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## Wednesday, 29 April 2015

### Time travel

If time travel to the past were possible (A good solution to the grandfather paradox)

Traveling back in time is one of the most important science fictional concept that most science fiction author wish to exploit. Any story that involves time travel, will always forget to answer certain questions that stand vital for the reader’s understanding of time travelling concept. The main reason to this is time travel concept gives raise to many unique paradoxes that are hard to solve. Solving such paradox might not always seem easy. One such paradox is the grandfather paradox.

What would happen if someone were to go back in time and kill his own grandfather? Will he die? If he dies, then he couldn’t have killed his grandfather and he should continue to exist. The moment I came across this, I got strongly reminded of Gödel statements (refer to Wikipedia for more information on Gödel statements). If you say “I am a liar” with a condition that you either only tell lies or tell only the truth, then you couldn’t have said that!

The moment you say “I am a liar”, you declare yourself to be a person who always tells lies. But if you really were a liar, then you wouldn’t confess the truth that you are a liar! Because, calling yourself a liar it becomes the truth (which you are forbidden to say if you are a liar) and hence declares that you are a person who always tells the truth (remember the first condition that you can only be a person who speaks only the truth or only lies).

This shows that there is a particular solution for a problem, such that the mere truth of it falsifies the statement. So if the statement is true, then the statement should be false and conversely, if the statement is false, then it should be true! So how is this related to grandfather paradox? (I believe that it is more likely that you already know the answer to this question). The mere of the grandfather falsifies the truth of his own existence. If you talk about digital logic, then it’s like a logical NOT-gate, with its input connected with its output.

One difference between a NOT-gate and the grandfather’s scenario is, a not gate processes one piece of information (either true or false) and inverts it, while the grandfather paradox is said to always be true, irrespective of the instant when his grandson exists. This causes all the problems; if the grandson should exist, then he shouldn’t have existed and if he shouldn’t exist, he should have existed. One possible way to reason out this is by saying that at one instant, he exists, and on another instant he does not exist.

So how do we solve the grandfather paradox? Actually, scientists haven’t found a direct solution to this problem, but perhaps have got something at hand to talk about. They use quantum mechanics or the parallel universe concept to resolve this paradox. One common explanation is, there is a feebly less probability that you land up in your own universe’s past rather, find yourself in a different universe. The other explanation is that, the behaviour of quantum particles are determined probabilistically; so if a subatomic particle was to travel back in time with a particular state, its behavioural outcome would not always be same. Instead, there would be a finite probability for each state it can change to.

Consider a hypothetical experiment where an electron is made to travel back in time. When an electron moves forward, it exhibits wave nature. This wave nature is because of the uncertainty of its position at each point in time. Let’s consider two identical electrons to travel back in time. Though both the electrons are identical, the actual path followed by each electron would differ because of the uncertainty in its position and velocity at each point in time. So if we talk about the grandson killing his grandfather before he was born, then it’s likely that the moment he cease to exist as a result of his action, there is only a probabilistic chance that he is born again.

Let’s elaborate further. During the first time, the grandson is born such that he kills his grandfather. That scenario cannot exist; because, the moment he is born, the grandfather ceases to exist, and so does he cease to exist. But once he ceases to exist, the grandfather has no one stopping him from existing, so again his grandson is born; but this time, he might have been born as a person who wouldn’t kill his grandfather. At the most fundamental level, we are all made of sub atomic particles. So if the behaviour of those subatomic particles are probabilistic, then there is a sure chance that our behaviour over time is determined probabilistically.

We can say that each time the grandfather ceases to exist and start existing again, his newer existence becomes slightly different from his previous existence. This changes him slightly each time until his existence is satisfied. So this shows that the quantum world evolves to aid our existence. Now how are we able to arrive at an answer!! This paradox is unsolved, isn’t it?

These are just theories and don’t have any experimental proof. Ok but still, if the grandfather’s behaviour changes each time he ceases to exist and continue to exist, then does it mean that when you travel back in time to meet your grandfather, you actually don’t meet the same grandfather you had met before when you were young, but someone different?

Yes! You will be meeting a slightly different grandfather, according to the above given theory. So this makes sense right, we haven’t solved the paradox yet, but jump to conclusions that prevent the arousal of the paradox. If you have read about Gödel’s incompleteness theorem, you can easily understand that certain problems cannot be solved without modifying the system we observe! To show that the person saying “I am a liar” actually says that sentence, we need to accept that the condition that that person who speaks this sentence partially speaks the truth and partially lies. If we don’t make this change, then he couldn’t have said the sentence “I am a liar”. The same way, if we hadn’t made changes to our usual assumption that time travel back to the past is possible and we meet the same grandfather we have always known, we wouldn’t have been able to conclude that travelling back in time is possible.

Conclusion
There is one thing that remains true until now. Grandfather paradox cannot be solved because you cannot decide if the person saying “I am a liar” is actually a liar or not a liar (assuming that that person either always speaks the truth or always the lies). So travelling back in time and killing one’s own grandfather before he was born cannot exist logically. To prove that travelling back in time is possible, we need to show that even if travel back in time, the information regarding our existence before we had travelled back in time and made the appropriate changes to our present life still remains.