TO: Professor Ellis
FROM: Sebastian Vela
DATE: October 8, 2021
SUBJECT: 500-Word Summary of “A computer program for simulating time travel and a possible ‘solution’ for the grandfather paradox”
The following is a 500-word summary of a master’s thesis about a program that simulates the grandfather paradox. The paradox explains that if a time traveler had gone back in time to kill his grandfather, then he would not have been born to travel back in time, thus allowing the grandfather to live and for the time traveler to be born. The program written by Doron Friedman uses automated reasoning to “modify” history and explore the consequences and propose possible solutions.
The actions and constraints in the simulation are labeled with the values “True”, “False”, or “Unknown”. For every person in the simulation, these values indicate whether the person is alive or not. The timeline of events can be changed by adding or removing actions in the simulation. A strong change is made when something that happened is changed, rather than adding actions. With each new event, the previous timeline is not erased. Instead, the program knows the consequences of the first timeline, and then sees the consequences of the second timeline.
A few hundred facts and constraints are included, with the paradox “solution” containing 229 facts and 344 constraints. Only 3 actions exist in each simulation: begetting, killing, and traveling in time (which is split into “depart” and “arrive”, with preconditions existing that for A to kill B, both must initially be alive, and B not being alive as the post-condition. The constraints “remains” and “appears” are introduced for continuity-of-existence.
The simulation is taken from the point of view of the time traveler, defined as S, and his actions toward his parent, F. The first action is the that F has a child, S. The system is aware of F needing to exist to beget S. Then, S travels back in time to kill F, creating the paradox and the system reports a logical contradiction. The proposed solution to repair this paradox is that S has a clone S1. They are two separate entities, so the contradiction is resolved, but they retain the same identity. Thus, S goes back in time and creates a clone that kills F. This also reports a contradiction: “The user (clone S1) kills his parent F; this introduces the parent paradox and, indeed, our reasoning engine reports a contradiction: F is supposed to be dead because he was killed, but he is also supposed to be alive to beget S” [1, p. 10].
The solution that follows is not as elegant as the researchers would like. “F gives birth to S and goes back in time. S, right after being born, goes back in time as well, and kills his parent F. Right after killing his parent, though, S (actually the clone, S1) gives birth to him. In this solution, therefore, S is F’s son, F’s father, and F’s killer” [2, p. 12]. A much more simplified solution to the paradox is given by having the system not assume any actions by the time traveler. “F travels to the future, begets S, and travels back just in time to be killed by a clone of S who also went back in time” [3, p. 12].
References
[1] D. Friedman, “A computer program for simulating time travel and a possible ‘solution’ for the grandfather paradox,” arxiv.org. [Online]. Available: https://arxiv.org/ftp/arxiv/papers/1609/1609.08470.pdf
