© iStockphoto/head-offGroundhog Day for particles. A quantum particle can travel around a loop in time and keep returning to the same moment of interaction with another particle without creating any paradoxes, but it must meet strict consistency criteria.
General relativity, Einstein's theory of space and time, allows the existence of closed timelike curves (CTCs)--paths that go forward in time, then back again to reconnect and form closed loops. Although it's unclear whether CTCs can be created, physicists have nevertheless explored their possible consequences, including their influence on quantum mechanics.
An ordinary quantum event might involve two particles moving forward in time, changing each other by interacting at some time, then going their separate ways into the future. However, if one outgoing particle enters a CTC, it can double back and become one of the ingoing particles--thus influencing its own transformation. In 1991, Oxford University physicist David Deutsch proposed a consistency condition to avoid time-travel paradoxes: a particle that loops back in time in this way should be in the same quantum state when in reappears in the immediate past of the interaction as it was when it departed the interaction for the immediate future.[1]
To see how this condition works, imagine a quantum particle having states labeled 0 and 1. It travels around a CTC and, on its return, interacts with an "external" particle in such a way that 0 becomes 1 and 1 becomes 0. Such a particle presents a quantum grandfather paradox: when it comes back around the loop, it flips its former self to the opposite state. However, Deutsch showed that consistency is possible if the particle is in a superposition--a state that is equal parts 0 and 1. The interaction exchanges the 0 and the 1, but the state overall remains unchanged. For this to work, the external particle must also be in a superposition that flips back and forth.
The paradox is avoided, but a difficulty arises if the external particle is measured. Then it cannot remain in a superposition but must become definitely either 0 or 1--which means that the CTC particle cannot remain in a superposition, either. To preserve consistency, Deutsch argued that the CTC particle must exist in two parallel universes--the "1-universe" and the "0-universe"--and continually switch between them, so that no contradiction occurs in either one.
Lorenzo Maccone, of the Massachusetts Institute of Technology and the University of Pavia, Italy, and his colleagues propose a more stringent condition that avoids these difficulties. They require that any measurement of the particle going into the future should yield the same result as measuring it when it returns from the past. So any state that would alter the past when it came around again is disallowed, and no grandfather-type paradoxes can arise.
Perhaps surprisingly, "we can still have CTCs even with this strong condition," Maccone says. Only states that avoid paradoxes after the interaction are able to exist beforehand, so the team calls their condition "post-selection."
To demonstrate these ideas, the team performed an experiment with photons showing that the consistency condition indeed picks out specific states and destroys all the rest. Lacking an actual CTC to perform the post-selection, the team created photons in a specific quantum state for the input, a state where the polarization was not known or measured but had a correlation with another property, associated with the photon's path. As the photon went through the experiment, it experienced changes that mimicked the 0-to-1 flipping that occurs in the imagined time-travel arrangement. The team found that only those photons that wouldn't lead to paradoxes made it through unscathed. Although the result is in line with expectation, no one has simulated time travel in this way before.
An odd consequence of post-selection is that because the presence of a CTC annuls paradoxical states completely, it can disallow some states that seem innocuous today but have unacceptable consequences later. "In principle, one could detect the future existence of time machines by ... looking for deviations now from the predictions of quantum mechanics," says Todd Brun of the University of Southern California in Los Angeles. Although, he adds, it's hard to know in advance what to measure.
David Lindley is a freelance writer in Alexandria, Virginia, and author of Uncertainty: Einstein, Heisenberg, Bohr and the Struggle for the Soul of Science (Doubleday, 2007).
Reference:
[1] D. Deutsch, "Quantum Mechanics near Closed Timelike Lines," Phys. Rev. D 44, 3197 (1991).
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