A.H. Reginald Buller

Introduction

The fascination with time travel has kept science fiction writers, physics students and the adventurous at heart deep in the rapture of endless equations, intricate plot lines and a yearning desire to contemplate how life would be if only they had chosen a different path. How many times has one heard the question "if you could live your life over, what would you change?" There have been hundreds, perhaps thousands, of books written and perhaps nearly as many television episodes and movies that depict some curious, intricate yarn about time travel. There have been three spin-offs of the Star Trek series that along with the original series contemplated dozens of interesting and twisted plots involving time travel and its problems.

This paper will look into the possibilities of traveling great distances and times. There are several possibilities for time travel including various types of black holes and both natural and man made worm holes. The paper will describe these phenomena free of mathematical equations and discuss the feasibility for such devices. An important part of the paper will also be the practicality and safety. Finally, the paper will address the issue of causality and the question of how a universe could be created that would permit such ridiculous paradoxes to exist that could perhaps cause the destruction of the universe itself?

We have for decades now referred to the world in which we live as "space-time". This refers to the fact that we exist in what appears to be a three dimensional world of space, that is length, width, height plus the dimension of time. Those who study relativity theory and quantum mechanics are familiar with space-time diagrams where one or two spatial dimensions are left off the physical representation of our universe. In these diagrams the dimension of time is usually represented as the vertical axis. And so it is usually perceived that time flows only in one direction as an arrow. Are there ways around this seemingly one way, metronomic existence?

Many have contemplated this possibility, and since Einstein's theories of Special and General Relativity the number has increased dramatically. Two major conclusions have resulted from these theories concerning the concept of time. One is that moving clocks tick slower than ones at relative rest. So therein lies the famous twin paradox where twins separate, one journeys into space at near the speed of light while the other remains on Earth. The adventurous twin returns only to find his brother to be much older than himself. Is this possible? According to general relativity it is. The rub here is that in order to travel more than a few nanoseconds into the future, we will have to achieve speeds much faster than today's technology permits. Even if we achieve speeds near half the speed of light we could only hope to jump a whopping few hours ahead. In order for time travel into the future to be a reasonable possibility we would have to get to just below light speed. This, however, would cost us dearly. Lawrence Krauss (1995) states that the Starship Enterprise, which weighs 4 million metric tons (they actually have technical manuals out there that give the specifications of the ship), uses nuclear fuel to travel at what they call impulse power which at maximum is one quarter the speed of light. This calculates out that "... over 300 million metric tons of fuel would need to be used each time the impulse drive is used to accelerate the ship to half light speed" (Krauss, 1995, p.25). It would take years to accelerate us to that speed unless we had some kind of "inertial dampers" as used by The Enterprise. Otherwise the acceleration required to do this is a short period of time, say a few hours, would definitely kill us with G-forces. If we had this type of technology to eliminate these gravitational forces and wanted to make this acceleration in a few hours " the power radiated as propellant by the engines would then be about 10²² watts - or about a billion times the total average power presently produced and used by all human activities on Earth" (Krauss, 1995, p.26). Clearly we have neither the time nor the energy to accomplish this. Again , this only achieves twenty five percent of light speed, and this is just not fast enough to make time travel worthwhile.

Warp speed is another means of travel in this science fiction series. This is another ball game all together. The concept here is not to increase the speed of the ship moving through space but to somehow bend space so that slower speeds could be used. These warp speeds do not affect the normal passage of time. Therefore, the effect is to travel through space by wrinkling or curving space in front of the ship while stretching it behind thereby taking distance out of the velocity equation. We do not violate the universal laws of physics by traveling at greater than light speed. The theory of how this works (a-la Star Trek and not real physicists) is that the annihilation of matter and antimatter provides the power required to bend space. Even though great distances could be traversed there would be no significant movement through time with this method. We have no idea if this is possible, and the author has not researched respected theories concerning this. Even though forward time travel is possible according to general relativity, the use of near light speeds to achieve significant temporal displacement does not seem realistic in the all but distant future due to the physical constraints and energy requirements (Krauss, 1995).

In 1676 the Danish Astronomer Ole Christenson, while observing the moons of Jupiter, discovered that light travels at a finite speed. "On this assumption, a Cambridge don, John Mitchell, wrote a paper in 1783 in the Philosophical Transactions of the Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape, any light emitted from the surface of the star would be dragged back by the star's gravitational attraction before it could get very far" (Hawking, 1988, p.81). A consistent theory of how light is affected by gravity was not postulated until Einstein in 1915 in his Theory of General Relativity. In the late 1920's an Indian graduate student, Subrahmanyan Chandrasekhar looked at stars and their ultimate fates. Stars shine by the nuclear fusion process which causes an emission of particles and radiation. This outward "pressure" combined with a powerful gravitational attraction of matter keeps the stars reactions going (Hawking, 1988). Gravity keeps the matter dense and hot enough to begin fusion and the expansion of gases and radiation (according to the Pauli exclusion principle) pushing outward balances this. For this reason stars can burn for extremely long periods of time.

Stars like our own are relatively small, and when their nuclear fuel is nearly exhausted they collapse into small dim star called a white dwarf. "Chandrasekhar calculated that a cold star of more than one and one half the mass of the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar limit)" (Hawking, 1988, p.84). Stars with masses above this limit have been calculated to violently explode upon burning the last of their fuel and collapse into an extremely dense object called a neutron star. Shortly after Einstein published his general relativity theory, a man by the name of Karl Schwarzschild used Einstein's field equations to predict that a spherical star with a mass larger than the Chandrasekhar limit (around three solar masses) would not just collapse to a smaller star but would continue to collapse to an infinitely small point called a singularity (Hawking, 1988). By collapsing the mass into an infinite space the density is then infinite, and the star would have an intense gravitational field. A mathematically defined region where the gravity would prevent any particles and even light from escaping would then surround this singularity. This Schwarzschild radius is now known as the event horizon. It represents the region of no return, and nothing that enters this highly curved region of space-time could escape. In 1969 a scientist named John Wheeler coined the term black hole to represent this object.

To understand this phenomenon a little better the writer will represent a space-time diagram where the infinite number of points along the world line of a particle or a person or perhaps even a spaceship is represented as a somewhat vertical line (figure 1).

Figure 1

Space-time diagram of world line and light cones

The x-axis of the diagram represents all the spatial aspects of the line with two of the three dimensions suppressed, and the vertical axis represents time. Since light is the ultimate speed limit and horizontal displacement on the diagram represents spatial displacement while vertical displacement represents time, a world line of more than 45 degrees from the vertical is not possible. This limit is shown in the diagram as a cone where the bottom or point of the cone represents an event (for instance a pulse of light) while the farther up the cone represents the area of expansion of the burst of light through space and time. The cones continue on forever but for the sake of convenience are cut short so as not to clutter the diagram. Travel outside of this cone (or at angles greater than the 45 degrees) is not permitted according to general relativity.

In the case of black holes, space-time is bent inward due to the intense gravitational field. Under this circumstance the light cones tip towards the black hole. Figure 2a depicts a space-time diagram near a black hole and three possible world lines.

The dotted line represents the event horizon. As a world line (a person perhaps) nears a black hole, the light cones tip towards the singularity and therefore escape becomes more difficult since more speed is needed. As the world line gets closer to the edge of the light cone, higher speeds are represented. Very close proximity to the event horizon requires very near light speed just to get away, and getting away is a very slow process. At this horizon the left edge of the light cone is parallel to the horizon, and even at the speed of light, the hapless adventurer is destined to spend the rest of his life at the speed of light trying to escape but getting no further away. Once inside the event horizon the light cones tip even further, and even when a traveler moves away at the speed of light his world line still continues toward the singularity. Figure 3 shows a 2D diagram of a black hole and the warping of space with tipping light cones.

Figure 3

Orthogonal view of wormhole with tipping light cones

(Website 1)

According to relativity as one approaches the vicinity of a black hole time slows down compared to areas farther from it. If one wanted to travel into the future and return home, a black hole would be the equivalent of near light speed travel. Einstein's twin scenario would apply in this situation but instead of traveling at near light speed, travel near a black hole would accomplish the same end. This situation is not without problems though. First of all, the event horizon is not a detectable region of space. You cannot see, feel or otherwise detect its presence. It is mathematical equation depending on the charge, mass and spin rate of the black hole. An astronaut crossing the horizon would not know he had done so until he realized that escape was proving futile. Second, there would likely be a large amount of radiation as Stephen Hawking points out (Hawking, 1988, p. 106). This radiation would be produced by the creation of virtual particles and their subsequent entry into the black hole. Scientists have theorized that x-rays would be produced in large quantities near black holes, and recent Hubble telescope photographs have spotted possible black holes complete with large fountains of radiation being emitted. Galaxy M87 and NGC 3115 are possible candidates for this phenomenon. ( websites 2 and 3) Hawking and Kip Thorne of Cal Tech have an ongoing bet concerning the existence of a black hole at Cygnus X-1.(since this paper was written Hawking has conceded the bet)

Since Einstein there have been a number of scenarios postulated about black holes concerning their characteristics. The simplest of black holes is called a Schwarzschild black hole and is defined as a non rotating, electrically neutral point-like singularity (Halpern, 1992). Even in this variety there are several possibilities. Stephen Hawking and others theorize that there might be primordial black holes left over from the very early and very wild beginnings of the universe. Calculations estimate that at most there might be 300 of these per cubic light year.

With primordial black holes being so scarce, it might seem unlikely that there would be one near  enough for us to observe as an individual source  of gamma rays. But since gravity would draw primordial black holes towards any matter, they should be much more common in and around galaxies. So although the gamma ray background  tells us that there can be no more than 300 primordial black holes per cubic light year on average, it tells us nothing about how common they might be in our own galaxy. (Hawking, 1988, p 110)

Hawking further states that if these primordial black holes were far more abundant there might be one in our solar system, but we would be unlikely to detect it since its radiation would be weak due to its extremely small size.

It has been theorized recently that matter that falls into a black hole may be emitted by another black hole in some kind of parallel universe or perhaps our universe is warped or curved sufficiently that one black hole may connect with another black hole elsewhere. (see figure 4)

Figure 4a

Diagram showing Einstein-Rosen Bridge

connecting two universes

( Gribbin, 1992, p. 156)

Figure 4b

Diagram showing Einstein-Rosen bridge connecting

different parts of the same universe.

( Gribbin, 1992, p. 157)

In this case a black hole would be considered a wormhole which will be discussed later.

If these passages exist through some sort of hyperspace to connect either two universes, or perhaps two places in our own universe, we may be able to use them to travel great distances or even through time since we may arrive elsewhere in our universe but at some other period of history. Could we travel through these black holes to get to "the other side"? It seems that primordial black holes, likely the most common in our universe, would be too small for travel. This does not necessarily mean that they are physically too small to squeeze through. That may be the case, but instead, because their event horizons are so close to the intense gravitational field of their singularity, a traveler would be torn to shreds due to tidal forces and accelerations; their heads for instance being farther from the gravitational source than their feet. A larger Schwarzschild black hole would be better. In fact, the larger the better as far as reducing tidal forces is concerned. "Only for black holes of ten thousand or more solar masses might survival be possible for an approaching astronaut. Then, the rate of velocity increase would be reduced to a "mere" five hundred feet per second per second or less, a value...possibly endurable by hardy explorers" (Halpern, 1992, p. 68). Passageways between these large Schwarzschild black holes "...sometimes called Einstein-Rosen bridges, would exist only for a brief period; hence the mouths of such gateways would be dynamic, not static" (Halpern, 1992, p70). A traveler would need to travel at speeds greater than light to get through since they mathematically exist for only an infinitely small moment. Even though super large Schwarzschild black holes could possibly be traversed, there still is the problem of escaping out the other side. There would be an event horizon there also, so faster than light speeds would be necessary to escape. This leaves the Schwarzschild black hole a poor candidate for space or time travel.

As it turns out the collapse of a star would not likely, according to most physicists, settle down into a static, non-rotating state but instead would likely be spinning. In the 1960's, Roy Kerr worked out some equations that predicted that a black hole spinning at a high velocity would assume a ring shaped singularity rather than a point singularity (Halpern, 1992). This would be due to the centrifugal force of the spin. Under the conditions of a Kerr-type black hole one could enter from a polar region and travel through the center of the ring thereby reducing the severe tidal forces exhibited by other types of black holes. Gribbin (1992) states that there are theories that seem to indicate that such a Kerr-type black hole could, like the Einstein-Rosen bridges of the Schwarzschild solution, produce a gateway to either another universe or some perhaps large displacement in our own, not as another black hole but as a "white hole" that repulses matter out into the "other" universe.

According to some recent work of mine, the  answer is that they (particles that enter black holes) will go off into a little baby universe of their own. A small, self contained universe branches off from  our region of the universe. This baby universe may  join on again to our region of space-time. If it does  it would appear to us to be another black hole that formed and then evaporated. Particles that fell into  one black hole would appear as particles emitted by the other black hole, and visa versa. ... In the  last few years, a lot of people have been working on baby universes. I don't think anyone will make a fortune by patenting them as a method of space  travel but they have become a very exciting area of research. (Hawking, 1993, p.121,125)

Gribbin further states that " An astronaut who dived through the ring but stayed close to it and circled around the center of the black hole in an appropriate orbit would be traveling back in time" (Gribbin, 1992, p.163). If the other side is a white hole where matter is forced out into the universe, then perhaps travel is possible. But is it a white hole in another universe or a white hole in the past of our universe? According the common belief, white holes may have been common in the early history of the universe but chances of finding one near our present timeline is unlikely. Others think that quasars could be white holes, but they are so far away that they represent light from many millions to perhaps billions of years ago. Remember that you cannot return to our universe due to the event horizon on our side. On the other hand perhaps these so called other universes may just be our own universe at some other time." Just as Schwarzschild's solution can be extended into an antiworld-another universe, where time runs backwards-so Kerr's solution extends into an infinity of other universes both worlds and anti-worlds" (Davies, 1995, p.244).

Another Kerr solution (Gribbin, 1992) involves a ring singularity spinning so rapidly that is flings off its event horizon thereby "exposing" it. This is called a naked singularity. If there was no event horizon to prevent relativistic escape from the black hole, and then an astronaut could theoretically enter, make a few passes around the ring and return on the same side. There would still be very powerful gravitational forces to overcome but at least sub-light speed is a viable escape velocity.

Godel's Spinning Universe

The commonly held view of the universe proposes that after the big bang the universe is expanding in a non-rotating fashion. In 1949 a scientist by the name of Curt Godel, working with some of Einstein's equations, came up with a theory of the universe that uses centrifugal force as part of the expansion process (Gribbin, 1992). This spinning universe idea gave him some interesting possibilities for closed time-like curves and time travel. "When massive objects rotate, they drag space-time around them, in a manner reminiscent of the way coffee will swirl around if you twiddle the spoon in your cup" (Gribbin, 1992, p.198). If the universe is rotating at a high enough speed, say once every seventy billion years (Halpern, 1992) then that speed may be enough so space time is swirling enough that light cones are tipped over sufficiently to allow a traveler to move in a large circle passing from one light cone to another. This tilting of light cones gives the effect that the future cone of an event intersects the past cone of another event and so on. This resembles a giant loop or a closed time-like curve (CTC). The traveler could then circumnavigate the universe in a way that he returns to his own history (see figure 5). The distances however would be enormous, and there seems to be no evidence that the universe is rotating in such a way or that there is any evidence for CTCs in nature.

Figure 5

Tipped light cones in rotation about the

universe (Gribbin, 1992, p.201)

Tippler's Rotating Cylinder

In 1974, Frank Tippler stumbled across an idea taking Godel's model into account and determined that instead of using the universe itself to rotate space-time, it may be possible to use an extremely massive very rapidly rotating cylinder to swirl space-time (see figure 6). This would seem to have the effect of Godel's model of tipping over the light cones and allow both forward and backward travel (Gribbin, 1992). The Time traveler would simply make revolutions with or against the rotation to travel either forward or backward in time. The cylinder would have the property of being a naked singularity so that event horizon would not interfere with escape. As it turns out, however, a cylinder of infinite length would be required for this to occur. Constructing such a time machine of "infinite" length would be a problem. How could we build something infinite? Where would we find an infinite amount of material with which to construct it?

Figure 6

Tippler's design of a massive cylinder

dragging space-time around itself.

(Gribbin, 1992, p.203)

Tippler's time machine would have another problem that would frustrate time travelers also; they could not travel backwards to a time before the machine was built. It's closed time-like curve, unlike Godel's rotating universe, does not extend into the past beyond the time the machine was created. So, travelers would be relegated to travel the future or to the past up until the time the machine began to exist. Tippler's machine doesn't seem too promising.

Worm Holes

In 1985, Dr. Carl Sagan, of Cornell University published his only work of fiction; Contact. In it he chronicled mankind's first contact with beings from outside the Earth. A signal was sent from the star Vega that after much analysis proved to be the blueprints for some kind of fantastic machine. Believing this machine to be some kind of interstellar transport device, the nations of Earth took decades to build it. In the novel, scientists, via a wormhole accessed by this machine, were rapidly transported not only to the star Vega, but also to a place somewhere on the other side of the galaxy.

When Sagan had written an earlier version that used a black hole, he sent a copy to his friend at Cal Tech, Kip Thorne, and asked him to review it for the purposes of scientific accuracy (Halpern, 1992). Sagan wanted his novel to be as realistic as possible using the most advanced scientifically sound ideas of the day. Thorne and several of his graduate students took to the task with vigor, and by using the latest field equations and some brilliant extrapolations, proposed the idea of using a wormhole. Now the idea of a wormhole is nothing new, but Thorne and his team devised theories and equations to predict that wormholes exist, may be able to be controlled and perhaps even created purposefully.

Einstein-Rosen bridges mentioned earlier are in effect wormholes. They may contain one or two black holes and connect one part of space-time with another. That "other" may be in some other universe or perhaps somewhere in our own. As also mentioned earlier, black holes are tough on human beings and their equipment so travel through them is difficult as best and usually fatal. Also, there is the problem of the event horizon preventing return. Any volunteers?

Researchers propose that worms holes may exist without the presence of black holes nearby. Perhaps these were left over from some earlier part of the evolution of the universe.

The flexible nature of Einsteinian space-time, in contrast to the rigidness of Newtonian space and time, seems to  permit the existence of geometries distorted greatly enough to allow for transuniversal links. According to the time-tested conclusions of theoretical general relativity,rips, tears and connections in the cosmic fabric do actually  exist. The presence of these geometric formations fuels  considerable speculation that traversable interstellar  short cuts, connecting widely separated parts of the  universe, may, in fact, be possible. (Halpern, 1992, p.43)

If these regions were connected by this wormhole, it would have the effect of bending space around thus shortening the distance. This could also be depicted in a somewhat different way ( see fig. 7) that seems to lengthen the distance but actually because space-time is infinite in the wormhole the distance is actually shorter.

Figure 7

The wormhole drawn in a differentway still represents a shortcut.

(Gribbin, 1992, p.158)

Advanced civilizations may be able to detect these phenomena and use them to their advantage. Finding these would be rather difficult since there doesn't seem to be any theories out there concerning what telltale signs to look for. Large black holes may give off enormous amounts of radiation as perhaps we have recently discovered with new Hubble telescope photographs, but we don't know what wormholes might look like. Natural wormholes may have other problems:

Gravitational radiation itself, traveling ahead of the space-ship and into the black hole at the speed of light, could be amplified to infinite energy as it approaches the singularity, warping space-time around itself and shutting the door on the advancing spaceship. In other words, even if a natural traversable wormhole exists, it seems to be unstable to the slightest perturbation, including the disturbance caused by any attempt to pass through it.

Perhaps the most reliable way to travel would be to build a wormhole of your own design, and this is exactly what Kip Thorne and Michael Morris had in mind for Sagan's novel. They set about to devise a strategy of how to build a wormhole and decided to work backwards. They had to determine first what the conditions of a traversable wormhole would be. They had nine of them. First, the wormhole must be static and spherical- meaning its shape and size must be the same at all times. Shifting wormholes would be dangerous if not fatal. Second, it must obey Einstein's equations for general relativity. Third, it must have some sort of hourglass shape as seen in previous figures. Fourth, it cannot have any event horizons. Fifth, the acceleration and tidal forces due to gravity must be small so we won't be crushed or stretched. Sixth, The time of travel should be less than one year for both the travelers and the crew left behind. Seventh, the matter and energy needed to create the wormhole must be physically reasonable. Eighth, the wormhole must remain stable as the spaceship passes through it. Small perturbations in the gravitational field surrounding the ship could cause the walls or mouth of the wormhole to collapse. And ninth, the assembly of the wormhole can't take too much matter or time to create (Halpern, 1992).

One problem that must be overcome with the building of these wormholes is the problem of the gravitational waves or a vibration pushing out in front of and around the spaceship as it enters the mouth. Gribbin suggests building a gravitational wave receiver/transmitter that is near the mouth that will read the vibration and transmit an inverse or opposite one to exactly cancel the wave generated by the ship (Gribbin, 1992). A major problem would be the material used to build the wormhole. In order to build a wormhole strong enough to withstand tremendous gravitational stresses, Thorne and his colleagues turned to antigravity! They needed some sort of material that would have numerous "opposite" effects of matter to build a wormhole to avoid the devastating effects of gravity. They needed some sort of exotic matter.

Normally, one of the basic tenets of elementary physics is that all objects have positive energy. Vibrating molecules, moving cars, flying birds and soaring rockets all have positive energy. (By definition, the empty vacuum of space has zero energy.) However, if we can produce objects  with "negative energies" (that is, something that  has an energy content less than the vacuum), then we might be able to generate exotic configurations of space and time in which time is bent into a circle.

The exotic material used to build the wormhole would have to have enormous tension strength to mass density ratio in order to keep the mouth open, and these properties exceed any known material's specifications.

Where to find such material is also a problem. Several theories have been postulated as a possible solution. Quantum mechanics gives us one. Hawking has demonstrated that black holes emit radiation. Some of this is thought to come from the appearance of virtual particles near the event horizon. Here, these virtual particles "appear" from infinity (hyperspace?). Far away from black holes they appear as a particle and it's antiparticle that separate momentarily and then come back together to annihilate each other and disappear. Near the black hole the antiparticle is drawn into the black hole having negative mass and energy. This decreases the mass of the black hole and reduces its total energy thereby causing it to evaporate. If we can devise a way to "harvest" these antiparticles, and some have devised some possibilities, and if we can contain them, we may be able to get enough to build our worm hole (Kaku, 1994).

It is well researched that wormholes could lead to other parts of the universe and serve as spatial passages. It is also believed that perhaps the "other side" leads not just to another region of space but of space-time, perhaps near us but at a different time. Knowing where and when a wormhole leads is a difficult situation. If we could build it, the other side would probably be a stab in the dark. We might not know where it goes, but if we could build a small one that leads to a region near the original opening, we could drag one mouth around at high speeds. This would slow time down at the moved opening while the static opening would forge ahead at our normal clocks. This, therefore, would have a relativistic effect of entering the static mouth and emerging from the dynamic one thereby making a closed time-like curve, a loop so to speak (Halpern, 1992). We still have the problem that the loop did not exist until we created it, so therefore we could not go back to a time before the device was created. A solution to this would be if some advanced civilization did this long ago in our history and left behind this device for us to find.

Cosmic Strings

Richard Gott of Princeton University has proposed a time machine using "cosmic strings". Very near the beginning of the big bang it is theorized that the universe may not have had the uniform expansion we have today and perhaps even had undergone a "...wild expansion, driven by negative-pressure antigravity in the form of a cosmological constant, which occurred during the first split second after the moment of creation" (Gribbin, 1992, p.180). It is thought that this initial wildness created domains in the universe with boundaries made of the exotic matter produced during this period. Some believe that these boundaries may still exist, and at these boundaries we might find infinitely dense negative materials with trillions of negative tons per inch densities (Lemonic, 1991). These have been called "cosmic strings". These would exist as large loops present today separating these domains of our universe. Astronomers looking at composite photographs of the known universe have noticed that matter is not evenly distributed but instead form huge clusters of galaxies separated by large regions of empty space. It is in these regions where cosmic strings are thought to exist. These strings present two scenarios for use; for the exotic material needed to construct wormholes, or perhaps to use as a Kerr-type black hole circling the strings to travel backward instead of forward in time since they would produce anti-gravity instead of the normal gravity that is used to propel time travelers into the future.

Gott has gotten enormous interest from other physicists and astrophysicists about his theory. The reason is not that physicists really believe that time travel can actually occur. But the fact that it appears possible in principle challenges the very foundations of physics.

Causality

Time is Nature's way to keep everything from happening at once. John Wheeler

Every time a new theory is proposed that seems to point to the possibility that closed time-like curves can exist someone manages to remind those beginning to feel excited that there still is the problem of cause and effect. Of course the classic tale of the time machine has been told even to the very young as the case of the time traveler who goes back in time and kills his grandfather before he conceived his father. He would have never been born!

Another well known story of causality is that of a destitute but brilliant man who is paid a visit by a mysterious wealthy man who gives him the plans and money to build a time machine. The man builds it, makes a fortune in the stock market by getting information from the future and returns into the past to give the plans to the poor destitute but brilliant young man (himself). Where did the idea of the time machine come from?

Robert Heinlein's "All You Zombies-" is a story where by twist of causality, a man goes back in time and has sex with himself. That alone does not seem to have any obvious effects except when you find out that "he" was a "she" during this time and only after the birth is he physically altered. What makes matters worse is he kidnaps the newborn child and takes "her" back to the past where "she" grows up to be the person (himself) he has an affair with… and ... it just gets worse from there. When you try to find who's who, it turns out that she is her own grandmother, grandfather, father, mother, son, daughter and probably much more (Kaku, 1994).

Most physics students have heard of the story where a wormhole exists on a billiard ball table. The ball rolls across the table, falls into a wormhole and emerges at the exit of the hole, which is in the line of the ball heading toward the wormhole entrance. The ball emerges in the past and knocks itself out of the way now missing the opening to the wormhole and never falls in.

There are dozens of stories of violation of causality. How could a universe exist with such goings on?Hawking is convinced that time machines are  impossible, because of the obvious paradoxes that might result, and he has proposed a "chronology-protection conjecture," to wit: "The laws of physics  do not allow the appearance of closed timelike curves. (Krauss, 1995, p.51)

Many have suggested that even if time machines have existed in the past and people have been traveling back and forth somehow, our history books would have to be constantly rewritten as the past changes. Stephen Hawking has often remarked that if time machines have existed, where are the hoards of tourists coming from the future to witness great catastrophes (Davies,1995). The infinite number of universes hypothesis as well as the microscopic world of quantum mechanics's uncertainty principles, gives rise to such television series as "Sliders" where a small group of scientists and adventurers keeps popping in and out of different universes all like ours but with different historical outcomes. If history is rewritten, no one will know since once a change is made the entire future is different for that universe. Perhaps the "other universe" where time travelers did not alter the past just keeps on going. Even Hawking who hates the idea of closed timelike curves likes the concept of multiple universes.

Conclusion

For centuries, mankind has dreamed of traveling great time and distances. Early in this century Einstein formulated his famous theories of special and general relativity. These addressed, among other things, the effects of travel near the speed of light and the influence of gravity on space-time. Since then physicists have extrapolated these equations to using near light speeds as time machines. Obviously we could travel great distances at these speeds but we also found that clocks slow for rapidly moving spaceships. Unfortunately, the energy required to bring such craft to these enormous speeds is quite prohibitive if not totally out of reach. We could travel at considerably slower speeds and find the energy to do that but the distance we could travel into the future would not warrant the effort.

Also, as a result of the exploration of these equations, physicists have been toying with the idea of black holes. The term is now a household word. This paper looked at several black hole scenarios. A recent search on the World Wide Web produced thousands of web sites that related to black holes. Black holes have pretty much the same effect on time travelers as near light speed travel in that it is one way. There were also some other problems associated with black hole time travel. Radiation is one of them. That gravitational field that permits the bending of space-time makes it difficult to get away from it thereby creating, again, a need for incredible power in the ship's engines and very elastic astronauts. Then there's that pesky event horizon which just won't let go. Traveling into the past is where the real fun is.

Enter wormholes. These clever little devices that connect either different universes or perhaps different times or regions in our own universe and seem to satisfy the laws of physics if we can do some pretty insurmountable things. We must collect antimatter in huge quantities and figure out where the exit will form. We also have to figure out the basic configurations of the holes themselves. Then there are cosmic strings. They are to glamorous movie stars as black holes are to the girl next door.

Although ultimate understanding of time and it's  manipulation remain beyond our grasp, physicists have  brought the issues to focus in a remarkable story of the exploration of time that has been carried out for the last28  few years. Time has always been a fundamental part of physics. The equations physicists use are chronologically symmetric - in other words, they do not differentiate a forward from a backward direction in time. (Wheeler, 1996, p. 52)

The biggest battle with these ideas today is that even though physics does not seem to prohibit closed timelike curves, causality makes the physics seem illogical. Most of the physicists who argue that causality prohibits backward time travel realize that these CTCs make no sense, and the nature of the universe itself would have to prohibit a timeline that could possibly lead to the ultimate fate that the universe itself will not begin let alone be here today. Until someone can prove that CTCs will not affect the operation of the universe and the physics within it, most physicists will be relegated to dreaming about time travel.

So far it has taken most of the twentieth century to get from general relativity to where we are now. The next hurdle is the so-called unification of quantum mechanics and gravity. If this can be done, then perhaps doors will begin to open. Stephen Hawking has make it his goal to do just this. This paper has explored some of the recent advances toward this project of time travel. The author feels that according to all sources used, the physics seems to say go ahead, but the energy and technology required are not attainable in even the distant future. Nevertheless, mankind will continue to search deeper and deeper into these mysteries and it will take the efforts of the great minds and visionaries of our time to help solve these riddles.

References

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