Rachel Phipps

Time Travel: Paradoxes and Probabilities

The idea of time travel is a complex issue. Proposed theories of time travel range from the basic to the bizarre. There are many paradoxes, or contradictions, that some say prove that time travel cannot be possible. One such paradox is called the Grandfather Paradox, also known as the autonomy principle. What would happen if a person went back in time to when their grandfather was a child and killed him? If this happened their grandfather would not become a man and marry their grandmother preventing the person from being born. If they are not born, then they could not go back into the past to prevent their grandparents from meeting, and so they would be born. This causes a time when the person was both born and not born. This creates a paradox – how could someone both have been born and not born?

"There is no contradiction," says David Deutsch, a physicist at the Center for Quantum Computation at the University of Oxford, "because the laws of quantum mechanics always arrange for you to go back in time to a different universe." (Crenson)

According to Sherrill Roberts, one attempt to resolve the grandfather paradox is Hugh Everett’s "many-worlds" interpretation of quantum mechanics. "Everett’s hypothesis is that, at the quantum level, all possible states potentially exist and that a universe confronted with a choice brings both realities into being." (Roberts) Everett’s theory is consistent with certain experimental findings that photons (light particles) exist simultaneously as particles and as waves, so the possibility of an infinite number of parallel universes is not as far-fetched as it may seem. "Physical reality consists of a collection of universes, a multiverse, so to speak, that contains its own copy of the observation and its outcome." (Samudrala)

Also, Fred Allen Wolf says that, "Any one universe is composed of potential or unobserved overlapping parallel universes so long as no resolution or observation is attempted. In this manner the whole range of unobserved phenomena represents a completely undivided universe. This whole undivided mess is greater than the sum of its possibilities, because the various possibilities are able to interfere with each other at a level existing before observation occurs." (Wolf)

Another attempt to solve the grandfather paradox is in two parts. First there is the Chronology Protection Conjuncture which suggests that it is impossible to make a Time Travel machine from something such as a wormhole. The second part involves free will and restraints of the Laws of Physics. This solution allows Time Travel to be possible but shows that the Universe is a pretty smart place and easily able to sort out any actions we Humans might cause! (Edwards)

One idea that is thrown around a lot by scientists and physics enthusiasts alike is the ability to travel faster than the speed of light and as a result travel backwards in time. It has been proven that it is possible to travel at speeds close to the speed of light, but whether someone could travel faster than the speed of light is yet to be proven. Travelling at a speed close to that of light, one could travel into the future. This brings about the idea of the twin paradox.

In this scenario, one twin stays on earth while the other twin travels into outer space at near the speed of light. When the travelling twin returns, he has only aged by a few years, while the other twin who stayed back on earth has aged by many years. How could this be possible?

The solution given is the idea of time dilation. "The mechanism for traveling into the distant future is to use the time-dilation effect of Special Relativity, which states that a moving clock appears to tick more slowly the closer it approaches the speed of light." (Hiscock)

This is the time dilation result. "The proper time will be the shortest interval – the time intervals measured by other observers will be longer. Note that in the case of travel it is the traveler who measures his/her own proper time, since he is a the beginning and end of his/her trip interval." (Hawkes) What this means is that to the twin traveler, their time on the ship is perfectly normal. However, to the twin left back on earth, the traveler’s time seems to be going much slower.

Why can’t a person travel at the speed of light? The reason is that, "according to Einstein’s special theory of relativity, objects gain mass as they accelerate to greater and greater speeds. If an object reached the speed of light, it would have an infinite amount of mass and need an infinite amount of push, or acceleration, to keep it moving. No rocket engine could do this." (Nova Online)

If it were next to impossible to travel at the speed of light let alone at faster than the speed of light, how would one then go back in time? One possibility is through the help of something called a closed timelike curve (CTC). A CTC is "a worldline that a particle or a person can follow which ends at the same spacetime point (the same position and time) as it started (Thaler) Suppose space-time becomes so distorted so that some worldlines form closed loops. Such worldlines would be timelike all around. By following a CTC, we could meet ourselves in the past, or if the loop were large enough, visit our ancestors (Samudrala). However, Stephen Hawking argues that quantum mechanical effects would either prevent CTCs from forming or destroy any would-be time traveler who approached one.

To further describe this point, Egils Sviestins says that, "except for special cases, in general relativity one cannot choose a global time coordinate and draw global light cones. Each observer has his own small local light cone. He can move within the light cone, draw a new light cone from that position, etc. And, believe it or not, the light cones may be "tilted" so that a huge closed timelike curve is formed. The figure here may illustrate the idea; don’t take it too literally as the meaning of the coordinate axes is not clear. A material object can travel from an event A, around the universe, and then back to event A. The curve can even be modified so that the object arrives before it was launched. If it then waits to see the launching, the timelike curve is closed."

Another possible way of going back through time is through something called a wormhole. "It’s not that easy to travel through a wormhole, because big wormholes don’t just arise out of nothing. They’re the result of an enormous gravity, and that’s the result of a huge concentration of energy, for example a black hole." In the early 1930’s, Albert Einstein and Nathan Rosen discovered that the gravity hole, in which the middle of the black hole lies should be bottomless, and that it should lead to another, hypothetical universe of another part of this time-universe. Such a hole is called an Einstein-Rosen bridge or a wormhole. Basically, a wormhole is "a tunnel through space-time linking one black hole to another one somewhere else and somewhen else." (Plato) There are some problems that arise with the issue of wormholes. In the middle of a black hole the gravity is so great that it would tear apart every spaceship that tried to enter it. Another problem is that you would need to go faster than the speed of light to reach the other side, because the speed you need to escape a black hole is bigger than light speed.(Vannoppen) As I mentioned earlier, this is next to impossible.

"If we have one entrance to the wormhole and one exit, and we adduce a model in which the ball coming out of the exit will collide with itself such that it will drive itself into the entrance, then we know intrinsically that if the collision does not happen, the billiard ball will never enter the wormhole initially, and so won’t exit in the past." The conclusion of this statement is that, "if it must have happened in order to happen, it is easier to suppose that it never happened." (Young)

Kelly L. Ross, Ph.D. talks about a third type of time paradox, that of the man (or idea) in the cycle of time and without future, or also known as the chronology principal.. One example, explained by John Gribbin, is the story By His Bootstraps by Robert Heinlein. "The protagonist in the story stumbles on a time travel device brought back to the present by a visitor from the far future. He steals it and sets up home in a deserted stretch of time , constantly worrying about being found by the old man he stole the machine from – until one day, many years later, he realizes that he is now the old man, and carefully arranges for his younger self to "find" and "steal" the time machine." (Gribbin)

Now in the movie "Somewhere in Time" starring Christopher Reeve and Jane Seymour, Reeve meets an older woman who gives him a watch and then he sees a picture of a beautiful young woman. After this encounter he goes back in time and meets the woman from the picture. He gives her the watch he was just given. This then becomes the watch that the older woman, actually Seymour, gives to Reeve. This in turn creates a paradox. Where did the watch come from? Seymour gave it to Reeve, and Reeve also gave it to Seymour.

"In a closed temperal loop, like the knowledge in the notebook in Heinlein’s story, the watch is uncreated. But this is impossible. The watch is an impossible object. It violates the Second Law of Thermodynamics, the Law of Entropy. If time travel makes that watch possible, then time travel itself is impossible." (Ross) The Second Law of Thermodynamics states that, "The entropy of a closed system shall never decrease, and shall increase whenever possible." (Lambert) In the loop, the watch would gradually get older and older. When Seymour gave the watch to Reeve it was brand new. But when he gave it to her in the past it was slightly older. And when Seymour gives the same watch to him back in the future it will be even older. It will continue this cycle indefinitely.

But, as she also points out, there are possible ways to go around this paradox. "First, we might think that entropy could be reversed by time travel, so that forms of matter would be restored to that state they would have been at the earlier period." (Ross) Her second thought is the idea of alternate universes, which I mentioned earlier.

Another paradox in time travel is the suicide paradox. One example of this is if a person would travel a short amount of time into the future and after meeting their future self, would in front of their future self commit suicide. This creates a paradox because if the person has committed suicide how would they be alive in the future to the see the act performed? The answer is they wouldn't be. My opinion in this matter is that the future self wouldn't be there to begin with, because when they traveled through time into the future, they had been "away." What I mean is that during the time period between when they had left (the present) and when they arrived (the future) they were not there. So in effect there would be no future self. M. Joseph Young agrees by saying, "Moving into the future has no effect on time or history, unless it is accompanied by a trip into the past. As far as anyone else is concerned, as far as history is concerned, as far as time itself is concerned, you went away for a while, and then you came back" (Young)

Charles Miller brings up an interesting issue. If we would travel in time, where would we end up? How do we start in one place and end up at that same place only in the future? "The answer is we don't. Instead, the moment we activate our fiendishly complex Time Machine, we sidestep physical law, becoming a stationary non-entity relative to the rest of the cosmos…Depending on the intensity and duration of our ‘time warp,’ we may find ourselves deep in interstellar space -- with no recognizable constellations to guide us home -- or even outside of the Milky Way altogether, lost in the intergalactic void." (Miller)That is definitely a valid concern, and something to take into consideration.

An interesting paradox is the train in the tunnel paradox. According to Michael Fowler, "Any object moving relative to an observer will be seen by that observer to be contracted, foreshortened in the direction of motion by the ubiquitous factor sqrt."

Fowler continues, Suppose that a train of length L is moving along a straight track at a relativistic speed and enters a tunnel, also of length L. There are bandits inhabiting the mountain above the tunnel. They observe a short train, one of length Lsqrt, so they wait until this short train is completely inside the tunnel of length L, then they close the doors at the two ends, and the train is trapped fully inside the mountain. Now look at the same scenario from the point of view of someone on the train. He sees a train of length L, approaching a tunnel of length Lsqrt, so the tunnel is not as long as the train from his viewpoint! What does he think happens when the bandits close both the doors?

The concept of simultaneity, events happening at the same time, is not invariant as we move from one inertial frame to another. The man on the train sees the back door close first, and, if it is not quickly reopened, the front of the train will pile into it before the front door is closed behind the train.

Stephen Hawking once said, "If time travelling will be possible, why haven’t we seen a lot of tourists from the future yet?" One possible answer to this is that once a time machine is created, you can only go back in time to the point at which the time machine was created. If you are using a closed timelike curve (CTC) to travel backward in time it only reaches as far back as it was created. This would explain the reason why there isn’t any evidence of visitors from the future.

Another way to look into the past is to travel to a distant star or galaxy many light years away and use a good telescope. You would be so far away from earth that the image that you would see would be from the past. This is close to impossible, again, because of having to travel faster than the speed of light. However, this would be another explanation of why we don’t see future time travelers here today. They are watching us from a great distance and thus would not be seen interacting with us.

As you can see, there are many paradoxes, or contradictions, that some say prove that time travel cannot be possible. There are the ones I discussed here, the Grandfather Paradox ( autonomy principle), travelling faster than the speed of light, the twin paradox, the man (or idea) in the cycle of time and without future (chronology principal), the train in the tunnel paradox, and the suicide paradox, and there are probably others that I haven’t even thought of.

There are many ideas why time travel cannot be possible, yet there are also ideas why it could be possible. If we keep an open mind and positive attitude, perhaps in the future we will be able to travel through time. As science fiction has become science fact before, like when man took his first step on the moon, then isn’t it possible that this is another aspect of science fiction that could become science fact? Only time will tell.

Bibliography

Crenson, Matt, Associated Press, "Time Travel: Fiction or Reality?"

http://www.msnbc.com/news/341850.asp

Edwards, Anthony, "Time Travel – Let’s Get Rich"

http://www.cix.co.uk/~antcom/1gr1.html

Fowler, Michael, "More Relativity: Trains, Twins, Doppler"

http://www.phys.virginia.edu/classes/252/srel_twins.html

Gribbin, John, "Time Travel for Beginners"

http://www.biols.susx.ac.uk/Home/John_Gribbin/Time_Travel.html

Hawkes, Bob, "Time Dilation"

http://aci.mta.ca/Courses/Physics/4701/Etext/TimeDilation.html

Hiscock, William A., "According to current physical theory, is it possible for a human