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Nov 16
2009
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As can be seen from the example above, there are possible fundamental problems of consistency and causality associated with time travel. The most prominent is the "grandfather paradox," in which you travel back in time and kill your grandfather before you were born, which means you could not have been born to then travel back in time to kill your grandfather.
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The grandfather paradox as stated is difficult to analyze since it deals with human actions and free will. It is typical of a physics problems to start with a simpler scenario. For example, to understand aerodynamics we first start with understand simple motion, like a ball tossed in the air. For time travel and the grandfather paradox, a simpler scenario is consider a ball tossed through a wormhole, with an exit wormhole nearby in space. A wormhole is a hypothetical tunnel through the fabric of spacetime. Since both space and time are being tunneled, it is theoretically possible to produce a wormhole that not only moves you from some place to another instantaneously, but also can move you back in time.
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So consider a wormhole with entrance A and exit B as shown below. If we toss a ball into A, it will exit B a few minutes before. We can also orient the wormhole such that the exit trajectory can intersect the incoming path. Thus, we have produced a simple, billiard-ball version of the grandfather paradox. If a ball is tossed into A such that its exit trajectory will intercept the incoming ball, then it prevents itself from entering the wormhole and produces a paradox.
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The origin of the paradox is a logical error in our discussion of the scenario. We have assumed that there was no ball coming out of B when we first toss the ball. But spacetime is a singular thing, it can't be cut up and changed to match our wishes. So our assumption that the ball enters A without interference is incorrect. In fact, if we setup the experiment correctly we find that we must take in the collision with our calculations of how to toss the ball. We end up with a `nudge' rather than a strong collision and all works out in the end.
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We could even make this scenario alittle harder by replacing the ball with a very sensitive bomb. One touch or nudge will cause it to explode. Now there is no direct solution, no glancing blow that allows a time travel interaction. However, under closer inspection, what would really happen is shown below, a fragment from the explosion would pass through the wormhole, to cause the explosion, paradox avoided.
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The results of these thought experiments has led numerous physicists to speculate that spacetime contains a chronology protection effect, much like the event horizon around a black hole. Where an event horizon prevents a singularity from being exposed to the Universe, a chronology protection effect would prevent time travel and the framework of causality by making time paradox's impossible.
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