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Time Travel: Ways Around Paradox

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.


Comments on this entry are closed.

  • MattC July 26, 2010, 9:57

    Do we need a SETI like SMFF project?? (Search for Messages From the Future!)

  • Matt Robare July 26, 2010, 10:04

    I find it preferable to use time travel in such a way that a spaceship at non-relativistic velocities arrives at its destination instantaneously.

    The real problem with time travel isn’t killing your own grandfather, but becoming your own grandfather . . .

  • Administrator July 26, 2010, 10:11

    MattC writes:

    Do we need a SETI like SMFF project?? (Search for Messages From the Future!)

    Nifty idea. We can also set up a Fermi Paradox analog: Feynman’s Paradox — i.e., where are the tourists from the future?

  • matt r July 26, 2010, 11:05

    I would like to know why grand-kids from the future are such dicks that they are all coming back to kill their grandfather.

  • djlactin July 26, 2010, 11:06

    Grandfather paradox, be damned. That’s a trivial problem. Here’s my argument that time travel is impossible. Consider your own existence. Nine months before you were born, your father shot 5 billion sperm cells into your mother. One of those five billion made you. (Actually, this is a gross underestimate: they got it on possibly dozens of times before ringing the bell.) Try to imagine of one of the others had been the lottery winner. You would not exist. (I find this to be a mind-f*cking exercise: what if someone else were thinking this thought?) So the chances that YOU exist, given that your parents met and got it on , is maybe one in a trillion. Two factors: your parents existed, and they met. The odds of each of your parents existing is also about one it a trillion (same argument as the one about you existing; of both of them existing, one in 10 18); the odds of them meeting (etc.) is larger but less than one. Extend this chain of improbabilities back 3.5 billion years (generations?): the likelihood of your existence is, well, zero. Any trivial event that prevented (say) one wormlike creature from mating with a particular partner 1.8 billion years ago would have precluded your existence.
    Here’s my point: visiting the past would perturb it. Even a small change would disturb the inhabitants; displace items, affect later opportunities for your ancestors to meet. Any change would eliminate your likelihood of having been born. By disturbing the past, the traveller would preclude his/her own existence. Time precludes its own existence.

    Oh, and here’s another one: traveling into a different time would violate conservation of matter. Suddenly, at some time in time (odd language, but what else?), two copies of every atom in your body would exist (whenever you are). I don’t see any way to get around that problem.

    Time travel is fascinating speculation, but I sincerely doubt that it is possible.

  • William Truderung July 26, 2010, 11:09

    The simplest way to have a physics consistent with paradox-free time travel would be for the “many-histories” interpretation of QM to be correct. As soon as a time traveler appeared, the universe would branch off into a separate time-line with no further causal connection to the original one, so that the time traveler could do anything (including killing grandparents) he/she pleased without causing any sort of causal paradox.

  • Tulse July 26, 2010, 11:40

    I admit I don’t understand the specifics being proposed, but I find the general notion that the universe would somehow “resist” paradoxes to be very unconvincing. I can understand time travel creating multiverses, where if I travel from my timestream A to the past I am actually creating timestream B, and thus anything I do there can’t interfere with my own existence. But the notion that travel back in time in the same universe would remain paradox-free seems to imply almost a sense of narrative on the part of the universe, which is just silly.

  • Qrystal July 26, 2010, 13:44

    I must point out that quantum teleportation can only be applied to quantum states that are simple enough that they can stay in a state of superposition without self-decohering; thus, this discussion applies to atomic or molecular states, not people.

    If it turns out that there is some way to create an experiment that teleports a quantum state into the past, it will probably happen in such a way that the recipient state had a probability of being in the state that that was transferred from the future. Uncertainties might be able to be exploited to give time-travel-like effects, but time travel of macroscopic entities is not going to be the end result, and so there will be no grandfather paradoxes to worry about (although they will surely continue to be used as analogies).

    I suspect that this notion of time travel will actually turn out to just be an illusion (or a barely-useful novelty, like teleportation) that results from a particular interpretation of quantum mechanical probability amplitudes.

  • Thomas July 26, 2010, 14:11

    @ djlactin

    That’s an interesting point about conservation of energy/mass.

    Of course, the time from which you came would find itself robbed of an equivalent amount of matter as has appeared in the past.

    How does conservation of energy/mass work with time travel? Is the appearance of mass in the past balanced by its dissapearance from the present so as to make the conservation an average over the history of the Universe? (i.e. despite conservation of energy, particles pop in and out of existence, such that the average is zero, can something similar work for time as well as space?)

    Or am I talking nonsense? (I don’t claim to know much about this kind of thign).

  • Rob July 26, 2010, 14:18

    I’d have to agree with William.

    Just simply appearing at a point in past would displace air molecules, and that would have SOME causal effect… or blade of grass is crushed… or an insect is forced to divert it’s course thereby depriving a larger animal of a meal etc.

    I imagine it would be more significant the further back you arrive.

  • Zen Blade July 26, 2010, 14:59


    I think your point regarding all sorts of changes (small and meaningless, but meaningful in the larger context) is also where my problem with time travel kicks in. Is there an auto-rewrite that kicks in for every little change? And what “is” a Time Paradox???
    Is it anything in your original time that would be changed by your actions in the past, such that your actions in the original time might be changed, thus changing your actions in the past, etc…
    Or, is it an action in the past that definitively creates an a different set of future conditions that we know what have a definitive effect on the future/past?
    The point being: let’s say your favorite color is orange because oranges are orange, and you build your time machine to be orange (and it accompanies you to the past). However, in the past you change something (at the molecular level) that makes oranges red! [assume no side effects on the popularity of the fruit, etc…] So…
    does that mean that your favorite color is still orange but for some other reason, which you should already know?
    does that mean that your time machine is now red because your favorite color is now red?
    Or, does that mean a new future was created in which red was your favorite color and you built a red time machine, which you traveled back in time with to some alternative past in which you already made oranges red?

    Granted, that whole series of events might NOT even be a paradox… But, if it is, that implies “fate”, much like the “really hard to kill grandfather”, which means that I can say and do whatever I want in life because free will does not supersede destiny?

    Viva el time machino!

  • david spencer July 26, 2010, 15:16

    I recall watching the movie ‘Sound of Thunder’ a while back and thinking if time travel were possible it could explain fermi’s paradox.

    With time travel I don’t see the paradox. The universe is made up of a massive number of particles each with a number of properties. Much like memory within a computer. When a future event affects the past it could be like resetting the universe back to that state. Just like memory within a computer can be reset back to a particular state. However a computer process that resets memory might alter that previous state just a little. And so the process within the universe that reset the universe back a previous state might make changes to that state, ie the time traveler. Though that time traveler wouldn’t necessarily be a human. It could just be a particle that in its interactions with other particles changes things.

    In ‘Sound of Thunder’ humanity nearly wipes itself out via a time travel incident back to the time of the dinosaurs. And that in itself could provide a selection mechanism that creates a universe where time travel never happens. If a species utilizes time travel either on purpose, or by accident while doing scientific experiments, then the state of the universe gets reset. Eventually it would come across a state where time travel never happens.

    Which would explains fermi’s paradox. Any species capable of interstellar space travel would also be capable of time travel and would reset the time line. So a universe which has reset itself to a state where time travel doesn’t happen would also be in a state where interstellar travel doesn’t happen.

    Which would mean the universe has few technological species. That those that do exist wipe themselves out before they are able to reset the time line.

    What fun to speculate on such things. And a bit scary since in the above case it means there can never be a species that is really technologically advanced.

  • Athena Andreadis July 26, 2010, 19:37

    As Qrystal pointed out, quantum teleportation cannot be used for macro objects. Decoherence sets in way below that scale. No time travel in that direction.

  • Ron S July 26, 2010, 19:41

    Regarding conservation of mass or energy (same thing), we need to be careful. First, it is a local phenomenon, which is not necessarily conserved over cosmological times and distances. Second, it is not a decree from on high: it is determined from experiment (data), and which appears to be true and consistent with some pretty strongly-tested theories. So while we call it a “law”, it doesn’t preclude an experiment tomorrow that will violate conservation.

    A further thought on the topic is that there are *no* paradoxes, just our incomplete understanding of physics. Finding a paradox in our thought experiments about time travel only shows that there is either stuff we don’t fully understand or that the experiment is impossible.

    There was once some wit (it may have been Douglas Adams) who observed that it is silly to imagine that the universe is so fragile that it cannot endure a bit of scar tissue due to some peculiar or seemingly-impossible outcomes due to poorly-executed (not causally consistent) time travel adventures. I suppose if we find a “bandage” lying around out there somewhere we’ll have a real puzzle on our hands.

  • kurt9 July 26, 2010, 19:48

    My understanding is that the paradoxes involved with time travel are resolvable only on the basis of the many worlds interpretation of quantum physics. If you go back in time and kill all of your grand parents prior to your birth, that “universe” branches off from the the past path of the universe you came from and continues on into the future as a separate universe. One where you are not “born” at all.

    If time travel were possible, I think there would be occasional visitors from the future dropping in on us. No one’s dropped in from the future as far as I know. Hence, I think it impossible.

  • NS July 26, 2010, 20:28

    Re “A Sound of Thunder”, IIRC in the original Ray Bradbury story, shortly after a presidential election between a mainstream and a far-right candidate a safari travels back in time to hunt dinosaurs. One of the party accidently steps off the designated trail and kills a butterfly. When the hunters return to their present they find out that (c0ntrary to the original timeline) the Hitler-like presidential candidate has won the election. The “sound of thunder” is the safari guide shooting the hunter responsible for altering history.

    Makes you wonder…

  • Nathan Currier July 26, 2010, 20:46

    Well then- I want America to be reborn as a free country. I want the Rothschilds to go the way of the Romanovs. And I want a spaceship to Alpha Centauri. If I don’t get these things, I swear to perform a self-cancelling time travel experiment or die trying.

  • William Truderung July 26, 2010, 23:02

    My understanding of the possibility of time travel is that it is only possible if the ‘many histories’ interpretation of QM is correct. If it is not, then this time line is the only one, meaning that either time travel is technologically impossible, or if it IS technologically possible, each time somebody (anywhere in the universe) travels backwards in time, the history of events in the single universal time line changes. This keeps happening until the time line settles down into a ‘steady state’, which can only happen if time travel never happens — which since it is technologically possible, must mean that every technological civilization in the universe never successfully achieves time travel, either willingly abstaining from time travel for their entire existence, or because they are destroyed before they have the technological ability to successfully achieve it. Given human nature, I would bet on human civilization being destroyed first.

    On the other hand, if the many histories interpretation of QM is correct, then I see no reason for time travel not to be technologically feasible and to be practiced, since no time travelers would ever alter the originating time line without splitting off into their own new time line, hence time travel paradoxes would never form, and the originating time line would remain stable. If we are indeed on the ‘first’ time line that originally leads to the development of true time travel, we would by definition never see an actual time traveler.

    Of course I am ignoring the fact that if the true interpretation of QM is indeed ‘many histories’, then there are countless trillion on new time lines splitting off from ours every microsecond. The logic remains the same in any case.

  • Jay Cee July 27, 2010, 9:30

    The tourists from the future are in the UFOs, joy-riding & “buzzing the primitives” ;-)

  • bigdan201 July 28, 2010, 20:07

    This is relevant to my interests.

    I played many video games growing up, and one of my favorites was Chrono Trigger for the SNES. It’s an RPG (role-playing-game) centered around saving the world through time travel, and it’s widely considered a classic.

    Although it came out in 1995, it still has a following, and people have seriously analyzed the themes in the game (you have to realize that the story and fictional world is very complex). One concept they came up with is “time travelers immunity” which states that the individual traveling through time is immune to the changes they make. Time travel creates a new timeline, either a new worldline branch or a replacement of the old, but the time traveler himself is unaffected by this. This conveniently avoids paradoxes. No matter how much you change history, you won’t be affected and you’ll remember the old timeline before it got replaced. There is also the “time bastard” theory, which states that other versions of a time traveler will also be displaced at the point of the originals time travel.. it is rather complicated though. The point of time bastard is to maintain conservation of energy in the universe.

    The question remains whether there would be numerous worldlines, or one worldline which is changed anytime someone travels back in time. But TTI/time travelers immunity addresses the grandfather paradox well, and it seems to work better than applying principles of quantum mechanics to a macro scale, although I can’t say for sure. It also makes the storyline of the game make sense.. otherwise, the travel to various eras, and the defeat of the last boss which erases the post-apocalyptic future (which you also interacted with) would be riddled with paradoxes.

    In any case, traveling backwards through time would make the universe a rather chaotic, embroiled place with either numerous worldlines or a single worldline being updated for every trip backwards in time. It is not likely that it can be done on a macro scale, although I can’t rule it out.

    It is certain that its possible to travel forward through time, thanks to relativity. That’d be a wild alternative to joining the french foreign legion.

  • djlactin July 29, 2010, 10:37

    We are all time travelers, moving at a rate of 1 s/s (less, if you’re actually moving through space).

  • Mark Oller September 16, 2010, 13:11

    If two objects are 1.1 light years apart and moving away from each other at 90% of the speed of light, both objects are two years in the past from the other’s perspective. If a signal could be sent instantaneously, it would travel two years backwards in time. With Burkhard Heim’s hyperdrive, it would be possible to send small unmanned probes, containg libraries of information, to and from the Earth at hundreds or thousands of times the speed of light. It could stop at a robot craft travelling ever closer to light speed.

    Soon, there would be more efficient ways to communicate with the future, so in a few years, we will know all there is to know. I am not a physicist, so I want to know if there is any fallacy in my reasoning.

  • ljk May 21, 2012, 17:06


    European Physicists Smash Chinese Teleportation Record

    The battle over distance records sets up a fascinating race to be the first to teleport to an orbiting satellite

    kfc 05/21/2012

    Just a couple of weeks ago, we discussed a Chinese experiment in which physicists teleported photons over a distance of almost 100 kilometres. That’s almost an order of magnitude more than previous records.

    Today, European physicists say they’ve broken the record again, this time by teleporting photons between the two Canary Islands of La Palma and Tenerife off the Atlantic coast of north Africa, a distance of almost 150 kilometres.

    That’s sets the scene for a fascinating prize. Both teams say the next step is to teleport to an orbiting satellite and that the technology is ripe to make this happen.

    The Canary islands experiment was no easy ride. In ordinary circumstances, the quantum information that photons carry cannot survive the battering it gets in passing through the atmosphere. It simply leaks away.

    Indeed, the European team say that unusually bad weather including wind, rain, rapid temperature changes and even sand storms all badly affected the experiment. “These severe conditions delayed our experimental realizations of quantum teleportation for nearly one year,” say Anton Zeilinger at the Institute for Quantum Optics and Quantum Information in Vienna and a few pals.

    (However, they are quick to point out that satellite-based quantum communication shouldn’t be as susceptible since there is less weather to pass through if you fire photons straight up.)

    To perform this experiment, Zeilinger and co had to perfect a number of new techniques to dramatically reduce noise, which would otherwise overwhelm the quantum signal.

    Perhaps the most significant of these is a way of using entangled photons to synchronise clocks on both islands. That’s important because it allows the team to send photons and then look for them at the receiver at the exact instant they are due to arrive.

    This significantly reduces the number of extraneous photons that could swamp the signal. The GPS system allows clocks to be synchronised in a way that allows a 10 nanosecond coincidence window. But entanglement-enhanced synchronisation allowed Zeilinger and co to use coincidence windows just 3 nanoseconds long.

    The results sets up an interesting race between east and west. These experiments are proof-of-principle runs for a much more ambitious idea–quantum teleportation to orbiting satellites.

    Since teleportation is the basis of more-or-less perfectly secure communication, the prize here is a global communications network that cannot be hacked, even in principle.

    “The technology implemented in our experiment thus certainly reached the required maturity both for satellite and for long-distance ground communication,” say Zeilinger and co.

    The questions, of course, is who will be first to orbit. The Europeans have a space agency that could be persuaded to test this idea but they won’t be in a hurry. China is currently showing great ambition in space and will want to show off its technological prowess. Both have the wherewithall to pull off this next step.

    The contrast with the US couldn’t be clearer.

    Ref: http://arxiv.org/abs/1205.3909: Quantum Teleportation Using Active Feed-Forward Between Two Canary Islands