What Are Some Famous Paradoxes?


What is a paradox? Simply put, a paradox is an argument whose conclusion cannot exist because of the prevailing conditions set forth in the argument but does exist because of those same conditions. While not all paradoxes have Earth-shattering implications, many can have interesting implications for our lives. If anything else, they provide a new viewpoint and perhaps spark the inquisitive nature of the mind.

Predestination Paradox

This is a paradox that results from time travel. In one of the generic forms, you come across a time machine (it does not matter if you invented it or happened upon it) and go back in time. While you are there, you meet someone you find attractive and together have a child. Later on, you find out that the child is a direct ancestor of you and without him/her you would not exist. But if the child was always required for you to live, then you were also always required for the same reason. But how could you be around to have the child in the first place if the child was necessary for your existence?

To describe this paradox in more encompassing terms, this paradox involves you completing some event in the past that is required for a future event that you are dependent upon in order to go back in time. Frequently this is used in the above-mentioned case, but it could also be a historical event, such as you replacing a founding father of the United States and taking his place. Whatever the example may be, the paradox always arises because the event that created you happens before you were created.

Grandfather Paradox

This is another infamous time travel paradox. On your adventure into the past you meet a man and for whatever reason (many exist, including an attempted theft to an accident) you end up killing him. You realize after he is dead that it is in fact your grandfather, specifically at an age where he had not yet met your grandmother. Because he is now dead he never will meet her, so your mother/father will not exist, so you cannot exist either. But then because you do not exist you could not go back in time and kill him. So he never died, so you did exist and you still went back in time. How can you exist and not exist at the same time?

In general, the grandfather paradox is simply you going back in time and preventing an event from occurring that is integral to your existence. Just like the predestination paradox, this deals with you being the source of a major event in your life but in this case an event of destruction.

A Possible Solution?

Most people say that because such events cannot happen and remain consistent with their timelines we need not even consider them in the first place. But the math does not lie and it says backward time-travel is possible. So how can we explain these possible problems?

Note that to travel back in time as we know it, we need a closed timelike curve, or a CTC. They are simply moments of spacetime that loop back onto themselves, generally caused by a large gravitational source. David Deutcsh in 1991 was able to show that when you go back in time to perform the grandfather paradox, you have a 50/50 shot of actually doing it and not. According to quantum mechanics, this is good enough to say that the not-chance happens. 20 years after David developed this idea Tim Ralph and his team were able to test out the theory using polarized particles. One particle would change states and a second particle would be given the same traits as the other before its evolution. These two photons would then interact and change. Using this system the team was able to show that the second particle would become the same as the first one after its evolution. Apply some math and you have an equivalent CTC example (Billings).

Another possibility developed by Seth Lloyd in 2009 combines quantum teleportation and post-selection. His theory eliminates the possibility of alternative universes that David's CTC method predicts and instead keeps the time-traveler in his own universe. But more solutions are sure to crop up, so keep an eye out!


Twin Paradox

This is a time-related concept and depending on how you define it is a time-travel event. Though not technically a paradox, it is frequently cited as one and thus merits a discussion.

One member of a set of the twins is an astronaut and is selected for a space mission. He/she will be put on a rocket ship and sent at nearly the speed of light to a distant star, collect data, and then return to Earth at the same speed. The astronaut launches and goes about the mission. Years pass by and finally the astronaut returns to Earth. Once they land, the astronaut exits the craft and meets up with their twin. But the astronaut is not as old as the person who stayed behind. In fact, they have barely aged! How is this possible?

This is a result of Einstein's Relativity. Specifically, an effect of going at near-light speeds is time dilation. The faster you go, the slower the time goes by for you relative to someone who is not moving at that speed. For the astronaut inside the spacecraft they are moving at normal speed and everyone else appears to move slowly. So even though the astronaut was in fact gone for all those years, the person aged slower than did their twin in our timeframe.

The race is on...or is it?
The race is on...or is it? | Source

Zeno's Dichotomy Paradox

Zeno was an ancient Greek philosopher, and he had many paradoxes he thought up of. This one may be his most famous work.

All the time we see people run races and complete them. They have a starting point and an ending point. But what if we thought of the race as a series of halves? The runner finished half of a race, then a half-of-a-half (a fourth) more, or three-fourths. Then a half-of-a-half-of-a-half more (an eighth) for a total of seven-eighths more. We can keep going and going on but according to this method the runner never finished the race. But we all know he does, so how can we reconcile the two viewpoints?

Poor Zeno never had calculus. If he had, then he could have thought of the limit of this series as it got smaller and smaller. We all know now that if we look at the overall pattern of this halving, it approaches a whole. But the Greeks did not have this tool at their disposal and thus were unable to solve this paradox.

Russell's Barber Paradox

This one was developed by the famous mathematician Bertrand Russel, whose work in logic and set theory is far-wide and still in use to this day. He came up with this paradox to describe an interesting facet of set theory.

Imagine a town full of people who need a haircut. No one is allowed to cut their own hair but fortunately a barber is in the town. He does in fact cut everyone's hair as promised, but now he needs a haircut, for is a member of the town and they all need a haircut. But he cannot cut his own hair, for no one is allowed to cut their own hair. What does he do?

In this example, something is a member of a set but by being a member of that set cannot exist in it. If a special set for barbers was made then he would be fine but since he is concluded in the town then he cannot violate that rule.

Works Cited

Billings, Lee. "New Time Travel Simulation May Help Resolve Grandfather Paradox." HuffingtonPost.com. HuffingtonPost.com, Sept. 03, 2014. Web. Oct. 25, 2014.

© 2014 Leonard Kelley

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