In 1905, an obscure Swiss patent office worker wrote a paper that caused an uproar in the scientific community. The paper refuted all the Newtonian physics that scientists knew. The writer of the paper was Albert Einstein. Scientists now accept his Special Relativity Theory and General Relativity Theory as the best theories to explain the universe, or as Stephen W. Hawking (1988, p. 175) put it, to "know the mind of God." If someone were to know the mind of God, he would be omniscient like God. If someone were omniscient, he would know how to take control of time and travel forward and backward at his whims.
Since 1895 when H. G. Wells published his book The Time Machine, the idea of time travel has enamored the American public. Large amounts of literature, usually science fiction, have been dedicated to time travel. On the humorous side of that literature, the Calvin and Hobbes cartoon above contains a truth about Einstein's equations that all physicists know: the Mathematics behind travel into the past and General Relativity is extremely difficult. Arthur Buller also used the ideas behind Einstein's theories in a humorous way in his limerick about "Miss Bright:"
- There was a young lady named Bright,
- Whose speed was far faster than light;
- She set out one day
- In a relative way,
- And returned on the previous night (Davies, 1992, p. 21).
Even though Miss Bright's trip may seem like an idea concocted by Star Trek writers, many respected theoretical physicists have published serious ideas using Einstein's Special and General Theories that may allow travel in time.
To understand how theoretical time travel is possible, one must understand the basics of Einstein's theories. Using Special Relativity, scientists know that time, length, and mass are "not absolute and universal but depend on the observer's state of motion" (Davies, 1992, p. 20). At the speed of light (which, according to Einstein's equations, cannot be reached or exceeded by a body with mass1), length decreases to zero, mass increases to infinity, and most importantly, time slows to a stop (Macvey, 1990). Therefore, time is not absolute. An event that took two seconds to a stationary observer would seem to take only one second to a person traveling at 0.87c (87% of the speed of light)2. Any length would also shrink to half its original length relative to the moving observer and the mass would double.
General Relativity is even more difficult to understand than Special Relativity. In General Relativity, Einstein said that gravity is not a force. Matter distorts and curves spacetime (commonly referred to as the "space-time continuum" by science fiction authors). Projectiles merely attempt to travel in the straightest line possible in the warped spacetime. Using Riemannian geometry (since planar Euclidean geometry does not encompass warped planes), Einstein improved upon Newton's equations of planetary orbit by more accurately describing the path that planets travel3. A mass, such as the sun, warps spacetime as a steel ball stretches a taught rubber sheet. (Theoretical physicists call this type of two-dimensional model of spacetime a "spacelike hypersurface.") The larger the mass, the more the rubber sheet stretches (Gribbin, 1983). The "pit" created by the sun catches the planets, which are trying to travel in a straight line. A black hole, which warps spacetime in special ways, can be described as a lead ball that ripped through the rubber spacetime sheet. Anything that falls into a black hole is compressed into a "singularity." Hawking (1993), who has done intensive research with black holes, defines a singularity as a point in spacetime where the spacetime curvature is infinite and where spacetime ends. Wormholes, another result of Einstein's equations that connect two distant points with a short path through spacetime, are thought to appear to be two black holes ("mouths") connected by a passage (a "throat"). However, the passage is very small and wormholes have not even been proven to exist (Lemonick, 1989).
 |
Many scientists in Einstein's day refused to accept his results because the equations led to the possibility of time travel. Theoretically, the Special Theory of Relativity allows travel into the future, while the General Theory, under exotic conditions, allows travel into the past. However, the energy and the technology required to accomplish either of these feats are far beyond what anyone in the foreseeable future can dream to use. Using Einstein's theories of relativity, time travel into the future and past are theoretically possible, but are not feasible.
Time travel into the future is commonplace. Humans have been adept at moving steadily into the future since their creation. However, moving appreciably faster into the future than others is more difficult. As already stated, if a traveler could move at a velocity of 0.87c, time on earth would move twice as fast as his time. Therefore, if he were to leave on his birthday and return on what he thought was his next birthday, two years would have passed on Earth. Although this may be useful as a "fountain of youth," it is not useful to serious time travelers. If this traveler could tweak his engine to get it to travel at 0.999 999 999 9c, or one hundred millionth of a percent less than the speed of light, he could travel to Andromeda and back in 55 years. If he were to return to Earth if it still existed, the Earth would have aged 4.7 million years (Macvey, 1990). Most travelers would not want to go that far into the future. However, traveling a 0.999 999 5c, the traveler would only go one thousand years into the future with one year of travel4, which could be extremely useful to potential time travelers.
No physical barriers have been proposed yet to prevent time travel into the future. However, no technology known comes even close to accelerating massive starships to such tremendous velocities. Many scientists look at the advancements that the human race has made in the last forty years and speculate that eventually such a ship could be built eventually. Realistically, even if the vehicle was built, the ship would consume enormous amounts of energy. John Macvey (1990) estimates that for a spaceship weighing one ton, the power needed to attain a velocity of 0.8c would be 215 billion kilowatt-hours. All the power stations on the earth combined would need several months to generate that much power. Also, traveling at such high velocities, the impact of the spaceship hitting even a particle of dust would be enormous. The particle could have the inertia of a planet (Davidson, 1990). The force of the collision would easily rip the ship apart. If the prospective time traveler was able build a spaceship, enslave the workers of the world and force them to produce power for himself for several months, he would probably die in his attempt to travel forward to a time where the people of earth had forgotten his tyranny by striking a speck of dust.
Time travel into the past is much more difficult than into the future. To travel into the past, "exotic conditions" are needed to change spacetime in a way that a traveler can go backwards in time (Freedman, 1989, p. 58). To warp spacetime enough to allow the functions of space and time to interchange, a person must travel at relativistic speeds, because no valid conditions are within a close range of the earth. If a traveler could reach suitable conditions, he would encounter many other obstacles. Many scientists believe that "causality" will prevent anyone from traveling to the past (Davidson, 1990). Causality is the normal relationship between cause and effect. If someone could travel back in time, the effect could influence the cause. For example, if Michael J. Fox in Back to the Future had killed his parents, then he would never have been born, which would render him unable to kill his parents. Some theoretical physicists believe that nature protects itself from time travel because of causality violations. Stephen Hawking (in Travis, 1992, p. 180) believes that since the Earth has not been "invaded by hordes of tourists from the future," time travel will never occur. Whenever a new theory is proposed about traveling back in time, other physicists attempt to prove that each is impossible. By playing with Einstein's complicated equations, scientists also learn more about the properties of the universe.
 |
Black holes have long been of interest since Einstein's theories predicted them. In a black hole, matter collapses to a point of infinite density, called a singularity. Around the singularity is an event horizon. Once a traveler passes the event horizon, the gravitational pull is so great that the traveler cannot pass back through the event horizon without traveling at a speed greater than the speed of light (Gribbin, 1983). However, another exit may be available. In a rotating black hole, an Einstein-Rosen bridge system develops (Parker, 1991). In this "wormhole," a shuttle could enter and, by orbiting around the singularity to avoid it, could arrive in another universe (Davidson, 1990). Scientists are not sure what this other universe might be. The other universe may be our own universe but in a distant location in space and time or it may be another universe, often called a parallel universe.
However, to reach the "other universe," the traveler must survive the hazards of the black hole. According to Barry Parker (1991), a spaceship attempting to travel through the wormhole in a black hole would be crushed by the wormhole passage pinching off, stretched out by the strong tidal gravitational waves, and "literally fried" by extremely high radiation levels. This grim forecast should deter most travelers from attempting to enter a black hole. If, for some foolhardy reason, a traveler attempted to enter a black hole, he would never reach the event horizon relative to an observer orbiting around the black hole. Time slows down in strong gravitational fields (Parker 1991). Therefore, the traveler's ship would at first accelerate toward the black hole. As the ship would approach the event horizon, however, it would slow down to a virtual stop. If the observer were to see a clock on the ship, the clock would slow down so much that it would appear to stop. The traveler, on the other hand, would feel as though he passed through the event horizon almost instantly (Parker, 1991). Unknown to the traveler, an infinite amount of time would have passed outside the event horizon and he would be cut off from the rest of the universe. The traveler would be forced to travel infinitely into the future and then travel back infinitely into the past to accomplish anything. Because of the number of difficulties associated with travel into a black hole, most theoretical physicists have given up on using black holes to go back in time. Hawking (1993) consoles potential black hole time travelers by stating that even though they would be ripped apart to atoms, their atoms may float into a time in the earth's past.
Although the wormholes connecting black holes are not likely to be useful for time travel, other types of wormholes may exist which do not have singularities in the middle of their throats. Scientists who work on the Plank scale (dealing with objects smaller than 10-33 cm long, which is smaller than an atom) have discovered that tiny wormholes lace spacetime, making a "spacetime foam" of millions of tiny wormholes (Davies, 1992). These wormholes connect different spots in time 10-42 seconds into the past (Deutsch, 1994). If one of these microscopic wormholes could be inflated into a macroscopic wormhole by some means, then it could be used to connect two different points in space and time. By taking one of the mouths and moving it at a relativistic speed away from the other mouth, one end of the wormhole would be younger than the other ("Wormholes," 1988). By traveling from the older one to the younger, a shuttle could go back in time (Allman, 1992).
 |
Problems still arise in a wormhole even without a singularity. Wormholes tend to be very unstable, and the if a spaceship entered one of the mouths, the throat would immediately pinch off, crushing the ship (Clarke, 1990). To keep the throat open, negative energy or "exotic matter" equal to the pressure in the center of a neutron star is needed ("Wormholes," 1989). Madhusree Mukerjee (1994) describes negative energy as a "no-no," meaning that physicists do not know how to produce negative energy. Scientists have no idea how to produce any of these "lozenges" to open up the throat. Also, since enlarging a microscopic wormhole would be extremely difficult, a natural wormhole could be used, but the ends of the wormhole would be separated by large expanses of space. Therefore, to return to earth within his lifetime, a traveler would have to travel at relativistic velocities. Even at those high speeds, he probably could not return before he left.
The most recent theoretical model of a time machine has sparked a great deal of dispute, some of which has been appropriately published in the popular newsmagazine Time. The model, proposed by J. Richard Gott III, involves cosmic strings. Cosmic strings are long, thin strings of pure energy left over from the beginning of the universe (Lemonick, 1991). The energy of a cosmic string converted to mass would yield a density of approximately 40 million billion tons per inch (Travis, 1992). By taking two of these strings, placing them parallel to each other, and accelerating each to 0.999 999 999 92c in opposite directions, spacetime becomes extremely curved. By traveling between the strings and then looping around them, Gott calculates that spacetime would be warped enough that when a traveler took off, he could see himself returning (Peterson, 1992). By repeatedly traveling between the strings, multiple spaceships could all be together at once. Edward Farhi of the Massachusetts Institute of Technology remarked that Gott's idea "was so simple that it was tantalizing" (Peterson, 1992, p. 202).
Many physicists were quick to attempt to prove that Gott's idea is impossible. The team of Farhi, Alan H. Guth and Sean M. Carroll from the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts developed a simplified model called "Flatland" (Peterson, 1992). Ignoring one space dimension and forming a three-dimensional spacetime, Farhi and his colleagues determined that if the universe was open, meaning that it did not contain enough matter to halt its expansion, not enough matter and energy would be present to construct the strings (Travis, 1992).
Gott quickly responded that this analysis may "eliminate his time machine from certain universes, but not necessarily from our own" (Travis, 1992, p. 179). He claims "physicists have a deep-seated belief that things should be causal" and believes that these physicists are saying, "We do not like what [Closed Timelike Curves] imply for physics, so CTCs are unphysical constructs" (Travis, 1992, p. 180). Despite this tirade, Gott himself admits, "Actually, before trying to locate a pair of cosmic strings, it would probably be helpful to locate a single string-something that no one has yet managed to do." He also wistfully states that the speeds that the strings are required travel at are "not any faster than we get electrons to move in the Stanford Linear Accelerator," ignoring that electrons are extremely light while cosmic strings are extremely massive.
Despite these restraints, Gerard 't Hooft of the University of Utrecht in the Netherlands is determined to grind any hope that cosmic strings may work under his heel. He warns, "Don't try [to go back in time using cosmic strings] . . . You won't just fail-you might destroy the entire universe" (Mukerjee, 1994, p. 32). The dilemma described by 't Hooft shows that in a closed universe, the strings cannot pass parallel to each other. Instead, they begin to orbit each other, moving closer and closer together spinning faster and faster. As the kinetic energy of the strings approached infinity, the universe would begin to crumble and collapse in onto the strings. Mukerjee (1994) described the event from the prospective of a potential time traveler: "A time-machine ticket-holder will see massive walls closing in while being shredded to spaghetti by the strings speeding through. . . The scene sketched by 't Hooft shows how such objects can act as Nature's dragons, guarding time machines from fools who would rush in" (p. 32).
Gott, not to be easily dismissed, has proposed a new theoretical puzzle: a finite, rapidly shrinking cosmic loop. This idea will prove more difficult to prove or disprove, because "Flatland" cannot be used. Complete four-dimensional spacetime is needed to fully analyze the phenomenon. However, Gott admits that the system will probably collapse into a black hole, and any time travelers attempting to travel through would be captured behind the event horizon (Peterson, 1992).
Theoretical physicists have been and will continue to introduce new ways to travel in time. Other theoretical physicists will continue to prove that time travel is impossible. Despite optimism from some prominent physicists and science fiction fans, mankind will never "know the mind of God," and therefore will never be able to control the passage of time. Travel into the future will be restricted by the absence of the technology needed to build vehicles capable of velocities close to that of the speed of light and the enormous energy requirements needed to operate the vehicles. Travel into the past will be more violently restricted. Natural phenomena such as crushing singularities, pinching wormholes and collapsing universe will prevent anyone from attempting to violate causality. Stephen Hawking (in Travis, 1992, p. 180) also believes that time machines in general "sow the seeds of their own destruction by creating a small feedback loop in which small fluctuations in the energy of the vacuum travel back in time" and amplify the distortions to astronomical proportions, destroying the time machine the instant it is created. Presently, Hawking is working on a "Chronology Protection Conjecture," which will rule out time machines altogether. Various parts of the conjecture have been proven, including one which states that unless a ship is surrounded by negative energy while attempting to travel back in time, singularities will form around the ship and cut it off from the rest of the universe (Allen, 1992). If a prospective time traveler ever wishes to enter a time machine, he should carefully take heed of the warning Dante to those entering Hell: "All hope abandon, ye who enter here."
Notes
1 Using the formula for mass dilation
where M0 is the rest mass, Mv is the mass of the object in motion, v is the velocity, and c is the speed of light (299 792 458 m/s), the fact that a massive body can only travel below the speed of light can be proven (Macvey 51). By plugging the speed of light into the equation for the velocity,
the rest mass is divided by zero to give the value of the mass in motion, which is undefined and approaches infinity. When a speed greater than the speed of light is used for the velocity, such as 2c,
the rest mass is divided by the square root of a negative number, which produces a complex or "imaginary" number (
2 Using the equation for the dilation of time,
with Tv (time to an observer in motion) equal to one second, and T0 (time to an observer at rest) equal to two seconds,
the formula yields a result of 87% of the speed of light as the velocity. At this velocity, the moving observer would see things as occurring twice as fast as an observer at rest.
3 Newton's equations stated that planets travel in a perfectly elliptical orbit around the sun. Einstein's, however, took into account that the perihelion of Mercury's orbit rotates around the sun at 43 arc seconds per century. (Macvey 64) The other planets' orbits, while not as observable as Mercury's, follow a similar path.
4 Again using the formula for time dilation,
with Tv equal to one thousand years and T0 equal to one year,
the velocity required is 0.999 999 5c.
Time travel is a concept much loved by science fiction writers, and Star Trek fans, but is it possible within the known laws of physics? To answer the question we shall take another look at quantum theory (Quantum Mechanics) bringing in the ideas of Richard Feynman, and re-examine the theory of relativity. After that we shall consider the difficulties involved in constructing a time machine, if such a thing can be done. But before we do any of this, let's first consider some of the problems that time travel raises. I have to say at this point that if ever a theory was riddled with problems, paradoxes, speculation and possibilities, then this is it, outright winner of my gold medal award!One of the stock answers to the question of time travel is to suggest that if time travel were possible it would have already happened. By way of explanation let's say that at some time in the future a clever scientist invents a time machine that can travel through time in any direction, just like the fictional time machine created by H. G. Wells. So where is our intrepid time traveller? History shows that no time traveller has ever visited us from the future, therefore it's never going to happen. This appears at first glance to be a good solid argument against the possibility of time travel, but the argument is flawed. It may be that time travellers from the future have visited us, but have not revealed themselves in order to avoid changing the future. Alternatively, time travel may be possible, but only into the future, the past already having been determined. Finally, time travel into the past may be possible, but only into a different (alternative) universe, thus avoiding paradoxes. The fact that we have no record of having been visited by time travellers does not exclude its possibility. Having dealt with that little problem we can now move on the fun part, paradoxes.
Paradoxes
This is where we start to run into some of the problems posed by time travel. The most commonly posed paradox is known as the 'grand parent' paradox. This states that if you could travel back in time you could murder your grand parents and thus prevent your existence, thus rendering it impossible for you to have gone back in time and killed them... no need to draw you a picture. Even more to the point perhaps, you could travel back in time and kill the person responsible for time travel before they discover it! However, popular though the grand parent paradox is, it only reveals the tip of the iceberg. Let's examine a theoretical time travel situation in more detail in order to highlight some of the problems involved.
Imagine that today you travel back in time to August 2001 and warn the authorities that the World Trade Centre in New York is going to be attacked on September 11th. They take the necessary action and as time unfolds the disaster is eventually averted. You are still in August 2001 at this point and the disaster has not yet been prevented, but it will be eventually because of the chain of events that you have put into motion, and you now wish to return to the time you came from. Here comes the Big Question - can you return to where you came from? Where you came from the attack had taken place, therefore where you came from no longer exists! If you do return to your original time, the World Trade Centre will still be standing (because you prevented the attack), so it cannot be where you came from. You will have changed the course of history, not just for yourself, but for the entire world. The question is, will the World Trade Centre still be standing when you return to your starting time? This is a major point of contention. According to one theory it both will and it won't! This is because your actions will have created an alternative possibility and in the process an 'alternative' universe, where we now have one universe with the World Trade Centre intact, and one with it destroyed, and we will all exist in both. The theory is firmly rooted in quantum theory that states that ALL alternative outcomes are possible. However, there is no evidence at this stage that the strange phenomenon found in quantum theory can be applied to the larger world.
Yet another theory suggests that alternative universes will not be created because events will conspire against you that prevent you (as in this scenario) from warning the authorities and changing history. This 'theory' it isn't really a theory as such, more an expression of a desire, because it is believed to be impossible (and very bad manners from the point of view of historians) to change history. The theory has no explanation as to how this 'prevention' could actually come about and has no solid theoretical basis.
The same arguments can be applied to travel into the future. Suppose I travel 24 hours into the future, armed with a loaded gun, (just in case, you never know) and happen to meet myself sitting at my computer, (can you meet and interact with yourself?) also armed with a gun, which would be most unusual for me as I do not own one. I am alarmed to see that the gun is pointed at me and warn my future self to put it down or I will shoot him. He prepares to fire the gun so I shoot him dead at the computer, then return. On my return, when tomorrow comes, I am sitting at my computer and receive a visit from 'me' from my past. He warns me that he will shoot me. I of course knew this would happen and took the precaution of keeping the gun beside me and aimed at the spot at the time I knew 'he' would arrive, and I shoot him first. Can I do that? That isn't what happened in my future, it was the 'me' at the computer that died. Even if I don't manage to shoot 'him' in time and still die at my computer, which one of us exactly is it that is still alive? We have created a nonsense scenario. Now this may sound like nonsense, and perhaps it is, but if the future really does exist then it does raise the prospect of meeting and interacting with yourself.
If we accept the idea that the future does exist, because time is just another dimension as discussed in the previous section, then these paradoxes would be unavoidable. If however, we take the view that only the dimension of time itself exists, and not the events within it, then this would suggest that time travel is impossible. Why? Because if future events do not exist, then it would be impossible to travel into the future to witness them, there would be no 'future' to visit.
We either have to accept that if time travel is possible we will, by our actions , create all sorts of paradoxes, or accept that we will create alternative universes. The paradox problem will not go away. As for alternate universes, the mind boggles!
Alternate Universes
The idea of having alternate Universes very conveniently solves the paradoxes raised by time travel, but is it a serious possibility? It sounds a bit far fetched, like something out of a science fiction paperback, but try not to dismiss the idea out of hand, it has some strong supporters.
The alternative universe theory (also known as the multiverse) suggests that for every possible outcome of an event, an alternative universe is created, with the result that somewhere out there I won the lottery last week, and so did you. If only we knew how to get there! This theory has the problem that there must be an infinite number of alternative universes existing to cover every possible outcome of every event. Which one, if any, is the 'real' one, or are they all equally 'real'? Furthermore, where does all the energy and mass come from that creates all these alternative universes? To try and find answers to these questions we have to return briefly to quantum theory.
We learned from the cat-in-the-box thought experiment that prior to observation the cat is in, what is termed in quantum speak, a 'superposition of states'. In plain talk, it is either dead or alive until the moment of observation, its fate is not determined beforehand. The explanation given for this strange state of affairs was the behaviour of the electron's probability wave spreading through first the box, then the room, and finally collapsing into an electron at the moment of observation. A different approach however, is to suggest that at the moment of observation both (or all, as the case may be) possibilities become realities. This is achieved by the creation of an alternate universe, in which the cat is in the opposite state to the cat in our universe. A refinement of this theory suggests that there are always two universes involved, but prior to the experiment they are identical in all respects. If three different experimental outcomes are possible, then we would have three initially identical universes, one of which would change. In general, we would need an infinite number of universes to cover all possibilities. When we were looking at the section 'can anything real be infinite?' we discovered that if the universe were infinite in size then every possibility of every possible outcome would exist within the universe. Perhaps the universe IS infinite?
We have looked at some of the problems associated with time travel, it is now time to look at the laws of physics.
Quantum theory
We shall now study another aspect of quantum theory, one that is directly related to time travel, and learn that particles can travel backwards in time!
We can look at an event that begins with a photon and an electron, and ends with a photon and an electron. We can say that what has taken place is a photon is absorbed by an electron, the electron continues on a bit, and a new photon comes out. This process is called the scattering of light. When calculations are made for scattering, we must include some peculiar possibilities. For example, the electron could emit a photon before absorbing one. Even more strange is the possibility that the electron emits a photon, then travels backwards in time to absorb a photon, and then proceeds forwards in time again. The path of such a 'backwards-moving' electron can be so long as to appear real in an actual physical experiment in the laboratory. The backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except it's attracted to normal electrons - we say it has a 'positive' charge. For this reason it's called a 'positron'. The positron is a sister particle to the electron, and is an example of an 'anti-particle'. This phenomenon is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. When a particle and its anti-particle collide, they annihilate each other and form other particles.
We have now learned that time travel is not only possible, it is a perfectly normal phenomenon, at least for particles. But is it possible in the macroscopic world?
Einstein's theory of relativity
Black holes, according to relativity theory, warp spacetime with their enormously powerful gravitation field. The effect of this gravitational field is that if an astronaut were to cross the event horizon of a black hole, time would slow down on board his spacecraft as he approached the singularity and eventually come to a stop. Similarly time slows down in proportion to speed, the faster our astronaut travels the slower time runs. The closer the astronaut travels to the speed of light the more time slows, until at the speed of light, time would stop. Both these effects of time being affected by speed and gravity have been discussed in the previous section, all of which illustrates that time is not a fixed constant, but is affected by gravitational fields and relative speed in the same manner as the other three dimensions of space.
The solutions to particular equations of the Special Theory of Relativity can be expressed mathematically in any direction of time without running into any problems. Does this mean that time travel is possible? There is nothing in relativity that rules out time travel, it would appear to be theoretically possible.
Constructing a time machine
Research carried out in the late 1980's showed that genuine time travel is not forbidden by the known laws of physics. This means that it may be possible to build a time machine, but not that it may be easy. Help may be at hand though, it is possible there are naturally occurring objects in the universe that act as time machines.
There are at least two ways to build a time machine. Frank Tipler published a possibility in the highly respected journal Physical Review in 1974. This involves making a naked singularity, a singularity that is not concealed from view behind the event horizon of a black hole. To make a naked singularity involves rotating a singularity extremely rapidly, and if rotated sufficiently fast it would fling away the event horizon and exposes the singularity. We know that spacetime is extremely distorted by the singularity's strong gravitational field and the effect of this rotation would be to twist spacetime, and tip it over so that one of the dimensions of the space dimensions is replaced by the time dimension. A carefully piloted spaceship taken close to the singularity would enter the time dimension and journey through time instead of space, although to the astronauts all would appear as normal. When the spaceship moved away from the distorted area around the singularity, it would be in a different time from when they had entered the area.
According to Tipler's calculations, the same effect could be achieved with a cylinder about 100 km long and about 10 km across, made of material compressed to just over the density of a neutron star, and rotating twice every millisecond. It would be like ten neutron stars joined pole to pole and given a strong twist. Curiously, there are objects in the universe which nearly fulfill the other requirements - so-called millisecond pulsars are known which contain almost the right density of matter and spin once every 1.5 milliseconds, at one-third the speed needed to make a time machine. Such objects are so close to being time machines that they hold out the tantalising possibility that an advanced civilisation might be able to tweak them up in the right way to allow time travel.
That such things as naturally occurring time machines exist in the universe, with only a little tweaking needed, raises the prospect that an advanced civilisation may have already done the trick! This raises the interesting possibility that such a civilisation would have the capacity to travel between the galaxies; a journey of a few million light years would be as nothing. Something for the UFO brigade to mull over!
The other possibility for building a naturally occurring time machine involves worm holes - tunnels through spacetime which may, according to relativity, connect a black hole in one part of the universe to a black hole in another part of the universe. Before the mid-1980's physicists believed that such objects as wormholes could not 'really' exist, and that a better understanding of Einstein's equations would prove this. They were forced to change their minds as a result of careful investigation of wormholes carried out by Kip Thorne and his colleagues at Caltech in 1985. It is interesting to note that this research was triggered by Carl Sagan, a well known scientist, who was writing the science fiction novel 'Contact', a best seller that went on to become a highly successful film. Sagan wanted his wormhole to be as scientifically accurate as possible and approached Thorne to check out the idea as presented in the book. What neither Sagan nor Thorne first realised from the results of Thorne's study was that this short-cut through space would also work as a short-cut through time. In 1988 Morris, Thorne and Yurtsever (Morris and Yurtsever were students of Thorne) published their conclusions in the journal Physical Review Letters, that Einstein's equations really did allow for the existence of wormholes that link different times, and could be used as time machines.
We have seen that the laws of physics do not preclude the possibility of time travel, and further, that it may be possible to construct a time machine by tweaking naturally occurring objects in the universe. It would appear that we only need the technology to make time travel a reality.
What do I think?
Regardless of the theories, I cannot believe that time travel will ever be possible. My main reason for this is because we have recorded history and we know what events happened in the past, and in our own recent past we even have our own memories of past experiences. If time travel were possible then we could not have a recorded history because it would be constantly changing. I can remember, for example, the day when Neil Armstrong set foot on the Moon, the first man to do so. If time travel were possible it would be possible to travel back through time and prevent that event from taking place. It would, for example, be possible for a Russian to travel back through time armed with the technical knowledge necessary to land on the Moon and give it to the Russians years before the Americans achieved it. That act would change history. After that it would then be possible for an American to travel back in time and prevent the Russians from using that information, and so on, and so on. History, however, is not subject to change, it remains constant, if it did change then it would not be history! In order to have a past that past must be unalterable, if it were subject to change then we may not be born to observe it, but we are here observing it. The following quote sums it up rather well I think - "This only is denied to God: the power to undo the past." Agathon (448 BC - 400 BC), from Aristotle, Nicomachean Ethics.
It has been argued that perhaps time travellers from the future have visited us, but being aware of the dangers of interfering with the past - that could have dire consequences for their future - they only observe in secret and do not interfere. However, it should be clearly understood that this policy of 'non-interference' does not help the situation at all. Imagine that today no time travellers have yet come back from the future to visit us. Now imagine that at some future time they do come back to today and visit us. Even though they may only be observing for a few minutes and then return to their own time, they have still changed the course of history. In the first instance no time travellers had visited us, but in the second instance they had. This alone has changed history, it doesn't matter whether or not anybody knew they were there, or if they physically changed anything or not, the fact is they were there. So what happened to our 'original' history, the 'today' with no visiting time travellers? It has been removed from history and never happened - but the problem is we know it did happen! Does this mean that when history is changed our memories are changed as well? Perhaps I only think that my memory of Armstrong walking on the moon has never changed, but in reality it may have been changed many times. I don't think so though, because it is recorded history, it is written down in black and white, and how could that change? Unless it has changed every time of course and I only think it is permanent? This is leading us on to the alternative universe theory, as it is beginning to sound a lot like it.
The alternative universes theory was designed to overcomes the problems of altering history, which of course cannot be altered. It is my opinion however, that this theory is an extremely complicated concept only offered up as a way of getting round a very real problem - that of changing history and associated paradoxes - and is based on strange phenomenon found only in the quantum world - which is not at all understood - and for which we have absolutely no evidence for being applicable in the larger world. Furthermore, I have yet to find any explanation of where all the matter and energy would come from that mysteriously creates all these very convenient alternative universes. I am also puzzled as to what would constitute a choice of outcomes that would generate a universe for every possible outcome. I can understand a photon being 'forced' by observation to go through either one slit or another, and this generating two possible outcomes both of which require its own universe, but what of other examples of a choice of outcome? What about my turning left at a road junction instead of right, does that create an alternative universe? Or what if I said 'yes' instead of 'no' when asked if I liked the colour pink, would that create an alternative universe? You can see where I am going here, if every choice resulted in an alternative universe, then the number of alternative universes created would be infinite and ever increasing at an infinite rate as all those alternative universes created their own alternative universes, and so on ad infinitum. All this just to avoid paradoxes! I think not.
I really cannot see how time travel could ever become a reality, for if it were possible it would have already happened, if you see what I mean? The only method I can envisage as workable, or possible, is to put a person into a state of suspended animation in order to arrive, eventually, at the future, because I don't think the future is already 'out there', I suspect it has to develop moment by moment.
Quantum theory is bizarre. In order to try and understand it we need to forget everything we know about cause and effect, reality, certainty, and much else besides. This is a different world, it has its own rules, rules of probability that make no sense in our everyday world. Richard Feynman, the greatest physicist of his generation, said of quantum theory
'It is impossible, absolutely impossible to explain it in any classical way'.
Quantum theory is much more than just bizarre, it is also without doubt the most amazing theory in existence. If after reading this section you are not totally amazed by it, then the fault will be mine, for I will have failed to reveal to you its deep underlying significance. This theory is not just about experiments and equations, it reveals something extraordinary about our very understanding of what constitutes reality.
This is a very complex theory, and in order to fully do it justice it would require at least a fair sized book. However, in order to grasp the basic principles involved it will suffice to study just three key experiments. The three experiments are generally known as: the 'Double Slit Experiment', Schrödinger's 'Cat-in-the-Box Experiment' and the 'EPR Paradox'.
We will start with the famous double slit experiment as it demonstrates beautifully the central mystery of quantum theory. Quantum theory however, needs some introduction before we get too involved in the experiment.
The standard explanation of what takes place at the quantum level is known as the Copenhagen Interpretation. This is because much of the pioneering work was carried out by the Danish physicist Niels Bohr, who worked in Copenhagen. Quantum theory attempts to describe the behaviour of very small objects, generally speaking the size of atoms or smaller, in much the same way as relativity describes the laws of larger everyday objects. We find it necessary to have two sets of rules because particles do not behave in the same way as larger everyday objects, such as billiard balls. We can, for example, say precisely where a billiard ball is, what it is doing, and what it is about to do. The same cannot be said for particles. They are, quite literally, a law unto themselves, and why this should be so is a source of much debate. The classic experiment to illustrate this is the famous double slit experiment, originally devised to determine if light travels as waves or particles. Feynman said of it:
'Any other situation in quantum mechanics, it turns out, can always be explained by saying, "You remember the case of the experiment with the two holes? It's the same thing."'
The double slit experiment.
If light travels as particles we can imagine particles of light (photons) as bullets fired from a rifle. Imagine a brick wall with two holes in it, each the same size and large enough to fire bullets through, with a second wall behind where the bullets will strike. After firing a few rounds you would expect to see on the second wall two clusters of hits in line with the two holes. This is of course precisely what you get with bullets, so if we get the same result with photons we can say they are particles.
Now imagine that instead of particles, that light travels as a wave, we can replicate that with a water tank. As the wave spreads out from its source it would reach both holes at the same time and each hole would then act as a new source. Waves would then spread out again from each of the holes, exactly in step, or in phase, and as the waves moved forward, spreading as they go, they would eventually interfere with one another. Where both waves are lifting the water surface upward, we get a more pronounced crest; where one wave is trying to create a crest and the other is trying to create a trough the two cancel out and the water level is undisturbed. The effects are called constructive and destructive interference.
If we carried out this procedure with light instead of water, and if light travels as waves, then the pattern on the second wall would appear as an interference pattern of alternate dark and light bands across the wall. Particles, on the other hand, would produce two separate areas of light (where the bullets would hit). This experiment has in fact been carried out many, many times, with the same results every time, and the results are nothing less than amazing.
When the experiment is set up as shown in the above diagram, with both slits open, the resulting interference pattern clearly shows that light behaves as a wave. Now if that was all there was to it we could all fold up our tents and go home happy in the knowledge that light travels as a wave; but there is much more to it than that. This is where the word 'weird' can become over-used.
If the experiment is set up to fire individual photons, so that only one photon at a time goes through the set up, we would not expect the same interference pattern to build up; we would surely expect that a single photon would only go through one hole or another, it cannot go through both at the same time and create an interference pattern. So what happens?
If we wait until enough individual photons have passed through to build up a pattern - and this takes millions of photons - we do not get two clusters opposite the two holes, we get the same interference pattern! It is as if each individual photon 'knows' that both holes are open and gives that result. Each individual photon, passing through the set up will place itself on the wall in such a position that when enough have passed through they have collectively built up an interference pattern, when there cannot possibly be any interference!
If we repeat the experiment, this time with only one hole open, the individual photons behave themselves and all cluster round a point on the detector screen behind the open hole, just as you would expect. However, as soon as the second hole is opened they again immediately start to form an interference pattern. An individual photon passing through one of the holes is not only aware of the other hole, but also aware of whether or not it is open!
We could try peeking, to see which hole the photon goes through, and to see if it goes through both holes at once, or if half a photon goes through each hole. When the experiment is carried out, and detectors are placed at the holes to record the passage of electrons through each of the holes, the result is even more bizarre. Imagine an arrangement that records which hole a photon goes through but lets it pass on its way to the detector screen. Now the photons behave like normal, self respecting everyday particles. We always see a photon at one hole or the other, never both at once, and now the pattern that builds up on the detector screen is exactly equivalent to the pattern for bullets, with no trace of interference. As if that was not bad enough, it gets even worse! We do not need place detectors at both holes, we can get the same result by watching just one hole. If a photon passes through a hole that does not have a detector, it not only knows if the other hole is open or not, it knows if the other hole is being observed! If there is no detector at the other hole as well as the one it is passing through, it will produce an interference pattern, otherwise it will act as a particle. When we are watching the holes we can't catch out the photon going through both at once, it will only go through one. When we are not watching it will go through both at the same time! There is no clearer example of the interaction of the observer with the experiment. When we try to look at the spread-out photon wave, it collapses into a definite particle, but when we are not looking it keeps its options open.
What the double slit experiment demonstrates is this: Each photon starts out as a single photon - a particle - and arrives at the detector as a particle, but appears to have gone through both holes at once, interfered with itself, and worked out just where to place itself on the detector to make its own small contribution to the overall interference pattern. This behaviour raises a number of significant problems! Does the photon go through both holes at the same time? How does a photon go through both holes at the same time? How does it know where to place itself on the detector to form part of the overall pattern? Why don't all the photons follow the same path and end up in the same place?
As a possible explanation it could perhaps be said that this is just one more example of the extraordinary nature of light, after all it does have some very unusual properties. Photons have no rest mass for example, a very odd property! Light is also unique in that it always travels at the same speed. However you move, and however the light source moves, when you measure the speed of light you always come up with the same answer. By way of comparison, two cars approaching each other and each having a speed of 30 mph will be approaching each other at a speed of 60 mph. Two light beams, both travelling of course at the speed of light, will be approaching each other at the speed of light, not twice the speed of light. Perhaps the weird behaviour of photons in the experiment is due to the weird nature of light. Unfortunately further experiments have demonstrated that this is not the case. Electrons have been used instead of photons, and they not only have mass, they have an electric charge, and furthermore they move at different speeds depending on circumstances, like normal everyday objects. The double slit experiments still gives the same result using electrons as it does using photons; electrons also alter their behaviour depending on whether or not they are being observed. The experiment has even been performed using atoms, again with the same result, and atoms are large enough to be individually photographed, they are very real solid objects. This odd behaviour of particles is a very real phenomenon.
The double slit experiment is not simply an oddball theory that has no application in the real world. This strange behaviour of particles lies at the very heart of our understanding of the physical properties of the world. Quantum theory is used in many applications, including television and computers, and even explains the nuclear processes taking place inside stars.
One possible explanation for quantum weirdness is a theory concerning the nature of the wave that is passing through the experiment. The key concept of the theory, which forms a central part of the Copenhagen Interpretation, is known as the 'collapse of the wave function'. The theory seeks to explain how an entity such as a photon or an electron, could 'travel as a wave but arrive as a particle'. According to the theory, what is passing through the experiment is not a material wave at all, but is a 'probability wave'. In other words, the particle does not have a definite location, but has a probability of being here or there, or somewhere else entirely. Some locations will be more probable than others, such as the light areas in the interference pattern for example, and some will be less probable, such as in the dark areas. In this theory, an electron that is not being observed does not exist as a particle at all, but has a wave-like property covering the areas of probability where it could be found. Once the electron is observed, the wave function collapses and the electron becomes a particle. This theory rather neatly explains the behaviour of the particles in the double slit experiment. When we are not looking at the particle, the probability wave, of even a single particle, is spread out and will pass through both slits at the same time and arrive at the detector as a wave showing an interference pattern. When we observe the electron by placing detectors at the slits, it is forced into revealing its location which causes the probability wave to collapse into a particle. If the theory is correct, its implications are staggering. What it suggests is that nothing is real until it has been observed!
Nothing is real until it has been observed! This clearly needs thinking about. Are we really saying that in the 'real' world - outside of the laboratory - that until a thing has been observed it doesn't exist? This is precisely what the Copenhagen Interpretation is telling us about reality. This has caused some very well respected cosmologists (Stephen Hawking for one) to worry that this implies that there must actually be something 'outside' the universe to look at the universe as a whole and collapse its overall wave function. John Wheeler puts forward an argument that it is only the presence of conscious observers, in the form of ourselves, that has collapsed the wave function and made the universe exist. If we take this to be true, then the universe only exists because we are looking at it. As this is heading into very deep water I think we will have to leave it there and move on to the next experiment.
Schrödinger 's 'Cat-in-the-Box Experiment'
According to the Copenhagen Interpretation, the probability wave of an electron requires the act of observation by a conscious observer to collapse it into a definite particle, and thus have a definite location. We can imagine a closed box containing just a single electron. Now until someone looks in the box, the probability wave associated with the electron will fill the box uniformly, thus giving an equal probability of finding the electron anywhere inside the box. If a partition is introduced into the middle of the box that divides it into two equal boxes, still without anyone looking inside, then common sense tells us that the electron must be in one side of the box or the other. But this is not the case according to the Copenhagen Interpretation; that says that the probability wave is still evenly distributed across both half-boxes. This means that there is still a 50:50 chance of finding the electron in either side of the box. When somebody looks into the box the wave will then collapse and the electron will be noticed in one half of the box or the other, but it will only at the moment of observation 'decide' which half it will be in. At the same time the probability wave in the other half of the box vanishes. If the box is then closed up again, and the electron no longer observed, its probability wave will again spread out to fill the half box, but cannot spread back into the other half of the box that was empty.
The way that a quantum wave moves is described by Erwin Schrödinger's wave equation and describes the probability for finding a photon, or electron, at a particular place. Schrödinger did not however, go along with the 'collapse of the wave function' theory, he thought it was a nonsense, and designed 'thought experiments' to prove his point. In an attempt to demonstrate the foolishness - as he saw it - of quantum theory, Schrödinger devised the cat-in-a-box thought experiment.
In Schrödinger 's original thought experiment he used radioactive decay because that also obeys the rules of probability. We however, shall use our box with the partition and electron again, as we are now familiar with it.
Imagine we have our box with the partition in place, and the electron's probability wave evenly spread between both halves of the box. We have now added a device that will, at a given time, automatically open up one half of the box to the room. There is a 50:50 chance that when opened the box will contain the electron that is now free to enter the room. The room is sealed and has no windows that would allow any outside observations to be made. Inside the sealed room there is a cat, a container of poisonous gas, and an electron detector. The experiment is so designed that if the electron detector detects an electron it will release the poisonous gas into the room, which would prove very unfortunate for the poor cat. If, on the other hand, that half of the box does not contain the electron, the poisonous gas will not be released into the room and our cat, henceforth known as Lucky, will continue to enjoy good health, providing it keeps away from busy roads.
Taking a common sense view of the situation, we would say that when the experiment has run its course, and an observer enters the room, they will find the cat either dead or alive. But we already know enough about quantum theory to realise that common sense doesn't apply here, and instead we have to turn to the Copenhagen Interpretation for an explanation.
According to the Copenhagen Interpretation, when the lid of one half of the box is opened, it is not an electron, or not as the case may be, that is released into the room, but the probability wave of the electron as it has not yet been observed. This raises the question of whether or not the cat can be regarded as a conscious observer. If it can be then where do we draw the line? Would a fly or an ant count? How about a bacterium? As this is again getting into rather deep and murky water, we will skip over this problem and continue with our experiment, otherwise we run the risk of becoming seriously side-tracked. So the probability wave spreads into the room, not an electron (or no electron). The electron detector is itself composed of microscopic entities of the quantum world (atoms, particles and so on) and the interaction of the electron with it would take place at this level, so the detector is also subject to the quantum rules of probability. Taking this view, the wave function of the whole system will not collapse until a conscious observer enters the room. At that moment the electron 'decides' whether it is inside the box or in the room, the detector 'decides' whether it has detected an electron or not, and the cat 'decides' whether it is dead or alive. Until that moment, according to the Copenhagen Interpretation, the cat is not either dead or alive, it describes the situation as a 'superposition of states'. Only the act of observation will cause it to become one or the other. Schrödinger described the situation as 'having in it the living and the dead cat mixed or smeared out in equal parts.' The Copenhagen Interpretation does not allow for the room to actually contain a cat that is both dead and alive at the same time, or a cat that is neither dead nor alive, suspended in limbo. But contains either a dead cat or a live cat, until someone looks, and it is then that the actual reality of the situation is determined.
Cat lovers please note. This experiment has never been carried out, and never will be. This is not only because it would be a very cruel thing to do, but because it wouldn't prove anything. An observer upon entering the room would find either a dead cat or a living one, but could not observe what processes preceded this event. Any previous observation would of course defeat the object of the experiment.
The problems highlighted by the cat-in-a-box experiment raise some very deep questions. What for example are the requirements needed to qualify as a 'conscious observer'? Do the probability waves of particles spread out again when not observed and particles somehow become less 'real', as described by the Copenhagen Interpretation? Does the universe exist only because we are here to observe it? Could a cat really be in a 'superposition of states', either dead or alive until the moment of observation? This goes entirely against all our common sense experience of life, we would naturally conclude upon finding the cat alive that it had 'obviously' been alive all the time. Quantum theory is telling us that we could be very wrong in our thinking regarding what reality really is.
Quantum theory has yet another surprise in store for us, and this time it's not simply another bizarre phenomenon that challenges our common sense. This time it contradicts one of the central principles of Einstein's theory of relativity, that nothing can travel faster than the speed of light. As you can imagine, Einstein was not amused.
The EPR Paradox.
The experiment is so named because it was a thought experiment devised by Einstein, Boris Podolsky and Nathan Rosen. As with Schrödinger's cat-in-the-box experiment, its purpose was to expose the 'foolishness' of the Copenhagen Interpretation. The experiment focuses on the phenomenon of quantum theory known as 'non-locality', which concerns communication between particles. A pair of protons, for example, associated with one another in a configuration called the singlet state will always have a total angular momentum of zero, as they each have equal and opposite amounts of spin. Just as we have seen in the other experiments, the protons will not collapse their probability wave and 'decide' which spin to adopt, until they have been observed. If you measure the spin of one proton, according to quantum theory, the other proton instantly 'knows' and adopts the opposite spin. So far so good, we have come to expect this sort of behaviour from particles, so what is the problem with this particular experiment?
It is possible, and has been carried out in laboratory tests over a short distance, to split the particles apart and send them in opposite directions and then measure one of them for spin. The instant it is measured, and the spin determined, the other particle adopts the opposite spin. The time interval is zero, the event takes place instantaneously, even though the particles are separated, and theoretically would still do so even if they were separated by a distance measured in light years. This is what upset Einstein, the implication that particles could communicate at faster than light speed, as it is impossible for this to happen according to Einstein's theory of relativity.
At the time this thought experiment was proposed, in the early 1930's, just about the time of Schrödinger's cat-in-the-box thought experiment, it was not actually possible to physically carry out the experiment. Einstein did not live to see it turned into practical reality, which is probably just as well in light of the results produced. This experiment has now actually been carried out over a distance of 10 kilometres and confirmed as correct. Something here is taking place at faster than light speed, although exactly what seems to be a matter of some debate. Regrettably, due to its very nature, no meaningful communication could be made using such a device. Whether or not it will ever have any useful application remains to be seen, but that is not the point. The point is the experiment has proved Einstein wrong, faster than light speed, at least in the quantum world, is a reality. However, in classical physics - at sizes above that of atoms - relativity still remains unchallenged, nothing has been detected at faster than light speed.
As I said at the outset of this section, these three experiments highlight the basic principles involved in quantum theory. I also said they would amaze you, and I hope that you feel that I have kept my word. If you are not amazed by quantum theory, then blame me, for the theory is truly amazing and any disappointment you may have with it can only be due to my inability to do the theory justice.
One last thing you need to know about quantum theory, and that is Heisenberg's Uncertainty Principle. Heisenberg said that the electron was a particle, but a particle which yields only limited information. It is possible to specify where an electron is at a given moment, but we cannot then impose on it a specific speed and direction at the setting-off. Or conversely, if you fire it at a known speed in a certain direction, then you are unable to specify exactly what its starting-point is - or its end-point. The information that an electron carries is limited in its totally. That is, for instance, its speed and its position fit together in such a way that they are confined by the tolerance of the quantum.
The principle of Uncertainty fixed once for all the realisation that all knowledge is limited, that there is no such thing as absolute certainty.
What conclusions can we draw from these experiments?
We need to be very careful in drawing any conclusions from the results of these experiments. All we can say with any confidence is that if we set up the apparatus in a certain way it will produce a certain result. How we interpret those results, the meanings that we attach to them, is nothing more than our way of attempting to make sense of them, and need have no relationship at all to the actual reality of the situation. To imagine that a probability wave passes through both slits in the double slit experiment helps us to understand what may be happening, but it is in fact nothing more than proposing an idea that meets the criteria of what has been observed; there may be no such thing as a probability wave. It may be the case that we are completely missing some fundamental property of particles, a property that as yet remains undetected by our equipment and experiments. There may be things going on that we are completely unaware of.
What quantum mechanics tell us is that nothing is real and that we cannot say anything about what things are doing when we are not looking at them. In the world of quantum mechanics, the laws of physics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. Einstein was so disgusted by the whole notion that he made his famous remark, "Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secrets of the Old One. I am at all events convinced that He does not play dice".
What do I think?
It seems illogical that we need two completely different laws to explain the behaviour of objects, dependent on how large or small the object is. Why is it that the laws of cause and effect, that work so well in the everyday world, breakdown in the world of the very small, when everything in the everyday world is made up of the very small?
It just does not make any sense, but like it or not, until a theoretical physicist comes up with a theory that incorporates both Quantum Mechanics and Relativity we just have to admit that we do not really know what is going on. However, one thing I am absolutely clear on is that an electron, or photon, doesn't 'know' anything, anymore than a frozen pea does. When you remove a frozen pea from the freezer and place it in a warm room you do not gasp in amazement when it defrosts and ask how did it 'know' to defrost. You do not try and trick it into not defrosting by leaving it in the freezer and turning off the freezer. This is of course because we understand the laws of thermodynamics. Particles do not 'know ' anything!
When physicists ask the question, 'how does a particle 'know' something'? they are of course using the term loosely. What they are really asking is 'what are the forces acting upon the particle that we have not detected? What interactions are taking place that we have not detected?'
That is the problem. Something is going on at a level that we are completely unaware of. However, the idea of probability waves as an explanation is nothing more than an attempt to describe what is observed in the quantum world by the Copenhagen Interpretation, and is of course a purely theoretical concept.
It may be possible that we need to develop a new form of logic to be able to describe what is happening at the quantum level. It may be that it is not enough to say that a statement is either true or false, we may have to introduce a three-valued quantum logic which allows the additional status of 'undecided'. This would mean that a statement that is not true need not be false.Reference research
Allen, B. & Simon, J. (1992, May 7). Time travel on a string. Nature, 357, 19-21.
Allman, W. F. (1988, December 19) Playing fast and loose with time. U.S. News and World Report, 105, 62.
Clark, C. J. S. (1990, November 22). Opening a can of wormholes. Nature, 348, 287-88.
Davidson, M. (1990, January). Is time travel possible? U.S.A. Today, 118, 60-67.
Davies, P. (1992, January). Wormholes and time machines. Sky & Telescope, 83, 20-21.
Deutsch, D. & Lockwood, M. (1994, March). The quantum physics of time travel. Scientific American, 270, 68-74.
Freedman, D. H. (1989, June). Cosmic time travel. Discover, 10, 58-64.
Gribbin, J. (1983). Spacewarps. New York: Delacorte.
Hawking, S. W. (1993). Black holes and baby universes. New York: Bantam.
Hawking, S. W. (1988). A brief history of time. New York: Bantam.
Lemonick, M. D. (1991, May 13). How to go back in time. Time, 137, 74.
Lemonick, M. D. (1989, January 16). Wormholes in the heavens. Time, 155, 55.
Macvey, J. W. (1990). Time travel. Chelsea, MI: Scarborough.
Mukerjee, M. (1994, February). Time-trippers beware. Scientific American, 270, 32.
Parker, B. (1991). Cosmic time travel. New York: Plenum.
Peterson, I. (1992, March 28). Timely questions. Science News, 141, 202-03.
Travis, J. (1992, April 10) Could a pair of cosmic strings open a route into the past? Science, 256, 179-80.
"Wormholes and Time Machines." (1988, November 5). Science News, 134, 302.
"Wormholes, Time Machines and Schrödinger's Cat." (1989, February). Sky & Telescope, 77, 132.
GnomeXGurl
ParaCrypt RSG
No comments:
Post a Comment