Thursday, January 02, 2014

Wormholes into the past

Last night, Nova Cinema, a Czech TV station, aired Frequency, a 2000 sci-fi thriller. Beware spoilers.

It's 1999 and John is still devastated because of his dad's death 30 years earlier. The father, Frank, was a firefighter. On the night before his fatal fire in 1969, he would turn his ham radio on. And the man on the other side was John calling from the year 1999 and from the same ham radio. It just happens that both men could listen to Brian Greene on TV who was just explaining that string theory had 10 or 11 dimensions and perhaps, the number of time dimensions could be higher, too. It is not explained in the movie how a mature Brian Greene got to 1969 when the actual Brian Greene was 6 years old. Maybe we should send an e-mail to Brian who could explain how he managed to do that.

This communication across time was possible due to the aurora borealis (northern lights) that surrounded their house both in 1969 and 1999, we're told. After an irritated beginning of the conversation, they convince each other that they're indeed the "father and son" calling from the same house across the 30-year time barrier.

Using valid "predictions" of baseball games, John ultimately convinces his father that he is the son calling from the future and tells him to choose a different escape route from the fire. Frank survives as a result and they create a new branch of the spacetime in which Frank didn't die in the fire. Instead, he would die of cancer 20 years later. Another detail: the son also convinces his dad to quite smoking 30 years earlier. However, Frank's wife i.e. John's mom is killed by a serial killer in the new branches, a consequence of the modifications they have caused. Finally, John (a cop) and his dad (firefighter) team up and neutralize the killer, a bad cop of a sort.

Finally, they manage to produce a satisfactory draft of the spacetime in which they are together in 1999 – including John's boy that wouldn't otherwise exist due to John's bitterness, either. A friend of John – a boy from 1969 named Gordo – was also given a great gift by the old John through the intertemporal ham radio. It was a secret word: Yahoo. In the optimized draft of the spacetime we see at the end, Gordo would probably buy stocks of Yahoo before they dropped.

The Yahoo stock went from $1 in 1996 to a high $108 in 1999 but it later returned up to $4 or so in 2001. Frequency was released in April 2000 ($60) so I guess that if its creators had known about the burst dot-com bubble, they would have been more careful about the timing in the portfolio recommendations. ;-)

Tons of science-fiction movies contain time machines of various kinds. They lead to paradoxes. People may usually "land" anywhere they want and modify anything they want. I would say that this "aurora borealis" wormhole through time is somewhat subtler although it is still inconsistent. Don't get me wrong: it is silly to identify deep and speculative wormholes that may be proposed in quantum gravity with mundane meteorological phenomena. But by localizing the bridge, one partially reduces its inconsistent implications. As the movie shows, such modifications still require several branches of the spacetime ("timelines" in the filmmakers' jargon) to exist.

First, why is the generic time machine with a single branch inconsistent?

It's inconsistent because of the closed time-like curves (CTCs). It's a closed i.e. "periodic" curve (its topology is a circle) that is time-like and non-singular everywhere (it therefore keeps the same future-past direction). What's wrong with CTCs? There are events along the curve whose probabilities may be calculated from the properties of the previous events. The events in 1999 follow from those in 1998 which follow from 1997, and so on. If the events in 1969 depended on those in 1999 in the same way (a loop), it would be pretty much impossible for the loop to close. The system of equations would be overdetermined.

More precisely, in classical physics, the deterministic laws just don't evolve the configuration in 1969 to configurations in 1970, 1971, ... and 1999 so that the 1999 configuration could be smoothly connected to 1969 again. Quantum mechanically, the evolution is not deterministic but similarly, the evolution at least at one point of the closed loop would have to include transformations that would be vastly unlikely according to the probabilistic laws of quantum physics.

So closed time-like curves – including their special examples such as Universes which respect the opposite arrows of time at different places – lead to a conflict with the dynamical laws of physics. At this moment, I must remind the dear reader of the incredible stupidity of the "deniers of irreversibility" such as Sean Carroll. I've done it many times but let me expose the incredibility of their stupidity in slightly newer way now.

Imagine that you have some basis of states \(\ket{\psi_i}\) at time \(t_0\) and some basis \(\ket{\psi_\alpha}\) at a later time \(t_1\). The evolution operator \(U\) (imagine the S-matrix) is composed of the matrix entries \(U_{\alpha i}\) which express the complex probability amplitude that the initial state \(\ket{\psi_i}\) at time \(t_0\) evolves to the final state \(\ket{\psi_\alpha}\) at a later time \(t_1\). The probability is computed as\[

P_{i\to\alpha} = |U_{\alpha i}|^2.

\] The probability with an arrowed subscript may sound a bit heuristic. Let's rewrite it a bit differently. The probability above is nothing else than\[

P(\alpha|i)\equiv P(\psi=\psi_\alpha\text{ at }t=t_1| \psi=\psi_i\text{ at }t=t_0).

\] It is the conditional probability that the state will be \(\alpha\) at the later time given i.e. if it were \(i\) at the earlier time; note that this statement is exact and kindly verify it. The irreversibility deniers who believe that the laws of physics may be used in both directions are pretty much explicitly saying that the same matrix elements \(U_{\alpha i}\) encode the probabilities for the opposite evolution as well. It means that they are saying that\[

|U_{\alpha i}|^2 = P(\alpha | i) = P(i|\alpha).

\] Because \(P(\alpha|i)\) is pretty much the most general form of a conditional probability, they are saying that\[

P(A|B) = P(B|A)

\] which, I hope you will agree, is breathtakingly stupid. Conditional probabilities just aren't symmetric at all. If the squared amplitudes \(|U_{\alpha i}|^2\) may be interpreted as \(P(\alpha|i)\), the forward evolution's probability, and the experiments show that they can, they just cannot determine the opposite conditional probabilities because the conditional probabilities \(P(A|B)\) aren't symmetric in \(A\) and \(B\). (More precisely, the pure-to-pure probability is indeed symmetric but the symmetry between \(A\) and \(B\) is broken as soon as these propositions start to represent ensembles of states i.e. "one pure state or another" etc.)

The most direct not stupid link between the two probabilities is Bayes' formula\[

P(A|B) = \frac{ P(B|A) P(A) }{ P(B) }.

\] The extra factor \(P(A)/P(B)\) is what guarantees that the processes with a decreasing entropy by \(\Delta S\) are \(\exp(\Delta S / k)\) times less likely than their increasing-entropy cousins. Retrodictions of the past don't have easily calculable probabilities. Instead, these probabilities must be determined by the Bayesian inference which always depends on some subjective priors and has other subtleties. The laws of physics only dictate well-defined probabilities in one direction, the forward-in-time direction! That's the logical arrow of time, a defining feature of time in any physical Universe. The future predictably (albeit probabilistically) follows from the past but not the other way around.

I was talking about the usual probabilities in quantum mechanics but it's important to know that everything I said would hold for the probabilities in statistical physics (even classical statistical physics), too. They also determine objective probabilities in the forward direction only. If you want to determine the past, you must "reverse engineer" the problem and due to reversibility, the laws of physics won't give you any clearcut canonical values of the probabilities.

The Frequency movie talks about the creation of several branches of the spacetime ("timelines"). I don't exactly understand how to physically interpret such a concept. I think it's inevitable that such a picture suffers from the same inconsistencies as the "many-worlds interpretation of QM taken too seriously". Even though a spacetime with branching points could possibly exist, I think that the branching points would be singular and therefore qualitatively different. The moment at which Frank's life is branching into several "timelines" – he is burned in one of them but survives in others – would have to look very different from other, generic moments of time. After all, we see the furniture in John's room as it is transforming in 1999. Proper physics of quantum gravity would probably require more dramatic events than changing clothes on the furniture – namely extreme firewall-like Planckian events.

To summarize: I do think that the laws of physics will always avoid closed time-like curves of all kinds. For this reason, they will also prohibit the 1969-1999 ham radio from the movie. However, in the discussions about time travel and similar things, people used to clump genuine time machines containing closed time-like curves with some other examples of an unusual spacetime topology. Some of those may be allowed by the laws of physics, despite their "superficial similarities" to the CTCs.

For example, the Einstein-Rosen bridge was legitimized by Maldacena and Susskind in 2013 (who presented evidence that such a bridge is as mundane as an ordinary entanglement – in fact, any entanglement is equivalent to such a bridge). This bridge contains a moment at which the horizons of the two connected black holes are directly touching – so they exist "at the same moment", too. Could you connect the interiors of black holes that existed at different times – in regions of the spacetime that look time-like-separated from the viewpoint of the surrounding spacetime? Could such a shared, intertemporal black hole interior resemble Peter Pan's Neverland (another movie playing with time we could watch a few days ago: trailer)? ;-) I remain mostly open-minded.

More detailed analyses of such questions don't reveal that "anything goes". There are things that remain forbidden. But "some things" that used to be assumed to be impossible sometimes become possible. Stereotypes sometimes melt and the newer picture of what is allowed and what is disallowed by the laws of physics is more structured than the previous overgeneralized, black-or-white beliefs.

For decades, it would be assumed in string theory that "really complicated" Penrose diagrams such as those on the picture above would be impossible. Cauchy horizons inside rotating or charged black holes are unstable, and so on. However, it's plausible that string theorists will return to these issues and they may find out that such dramatically nontrivial Penrose diagrams describe a legitimate way how to "perceive" some quantum information.

Yes, this blog post is just a less religious, more sci-fi-oriented cousin of Quantum gravity and afterlife.


  1. kashyap vasavadaJan 2, 2014, 3:03:00 PM

    Interesting fictional movie. But I have a kind of serious question. Is it still believed that you need a big negative energy blanket to keep the neck of a wormhole open or there are alternative models?

  2. kashyap vasavadaJan 2, 2014, 3:07:00 PM

    Sorry .I thought I had reached the end of the article. But there is more! I withdraw my question for a while.

  3. You need a negative energy for traversable black holes - but not for Einstein-Rosen bridges which are non-traversable.

  4. Dear Luboš, time-travel stories are fun, and the efforts of notable science-fiction writers such as Robert Heinlein to manage the paradoxes often entertaining.

    In the movies, my favorite treatment of the topic is Primer, a no-budget indy made by Shane Carruth, who also wrote the script and the music plus he is one of the two lead actors. Rent or buy the DVD if you can, alternatively view it as a stream on Youtube (with Portuguese subtitles! Lol):

    But first, fair warning: the first ten minutes are probably the most viewer-unfriendly, un-welcoming of any movie I have seen. People talk in a rush, swallow half their syllables, use shorthand to refer to concepts only they know, the action (what little there is) is totally confusing. After that, it only gets worse :)

    However, if you do stick it out through to the end (plus the inevitable second, and third, viewing), you may find the experience strangely rewarding. A small cottage industry, of websites purporting to explain the plot of the movie, has sprung up around it but I'll let you discover them on your own if you're so inclined.

    What I liked about it: other Hollywood movies (including such supposedly cerebral sci-fi features as Contact or Inception) are embarrassingly simple-minded by comparison. It's nice to be treated as an adult for a change. Which is not to say that this is science! It's entertainment, but the kind that does not drop your IQ by ten points for having watched it.

  5. kashyap vasavadaJan 2, 2014, 3:44:00 PM

    Thanks. I should go back and understand the difference between the two situations. Does the difference lie in the way information about the two sides is related and the way actual material travels between the two sides?

  6. An account by another eyewitness, an (Australian) Green Party senator-elect Janet Rice:

  7. Repeat Performance (1947) is a time-travel film that I recently came across on YouTube. It only travels back one year in time, which is a bit unusual. It's also a bit unusual to find a film noir classic that deals with time travel.

  8. Dear Ladislav, that is just wonderful that you're sharing with us your priceless insights. However, I fear that the present-day society is insufficiently far advanced to appreciate your wisdom.

    Accordingly, I would ask you to hold still while I immobilize you and place you inside this machine. What? I guess you could call it an "Anti-Warming" device, heh heh. This will cool you down to 0.0000001 of a degree above absolute zero. In other words, you are now a Bose Einstein condensate and fit inside this little thimble... which will be passed on to future generations, one of whom will surely decide to thaw you and restore you to normal size.

    Greetings to the future, my frozen friend!

  9. “Searching the Internet for evidence of time travelers”

  10. kashyap vasavadaJan 2, 2014, 9:53:00 PM

    Interesting statement Lubos: "But
    “some things" that used to be assumed to be impossible sometimes become
    possible.” Are you talking about which are traversable and which are non -traversable wormholes? Also I understand, in rotating or charged wormholes there are branch cuts, so instead of blowing up you may just end up on a different Riemann sheet (different universe?)!!! Is this what the right Penrose diagram shows?

  11. We are seeing a high-melting ice polymorph appear as the Earth is burned to desiccated cinder. As warming spreads, the polymorph seeds liquid water and spreads with it. Besides, weather is not climate. Ask the US East Coast about it local 03 January 2014 when they are due for about 8 inches and single digits Fahrenheit of not climate.

  12. kashyap vasavadaJan 2, 2014, 10:43:00 PM

    Hi Lubos: Is there a way to search your blog-posts by key words? That would be nice instead of searching manually month by month. In particular I was looking for everything you wrote in past about Einstein-Rosen bridge.

  13. Just when I think I'm in the loop, the farkers get rescued.

    Still a chance their ship will sink, but it would be unseemly to hope for that outcome just to assuage my ego.

  14. Very nice article. Thanks for the fun :-)

  15. How does it feel to be One of the beautiful people?

  16. Yes, the traversable vs non-traversable is the best understood example of my sentence. Non-traversable wormholes were legalized, traversable ones have not.

    And yes, the possibility to have new sheets (a better word than "branch", thanks) in Penrose diagrams is what the right interpretation of some quantum processes could be, possibly legalizing something similar to the sci-fi movies, but this claim is much less established than the ER-EPR. ;-) So it's just a vague prophecy "morally similar" to ER-EPR and other developments, a prophecy you may choose to ignore.

  17. Hi, Lumo,

    I'm still wondering about the details of ER-EPR. Does the ER bridge have any energy content of its own? If so, does it depend on the distance between the two entangled objects? If not, is there an easy way to illustrate why not?

  18. I am tempted to think of these things in terms of systems that can have identical microstates. These systems can be viewed as occurring simultaneously. For instance, poincare recurring systems have some periodicity that can allow for a type if time travel. Another example are bosons which can have identical states, but particles such as photons can only interfere with themselves. So I imagine black holes that have identical macro properties must have identical sets of microstates, or perhaps very complementary microstates

  19. kashyap vasavadaJan 3, 2014, 1:41:00 PM

    Thanks. I am still trying to understand what makes a wormhole traversable and what makes it non traversable. Somehow to make it useful, information on both sides have to be correlated as in ER=EPR. So is it the pinching argument i. e the neck closes very fast or not, the distinguishing factor? Another thing: Is there a way to search on your blog for past articles by key words or one has to go manually month by month?In particular I was looking for all the articles you wrote in past about ER bridge.

  20. Dear Luboš,

    I dont know if you mean Dr. Ladislav Metelka, but is he a "member" of Czechglobe? I dont see him there...:

    Cheers and all the best in the new year! ;-)

  21. All characters appearing in this work are fictitious. Any resemblance to real persons, living or dead, is purely coincidental.

  22. kashyap vasavadaJan 3, 2014, 2:52:00 PM

    Thanks. I am still trying to understand what makes one wormhole traversable and another non-traversable. Is it that in some wormholes, the neck may close so fast that material cannot get through? For ER=EPR, somehow
    the information on the two sides have to be correlated. Another thing: is there a way to search for a past article on your blog by key words or one has to go back month by month? In particular, I was searching for your old posts on ER Bridge.

  23. Ah... thats all right then ;-)

  24. But I may be wrong, please feel free to verify my words. You may always ask whatever candidate you suspect could be the author of the text above: Hi, are you Mr Mrdelka?

  25. Thats definitely not me, as far as I know, but you are skilled enough writer you can convince me otherwise.

    BTW, I still wait for the proper brutal winter, even though the house where I live right now is not well isolated :-)

  26. Hi, searches are via URLs like

    The search boxes are everywhere in the sidebar in the green template - and at the bottom of the pink mobile template (e.g. page above).

    In Chrome, every TRF reader should create a custom search engine where Einstein+Rosen+bridge above is replaced by %s

    ER bridges are non-traversable because their "boundary" is an event horizon, a null surface, so it is a one-way membrane, like for a normal black hole.

  27. Lol! I love this type of fiction.
    Is it possible to convince ourselves to death ? :

    In the film I watched yesterday ("Promised Land") Matt Damon is trying to buy land from some villagers in Pennsylvania for his company for fracking, with a promise of big money... he is overtook by an environmentalist guy who wants to stop him by turning the whole village against him. Only it turns out that the green guy himself has been sent by the same company to do this job! A few clues show this guy is a lier... The whole campaign is a stage to manipulate the villagers into discrediting the environmentalists. Anyway this film shows how far big companies would go to manipulate people to get their way... or to put it mildly: to prepare people.

    The fracking company's strategy in the film is interesting. You inoculate the opposite ideology in order to better control the opinion... when you confuse people a little bit it is the beginning of a negotiation.

  28. A very interesting film, Shannon!

    I sort of started to like the new twists in the Antarctica:

    Recall that the AGW idiots went on the Russian ship. The Chinese ship sent them a Chinese helicopter. But this helicopter took them to the Australian ship.

    Now, the Chinese ship that sent the helicopter is stuck in ice itself! ;-) So it also means that the Australian ship that now carries the AGW idiots has to be around because it must be ready to help the Chinese ship.

    The AGW idiots won't go home yet. ;-) A lesson is that whoever tries to help these stuck idiots becomes a stuck idiot himself.


    Kim Jong Un's executed uncle was eaten alive by 120 hungry dogs

  30. Wow, some leftists are disgusting, perhaps even creatively so.

  31. Lol, unbelievable... They are cursed !

  32. Uuh... sick. I am confident Kim Jong Un's death will be extremely violent too.

  33. Apparently so. Given that Koreans eat dogs I assume this is a plan to feed his people


    New essay by David Gelernter here.

  35. MoptopTheLibertarianJan 3, 2014, 9:18:00 PM

    You are aware that the movie is fiction?

  36. Of course it is fiction, but investing time and money into a well targeted communication can be extremely beneficial.

  37. You do understand that the tactic works both ways? The environmentalists use the same tactic in the real world. It fascinates me that people think only the evil corporations would use this technique.

  38. Of course this interesting tactic could be used by anyone, anywhere.

    I didn't make this movie btw, I only watched it and described what the story is about.

  39. With all this ice they will soon be able to walk all the way home. Or someone will send a bus to pick them up.

  40. April 1st came early this year.

  41. This reminds me the demonstration in vol. I of Weinberg's QFT, that unitarity essentially implies Boltzmann's H-theorem. Irreversibility as a mystery in physics seems to be simply a myth. It's interesting to see that well-founded arguments like the ones in Weinberg's book, or its simplified version as explained in your post, are often ignored by some physicists...

  42. Interesting video

    What Is Time? Determinism, Quantum Physics, Consciousness

  43. Youtube link above show different video here , i this this link show right video.