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Quantum Mechanical Model Of A Time Travel Paradox

David Thomas Pegg

Published Jan 1, 2014• 0 citations

Abstract

The retrocausality inherent in the retrodictive description of a quantum optical device called the quantum scissors allows this device to be used as a non-deterministic time machine. We show how the device can be used to model the time travel paradox of retrospective suicide. Here a man goes back in time and interferes with his own birth, weakening his infant self in such a way that he is killed by the time machine and is unable to interfere with his own birth. We find that the paradox is avoided by interfering quantum mechanical amplitudes making the time travel event impossible in this case. A slight modification that limits the interference with the birth so that the infant is only injured by the time machine to give a self-consistent cycle does, however, render the time travel event possible. This lends support to the idea that time travel is only possible if it yields a self-consistent cycle that avoids a paradox.

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The retrocausality inherent in the retrodictive description of a quantum optical device called the quantum scissors allows this device to be used as a non-deterministic time machine. We show how the device can be used to model the time travel paradox of retrospective suicide. Here a man goes back in time and interferes with his own birth, weakening his infant self in such a way that he is killed by the time machine and is unable to interfere with his own birth. We find that the paradox is avoided by interfering quantum mechanical amplitudes making the time travel event impossible in this case. A slight modification that limits the interference with the birth so that the infant is only injured by the time machine to give a self-consistent cycle does, however, render the time travel event possible. This lends support to the idea that time travel is only possible if it yields a self-consistent cycle that avoids a paradox.

A time machine that sends information back to the past may, in principle, be built using closed time-like curves. However, the realization of a time machine must be congruent with apparent paradoxes that arise from traveling back in time. Using a simple model to analyze the consequences of time travel, we show that several paradoxes, including the grandfather paradox and Deutsch's unproven theorem paradox, are precluded by basic axioms of probability. However, our model does not prohibit traveling back in time to affect past events in a self-consistent manner.

The Delayed-Choice Quantum Eraser experiment is commonly interpreted as implying that in quantum mechanics a choice made at one time can influence an earlier event. We here suggest an extension of the experiment that results in a paradox when analysed in a local realist interpretation combined with backward causation (``dynamical retrocausality''). We argue that resolving the paradox requires giving up the idea that, in quantum mechanics, a choice can influence the past in this way, and that it instead requires a violation of Statistical Independence without (what most people think of as) retrocausality. Finally, we propose an implementation of the experiment that we believe to be possible with existing technology. This new experiment can distinguish between different types of hidden-variables theories in a way that Bell-type tests cannot: unlike in a Bell test, the measurement setting here is set by an earlier outcome, which makes the consistency of the backwards influence itself testable. We classify the fixed-point (consistency-enforcing) hidden-variables models of the experiment, which can reproduce quantum mechanics only if the backwards influence has no observable effect.