Time travel holds such perennial fascination that even though its relationship with interstellar issues is slim, I can’t resist reporting on new ideas about it. John Cramer’s time experiments seem stuck in limbo, but now we have new work from Seth Lloyd (MIT) and colleagues about one way out of the paradoxes time travel seemingly creates. The ‘grandfather paradox,’ returning to the past to kill your own grandfather and thus causing your future self not to exist, seems inevitable if we grant the existence of what are called ‘closed timelike curves’ (CTCs), the paths through spacetime that would let a time traveler interact with his or her self in the past.

Ways Around Paradox

Lloyd’s team gets past that problem by describing a particular version of closed timelike curves formed with what is called ‘post-selection.’ The idea is to describe these CTCs in terms of quantum mechanics, starting with the assumption that time travel is a communications channel from the future to the past. Is there, then, a quantum communication channel to the past? The researchers consider quantum teleportation, in which a quantum measurement combined with classical communication lets quantum states be transported between sender and receiver.

The paper then applies quantum teleportation to timelike curves with postselection (P-CTCs):

We show that if quantum teleportation is combined with post-selection, then the result is a quantum channel to the past. The entanglement occurs between the forward- and backward-going parts of the curve, and post-selection replaces the quantum measurement and obviates the need for classical communication, allowing time travel to take place. The resulting theory allows a description both of the quantum mechanics of general relativistic closed timelike curves, and of Wheeler-like quantum time travel in ordinary spacetime.

As best I can untangle this (and we’ll deal with Wheeler in a moment), the post-selection idea means that time travel paradoxes are ruled out. Try to perform the event causing the paradox and something will happen to make the action fail. Moreover, although this theory of post-selection in timelike curves was created to deal with quantum mechanics in CTCs following the principles of general relativity, the authors think it extends to other contexts. Quantum theory that allows entanglement, in other words, seems to allow time travel even when no spacetime closed timelike curve exists.

Tunneling Through Time

Lloyd’s team says this quantum time travel can be thought of as ‘a kind of quantum tunneling backwards in time, which can take place even in the absence of a classical path from future to past.’ That’s a helpful thought, given that the extreme distortions of spacetime required by more traditional time travel thinking in a relativistic context are all but impossible to create.

Interestingly, there already exists a growing literature on entanglement and projection in the development of timelike curves, all described briefly in this paper. But the authors are particularly careful to note John Wheeler’s ideas impinging on quantum time travel, ideas that Richard Feynman described in his Nobel Prize lecture. This is worth repeating:

‘I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, “Feynman, I know why all electrons have the same charge and the same mass.”
“Because, they are all the same electron!”
And, then he explained on the telephone, “Suppose that the world lines which we were ordinarily considering before in time and space – instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time – to the proper four velocities – and that’s equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron.”’

And now we’re really in Wonderland. Post-selection accepts only particular results, meaning that the only states that can be teleported via quantum entanglement are those that are consistent with the world we know. Time travel in this guise is necessarily consistent with our reality and forbids any actions that would create paradoxes. The authors put it this way: “…although any quantum theory of time travel quantum mechanics is likely to yield strange and counter-intuitive results, P-CTCs appear to be less pathological. They are based on a different self-consistent condition that states that self-contradictory events do not happen…”

Ratcheting Up Improbabilities

In an article on this work in Science News, Laura Sanders takes note of the fact that ruling out paradoxes means that unlikely events may happen with greater frequency:

“If you make a slight change in the initial conditions, the paradoxical situation won’t happen. That looks like a good thing, but what it means is that if you’re very near the paradoxical condition, then slight differences will be extremely amplified,” says Charles Bennett of IBM’s Watson Research Center in Yorktown Heights, N.Y.

For instance, a bullet-maker would be inordinately more likely to produce a defective bullet if that very bullet was going to be used later to kill a time traveler’s grandfather, or the gun would misfire, or “some little quantum fluctuation has to whisk the bullet away at the last moment,” Lloyd says. In this version of time travel, the grandfather, he says, is “a tough guy to kill.”

So we have no paradoxes but we seem to be distorting probability, a very strange result but maybe a bit less strange than the paradoxes we’ve avoided. Time travel makes for eerily seductive fiction — who would not wonder about traveling into the past to see loved ones again, or to remedy some unintentional wrong — and judging from the number of emails I received pointing me to this paper, the idea is as compelling now as it has ever been. I hadn’t realized how far back time travel has resonated in history, but the paper notes an account in the Hindu epic called the Mahabarata in which King Revaita visits the Brahma’s palace, stays for only a few days, and returns to Earth only to find that many eons have passed in his absence.

This is more or less the idea behind the creaky science fiction story “Out Around Rigel” (Astounding Stories, December 1931), in which Robert H. Wilson imagines the first journey to another star and uses the event as a way to teach Einsteinian special relativity (the first time this was done in science fiction, to my knowledge). The crew returns to find a thousand years have passed during their six-month journey. But this is a time travel account from the standpoint of relativistic spacetime. Quantum mechanics, in this paper’s estimate, might give us options other than that one-way ticket to the future.

How post-selection would work in quantum mechanics has yet to be determined, but the authors discuss the possibility of testing their theory experimentally by using quantum teleportation. Can people ever hope to take a journey into their own past with a self-consistent, non-paradoxical outcome? Science fiction writers will want to mull over the findings of this thorny, mind-bending paper and especially note the extensive literature treating entanglement and projection in the creation of closed timelike curves.

The paper is Lloyd et al., “The quantum mechanics of time travel through post-selected teleportation,” available as a preprint. Be aware as well of Lloyd et al., “Closed timelike curves via post-selection: theory and experimental demonstration” (preprint). This story on Physorg.com also discusses Lloyd’s work and ponders non-linearity in quantum mechanics.