Of all the weird consequences of quantum mechanics, one of the strangest is the notion of postselection: the ability to trigger a computation that automatically disregards certain results.

Here’s an example: suppose you have a long, tortuous expression in which there are a frighteningly large number of variables. The question you want answering is which combination of variables makes the expression logically true. And the conventional way to solve it is by brute force: try every combination of variable until you find one that works. That’s hard.

Postselection, however, makes the solution easy to find. Simply allow the variables to take any value at random and then postselect on the condition that the answer must be true. This automatically disregards any wrong’uns that come up.

Postselection is controversial because it leads to all kinds of fantastical predictions about the power of quantum computers. Nobody is quite sure if these kinds of computations are possible or how to achieve them but quantum mechanics seems to allow them.

Now postselection gets even weirder thanks to some new ideas put forward by Seth Lloyd at the Massachusetts Institute of Technology and a few buddies. They say that if you combine postselection with another strange quantum behaviour called teleportation and you can build a time machine.

Before we look at how this idea works, a quick reminder about quantum teleportation. This uses the phenomenon of entanglement to reproduce in one point in space a quantum state that previously existed at another point in space.

Lloyd and cos idea is to use postselection to make this process happen in reverse. Postselection ensures that only a certain type of state can be teleported. This immediately places a limit on the state the original particle must have been in before it was teleported. In effect, the state of this particle has travelled back in time.

What’s amazing about this time machine is that it is not plagued by the usual paradoxes of time travel, such as the grandfather paradox, in which a particle travels back in time and some how prevents itself from existing in the first place.

Lloyd’s time machine gets around this because of the probabilistic nature of quantum mechanics: anything that this time machine allows can also happen with finite probability anyway, thanks to these probabilistic laws.

Another interesting feature of this machine is that it does not require any of the distortions of spacetime that traditional time machines rely on. In these, the fabric of spacetime has to be ruthlessly twisted in a way that allows the time travel to occur. These conditions may exist in the universe’s extreme environments such as inside black holes but probably not anywhere else.

The fact that similar time machines may also be possible when quantum mechanics is pushed to its limits suggests an avenue that may prove fruitful in uniting this disparate areas of science. “Our hope is that this theory may prove useful in formulating a quantum theory of gravity,” say Lloyd and buddies.

So where might their time machine be built. That’s a tricky question too. Postselection can only occur if quantum mechanics is nonlinear, something that seems possible in theory but has never been observed in practice. All the evidence so far is that quantum mechanics is linear. In fact some theorists propose that the seemingly impossible things that postselection allows is a kind of proof that quantum mechanics must be linear.

However, if nonlinear behaviour is allowed, time travel will be possible wherever it takes place. As Lloyd and co say: “It is possible for particles (and, in principle, people) to tunnel from the future to the past. “

Fire up the Delorean.

Ref: arxiv.org/abs/1007.2615: The Quantum Mechanics Of Time Travel Through Post-Selected Teleportation

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