my feeling is that any scientifically plausible mechanism for a wormhole would require a prohibitive amount of energy to use. And I mean the word prohibitive literally: the amount of energy required would be so high, it would effectively prohibit the possibility of using a wormhole.

Since that doesn't make for good science fiction stories, we have to assume that the energy requirement is modest enough that we are able to produce and use wormholes. The question then becomes, how much energy is required? This question is related to the earlier question about cost, in that if a wormhole requires a relatively large amount of energy to operate, that could restrict its operation to a small number of controlling entities. Whereas if I can run it with a D-cell battery, there would be many more interesting things I could do with it.

It may not matter how much energy it requires to operate a wormhole, because, as discussed in some of my comments below, it seems likely that once you have a wormhole you could get as much free energy as you want.

What shape is a wormhole portal?

In most stories, wormholes portals are portrayed as circular areas that you step through, much like the entrance to a common tunnel. This is very convenient for imagining things like train lines that run through wormholes, and for thinking about the equipment that might be required to hold open a wormhole portal. That equipment is sometimes described as a torus with massive structures around it.

I think it is more likely that a wormhole would be spherical. You could enter it from any direction, and you would exit in a direction based on the direction you entered. This is a bit harder to visualize, which may be one reason it is not often described this way.

If a wormhole portal is a sphere, how does that impact the equipment required to maintain it? It would be tough to have equipment symmetrically on all sides and still have something that allows easy access. But maybe it doesn't all have to be completely symmetrical, so you can leave a few holes to let the trains get through the equipment so they can enter the portal.

Can I make a wormhole as large or as small as I want?

In most stories, wormholes are of a size that makes them convenient to step through, or drive a car or train through. Is this an essential feature of wormholes, or is it just that that happens to be the most convenient size? Could we make them any size if we wanted to? Perhaps big wormholes would be harder, but I would think smaller wormholes would actually be easier to make. And I can think of lots of interesting uses for small wormholes, depending on the answers to the other questions.

One example of a good use for a tiny wormhole would be to shine a laser through it and have a high capacity communication channel.

How do you control the location of the wormhole portals?

Some stories postulate that maintaining a wormhole portal requires physical equipment at both ends. In this case, the question of how to control the location of the portal is clear: you have to move the equipment to move the portal.

In other stories, the two ends of the wormhole are created at one location, after which one end can be moved to another location. In considering the geometry of wormholes, I would guess that it is possible to move one end of a wormhole through another wormhole, but perhaps only if the wormhole being transported is sufficiently smaller than the one it is being moved through.

If equipment is required at both ends of the wormhole, establishing a wormhole from A to B requires first traveling from A to B through normal space to deliver the necessary equipment, or possibly from C to B if the two ends of the wormhole don't need to be created in one place. This constrains the expansion of an interstellar civilization to the speed of light, which is annoyingly slow to some authors.

The more interesting case, as postulated in some stories, is that you can project the other end of the wormhole to a desired location without first having to get there some other way. This is, of course, a much-preferred mechanism if you want to quickly expand your network of gates, since who wants to wait many years while the slowship takes your gate to the next star? But what could we do if we could project the other end of our portal to anywhere we wanted in space?

If I can project tiny wormholes, I could do cut-less surgery. Mining would be much cheaper, as I could just project a wormhole down to where the ore is without having to tunnel or strip-mine down to it. I could make a great vacuum pump by putting one end out in space.

At a more banal level, I could eat as much as I want and not gain weight. I just need to project a tiny wormhole into my stomach and remove the food I just ate before my body digests it. I get all the pleasure of eating without suffering the problems of obesity.

I read one story in which a little wormhole was located on the bottom of a drinking glass, with the other end at the bottom of a vat of beer, wine, or whatever drink was selected. Each time the glass was set down, the wormhole would open to fill the glass, then close once the glass was full.

If I put on my black hat, the most obvious nefarious deed is, I project the other end of my wormhole into a bank vault and walk off with the cash. Or into a collection of classified documents and walk off with the secret plans. Or into my enemy's bedroom and kidnap him or kill him. I really only need to project a tiny wormhole, big enough for a bullet, to do a dastardly deed. Or so small it's only big enough for a packet of viruses that I inject into his bloodstream without him even knowing it.

If we can project one end of our wormhole to any desired location in space, perhaps we could project both ends. This would allow us to establish a wormhole between any two points anywhere in space, without having to have equipment at either end. This could actually be an interesting premise for a story, as it would allow for the case where there is a single wormhole-generating facility that creates all of the wormholes used throughout the civilization. That facility would presumably be controlled by some now-very-powerful entity, and would be both heavily secured and heavily attacked, so there are lots of opportunities for story lines.

The ability to create a wormhole between any two other points in space also opens up lots of additional opportunities for mischief. One could create a pretty effective weapon of mass destruction by creating a wormhole with one end in the middle of the sun and the other end where you want the destruction. Or put one end in the middle of a magma reservoir, or deep in the ocean, depending on the type of destruction desired. Or put one end in space to suck everything into the vacuum.

On the positive side, one could create a really nice package delivery system. Open a wormhole between the package source and destination, drop the package in for instant delivery, and close the wormhole.

Assuming we have the ability to create a wormhole portal anywhere in space, there is still the question of how we figure out where it gets created. Do we have to use trial and error to place the wormhole in just the right place? If we are trying to create a wormhole portal in a distant location, do we have to worry about the precision of our equipment, in the same way that launching a spaceship to land on Mars requires more precise equipment than launching one to land on the moon? Can we create the remote wormhole portal and then move it around at will, and if so, can we move it faster than the speed of light?

Is energy conserved when traversing a wormhole?

In most wormhole stories, one can step through a wormhole to get from one end to the other with no more effort than walking across the room. There is no explicit discussion of conservation of energy, and my assumption is that the authors don't worry about it because that detail doesn't advance the story. But I worry about it.

If I open a wormhole between Earth and its moon, there is a pretty big difference in the gravitational potential energy between those two points. When I want to put something in the wormhole portal on Earth and have it come out on the moon, do I need to supply the difference in energy between those two points? That would mean supplying a whole lot of energy to move in that direction. Conversely, if I step through the wormhole from the moon back to the Earth, what happens to all that gravitational potential energy?

If I can move from one end of a wormhole to the other end without having to supply that extra energy, then I can get free energy. Here's one way: go find a big dam with a hydro generating plant and install a wormhole with the entrance portal under the water at the bottom of the dam, just past the outflow of the generator, and with the exit portal just above the surface of the lake at the top of the dam. Since the entrance portal is underwater and the exit is above, water flows into the entrance portal and comes out at the exit portal. Thus the lake is ever refilled and our hydroelectric generators can keep running.

Maybe the wormhole technology works like a battery with regenerative braking on electric cars: it supplies the energy needed when traveling in one direction, and absorbs the excess energy when traveling in the other direction.

Is momentum conserved when traversing a wormhole?

If I am in New York City, the Earth's rotation is moving me at about 700 miles per hour relative to the center of the Earth. At the same time, Sydney is also moving at about 700 miles per hour, but in roughly the opposite direction, as it is almost on the opposite side of the Earth. If I open a wormhole between New York City and Sydney, and I step through, what happens to that 1400 miles per hour difference? Do I splat into the nearest wall at supersonic speed, or do I casually step through and continue walking to my destination?

If momentum is conserved, then I would be moving at a high speed relative to the exit point of the wormhole. If I put the appropriate mechanical devices next to the wormhole exit, I could send through a rock, catch it moving at 1400 miles per hour, and convert that kinetic energy to electricity. Then I could toss the rock back and do the same thing on the other side. Free energy.

The question of conservation of momentum is subtler than it first appears. If I want to conserve momentum, I come out of the wormhole in Sydney with that supersonic velocity relative to the city. But what does that mean for the angular momentum of the system? If I just moved that mass over to a new location and nothing else changed, then I have changed the angular momentum of the system. If the whole earth moves a tiny bit in the other direction, to keep the same center of mass, that could take care of that issue, but why should the whole Earth move when I use a wormhole? Would that happen if I were in an airplane? In a spaceship in low orbit? In a spaceship in high orbit? In a spaceship at the orbit of the moon, or beyond?

As with conservation of energy, perhaps the wormhole portals absorb or supply momentum as needed, transferring it to the surrounding masses. This could mean that wormhole portals would most effectively be placed on large masses such that they had a reservoir of momentum to transfer to or from. The larger the masses that were transferred through a wormhole, and the larger the relative velocity of the portals, the more momentum would have to be transferred, and the larger the attached mass would have to be.

How do physical forces propagate through a wormhole?

In every wormhole story I have read, light traverses a wormhole with no problems. I assume that means all forms of electromagnetic radiation traverse a wormhole equally easily. This presents another opportunity for a good energy source: put a wormhole portal in close orbit around the sun, then put the other wormhole portal on Earth. Stream that high-intensity light through and use it to drive solar cells for direct production of electricity, or as a heat source for standard steam turbines. If no equipment is required at the solar end of the wormhole, you're all set. If equipment is required, you might have to build some kind of refrigerator that brings that heat back to Earth and keeps the equipment cool.

How about gravity? How does that propagate through a wormhole? Most wormhole stories I have read describe travelers stepping through a wormhole and experiencing a discontinuity in the gravity field, meaning gravity is not propagating through the wormhole. This seems odd to me. Why would light propagate through a wormhole but not gravity?

The intensity of light from a point source drops off proportionally to the distance squared, which makes sense because the light is spreading out at that rate, and a fixed-size object intercepting the light will thus get less of it when it is further away. Because of this behavior, it makes sense to me that the amount of light that would come through a wormhole would be proportional to its size. If the wormhole is very small, only a small amount of light would come through.

Gravity also drops off proportionally to the distance squared, but not quite for the same reason. Given a particular mass, the gravitational force on that mass is independent of whether it is small and dense, or larger and less dense. The amount of area covered by the mass is not important, only its mass and its distance from another mass. If there is a tiny wormhole and I can measure a distance through that wormhole from my object to a large mass, wouldn't that mean the gravitational force is proportional to the square of that distance?

If gravity does propagate through a wormhole, perhaps I could make a null-gravity region by creating a pair of wormhole portals, then putting each one slightly above the surface of the Earth and upside down from each other. If you were to stand under one portal and look up, you would see the Earth above you. You have one Earth gravity below you and one above, so they cancel out and you have no gravity. A nice tourist attraction. Then again, the two Earths would also be exerting a gravitational pull on each other, so whatever is holding up each wormhole portal might be carrying the weight of the world.

On the other hand, given that General Relativity says that mass causes curvature of space, and thus gravity, and wormholes are usually described as some way of warping space, that seems to imply that being able to control wormholes means being able to control the curvature of space and thus being able to control gravity. So perhaps based on that we can choose how we want gravity to propagate through wormholes for our stories.

If you can turn wormholes on and off at will, you might be able to use this effect to get some free energy. You turn on a wormhole, have it pull up a weight, then turn it off, let the weight fall, and use that to generate energy.

What is the geometry of the wormhole connection?

A wormhole is usually described as a connection that goes through a higher dimension than the three dimensions in which we live. Those higher dimensions may present degrees of freedom that can lead to some curious and unpleasant results. Let me try to explain with a flatland analogy.

If I live in a two dimensional space, I can create a wormhole by folding that sheet of space until two points meet, then punching out a circle around those two points, and sewing those two circles together. This is topologically equivalent to attaching a hose that stretches up from a circle around one of those points and comes down at a circle around the other, with the assumption that the hose represents no distance (or a very short distance). A 2D creature could move from regular space onto the surface of that hose (assuming the hose diameter is much larger than the creature), then to regular space on the other end, then return to its original location via regular space, and all is well.

Now consider what happens if I take that same hose, but instead of going up from the first point and down at the second, I go up from the first point, then go around to the under side of the plane (which I can do without going through the plane if I have yet another dimension) and come up from the bottom side of the plane to meet the second point. Consider again what happens to that 2D creature who travels into the wormhole, out the other end, and returns to its starting point in normal 2D space. The result is that it comes back inverted. What was left is now right, and vice-versa.

I once read an old science fiction story in which there was a place deep within the Amazon where, if you navigated a certain course, it would reverse everything left to right. An enterprising businessman heard this and figured he could more efficiently make shoes by manufacturing only left shoes, then shipping half of them around this circuit, so he went exploring to find it. After going around the course, he looked at his sample left shoes, but they were all still left. Frustrated, he threw them all away, destroyed the worthless maps, and returned to civilization - only to discover that in fact the trick had worked, but he had not recognized it because he, too, had been reversed. But he could never find the place again.

Getting your body flipped left to right would probably be fatal. Almost all of our body chemistry is chiral, so you would not be able to extract any nutrition from most foods, and you would starve to death or die of malnutrition.

If there is an extra dimension in which a wormhole exists, why not two extra dimensions? If there are two or more extra dimensions, you now have the issue described above, and you will need to make sure you get the two ends of your wormhole attached with the right geometry, or things that move through the wormhole might not come out quite as expected.

Of course, a black-hat could surely come up with evil things that could be done with that kind of wormhole.

When considering wormhole geometry, another potential problem is the curvature of space in the wormhole. According to Einstein's Theory of General Relativity, curved space causes uneven acceleration. Too much curvature can lead to disastrous gravitational tidal effects that can tear things apart. Small wormholes would be most likely to have this problem. Larger wormholes, like South Pass through the Rockies, would allow that curvature to be spread out enough to be hardly noticeable.

In what reference frame is traversal of the wormhole instantaneous?

This is the issue which to me is the killer.

Einstein's Theory of Special Relativity is quite well supported by experimental evidence. According to that theory, there is no such thing as universal simultaneity, so we have to ask what instantaneous travel means.

You may have heard that, according to Special Relativity, if observer A with clock A in spaceship A is moving near the speed of light relative to observer B, clock A will run more slowly than observer B's clock B, according to observer B, due to time dilation. But at the same time, according to observer A, observer B with clock B is moving near the speed of light relative to A, so observer A sees clock B as moving more slowly. This effect is the core of the twin paradox, where one twin gets on a spaceship from Earth, flies away at near light speed, and returns, while the other stays on Earth.

The twin paradox is resolved by noting that there is an asymmetry between the twins: one stays at rest on Earth, whereas the other accelerates three times during the trip (takeoff, turnaround, and landing). This difference is the key to understanding the paradox and determining that the twin on the spaceship ages more slowly than the one left on earth.

In 1971 a couple of scientists ran an experiment where they took some atomic clocks with them on commercial flights around the world and confirmed that they really did slow down as compared to the stationary atomic clocks left behind, just as predicted by Special Relativity (and by General Relativity, which predicted time dilation due to gravitational differences).

For instantaneous travel between wormholes, it seems like we can set up a symmetric situation so that we can't resolve our paradox the same way as for the twin paradox. Consider the situation where we have a wormhole between two spaceships (or planets, if you prefer) A and B that are moving at near the speed of light relative to each other. As noted above, the observer in each location observes the clock moving more slowly at the other location. If person C with clock C steps from spaceship A to B through the wormhole, spends a bit of time on spaceship B, then comes back to spaceship A, observer A will calculate that clock C will be behind clock A, having moved more slowly than clock A while it was on spaceship B. If person D with clock D steps from spaceship B to A through the wormhole, spends a bit of time on spaceship A, then goes back to spaceship B, observer A will calculate that clock D will be ahead of clock B, having moved more quickly than clock B while it was on spaceship A. But in this symmetric situation, observer B will calculate that clock C will be ahead of clock A, and clock D will be behind clock B, the opposite of what observer A calculates. So which is it?

The problem here is that statement that travel between wormholes is instantaneous. According to Special Relativity, two events that occur at the same time but different locations in one reference frame will occur at different times in a reference frame that is moving with respect to the first. For our example, this means that if observer A sees person C moving instantaneously through the wormhole from A to B, observer B does not see person C moving instantaneously through the wormhole except for when A and B are right next to each other. And since A and B are moving with respect to each other, they will not be right next to each other for at least one leg of the wormhole round trip. When A and B are not right next to each other, what appears as simultaneous in one reference frame is not simultaneous in the other reference frame.

The only way I know of that is consistent with Special Relativity that would allow wormhole travel to be instantaneous according to both ends of the wormhole would be to constrain wormholes to be stationary relative to each other. But this would be a pretty strong constraint for stories, since essentially everything in the universe is moving relative to each other, and even the rotation of a planet is enough velocity variation to cause measurable time issues across the kind of distances wormholes sometimes connect.

But wait, it gets crazier. By the laws of Special Relativity, if you have any mechanism that lets you move between two points faster than the speed of light, in any arbitrary frame of reference, you can use that mechanism to travel backwards in time. The Tachyonic antitelephone is an example of how being able to send a message faster than light allows sending a message backwards in time, and this same principle applies to sending an object rather than a message.

One way to explain this is based on the assertion of Special Relativity that two events that are not at the same location in space that occur simultaneously in a frame of reference A will not be simultaneous in a frame of reference B that is moving with respect to A. In frame B, one of those two events will happen before the other. Let's assume that we have a wormhole with a pair of distant portals that are stationary in frame A, and another wormhole with portals stationary in frame B, moving with respect to frame A in the direction from one of the A portals to the other. We arrange the portals such that wormhole portal B2 is immediately adjacent to wormhole portal A2 at the starting time of our experiment according to observer A located at A1, and we arrange that B1 and B2 are adjacent to A1 and A2, respectively, at the same time in frame B. At the starting time in A, we step from portal A1 to A2. Since we arranged for B2 to be adjacent to A2 at this time, we can immediately move over to B2 and step through to B1, which we assume is instantaneous in frame B. Because we have arranged that B1 is adjacent to A1 at the same moment as B2 is adjacent to A2 in frame B, when we exit B1 we can then hop back over to A1 and complete our circuit in space. Since our trip through the wormhole B is instantaneous in frame B, it will not be instantaneous in frame A. For the traveler, all four legs of the trip are nearly instantaneous, but for an observer who remains in A only three legs are, with the leg through wormhole B not being instantaneous. Depending on which direction travelers takes around this loop, they will return to A1 either well after or well before the time they left.

The amount of time is proportional to the distance traveled through the wormholes and is related to the velocity of one frame with respect to the other. If frame B is traveling near the speed of light relative to A, the amount of time will be close to the light-distance between the two ends of the portal, so even if you are "just" traveling to Proxima Centauri B near Alpha Centauri, the closest extrasolar star group to Earth at four light years away, you could travel up to four years into the future or the past. The effect is less pronounced, but still present, at lower speeds.

Note that Special Relativity itself doesn't preclude faster-than-light messages or travel, it just says that being able to do so allows sending a message or traveling backwards in time, as demonstrated above. Our current theories do not say this is not possible, but most people believe in causality and thus find time travel problematic.

If you want to get a better intuitive feel for some of the weird things that happen when you start moving at near the speed of light, check out the free video game A Slower Speed of Light from MIT.

Potential Answers

Given that typical science fiction wormholes are based on new science beyond our current theories, we have a lot of leeway in deciding how that science works so as to create the conditions that best advance our story. We could say that managing wormholes requires an amount of money and energy that are only available to large organizations, or we could say that, once the science is known, wormholes are easy and cheap and anybody can make them, and see what kind of havoc is wreaked. We could say that small wormholes are easy to make, or that larger wormholes are easier. We could choose the geometry of the wormhole and portals to be troublesome or trivial. We could say that wormhole portals require equipment to maintain, or that we can cast them anywhere with ease.

All of the above choices are pretty easy in the sense that they are about the fictional new wormhole science and don't conflict with our existing science. Things get a little harder when we try to decide how conservation of energy and momentum work with wormholes, but even there we should be able to postulate something that allows us to remain consistent with known science, such as the wormhole absorbing or supplying the difference, or perhaps even requiring an exchange of equal mass from either end of the wormhole.

Propagation of gravity through a wormhole seems to me a little more difficult to deal with. As mentioned above, you might be able to claim that wormhole technology allows controlling the curvature of space. But another view of mass and space is that mass is the curvature of space, in which case making space curve is equivalent to creating mass, and at that point we get into all the questions of conservation of mass and energy and where it comes from when curving space for a wormhole.

The one that I really can't figure out how to make consistent is, as mentioned above, the question of time. The main reason wormholes are typically introduced is to allow faster-than-light travel, which, as described above, is what leads directly to the potential of time travel, according to Special Relativity. For all of the other questions, it seems like it may be possible to define some new science that answers those questions in a way that does not require us to discard any of our current well-established scientific theories, but for faster-than-light travel, I don't see any way to do this.

I can't even just assume that Special Relativity doesn't apply in that universe. There is a deep connection between having the same laws of physics everywhere, electromagnetism, and having a maximum velocity for any matter or information. Special Relativity builds on the work of Newton and Maxwell. and discarding it would require some other significant changes to the way the universe works.

A science fiction author might choose to focus on how wormholes allow time travel, as Robert L. Forward does in some of his stories. For the other stories, the ones that don't mention time travel, I just have to suspend my understanding of Special Relativity and enjoy the story as told.