The Time Traveler's Note

The grandfather paradox states that a person goes back in time and kills his grandfather before the grandfather has the opportunity to have children. This would mean that the time traveler could not have been born resulting in his paradoxical existence. This paradox is often resolved by a theory in which we assume that we can find ourselves in different universes depending on the actions we take.
To understand this multiple universe theory better we can look at the following simple example. Assume a person is at a crossroads with the option of turning left, turning right, or going straight. After the action has been chosen we find ourselves in one of three different parallel universes. Each universe is the result of the person choosing one of the three aforementioned actions. This theory is naturally intertwined with causality.
Now for the paradox... Consider the following scenario: A person writes a note which records their current geographical location, the date, and the time. The note further says, "if I ever have access to time travel, I will return to the place and time noted here." Now the person waits to see if a copy of themselves appear. If in fact the person does reappear then it can be already concluded that time travel can exist! If the person does not reappear, then it can be concluded that time travel does not exist and hence the note can be destroyed because it will be of no use in a world without time travel! But how will the person know where (or when) to return if they destroyed the note?
This paradox gives some insight into the multiple universe theory through the fact that the paradox only arises if the note is destroyed AFTER the time at which the person is supposed to return. If the note were to be destroyed before the critical point in time, then we cannot conclude anything since it would not be known whether the absence of a time traveler is due to the note's destruction or the fact that time travel does not exist. If, on the other hand, the note is destroyed after the critical point in time then we can (under the multiple universe assumption) conclude that the absence of a time traveler was, in fact, due to the impossibility of time travel. This is because the assumption of multiple universes tells us that there exists a universe in which the person kept the note. The person who destroys the note before the critical point in time is already in a branch of the tree of universes which excludes the time travellers return.

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