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Space Warps And Time Machines

 

In the previous chapters on "Antigravity" and "Black Holes", I discussed the physical meaning of some of the solutions to the equations of the Einstein Theory of Gravity, the General Theory of Relativity. In this chapter, I discuss how these and other solutions to the Einstein equations produce some bizarre predictions for the behavior of certain of these structures, including behavior that emulates such science fiction concepts as space warps and time machines.

 

There are two basic ways to get from "Here" to "There" in a hurry. One way is to find some future technology that allows movement through the space between Here and There faster than the speed of light. The other way is to obey the cosmic speed law, but find some method of getting from Here to There without having to go through all that empty space in between. To do that, what is needed is that good-old science fiction plot-speeder-upper, the space warp.

It turns out that there are a number of possibilities for space warps based on the Einstein Theory of Gravity. These space warps are "bridges" or "tunnels" that shortcut through higher dimensions from one point in our space to another. All of these space warp concepts have some theoretical problems, yet those problems might not be unsurmountable for a sufficiently advanced technological civilization. Of the many types of space warps produced to date using the Einstein Theory of Gravity, the one that Hollywood likes best is the black hole.

As I discussed in the chapter "Black Holes", shortly after Einstein published his Theory of Gravity, Schwarzschild found an exact solution to the equations for a nonrotating spherical mass. The solution correctly predicts the precession of the axis of Mercury's orbit about the sun. It also predicts that a sufficiently dense star will create an optically black "event horizon" in the space around itself, a black shield in space and time that forever prevents anything from getting out. This is the infamous "black hole". The full mathematical solution found by Schwarzschild not only describes the shape of space and time in this universe, right down to the center of the black hole, but it also includes a mirror image solution that exists in the "other universe" on the "other side" of the center. In essence, the Schwarzschild solution to the Einstein Theory of Gravity describes a "Wormhole" through space from one universe to another.

There are some significant problems with this Schwarzschild Wormhole Space Warp much loved by Hollywood. First, there is the event horizon that forms the black hole shield around the mouth of the wormhole in this universe. It only allows one-way travel. You can enter the Wormhole, but you can never come out. Second, even if you enter the Wormhole by falling through the event horizon, you will find that the Wormhole is not a true "hole" since the collapsing star that formed the black hole is blocking the throat and preventing your passage to the universe on the other side. There is no way to "avoid" or "tunnel through" the collapsing star, since both you and it are inexorably falling toward the center where a singularity in space and time is forming that will crush both you and the star.

The fact that a user of a Wormhole must hit the singularity at the center of the black hole is strongly emphasized by the mathematically oriented physicists who study black holes. They point out that although Einstein showed us that space is equivalent to time, there is a major difference between a space-like dimension and a time-like dimension. If you get far away from everything and don't do anything, then you can stand still in space—but you can't stand still in time. You can slow down time by flying off into space in an ultrafast rocketship or by setting up housekeeping on a very massive planet, but you can't stop time. You must keep on moving inexorably through time (t), in one direction only (+t), until you come to the end of time (t=infinity).

In the Schwarzschild solution describing the Wormhole Space Warp, there are three space dimensions and one time dimension. But at the event horizon, the radial space dimension takes on the behavior of a time dimension, while the time dimension takes on the behavior of a space dimension. [See the left side of Figure 13.] This means, that, once inside the event horizon, despite all the rockets, all the forces, all the future magic you can command, you must keep on moving inexorably through space in the radial direction (r), in one direction only (-r), until you come to the end of space at the singularity (r=0). From this mathematical point of view, you can no more increase your radial distance from the Schwarzschild singularity at the center than you can turn back the hands of time. Thus, the Schwarzschild Wormhole, despite its popularity with Hollywood, is not a very useful space warp. Fortunately, there are a number of ways to modify the Wormhole to make it more user friendly.

If the collapsing star is electrically charged, then the Schwarzschild solution converts into the Reissner-Nordstrom solution. This solution, found shortly after the Schwarzschild solution in 1918, describes the structure of spacetime outside a massive object that also contains an excess of charge. There are now two event horizons, an outer event horizon which is slightly inside of where the event horizon would be if the collapsing mass were not charged, while outside the singularity is an inner event horizon. [See the right side of Figure 13.] The greater the charge, the greater the radius of this inner event horizon.

 

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Fig. 13 - Schwarzschild Wormhole Space Warp
and Reissner-Nordstrom Chargewarp.

 

To use this charged black hole space warp, or "Chargewarp", a spaceship would follow the collapsing charged star and pass through the outer event horizon. Once inside the first event horizon, the radial space dimension will have taken on time-like qualities, in that the spaceship must inexorably continue moving inward to constantly decreasing radial dimensions, following the collapsing charged star down toward the singularity. As the collapsing star becomes smaller and smaller, a second event horizon would form. Once inside the inner event horizon, the matter in the collapsing star would continue falling inward toward the center under its self-gravitation, where it would form the singularity. The spacecraft would also have to pass through this inner event horizon. Inside the inner event horizon, however, time and space have once again reversed roles and it is now possible for the spacecraft to turn on its rockets, halt its motion in the radial direction, and go into orbit about the singularity.

The mathematics then says that, if the spacecraft has enough energy, there is no mathematical reason why the spacecraft cannot circle around the still collapsing star and then head back out through the inner event horizon and the outer event horizon, and emerge back into the outer universe again. The mathematics also tells us that the universe that the spacecraft emerges into is not the universe that it left. The spacecraft has traveled through the Chargewarp, and emerged somewhere else.

Still another space warp concept is based on the Kerr solution to the equations of the Einstein Theory of Gravity for a dense, spinning mass in the form of a rotating ring. Since all stars have some rotation, when a star reaches the end of its life and collapses, one would expect it to turn into a dense spinning mass. Left to itself, however, a collapsing star will find ways to shed its angular momentum, usually by throwing material off from its rapidly spinning equator. With the excess angular momentum gone, the star will finally form into a rotating pancake shape, not a rotating ring.

However, it is possible (and given the human race's proclivity for fooling around with nature, probable), that this pancake shaped collapse could be induced to form a ring-shaped collapse, with all the dense mass out in a rotating ring. This Kerr solution to the Einstein Theory of Gravity then describes a space warp—a Ringwarp. The gravity tides are strong near the surface of the ring and it is dangerous to approach too closely to the ring. There is no mass in the center of the ring, however, so there are no gravity tides there. If you go through the center of this rotating ring you do not come out the other side. [See Figure 14]. Instead, as you pass through the ring in either direction, you will enter a hyperuniverse. In this hyperuniverse the spacetime has different properties than the normal spacetime of this Universe. Mass in the hyperuniverse is negative and repels instead of attracts. To get out of the hyperuniverse back into our Universe, merely traverse the Ringwarp again. Either direction is okay.

 

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Fig. 14 - The Kerr Ringwarp.

There is a problem with the Kerr Ringwarp, in that in order to open up the Ringwarp enough to allow two-way travel, it is necessary that the mass in the rotating ring be moving at the speed of light. If, however, the rotating massive ring source for the Ringwarp also carries an electrical charge, then the charge and angular momentum augment each other. The requirement for rotation is lessened and the event horizons can be eliminated at a rotation rate that produces a peripheral velocity of the ring slightly less than the speed of light.

Thus, according to our present understanding of this solution of the Einstein field equations, a highly charged, rapidly rotating, ultradense ring, warps space enough to form Ringwarps that can be used without leaving this Universe. We do not know if the hyperuniverse opened up by a Ringwarp is the same for all such Ringwarps. If it is, then by making and opening Ringwarps in orbit around distant stars we can travel from one star system to another by merely popping into the Ringwarp in our solar system and popping out again in another Ringwarp around some distant star system. We do not yet know whether the theory for interconnection of Ringwarp hyperuniverses will allow the distance between the Ringwarps in the hyperuniverse to be made less than the distance between the Ringwarps in this Universe. If it can be made significantly less, then we have a new method of space travel that allows us to travel faster than the speed of light.

Any of the space warp concepts that involve singularities in spacetime will always have problems. The mathematically oriented physicists that study the exotic behavior of black holes can easily show that even minor perturbations, such as that caused by a spacecraft trying to use a space warp, should cause the space warp to distort or collapse. Although one could argue that a technological civilization that is sufficiently advanced to create a stellar-sized space warp should be able to control any potential instabilities in the space warp, the mathematicians are probably correct. Fortunately, there is a space warp concept that is an exact solution to the equations of the Einstein Theory of Gravity, and yet does not involve singularities, or even stellar masses. This is the Morris-Thorne Field-Supported Space Tunnel. [See Figure 15.] These are tunnels through space that are kept from collapsing to a singularity by threading the throat of the tunnel with special fields.

The fields holding up the Space Tunnel have to be exotic fields that have a tension greater than their energy density (electric and magnetic fields have a tension that is equal to the energy density). Such fields are known to exist in high energy density matter such as is found in neutron stars. Other versions of these fields have been made in the laboratory at low energy densities.

 

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Fig. 15. Morris-Thorne Field-Supported Space Tunnel.

 

The best example of an exotic field that has the proper properties are the vacuum fluctuation fields between two closely spaced metal plates. According to quantum mechanics, the vacuum is not empty. It is full of random fluctuations of the electromagnetic field. [See the top half of Figure 11 in the Chapter "Black Holes".] When two conducting metal plates are brought very close together, the vacuum between the plates is limited in the number of fluctuations it can support, and thus becomes "emptier" than the vacuum outside the plates. This energy difference forces the two plates together, creating a force that is large enough to be measured in the laboratory. Since the energy of the vacuum is defined as zero, this means that the space between the plates has negative energy density. Being negative, the energy density is automatically less than the tension, and the field between the plates has the desired exotic properties needed to hold a Morris-Thorne field-supported Space Tunnel open.

Thorn and his students have "designed" a space warp that consists of two perfectly conducting spheres completely covering the spherical holes in spacetime that form the "mouths" of the Space Tunnel. [This is hard to visualize unless you are used to thinking in four dimensions.] Although the two spheres are quite large, and have a comparatively small door in them to let a spacecraft to pass through, their inner surfaces are only a microscopic distance apart, since the distance as measured through the Space Tunnel is very small, while the distance between the mouths in our outside Universe can be lightyears apart.

The two spheres have a large amount of identical electric charge on them. This has two effects. First, the identical charges on each sphere causes them to electrically repel each other. This electrical repulsion force is sufficient to exactly counterbalance the vacuum fluctuation forces that are trying to pull the two closely spaced conducting spheres together. Second, the strong electric fields on the outside of the spheres act to keep the Space Tunnel throat open in the region from the outside surface of the sphere off into flat space at infinity. These electric fields are what keeps the Space Tunnel open.

Electric fields are not quite exotic enough, however, to hold the Space Tunnel open at its throat. Right at the throat, in the microscopic region between the interiors of the two spheres, an exotic field with a tension greater than its energy density is needed. That exotic field is supplied by the vacuum fluctuation forces between the two spheres. The equations obtained show that the smaller the spacing between the spheres through the Space Tunnel, the smaller the spheres need to be to keep the Space Tunnel throat from collapsing, and the easier the space warp will be to build.

If you assume that the minimum spacing between the two conducting spheres will be determined by the fact that the conducting spheres have to be made of atoms, then with a spacing between the spheres of one percent of the radius of an atom, the diameter of the spheres required is one astronomical unit (the distance from the Sun to the Earth). To get the size of the Space Tunnel down closer to the size of a spacecraft would require much smaller spacing between the spheres, and they would have to be made of some form of collapsed matter that wasn't made of atoms, just the nuclei of atoms.

Although still nearly impossible to build from a technological point of view, the Morris-Thorne Field-Supported Space Tunnel design has the many nice features that: mathematical singularities are not involved in the construction, the amount of mass needed is less than a stellar mass, the throat of the space warp is large enough to pass a spacecraft, there are no tidal effects to damage the ship or crew, there are no infinite blue shift horizons to fry the crew with radiation, and the distance through the Space Tunnel can be made much shorter than the separation of the Space Tunnel mouths, allowing for faster-than-light transport from one part of space to another. For a description of how one might build a Space Tunnel and use it for travel through space and time, and a discussion of how the resulting causality paradoxes will be resolved, read my novel Timemaster, which in turn is based on the more mathematical papers by Morris, Thorne, Friedman, Novikov, Echeverria, Visser, Garfinkle and myself in the Recommended Reading list at the end of the chapter.

 

It is an axiom of relativity, where time and space are treated on an equal footing, that a faster-than-light space warp is operationally equivalent to a time machine. If one observer sees you using a space warp to move from one place to another faster than the speed of light—say, entering the space warp at Sol and arriving at Alpha Centauri one hour later—a different observer, who just happened to be passing by in a spacecraft moving in the right direction at a fast enough speed, would swear that you arrived at Alpha Centauri before you left Sol. Thus, if space warps are theoretically possible, then time machines should be too.

One of the technologies I see in our future that is presently indistinguishable from magic is the ability to travel in time. If a present-day scientist were confronted with a real time machine, he would certainly say that the machine had to be run by the rules of magic. His argument would go like this: Science is based on logic. Anything that produces logical paradoxes is not science. Time machines produce logical paradoxes. Therefore, if time machines exist, they must use magic, not science.

Yet, two of the most respected and tested theories of physics, both the Einstein Special Theory of Relativity and the Einstein General Theory of Relativity, allow time to be manipulated. Although we are presently far from being able to control the energies and masses that will be required to make a time machine suitable for human use, these theories give us the physical principles behind time travel.

How do we make a time machine?

What most people don't realize is that one type of time machine already exists. Various versions of these machines can be found in university and government laboratories. They are used every day by the scientists there, but they do have some limitations. They are only good for one-way time travel, and they can only handle a few atoms at a time. These present-day time machines are based on the Einstein Special Theory of Relativity. To understand how they work we need to know a little bit more about this remarkable theory that is now almost a law of nature.

Einstein's Special Theory of Relativity should really be called the Einstein Theory of Mechanics at high velocities. The Einstein Theory of Mechanics replaced the old Newton Theory of Mechanics. The Newton theory described how matter moves through space and time. The matter gains and loses heat energy and kinetic energy as various forces act upon it, but nothing else happens to the matter. The Newton theory worked very well for objects moving at ordinary speeds, but it was not adequate when the velocities of the masses began to approach that of the speed of light. The newer Einstein theory correctly predicts the behavior of matter and energy, while Newton's old theory fails when the amount of energy in a particle becomes large and the particle is moving near the speed of light.

The Einstein Theory of Mechanics is called a theory of relativity because that is the way that Einstein stumbled onto the correct theory. In his usual insightful manner, Einstein didn't try to think about planets in orbit, or falling spheres, or billiard balls, or the other mechanical things that occupied the thoughts of Newton and other theorists thinking about mechanics. Instead, he asked a more personal question: "What does a person see and sense when they are moving?"

Einstein knew that experiments had shown that there was no way for a person to tell that they were in motion, as long as it was constant motion. For example, suppose we had two observers: Jill in a rocket ship and Jack floating lazily in space. Jill turns on her engines for a while and accelerates up to a high velocity toward Jack, then turns the engines off. She is left floating in free-fall just as Jack is. She looks out her cockpit window to see Jack flashing past. It is obvious to both Jack and Jill that they are in motion relative to each other, but since both are floating in free-fall neither can prove which is moving and which is standing still. They can both see the stars, and perhaps Jill would be moving with respect to the stars and Jack wasn't. Jack might argue that he was the one that was standing still because he sees the stars stationary. To Einstein, however, each observer is just as important as the other. It doesn't matter that all the stars in the universe would have to be moving to make Jill stationary.

To the genius mind of Einstein, an observer like Jill was just as important as the rest of the universe. This was no time for a democratic vote as to who was moving and who was not. The only thing that counts is a physical measurement, and since there was no method of measuring absolute velocity, both Jack and Jill's points of view were equally valid. Jill in the rocket ship could be moving and the universe is sitting still, or Jill could be standing still and the rest of the universe is in motion. All points of view and all frames of reference are equally valid. Everything is relative—and that's where the name "relativity theory" came from.

At first glance, the Einstein Theory of Mechanics doesn't seem to follow common sense. Of course Jill's rocket ship is moving and the rest of the universe is standing still. But Einstein just continued on in his methodical way, saying, "But suppose it is true that we can't tell the difference between a spaceship moving one way and the whole universe moving the other way?"

In his usual technique of thinking unthinkable thoughts, Einstein then asked himself, "What would I see if I could travel at the speed of light and were to look at a light wave traveling alongside of me?" If Einstein used the Newton picture of the way things worked, the answer would be that he would see the electric and magnetic fields in the light standing motionless—not vibrating. Yet it was the vibration of the fields that gave the light beam its frequency . . . its energy . . . its very existence. According to the laws of electromagnetism, unless a light beam vibrates, it cannot exist. Newton's law led to a paradox.

Einstein thought other unthinkable thoughts. "Suppose I were traveling at nearly the speed of light and I sent out a beam of light ahead of me. Being light, it would seem to me to be moving at the speed of light, but since I am sending it off from a moving platform, would not some other observer see the light beam moving faster than the speed of light?" Yet the velocity of light coming from fast-moving stars had been measured by astronomers and was always the same, no matter what the velocity of the star was—another paradox.

To Einstein, the only consistent answer to any of these questions was: "No. No matter how fast or slow I am going, the result of any experiment (especially a measurement of the speed of light) must be the same for all observers whose frames of reference are moving at a constant velocity, no matter what that velocity is."

Now according to any reasonable extrapolation of Newton's laws, this was impossible. Different observers should measure different velocities of light, depending upon whether the motion of their frame of reference added or subtracted from the motion of whatever was being observed. Yet—Einstein accepted his own "impossible" answer and proceeded to produce a set of mathematical equations describing space, time, matter, and energy that would produce the desired result of a constant velocity for light no matter what speed the frames of reference of the observers were moving at.

The equations that Einstein came up with were awkward. They even involved square roots. Ignoring their strange looks, Einstein proceeded to examine the implications of those equations. The results predicted by those strange set of equations are astounding in their abandonment of common sense, yet, all of the predicted results have been proven to be true time and time again.

They are: Space can be converted into time—and vice versa. Mass can be converted into energy—and vice versa. As you travel near the speed of light; space shrinks, time expands, and mass increases. If you travel at the speed of light; space shrinks to nothing, time increases to eternity, and your mass (if you had any to start with) increases to infinity.

The impossibility of the last means that it is impossible for any material object (like Einstein himself) to attain the speed of light because it would take an infinite amount of energy to accelerate an infinite mass. Light, being a form of pure energy, has no rest-mass per se, and so can (and to exist—must) travel at the speed of light. Yet what a queer universe the photon lives in. Since its space has shrunk to zero and its time has expanded to eternity, the photon exists everywhere along its trajectory at all times!

The most amazing result from the Einstein Theory of Mechanics that is hardest for people to accept is the slowing down of time at high velocities. This is best illustrated by the famous twin paradox: There are two astronauts, Jack and Jill. They are twins. One astronaut, Jill, travels off on an interstellar spacecraft and spends a long time traveling at nearly the speed of light, while her twin, Jack, stays at home. Upon the return of the traveler, Einstein's equations say that while the stay-at-home Jack has aged considerably, Jill is still young since she has been traveling in her time-machine, the relativistic spacecraft.

Thus—one way to make a time machine is to find a way to move at velocities close to that of light. Unfortunately, this special-relativity time machine only works one way. It can allow you to go into the future at a slower rate than normal, but you cannot go back in time. Still, this kind of time machine would have its uses. If you were sick and there was no cure for your disease, a short sojourn in a relativistic rocket ship could keep you from dying until the medical researchers could find the cure for what was ailing you. If you had a rich but very healthy aunt, then a few days spent at 99.99998% the speed of light could insure that you would be able to enjoy your aunt's inheritance while you were still youthful.

These special-relativistic time machines are being used today. In many of the laboratories studying the properties of the atomic nucleus, there are large machines called "atom smashers" that use electric, magnetic, and radio fields to accelerate tiny charged particles to very high velocities. These particle beams are then shot into metal foil targets. Most of the high speed particles pass right through the foil, but occasionally one of the particles plows head-on into the nucleus of one of the metal atoms, smashing the nuclei into bits.

Some of the "bits" are very interesting, since they are particles that exist inside the nucleus, but we normally don't see them because they have a very short lifetime. Some of the particle lifetimes are so short, a trillionth of a second, that the particles would travel less than a millimeter before they decayed if it were not for the time machine that kept them alive. For the atom smasher is also the time machine.

The energy that the atom smasher puts into its beam is so high that the bits of smashed nuclei that come out of the miniature explosion are moving at nearly the speed of light. Since the bits are moving so fast, their lifetimes are increased 10,000 times or more, and instead of living only a trillionth of a second, they now live a few hundred millionths of a second and can travel tens of meters from the highly radioactive target chamber out through the steering magnets and into carefully designed instruments that measure the mass, charge, spin, and other exotic properties of that short-lived bit of nuclear stuff.

When the time machine properties of the Einstein Theory of Mechanics were first discussed, many people refused to believe that such a thing could happen. How could one twin stay young while the other grew old? If such a thing could be done, it wouldn't be done by scientists, but by magicians using some magical youth potion. But the true magical elixir of eternal youth was brewed by a scientist, Einstein, who gave us a new picture of the basic fabric of the universe, the space and time we live in.

The reason that the paradox of the twins is hard for us to believe comes from our limited experiences with high velocities. Our supersonic jets and rockets may go fast enough for most of us, but even our fastest rockets, boosted to their highest speeds by close encounters with the rapidly moving planets of Jupiter and Saturn, still travel at only one-ten-thousandth of the speed of light. Unfortunately, the unusual effects predicted by Einstein's Special Theory of Relativity only become significant when you are traveling at speeds greater than half the speed of light. Because of this limited experience with high velocities we have developed a "common sense" that says that time is some absolute quantity that ticks the same way for all things.

This strong, but erroneous belief in "common sense" is often backed up by people trying to use the principle of "relativity" to prove their point. "If everything is relative . . ." they would say, ". . . and all points of view are equally good, then the idea of the traveling twin Jill living longer than the stay-at-home twin Jack leads to a logical paradox."

Their argument goes like this: "Jill takes a ride on a relativistic rocket ship, while her lazy twin Jack stays curled up in front of his fireplace on Earth reading War and Peace. Jill returns some decades later just as Jack is reading the last page. (Jack is a slow reader.)

"According to Einstein, Jill will be young and perky, having aged but a few years, while Jack looks and feels like Rip Van Winkle.

"Well, if everything is relative, and Jack's point of view is just as good as Jill's point of view, then according to 'relativity' it would be equally good to say that while Jack was reading in front of the fireplace, the Earth was taking him on a relativistic ride, while Jill sat cooped up in her motionless rocket. The situation would be even more symmetric if we imagined Jack and Jill meeting out in empty space in two identical rocket ships, then flipping coins to see who travels and who waits. Since the 'all points of view are equally good' relativity principle says that we can either assume that Jack is moving while Jill is standing still, or that Jill is moving while Jack is standing still, then the Einstein "time dilation" effect leads to the paradox that: depending upon which point of view you choose, Jack ages slower than Jill, or Jill ages slower than Jack. These results are mutually contradictory, thus, there is a logical paradox generated. Since the Einstein idea of "time dilation" is what caused the paradox, it must be wrong, and the time that a person lives does not depend upon their velocity."

To resolve the Twin Paradox problem, let us set up a carefully designed experiment. Jack climbs into his rocket ship "FRAME 1" (short for Frame of Reference 1), and goes out into space and turns off his rocket so he is no longer accelerating and is moving at a constant velocity. Once he has stopped the engines, the name of his rocket ship now means something real—the unique frame of reference in which Jack resides. Jill also takes off in her rocket ship "FRAME 2" and after getting up speed relative to Jack, she aims her vehicle carefully at Jack's spacecraft so that their side port holes will pass facing each other. She then turns off her engines, leaving her floating in space. They both go to the side port holes in their vehicles. They set up their cameras and clocks (digital quartz chronometers with microsecond accuracies and large numbers on the readout). Fortunately Jill is a good pilot and the ships pass each other with a relative velocity of 99.9% of the speed of light and with their port holes within a few centimeters of each other. There are simultaneous clicks of their two cameras and each sees that the readouts on both clocks indicate the same time.

Jill now continues off into space, and within a few hours is out in the outer regions of the solar system on her way to the stars. They compare clock ticks by radio signals, but they both know that you can't tell anything definite by that technique, for both think that the other's clock is slow.

The resolution of the paradox comes at the turnaround point. Up until that point, special relativity says that the aging question is ambiguous. In order to compare the relative times of the two clocks (or the ages of the two twins), they must both be at the same place. Now instead of having Jill turn on the rocket engine in "FRAME 2" and destroying the validity of her rocket ship's name, let's have her hitchhike back. For the purposes of the experiment, we have sent David out earlier in his rocket ship "FRAME 3". David went out a few light years, then turned around and headed back into the solar system at 99.9% light speed, right next to the track Jill would be coming out on. Jill contacts David and arranges for a ride back in on "FRAME 3". As they pass, Jill hops off "FRAME 2" and onto "FRAME 3", carrying her clock with her. "FRAME 2" continues on its way out into the starry sky, keeping true to its name.

(One might think it would be difficult for Jill to make the transfer from a frame of reference moving at +99.9% of the speed of light to a frame of reference moving at -99.9% of the speed of light carrying a heavy quartz chronometer, but Jill, like Jack, is quite nimble.)

Jill rides back in with David in "FRAME 3", and when David zips by Jack, Jill is down at the side port hole, her youthful face grinning in exuberance as she snaps a picture of her gray-haired twin Jack and his aging quartz chronometer with a time indicated on it that is many years later than the time on Jill's clock.

We know that Jill will be the younger twin because she is the one that violated the "principle of equivalence of reference frames" by jumping off "FRAME 2" and coming back on "FRAME 3". By abandoning her original coordinate system that she started with, Jill can no longer claim "everything is relative". The stay-at-home twin Jack is still with his original coordinate system "FRAME 1" and thus has not moved, paying a price for this stodginess by aging at a precipitous rate compared to the traveling twin.

Suppose David had gone the other way, and had arranged to pass by Jack at 99.9999% of the speed of light, and Jack and his chronometer had left "FRAME 1" and jumped on "FRAME 3". Then sometime later when "FRAME 3" had caught up with and passed Jill in "FRAME 2", then it would have been Jack that was younger. (At 99.9999% of the speed of light, Jack is aging slower than Jill moving at 99.9% of the speed of light).

Except for a few who still cherish the idea of an inviolable, unchangeable time, the human race has absorbed this unusual behavior of nature at high velocities, and has learned not only to live with this "one-way" time machine, but to use it.

There is yet another type of "one-way" time machine. You are living on it—the Earth! This type of time machine uses one of the magical properties of gravity predicted by the Einstein Theory of Gravity, the General Theory of Relativity. According to the Einstein Theory of Gravity, a high gravity field causes time to run slower, just as high velocities do. The amount of time slowing in the field of the Earth is not very much, although it is measurable if you have an accurate enough clock. A clock in the basement of a building will run slightly slower than one on the top floor of the building. To get a significant amount of slowing, the gravitational field has to be very strong.

One way to obtain a strong gravitational field is to find a neutron star or a black hole and send your spacecraft into a close orbit around the mass. You are now down in the gravitational potential well of the star and are living slower than those further away. Since you are in a free-fall orbit, the strong gravitational forces pulling on you are canceled by the centrifugal force of your orbital rotation. The problem is that when you are in orbit about a dense star, the only place where the gravity and centrifugal forces exactly cancel is at the center of mass of the spacecraft (or you!). The other points are not quite in free-fall and are subject to the tidal forces due to the change in the gravity field of the star with distance and angle. For an orbit around a neutron star or black hole, these tidal forces can reach hundreds of Earth gravities per meter. These tidal forces are strong enough to literally tear you limb from limb. If you go even closer, the tides will be strong enough to straighten out the helical twist in your DNA!

In the very distant future, however, it may be that our future magicians will be able to make a one-way gravitational time machine that won't kill you with its crushing tidal forces if you try to use it. This time machine would be a hollow ball of ultradense material. The gravitational potential inside such a hollow ball is uniform. The gravitational potential can be quite high, giving a strong time slowing effect, yet, because there are no variations in it, there are no gravitational forces, since it is the variations in the gravitational potential that cause the accelerations.

Many people think that the slow-down of time in gravitational fields and for fast moving objects has only been confirmed for high-speed elementary particles. In one of the better justified boondoggles in the annals of science, however, nothing can beat parlaying a test of Einstein's theories of relativity into a trip around the world. In 1971, American physicists Hafele and Keating borrowed two identical, highly accurate portable clocks from the U.S. Naval Observatory, and obtained a grant from the Office of Naval Research to pay for three around-the-world tickets (one seat for each of them and a seat for one of the clocks). The twin clocks were set to the same time in Washington, DC. One clock-twin stayed in Washington where it was only subjected to the slow-down in time due to its position in the gravity field of the Earth. The other clock-twin took off at a speed of 1000 kilometers per hour (600 mph) and went in a round-trip journey around the Earth at an average height of ten kilometers (six miles) above the Earth's surface.

The time as measured by the moving clock twin was slowed down by the fact that it was moving at a velocity close to that of light (well . . . it was closer to the speed of light than the stay-at-home twin). The time as measured by the stay-at-home twin was slowed by the fact that it was subjected to a much greater gravitational field than the elevated twin (well . . . it was 1.0016 times greater). However, the velocity effect was larger than the gravitational effect, so upon return to Washington, the moving clock was found to be slower by exactly the amount predicted by the two theories of relativity. Just to check, the scientists and the world-traveling clock went back around the Earth the other way, where the rotational speed of the Earth subtracted from the airplane's speed rather than adding to it. Again the scientists got the correct result. (This was probably the cheapest test of relativity ever made; it only cost $8000, of which $7600 was spent on air fares.)

Scientists have already built a magic time machine that stretches the life-times of tiny particles by 10,000 times. When will we be able to build a time machine big enough to keep large particles (like us) forever youthful? We have already built and are using the first model of that magic time machine. It's called the Space Shuttle.

The Space Shuttle is a great space-travel machine, but as a time-travel machine this first version leaves something to be desired. The orbital velocity of the Shuttle is nearly eight kilometers per second (26 millionths of the speed of light). If you stayed in an orbiting space shuttle for a year, you would age more slowly than your twin on the ground, but only by about one-hundredth of a second. To make real time machines out of our space-traveling rocket ships, we need to make them go at nearly the speed of light. It will be difficult, but we can see the technology to build these magical time machines coming in our future. They are discussed in more detail in the chapter, "Starships".

The Einstein Theories of Mechanics and Gravity have given us one-way time machines that allow us to slow our rapid progression into the future. What about a time machine that will allow us to go into the past as well as the future? The Einstein Theory of Gravity allows many shapes for such a time machine. In fact, it seems that any rotating object that is dense enough to produce a region with a twisted ultra-gravity field can produce time-confusing regions. There are some shapes, however, that can produce time-travel regions that might be usable by humans.

One gravitational mass configuration that can act as a time machine is a large, rapidly rotating, dense object that is collapsing to a black hole just as its spin speed is rising to that of the speed of light. This is the Kerr Ringwarp. [See Figure 14.] The Ringwarp is not only a space warp, but a time machine. The mathematics of the Kerr solution indicate that as you come down from overhead and start to approach the plane of the ring, the strong gravity field of the ring starts to change your space and time compared to that of an observer far away. Your space becomes smaller and your time becomes longer. The spinning of the dense ring causes even stranger things to happen. The twist that the rotation puts into your spacetime converts part of what you would call space into what the outside observer would call time, and converts part of what you would call time into what he would call space. The Kerr solution then says that as you pass through the plane defined by the dense ring, the spacetime conversion becomes complete. Your forward space dimension has been turned into a time dimension while your time dimension has turned into a space dimension.

What is more amazing, is that when you go through the hole in the ultra-dense ring, you don't come out on the other side! Instead you find you have entered a strange type of hyperspace. In this hyperspace you feel perfectly normal, even though one of your three space directions has been interchanged with time. If you go in the hyperspace up near the rotating ring and move in the direction against the rotation of the ring for a number of rotations, you will observe nothing unusual happening to you. In your travels near the rotating ring, however, you will have traveled backward in space (the forward direction being determined by the direction of rotation of the ring). If you then return back through the hole in the ring, your time and space dimensions will be restored to normal. But don't forget that while in hyperspace you went backwards in space and what used to be space is now time. Although you have returned back to your original position in space, you will find that your position in time has moved backwards a number of years!

This magical result obtained from the Kerr solution to the Einstein equations can be found in a highly mathematical paper published by Brandon Carter in the Physical Review, the most prestigious scientific journal in the field of physics. In that paper Carter concludes: "To sum up . . . the central region has the properties of a time machine. It is possible, starting from any point in the outer regions of the space, to travel into the interior, move backwards in time . . . and then return to the original position."

Now, there are many mathematical theorists who insist that such a special shape for a rotating mass will not happen. It may be true that nature will not naturally form a ring-like time machine from a collapsing star, but with a little guidance and some presently indistinguishable from magic technology applied by our far-future ancestors, perhaps a star bigger than our sun can be made into a ring-shaped time machine one hundred kilometers (sixty miles) in diameter—and maintained despite the fact that it would not be stable if left alone. At a size of one hundred kilometers, the gravitational tides from the dense mass of the ring are weak enough that they will not cause damage to people and well-built spacecraft passing through the center of the ring. A time machine of this size would be big enough and safe enough to send an entire rocket ship back in time.

The Kerr time machine does have the problem that in order to get the time-travel effect, the mass in the spinning ring has to move at a speed equal to that of light, and that can never be attained, just approached. There are other solutions to the Einstein field equations, however, that improve upon on the Kerr solution. A rapidly spinning dense ring with a large electric charge on it will form a time machine even when the speed of the mass in the ring is below that of the speed of light. Since the original star has enough rotational energy to reach near-light speeds after collapsing from a diameter of ten million kilometers to a diameter of one hundred kilometers, all our far-future magicians have to do is make sure that the star stays highly charged as it collapses and it will form a time machine.

Even if it turns out that a ring-shaped time machine can't be built, it isn't all that important. A spinning ring is not the only shape for a time machine. Another configuration for a time machine is a spinning cylinder. [See Figure 16.] First described by Frank Tipler, the theoretical model for this time machine uses a mathematical approximation, so it is not as rigorous as the Kerr model. The approximation used is to assume that the long spinning cylinder is infinitely long. It is equivalent to saying that you are concerned only about the gravitational fields near the middle of the cylinder and the ends of the cylinder are so far away that the slight differences in the gravity field due to the fact that the cylinder is finite are not large enough to worry about.

 

067187686416.jpg
Fig. 16 - The Tipler Two-Way Time Machine.

 

Tipler's time machine is a long cylinder of ultra-dense mass with a spin speed at its surface that is one-half that of light. The time-mixing region is near the mid-point of the cylinder, but outside the mass of the cylinder. The important feature of the Tipler Time Machine is that it allows travel both backward and forward in time (depending upon whether you circle with or against the spin of the cylinder), and neither the time traveler or the time machine has to move at velocities close to that of light. In his paper, Tipler concludes: "In short, general relativity suggests that if we construct a sufficiently large rotating cylinder, we create a time machine."

The Morris-Thorne Field-Supported Space Tunnel can also be converted into a time machine. If the two mouths of the tunnel are generated side-by-side, they are like twins born at the same time. If you enter one mouth of the tunnel, you instantly exit the other mouth. Now, if one of the tunnel mouths is taken on a relativistic journey by a space tug, then, on its return, it will be "younger" than the stay-at-home tunnel mouth. If you enter the older mouth you will exit the younger mouth some time in the past, and if you enter the younger mouth, you will exit the older mouth sometime in the future. If the younger mouth is still there upon your exit from the older mouth, the process can then be repeated and you can continue to make time jumps into the future. The amount of time you jump over on each traverse is the difference in age of the two mouths.

Notice that this time machine, like all the other time machines that are allowed by the Einstein Theory of Gravity, can only take you backward in time to the moment that the machine is turned on, and forward in time to the moment that the machine is turned off. Einstein's laws do not allow a future time-machine maker to go back into time to tell himself how to make the machine. Thus, at least one of the possible time-machine paradoxes is avoided.

Once we have a time machine that allows us to go both forward and backward in time, however, then other paradoxes arise that are even more confounding than the twin paradox. Exhuming an old cliche: "What is to prevent you from going back in time and killing your grandfather before he has any children?"

It doesn't take time travelers to cause trouble. Even messages sent back and forth in time can produce logical paradoxes. For instance, you could send a message to your future self asking it to send a message to your past self telling you not to send any messages in the present. If you sent the message, you would have been told in the past not to send the message, so you wouldn't, but then the future wouldn't have told you not to send the message so you would have . . . and another logical paradox arises.

Once a time machine exists, then decisions made at one point on the time-line of an individual can affect not only the future of that individual, but also the past of that individual. Time machines will also raise philosophical questions. If you in the future had sent a message back in time to yourself in the past, then does the "you" in the future have any free will? For you know that you must and will send the message at the proper time in the future.

Yet, "free will" has always been limited by the laws of nature. For instance, if your past self has made the decision to jump off a bridge, your future self is bound by that decision. When time machines exist, your future decisions, in the same way, can bind your past self to the consequences of that "yet-to-be-made" decision.

There are other paradoxes brought about by the assumption of the existence of a two-way time machine, but they all boil down to the violation of a strict time-ordered cause-and-effect relationship. There are those who would argue that this alone is enough. The very fact that causality would be violated means that time travel is impossible. Nothing more needs to be said. (I'm sorry, young man, I can't buy your story that you came from the future to warn us about an asteroid about to strike the ocean off the East Coast. You are logically impossible. Go away!")

Amazingly enough, there are presently a series of papers appearing in the scientific literature that discuss in great mathematical detail the problem of paradoxes created by time machines. The first of these papers are those by Friedman et al., Echeverria et al., and Novikov to be found in Recommended Reading at the end of this chapter. To everyone's amazement (including the amazement of the scientists writing the papers), they find that instead of their mathematics showing that the existence of logical paradoxes proves that time machines cannot exist, their mathematics indicates that the logical paradoxes cannot exist! For every paradox that they can dream up (for example, someone deciding to go back into time to shoot himself), a detailed mathematical analysis of the way that nature will behave according to the known laws of physics shows that nature will automatically adjust itself so that the paradox will not occur!

These results are now embodied in the Novikov Principle of Self Consistency, which states that: "The only solutions to the laws of physics that can occur locally in the real universe are those which are globally self consistent."

In the example of the person deciding to got back into time and shoot himself, either he changes his mind, or the gun doesn't work, or the bullet misses, or he kills someone who looks just like him, or something else happens to prevent the paradox. Admittedly, the event that prevents the paradox may have a low probability of happening, but once a time machine exists, then possible physical events around that time machine are constrained so that the Principle of Self Consistency is observed, and low probability events become high probability events.

Once you have made a decision to jump off a bridge, nature will severely limit your possible future courses of action. In the same way, once you have made a decision to turn on a time machine, nature will severely limit your future courses of action to prevent you from creating any paradoxes.

The scientists involved in these publications are continuing their research, trying to come up with a paradox that has no escape routes, like the gun not firing. So far, they have been unable to find any. Those of you that think you can come up with an unbeatable paradox are encouraged to read the technical papers. You will find out there, how nature will conspire against you to prevent the paradox from occurring.

 

Suppose there was a time machine. Suppose it were something as simple as a time-phone, a telephone that allowed messages to be sent into the past. The time-phone would only be used after the occurrence of some disaster, such as an asteroid hitting the Earth. After the disaster had occurred, a message would be sent into the past to warn the people of the impending problem so that they could evacuate the affected area and at least save lives. In the future, the evacuation has already taken place, the asteroid struck, and the people have come back to rebuild. One of their first jobs would be to send the evacuation message back in time, for if it is not sent, then they would all be dead. Although there might be some thoughts about testing the paradox by not sending the message, I'm sure in this case it would be sent, for the consequences of not doing so would be too great. Besides, the Principle of Self Consistency will ensure that the message gets sent.

A time-phone will also give us a broader perspective of events before any major political or social decision is made. As a result of the existence of a time-phone, we will have an "awareness" that extends further into the future than the merest instant that you and I are presently limited to. By using the time-phone, we can be made aware of future events and avoid their consequences. Just as modern airplanes use long distance radar to search the space ahead of them for storms, and change their routes to avoid them, so time machines will allow the pilots of the nations to search the time ahead of them for disaster and avoid their consequences.

It may be tens of thousands of years before the human race has turned what is now future magic into future technology. It will be a long time before our engineering technology can control collapsing stars in order to make a time machine big enough for a vehicle loaded with human time travelers. Long before that time, however, our gravitational engineers may be able to make miniature time machines with the dimension of an atomic nucleus that will allow messages encoded on gamma rays to be sent backward and forward in time.

To make a time-phone we would need to make a superheavy nucleus and strip all the electrons off it to be able to get at the dense, highly charged nucleus inside. Them, using whirling electric and magnetic fields, we would spin up the supernucleus like the rotor of a motor. The rapidly spinning, highly charged supernucleus will then create a north and south magnetic pole at its spin poles. A super-strong magnetic field can then pull or push on the magnetic poles until the nucleus is stretched out into a long spinning cylinder or spread out into the shape of a rapidly rotating ring. [See Figure 17.] These high density, highly charged, rapidly rotating objects would be time machines for nuclear-sized time travelers, extremely short pulses of gamma rays with wavelengths smaller than the time-transfer region.

 

067187686417.jpg
Fig. 17 - Miniature space warps and time machines
for gamma ray signals using dense, highly charged,
rapidly rotating superheavy nuclei.

 

A message would consist of a small number of gamma rays, each at a slightly different frequency corresponding to its "code word" in the message. At these high energies, gamma ray detectors are quite efficient, and the decoding of the cluster of photons that emerged a few weeks in the past or future would be relatively easy.

In the far future when our present technology evolves and makes possible what we now consider magic, our gravitational and time engineers will construct time-phones and time-craft as easily as we now construct space-phones and space-craft. One of these days, instead of being a slave to the ever-ticking clock, we will be able to send our time-craft on a journey through sixty minutes of time into the past or future as easily as we now send our space-craft through the sixty light-minutes of space to Jupiter.

 

Recommended Reading

Brandon Carter, "Complete Analytic Extension of the Symmetry Axis of Kerr's Solution of Einstein's Equations," Physical Review, Vol. 141, #4, pp. 1242-1247 (January 1966).
 

Brandon Carter, "Global Structure of the Kerr Family of Gravitational Fields," Physical Review, Vol. 174, #5, pp. 1559-1571 (25 October 1968).
 

Fernando Echeverria, Gunnar Klinkhammer, and Kip S. Thorne, "Billiard Balls in Wormhole Spacetimes with Closed Timelike Curves—Classical Theory," Physical Review, D44, #4, pp. 1077-1099 (15 August 1991).
 

Robert L. Forward, "How to Build a Time Machine," Omni, Vol. 2, #8, pp. 92-94, 122-123 (May 1980).
 

Robert L. Forward, "Space Warps: A Review of One Form of Propulsionless Transport," Journal of the British Interplanetary Society, Vol. 42, pp. 533-542 (November 1989).
 

Robert L. Forward, Timemaster (Tor Books, NY, 1992). (Contains a detailed description of the construction of a Morris-Thorne Field-Supported Space Tunnel using frames of negative matter—following the prescriptions of the papers by Morris and Thorne, Garfinkle and Strominger, and Visser; its conversion into a time machine following the prescription of the paper by Morris, Thorne, and Yurtsever; and a resolution of the time machine paradoxes that result using the arguments of the papers by Friedman et al. and Novikov. During my research prior to writing the novel, I invented a defensive "weapon" based on a time machine, called the "Timetrap". When I sent my notes to Thorne for comment, he realized that I had found a new set of solutions to a problem that he and his students were working on at the time. He incorporated my notes into their scientific paper, "Billiard Balls . . ." by Echeverria, Klinkhammer, and Thorne, and referenced my science fiction novel as the source.)
 

John Friedman, Michael S. Morris, Igor D. Novikov, Fernando Echeverria, Gunnar Klinkhammer, Kip S. Thorne, and Ulvi Yurtsever, "Cauchy Problem in Spacetimes with Closed Timelike Curves," Physical Review, Vol. D42, pp. 1915 ff (1990).
 

David Garfinkle and Andrew Strominger, "Semiclassical Wheeler Wormhole Production," Physics Letters, Vol. B256, #2, pp. 146 ff (7 March 1991).

 

William J. Kaufmann, III, The Cosmic Frontiers of General Relativity, p. 238 (Little, Brown and Co., Boston, 1977).
 

Michael S. Morris and Kip S. Thorne, "Wormholes in Spacetime and Their Use for Interstellar Travel", American Journal of Physics, Vol. 56, #5, pp. 395-412 (May 1988).
 

Michael S. Morris, Kip S. Thorne, and Ulvi Yurtsever, "Wormholes, Time Machines, and the Weak Energy Condition," Physical Review Letters, Vol. 61, #13, pp. 1446-1449 (26 September 1988).
 

I. D. Novikov, "An Analysis of the Operation of a Time Machine" (English translation), Soviet Physics JETP, Vol. 68, #3, pp. 439-443 (March 1989).
 

Frank J. Tipler, "Rotating Cylinders and the Possibility of Global Causality Violation," Physical Review D, Vol. 9, #8, pp. 2203-2206 (1974).
 

Matt Visser, "Traversable Wormholes: Some Simple Examples," Physical Review, Vol. D39, #10, pp. 3182-3184 (15 May 1989).

 

 

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