Time travel is a fascinating subject. Can we really go back in time and maybe change it? Suppose I can go back in time, would I be able to kill my own grandfather thus preventing my own birth? Here opinions are split. Some think that precisely because of this "grandfather paradox" time travel is unphysical. Others, state that if you go back in time you cannot change the past no matter how hard you try. And this is elevated to the status of a principle, called the Novikov principle.
But why do we even consider such things? Obviously we are not seeing any time travel tourists from the future visiting us, as Hawking observed. There are good reasons to ask such questions, besides a wish to deflate our egos by stating that we are not seeing time tourists from the future because we are uninteresting.
The first reason came from Einstein's general relativity which under certain conditions can develop whirlpools in the fabric of spacetime, bending it so that the future meets the past. The theoretical possibility of creating a general relativity time machine is in serious doubt, but even if it could be done, there are problems putting it into practice. It turns out however, that the energies involved in developing these whirlpools are truly enormous and lie beyond our current or foreseeable technological capabilities. Also time travel is possible only from the moment the first time machine was created anyway.
Maybe we can settle for something less ambitious.聽 Quantum mechanics is really strange. It allows for teleportation, and if we can teleport anywhere, why not "anywhen"? This fantastic possibility has been analyzed by FQXi's Seth Lloyd and collaborators (arXiv:1007.2615v2, blogged about by arXiv blog here) and it has even been demonstrated in an actual experiment (arXiv:1005.2219).
So is time travel real? Well, not quite--it depends on the definition of "is." But to see what I mean, let's start at the beginning with teleportation.
A quantum state is a very brittle state, and any questions you ask of it, can destroy it. Moreover, it is impossible to extract all relevant information due to Heisenberg's uncertainty principle, and in general, it's well known that you cannot clone a quantum state. So how can you actually teleport a quantum state when you cannot really make a copy of it? The best way toexplain this (and also a most entertaining way of doing it) is to quote Charles Bennett's description of it. First consider 2 twin pupils, Remus and Romulus (a Bell entangled state), each completely ignorant of all subjects, answering randomly, but always giving the same answer, even when questioned separately.
"Teacher A: Remus, what color is growing grass?
Remus: Pink, sir.
Teacher B (in another classroom): Romulus, what color is growing grass?
Romulus: Pink, ma'am."
This Romulus-and-Remus Bell state can be used to teleport an unknown quantum state. For example,paraphrasing Bennett, here is how Remus and Romulus can help solve a crime that they did not witness:
Suppose someone, called Alice, had seen her best friend Bob murdered in Boston. Under shock, although she can recall the details, any questions can confuse her and erase critical pieces of her memory. Fearing that, the FBI wants to take charge and fly Alice to Washington DC to be interrogated by experts. But Alice is busy and the FBI comes up with a compromise: They know that Remus and Romulus share a special bond, and conveniently enough Romulus is currently located in Washington DC, while Remus lives in Boston. Therefore they instruct the local police to let Alice talk with Remus and see if they "get along" or not. (Alice and Remus will not be talking about the crime she just witnessed, but about other topics.)
Alice spends some time with Remus and she decides that she does not get along with him 100% of the time. Moreover, the stress of this meeting has erased all her memories of the murder. The Boston police phone the FBI and tell them that Alice and Remus don't get along. The FBI use this information by talking to Romulus and asking him about the murder. They know that Alice and his brother did not get along and whenever Alice would say yes, Remus (and his brother Romulus) would say no, and the other way around. So by carefully reversing every single response they get from Romulus, they can extract all the information Alice had about the crime.
What we have here is teleportation of Alice's brittle knowledge from Boston to Washington. In the process, the original state of Alice was destroyed, and the no cloning constraint is obeyed.
Now that we have a more intuitive description of how quantum teleportation works, we can proceed with explaining Lloyd's experiment and analysis. In quantum teleportation there is one bit of classical information transmitted from past to future: "Then the Boston police phone the FBI and tell them that Alice and Remus don't get along." To achieve teleportation to the past, this step has to be eliminated. How does Lloyd do it? By projection to another Bell state followed by postselection. (Postselection is what is being invoked by FQXi's Paul Davies to explain how the universe's set fate could be influencing its present state. For more details, see Julie Rehmeyer's article, "The Destiny of the Universe.")
To see what is happening in projection and postselection, we have to meet Alice, Romulus and Remus again. Alice likes songs, and Romulus likes to write down lottery number guesses. Today Alice hears a song on the radio: "Mary had a little lamb..." while a year ago (last time) Romulus wrote: "13,1,18,25,0,8,1,4,0,1,0,12,9,20,20,12,5,0,12,1,13,2,..."
Then Alice meets Remus and spurred by the song, they fall strongly in love, discovering to their amazement that now they share the same psychic bond as Romulus and Remus did in the past. Moreover now the original bond between Romulus and Remus is lost.
Together Alice, Romulus and Remus make a three way system: Alice is system 1 entering the time travel loop, Romulus is system 2 emerging from the time travel, and Remus is system 3, its purification (see Eq. 2 in arXiv:1007.2615v2). Here the projection to another Bell state takes place when the Alice-Remus pair is formed. Postselection eliminates the cases when Alice falls only weakly in love with Remus, meaning that the state of Alice-Remus link is not in the precise prior state of Remus-Romulus.
All this excitement made Alice completely forget about the original song. But that information from today is not get lost. It is now in the past as the state of Alice from earlier today is teleported to Romulus one year in the past. And indeed there is a simple cipher key translation between the song and the lottery numbers: A = 1, B = 2, C = 3, D=4, etc.
This is "effective time travel to the past" (see George Svetlichny (arXiv:0902.4898)).聽 Time travel is only a possible narrative of what is going on, but it is not falsifiable one way or another. The best way to understand this is in Bob Coecke's pictorial formalism where tracing the path of the information sometimes moves backwards in time (arXiv:quant-ph/0402014v2). (A similar scheme was proposed by Horowitz and Maldacena (arXiv:hep-th/0310281v2) as a way to teleport the infalling information into a black hole outside the black hole in outgoing Hawking's radiation using the Bell state of correlated infalling and outgoing Hawking radiation (there the postselection is replaced by the mirror effect of having a unique singularity state).)
At this point you may cry, "nonsense, this is like tea leaf reading!" But here is the amazing thing: change the song today and you'll get another cipher key whenever Alice falls strongly in love with Remus. And look at this from an information conservation perspective: in one instance you have a Bell state in the past and a song in the future, in another instance you get the same Bell state in the future and the lottery numbers in the past. Therefore there must be a direct translation between the lottery numbers and the song. If the song is changed to the point that no such translation is possible, then it is guaranteed that Alice will not fall strongly in love with Remus, and those cases are pruned by postselection.
So is this genuine time travel? What if I write down on a piece of paper today all possible lottery numbers and tomorrow after the actual drawing I postselect only the winning number, erasing all the others. Would this be considered time travel to the past? Not at all, but quantum mechanics is subtler. This situation is reminiscent of the question Aharonov asked about quantum mechanics: Can quantum mechanics be derived from non-signaling and non-locality? The answer came back negative with the discovery of the Popescu-Rohrlich box. Similarly, can time travel be banned by energy conditions in general relativity? No, because teleportation with postselection does allow it in the absence of general relativistic closed timelike curves, and it is experimentally confirmed. And it IS time travel because a quantum state is all about information and the information did get erased from present and did travel to the past. However, it could not alter the past obeying Novikov's principle, and also it is not a falsifiable time travel. Also it IS NOT time travel because it can be also understood as a narrative for selecting the appropriate communication channel between past and future by projection and postselection. In the little charade above is about having the right conditions for falling in love, losing your head, and the hindsight of the inevitability of that happening. As stated in the beginning, it depends on the meaning of "is."
There are other proposals beside Lloyd's to deal with the grandfather paradox. For example the leading explanation is Deutsch's (D. Deutsch, Phys. Rev. D 44, 3197 (1991)). Deutsch imposes a self-consistency condition which is different than Lloyd's teleporting condition and in general is generating a different resolution of the grandfather paradox. In his analysis, (arXiv:1007.2615v2), Lloyd points out that like in the weak measurement case, because of the nonlinearities involved in postselection, in his case there is no quantum state description available at any given time, and that you do not succeed in killing your grandfather no matter how hard you try. In comparison, Deutsch's condition leads to the existence of a quantum state at all times, and that you do manage to kill your grandfather with 50% probability, and your grandfather is 50% dead and 50% alive. In Everett's interpretation for Deutsch's solution you are splitting into 2 parallel universes and you manage to kill your grandfather from the parallel universe, which prevents you from being born there which prevents your self from that universe killing your grandfather from your universe, and in the end everything is consistent.
The advantage of Lloyd's condition over Deutsch's condition is that nature has validated teleporting to the past, while Deutsch's condition is only speculative at this point. However, Lloyd's resolution of the grandfather paradox is rather unimpressive because the inconsistent case is automatically discarded by projection and postselection. It is like drawing random numbers, postselecting only even numbers and then observing that you don't get odd numbers no matter how hard you try. Other authors proposed other solutions to the grandfather paradox, like Greenberger and Svozil for example (arXiv:quant-ph/0506027), and in all those proposals, causality is respected. What this shows is that in order to ban causality violations (or standard time travel in general relativity settings) one needs an additional ingredient besides quantum mechanics. (General relativity does not do it, and neither does quantum mechanics in certain circumstances.) This missing ingredient is most likely free will, for if I can choose to change the past after knowing the future, I would be able to create a paradox. For people believing the Novikov principle under all circumstances, free will is just an illusion, and this argument may not sway them. What is really needed is a full theory of quantum gravity. But can we do better and find additional arguments against "falsifiable time travel" without solving the hard problem of quantum gravity? I believe that we can. Time will certainly tell.
In the meantime, here is a question for you: is post selected quantum teleportation to the past time travel or not? Or if it swims like a duck, quacks like a duck, but is not falsifiable as a duck (and sometimes could be described as a goose), is it a duck? If not, what is it?