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Why time travel is a paradox?

A paradox is a statement which seems absurd but may be true (or false). Time travel seems absurd because if you can go back in your past, you can kill your forefathers. But then you would not have born and could not have killed your forefathers.
We do not need much investigation to establish that this statement is false. Then why there is doubt on time travel?
It is because of ‘Time Dilation’ proposed by Einstein in his Special theory of Relativity and proven by practically measuring the time dilation in 1971. But, we should not connect time dilation with Time travel. Time dilation is only slow down of time as measured by precise atomic clocks by observers moving at very high velocity, it is not going back in time. For example, two observers (one stationary and other moving) start measuring time for an event simultaneously at morning 0600 hrs. If the event is completing at 1800 hrs same day, then stationary observer will measure 1800 hrs in his/her clock while moving observer may measure a time anywhere between 0600 hrs and 1800 hrs, he/she cannot measure it less than 0600 hrs , which is required for going back in past. Even when the moving observer measure time between 0600 hrs and 1800 hrs, we cannot say that he/she has gone in past as compared to the stationary observer. Difference is only in the recording of time by their instruments, actual time passed is same for both observers. If the moving observer stops instantaneously after completion of event and matches his watch with the stationary observer, their watches will show different times, that is time dilation but it cannot be called time travel because time taken for both observers will be 12 hours, one will be measuring by normal clock while other (moving observer) will be measuring it with a clock that runs slow due to its motion at high velocity through space.
So, time travel is not a paradox, in fact, it is simply not possible.

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