Category Archives: Quantum Quandaries

The Church Of The Smaller Hilbert Space Needs Your Vote!

Chad Orzel has posted a poll about the “religious” beliefs of scientists. In case you need a reminder, this is the Church of the Larger Hilbert Space and this is the Church of the Smaller Hilbert Space (see my comment on Chad’s post for further discussion).

Use your vote wisely.

Time Travel and Information Processing

Lately, the quant-ph section of the arXiv has been aflurry with papers investigating what would happen to quantum information processing if time travel were possible (see the more recent papers here). I am not sure exactly why this topic has become fashionable, but it may well be an example of the Bennett effect in quantum information research. That is, a research topic can meander along slowly at its own pace for a few years until Charlie Bennett publishes an (often important) paper1 on the subject and then everyone is suddenly talking and writing about it for a couple of years. In any case, there have been a number of counter-intuitive claims that time travel enables quantum information processing to be souped up. Specifically, it supposedly enables super-hard computational problems that are in complexity classes larger than NP to be solved efficiently2345 and it supposedly allows nonorthogonal quantum states to be perfectly distinguished67. These claims are based on two different models for quantum time-travel, one due to David Deutsch8 and one due to a multitude of independent authors based on post-selected teleportation (this paper9 does a good job of the history in the introduction).

In this post, I am going to give a basic introduction to the physics of time-travel. In later posts, I will explain the Deutsch and teleportation-based models and evaluate the information processing claims that have been made about them. What is most interesting to me about this whole topic, is that the correct model for time travelling quantum systems, and hence their information processing power, seems to depend sensitively on both the formalism and the interpretation of quantum theory that is adopted10. For this reason, it is a useful test-bed for ideas in quantum foundations.

Basic Concepts of Time-Travel

Everyone is familiar with the sensation of time-travel into the future. We all do it at a rate of one second per second every day of our lives. If you would like to speed up your rate of future time travel, relative to Earth, then all you have to do is take a space trip at a speed close to the speed of light. When you get back, a lot more time will have elapsed on Earth than you will have experienced on your journey. This is the time-dilation effect of special relativity. Therefore, the problem of time-travel into the future is completely solved in theory, although in practice you would need a vast source of energy in order to accelerate yourself fast enough to make the effect significant. It also causes no conceptual problems for physics, since we have a perfectly good framework for quantum theories that are compatible with special relativity, known as quantum field theory.

On the other hand, time travel into the past is a much more tricky and conceptually interesting proposition. For one thing, it seems to entail time-travel paradoxes, such as the grandfather paradox where you go back in time and kill your grandfather before your parents were born, so that you are never born, so that you cannot go back in time and kill your grandfather, so that you are born, so that you can go back in time and kill your grandfather etc. (see this article for a philosophical and physics-based discussion of time travel paradoxes). For this reason, many physicists are highly sceptical of the idea that time travel into the past is possible. However, General Relativity (GR) provides a reason to temper our skepticism.

Closed Timelike Curves in GR

It has been well-known for a long time that GR admits solutions that include closed timelike curves (CTCs), i.e. world-lines that return to their starting point and loop around. If you happened to be travelling along a CTC then you would eventually end up in the past of where you started from. Actually, it is a bit more complicated than that because the usual notions of past and future do not really make sense on a CTC. However, imagine what it would look like to an observer in a part of the universe that respects causality in the usual sense. First of all, she would see you appear out of nowhere, claiming to have knowledge of events that she regards as being in the future. Some time later she would see you disappear out of existence. From her perspective it certainly looks like time-travel into the past. What things would feel like from your point of view is more of a mystery, as the notion of a CTC makes a mockery of our usual notion of “now”, i.e. it is a fundamentally block-universe construct.

The possibility of CTCs in GR was first noticed by Willem van Stockum in 193711 and later by Kurt Gödel in 194912. Perhaps the most important solution that incorporates CTCs is the Kerr vacuum, which is the solution that describes an uncharged rotating black hole. Since most black holes in the universe are likely to be rotating, there is a sense in which one can say that CTCs are generic. The caveat is that the CTCs in the Kerr vacuum only occur in the interior of the black hole so that the physics outside the event horizon respects causality in the usual sense. Many physicists believe that the CTCs in the Kerr vacuum are mathematical artifacts, which will perhaps not occur in a full theory of quantum gravity. Nevertheless, the conceptual possibility of CTCs in General Relativity is a good reason to look at their physics more closely.

There have been a few attempts to look for solutions of GR that incorporate CTCs that a human being would actually be able to travel along without getting torn to pieces. This is a bit beyond my current knowledge, but, as far as I am aware, all such solutions involve large quantities of negative energy, so they are unlikely to exist in nature and it is unlikely that we can construct them artificially. For this reason, CTCs are currently more of a curiosity for foundationally inclined physicists like myself than they are a practical method of time-travel.

Other Retrocausal Effects in Physics

Apart from GR, other forms of backwards-in-time, or retrocausal, effect have been proposed in physics from time to time. For example, there is the Wheeler-Feynman absorber theory of electrodynamics, which postulates a backwards-in-time propagating field in addition to the usual forwards-in-time propagating field, and Feynman also postulated that positrons might be electrons travelling backwards in time. There is also Cramer’s transactional interpretation of quantum theory13, which does a similar thing with quantum wavefunctions, and the distinct, but conceptually similar, two-state vector formalism of Aharonov and collaborators14. Finally, retrocausal influences have been suggested as a mechanism to reproduce the violations of Bell-inequalities in quantum theory without the need for Lorentz-invariance violating nonlocal influences15.

However, none of these proposals are as compelling an argument for taking the physics of time-travel into the past seriously as the existence of CTCs in General Relativity. This is because, none of these theories gives provides a method for exploiting the retrocausal effect to actually travel back in time. Also, in each case, there is an alternative approach to the same phenomena that does not involve retrocausal influences. Nevertheless, it is possible that the models to be discussed have applications to these alternative approaches to physics.

Consistency Constraints and The Interpretation of Quantum Theory

Any viable theory of time travel into the past has to rule out things like the grandfather paradox. Consistency conditions have to be imposed on any physical model to so that time-travel cannot be used to alter the past. This raises interesting questions about free will, e.g. what exactly stops someone from freely deciding to pull the trigger on their grandfather? Whilst these questions are philosophically interesting, physicists are more inclined to just lay out the mathematics of consistency and see what it leads to. The different models of quantum time travel are essentially just different methods of imposing this sort of consistency constraint on quantum systems.

That is pretty much it for the basic introduction, but I want to leave you with a quick thought experiment to illustrate the sort of quantum foundational issues that come up when considering time-travel into the past. Suppose you prepare a spin-\(\frac{1}{2}\) particle in a spin up state in the z direction and then measure it in the x direction, so that it has a 50-50 chance of giving the spin up or spin down outcome. After observing the outcome you jump onto a CTC, travel back into the past and watch yourself perform the experiment again. The question is, would you see the experiment have the same outcome the second time around?

A consistency condition for time travel has to say something like “the full ontic state (state of things that exist in reality) of the universe must be the same the second time round as it was the first time round”, albeit that your subjective position within it has changed. If you believe, as many-worlds supporters do, that the quantum wavefunction is the complete description of reality then it, and only it, must be the same the second time around. Therefore, it must be the case that the probabilities are still 50-50 and you could see either outcome. This is not inconsistent because the many-worlds supporters believe that both outcomes happened the first time round in any case. If you are a Bohmian then the ontic state includes the positions of all particles in addition to the wavefunction and these, taken together, can be used to determine the outcome of the experiment uniquely. Therefore, a Bohmian must believe that the measurement outcome has to be the same the second time around. Finally, if you are some sort of anti-realist neo-Copenhagen type then it is not clear exactly what you believe, but, then again, it is not clear exaclty what you believe even when there is no time-travel.

There are some subtleties in these arguments. For example, it is not clear what happens to the correlations between you and the observed system when you go around the causal loop. If they still exist then this may restrict the ability of the earlier version of you to prepare a pure state. On the other hand, perhaps they get wiped out or perhaps your memory of the outcome gets wiped. The different models for the quantum physics of CTCs differ on how they handle this sort of issue, and this is what I will be looking at in future posts. If you have travelled along a CTC and happen to have brought a copy of these future posts with you then I would be very grateful if you could email them to me because that would be much easier for me than actually writing them.

‘Till next time!

References

  1. Bennett, C. H. et. al. (2009). “Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems”. Phys. Rev. Lett. 103:170502. eprint arXiv:0908.3023. []
  2. Brun, T. A. and Wilde, Mark M. (2010). “Perfect state distinguishability and computational speedups with postselected closed timelike curves”. eprint arXiv:1008.0433. []
  3. Aaronson, S. and Watrous, J. (2009). Closed timelike curves make quantum and classical computing equivalent. Proc. R. Soc. A 465:631-647. eprint arXiv:0808.2669. []
  4. Bacon, D. (2004). Quantum Computational Complexity in the Presence of Closed Timelike Curves. Phys. Rev. A 70:032309. eprint arXiv:quant-ph/0309189. []
  5. Brun, T. A. (2003). Computers with closed timelike curves can solve hard problems. Found. Phys. Lett. 16:245-253. eprint arXiv:gr-qc/0209061. []
  6. Brun, T. A. and Wilde, Mark M. (2010). “Perfect state distinguishability and computational speedups with postselected closed timelike curves”. eprint arXiv:1008.0433. []
  7. Brun, Todd A., Harrington, J. and Wilde, M. M. (2009). “Localized closed timelike curves can perfectly distinguish quantum states”. Phys. Rev. Lett. 102:210402. eprint arXiv:0811.1209. []
  8. Deutsch, D. (1991). “Quantum mechanics near closed timelike lines”. Phys. Rev. D 44:3197—3217. []
  9. Lloyd, S. et. al. (2010). “The quantum mechanics of time travel through post-selected teleportation”. eprint arXiv:1007.2615 []
  10. I should mention that Joseph Fitzsimons (@jfitzsimons) disagreed with this statement in our Twitter conversations on this subject, and no doubt many physicists would too, but I hope to convince you that it is correct by the end of this series of posts. []
  11. Stockum, W. J. van (1937). “The gravitational field of a distribution of particles rotating around an axis of symmetry”. Proc. Roy. Soc. Edinburgh A 57: 135. []
  12. Kurt Gödel (1949). “An Example of a New Type of Cosmological Solution of Einstein’s Field Equations of Gravitation”. Rev. Mod. Phys. 21: 447. []
  13. Cramer, J. G. (1986). “The transactional interpretation of quantum mechanics”. Rev. Mod. Phys. 58:647-687. []
  14. Aharonov, Y. and Vaidman, L. (2001). “The Two-State Vector Formalism of Quantum Mechanics: An Updated Review”. in “Time in Quantum Mechanics”, Muga, J. G., Sala Mayato, R. and Egusquiza, I. L. eprint arXiv:quant-ph/0105101. []
  15. For example, see Price, H. (1997). “Time’s Arrow and Archimedes’ Point”. OUP. []

Return to blogging

I have decided to try to make a return to blogging and I am intending to write new posts about once or twice a week. Making a statement like this is dangerous, as veteran bloggers know well, as it usually leads to several month’s radio silence. Nevertheless, I hope that making this announcement will give me enough motivation to actually go through with it.

For those of you who are not up-to-date with the latest Matt Leifer gossip, I essentially gave up blogging at the end of 2007 because I came down with a mysterious illness that, amongst other things, ruined my ability to do anything that requires concentration. I had to take an indefinite leave of absence from work in April 2008 and I can attest that this is not a fantastic thing to do for your academic career when you are still a postdoc. I have since been diagnosed with Chronic Fatigue Syndrome, a controversial syndrome that does not have any very effective treatments (at least none of them have really worked for me so far). Although I am not really feeling any better, I have decided to try and work part-time for a couple of days a week and I am in the process of transferring the remainder of my FQXi grant to University College London to pay my salary for about eight months.

As you can imagine, I have built up a lot of internal rants about quantum theory in the couple of years since I stopped blogging, so I do not think I will have much trouble coming up with topics to write about. One person who should be especially glad about my return to blogging is Chad Orzel, because it means that I will have far less time to write overly long comments on his blog whenever he writes something about that touches on the foundations of quantum theory.

Hope to see you round here sometime soon!

Strange happenings at arXiv.org

Update: All seems to be well at the arXiv site now. Still no word about what happened.

This morning I read a tweet from Daniel Lemire saying that some papers have gone missing from arXiv.org, the primary repository for preprints in physics and some areas of mathematics and computer science. I checked and it seemed that a lot of more recent papers were missing in several searches that I tried.

Just now, I heard from Martin Roetteler that arXiv.org is redirecting to a random mirror site, e.g. the Australian, Brazilian or Chinese mirror. At the time of writing, at least the mirror sites seem to be working correctly.

Speculation is that perhaps the arXiv has been hacked, but at the very least least they are having some pretty major problems with the main servers at Cornell. It comes as a big shock because the arXiv has always been one of the most stable sites that I use regularly and the physics community depends on it. I can’t remember anything like this having happened before.

At the time of writing there is no official comment from the arXiv.

Debunking the Quantum Mystics

Update: Stenger’s book has been reviewed by Steve Esser.

I interrupt the current hiatus of this blog for news of what I think is an important new quantum foundational book.

One of the ways that I follow the latest hot topics in Quantum Schmantum is via a carefully crafted Google Alerts feed, which is quite good at throwing up articles that are getting attention in the mainstream science press. It does need to be carefully crafted though, because a basic search on the word “quantum” is dominated by a James Bond movie, a video game, a 1990’s television series and, worst of all, a whole lot of quantum mystical mumbo jumbo influenced by things like What the Bleep Do We Know, The Secret, Deepak Chopra, etc. Unfortunately, this sort of stuff seems to be more popular than ever and is even getting celebrity endorsment from the likes of Carmen Elektra

.

Unfortunately, however carefully crafted your search is, quite a lot of quantum nonsense will always make it through, so I usually just ignore links with suspect titles. Recently though, the feed has been turning up a lot of links with titles like “Quantum Physics and God”, so much so that I was eventually tempted to click through to see what all the fuss was about. It turns out that these articles were all referring to a new book Quantum Gods: Creation, Chaos, and the Search for Cosmic Consciousness by Victor Stenger who is perhaps best known for his nu athieism book God: The Failed Hypothesis. How Science Shows That God Does Not Exist. Amongst other things, the new book is aimed at debunking the claims of the quantum mystics.

For a long time, I have thought that a book that clearly sets out the case against the quantum mystics is a good idea. I don’t imagine that many people who actually believe in this stuff will read the book, although some may get drawn in by the fact that the title does not suggest that the ideas are going to be debunked. More importantly, however, this is ammunition for scientifically literate people, who may not be well versed in quantum theory, to use when they come up against quantum nonsense.

I have not read the book yet, and I am unlikely to do so in the near future due to my current illness. I would like to add it to my carefully curated Amazon Store of books about quantum theory, but I have a policy of not including any books that I haven’t read, since there are a lot of bad expositions of quantum theory in the popular literature. My main concern is whether Stenger manages to clearly separate the argument against quantum mysticism from his more general concerns about whether or not science is compatible with new age mystical beliefs. In my view, it is one thing to hold a set of new age mumbo jumbo beliefs and quite another thing to believe they are supported by quantum theory. The latter is clearly false, independently of the general debate about new age ideas. For one thing, a large part of the message of things like The Secret and What The Bleep… seems to be that you can make good things happen by the power of positive thinking. I can certainly imagine that this is true to an extent in the realm of human affairs, but that is a matter of psychology and sociology rather than quantum physics. I am encouraged by the fact that Stenger is also the author of a 1997 article from the Skeptical Inquirer, which was my previous go to link for people in need of some quantum debunking. Since I think this is likely to be an important book, I may decide to relax my policy and add the book anyway, provided enough of my trusted colleagues and commenters tell me that the book is accurate. So go out and read!

I’ll leave you with a confrontation between Richard Dawkins and Deepak Chopra, which I couldn’t resist adding to this post.

The three scientific we’s

I am a grammatical pedant. Therefore, for the record, here is the definitive style guide to using “we” in your scientific writing.

There are three different common uses of “we”. Only one of them is evil. Writers on this subject do not usually distinguish them properly, so the discussion often gets horribly confused. I don’t know the correct grammatical terminology (I’m not that much of a pedant), so I’ll just make up my own.

  • “We” used correctly as a pronoun: If there is more than one author on the paper and you are describing something that you actually did as a group, then this is an unambiguously correct usage of “we”.
    Examples:

    “We placed the beaker on the tripod and turned on the bunsen burner.”

    “We ran a numerical optimization algorithm to generate the data in fig. 1.”

    I don’t think there is any problem with this usage of we. If you want to eliminate it then you have to write in the past passive tense, e.g. “The beaker was placed on the bunsen burner and the tripod was turned on.” This might be what you were told to do in high school, but it just makes the text sound cumbersome and boring. Modern style guides do not recommend this any more. The era of past passive tyranny is long gone and I say good riddance!

  • The Royal “we”: There is only one author of the paper and you are describing something that you actually did. The examples are exactly the same as in the previous case.

    I’m not a big fan of this sort of “we”, as it makes you sound like Queen Victoria. Personally, I make a point to use “I” in this context. It sounds funny to me, but a lot of people do it and it is not a very big deal.

  • “We” as in “you and I, dear reader”:
    Examples:

    “In section 20, we show that quantum theory is even weirder than we thought before”

    “Substituting eq. (5) into eq. (4), we see that Newton’s second law is obtained.”

    “If we plot luminosity against distance from the Earth, we obtain fig. 3.”

    This is the evil “we” and should be eliminated at all costs. Eliminating them does not make your writing sound more passive. In fact, the opposite is true because it usually forces you to bring the object to the beginning of the sentence. Most people, including myself, use a lot of “dearest reader we’s” when writing a first draft. OK, maybe it’s not a big crime to let one slip occasionally, but in general I think it is a sign of lazy writing. You will find your sentences shorter, punchier and more direct if you eliminate them completely. In case you don’t believe me yet, here are the de-“we”d examples:

    “Section 20 shows that quantum theory is even weirder than previously thought.”

    “Newton’s second law is obtained from substituting eq. (5) into eq. (4).”

    “Fig. 3 shows a plot of luminosity against distance from the Earth.”

You may be thinking that this post is rather aggressive. If so, I apologize. My Ph.D. thesis advisor made me remove every single “we” from every paper I wrote with him, so I still have some scars from that process.

WARNING: Do not write a comment unless you have understood the distinction between the three uses of “we” described above.

Get Paid to do Foundations III

‘Tis the season to get employed as a foundations researcher.  Perimeter Institute is currently advertising vacancies for Junior Faculty positions in Quantum Foundations.  See here for more details.  Deadline for applications is Jan 15th.

Get paid to do Foundations II

It seems that this blog is becoming the official website for Quantum Foundations job announcements.  Sadly, in the current climate this still means that I don’t have to bug you with job adverts too often.  In any case, there are two postdocs available via the PIAF (Perimeter Institute — Australia Foundations) partnership, which look like a pretty sweet deal for any finishing postdocs/grad students in Foundations.  They involve spending 9 months of the year in Sydney and 3 months here in Waterloo.  Theoretically, this means that you could completely avoid experiencing winter for the three years of the postdoc.  The job ad is posted here and the deadline is 7th December 2007.

Get paid to do quantum foundations

It’s not often that I get to write a post with a title like this, but right now there are two opportunities worth mentioning. Firstly, if you are a student looking for a Ph.D. position in foundations then Caslav Brukner has one available in Vienna. The advert is attached below.

Secondly, the application process for the next round of fqxi grants now appears to be open. I haven’t received an email from them about this yet, but I just noticed that the form was up on their website. They have funded quantum foundations projects in the previous round, along with projects on many other foundational questions in physics.

OK, here is the Vienna advert:

PhD position in the group “Quantum Optics, Quantum Nanophysics, Quantum
Information” (www.quantum.at) at the Faculty of Physics, University of
Vienna is available immediately. The student will undertake research on
the foundations of quantum physics and theoretical quantum information
in collaboration with Prof. Caslav Brukner
(http://homepage.univie.ac.at/Caslav.Brukner/).

Candidate is expected to have an undergraduate degree in Physics, Maths,
Computer Science or Engineering. She/he will be able to work
independently and collaboratively. Interest to work on foundations of
physics and experience in quantum theory and/or information theory will
be advantageous. Enthusiasm will be essential.

The position is supposed to be fully integrated into the Doctoral
Program “Complex Quantum Systems” (www.coqus.at). Applications, prepared
to meet the standards (http://www.coqus.at/index.php?id=333) of the
application to the CoQus Doctoral Program, should be sent to Canan
Goeser (Secretary) (canan.goeser@univie.ac.at).

The position is funded by the FWF-Project “Quantum Information:
Foundations and Transition to Classicality” of the Austrian Science Fund
(FWF).

Quantum Cryptography to be used in Swiss Election

According to Wired, one of id Quantique‘s quantum cryptography systems will be used to transmit votes securely from voting machines in Geneva in the upcoming national election.  This is certainly good PR for quantum crypto, especially given the security issues surrounding the use of automated voting machines.  Maybe I’m missing something though, because I thought that the main security problems had to do with the possibility of hacking the machines themselves rather than with the transmission of votes.  Public key crypto would probably have been just as good in practice, unless the Swiss government believes that someone in the locale has built a quantum computer.