Hiding in the Mirror

I’ve just finished reading Lawrence Krauss’s new book Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond, and it’s very, very good. Scientifically, the book covers a lot of the same material as Lisa Randall’s Warped Passages, but it’s about half as long and has a wider perspective, with writing that is pithy and entertaining. Krauss’s topic is not just the science of extra dimensions, but the history of various ways the idea has turned up in art and literature, and the whole question of why people find it so fascinating.

He begins by telling the story of an episode of the Twilight Zone TV program that had quite an impact on him when he was very young. It involved a little girl who falls into another dimension and is saved by intervention of a physicist. Krauss notes that “We all yearn to discover new realities hidden just out of sight”, but that “Ultimately our continuing intellectual fascination with extra dimensions may tell us more about our own human nature than it does about the universe itself.” He writes about a wide range of different writers and artists who have been fascinated by the idea of extra dimensions, and some of the historical and cultural context for their work. Much of this I didn’t know anything about, although his description of the science fiction short story “And He Built a Crooked House” by Robert Heinlein brought back memories of my childhood, since I had found that story very striking, but hadn’t thought about it in a very long time (it involves a house based on a tessaract, a 4d version of a cube). Another interesting piece of history he unearths is that Marcel Duchamp’s famous piece The Bride Stripped Bare by Her Bachelors, Even (also known as the Large Glass), was heavily influenced by ideas about projecting from four dimensions, and that Duchamp spent a lot of time trying to learn about this, including reading Poincare.

Krauss writes that, while fascinated by the idea, he himself remains a skeptic (or at least agnostic) about the actual existence of physical extra dimensions. He tells the history of attempts by theorists to use extra dimensions, from 19th century conjectures that atoms were points where a four-dimensional etherlike field leaked into three-dimensional space, to Kaluza-Klein models and the heterotic string, ending up with recent braneworld scenarios. He describes the ideas behind this research concisely, and also explains exactly what some of the problems with these ideas are. Along the way he comes up with various obscure and interesting pieces of the history of physics I’d never heard before, for instance that in 1928 an English experimentalist named R. T. Cox found evidence of parity violation, but his results were not taken seriously.

On the topic of string theory and braneworlds, Krauss promises to be not like Fox News (i.e. actually “Fair and Balanced”), but he has truly scathing things to say:

But in the ever-optimistic string worldview, there are no embarassments… For these ‘true believers’, every new development provides an opportunity to confirm one’s expectations that these ideas ultimately reflect reality.

… string theory might instead do for observational cosmology what it has thus far done for experimental elementary particle physics: namely, nothing.

In short, the as-of-yet hypothetical world of hidden extra dimensions had, for many who called themselved physicists, ultimately become more compelling than the world of our experience.

This embarassment is solved in the way other similar confusing aspects of string theory and M-theory are sometimes dealt with: Namely, it is assumed that when we fully understand the ultimate theory, everything will become clear.

Over the past five years, hundreds if not thousands, of scientific papers have been written considering cosmological possibilities that might be associated with Braneworld scenarios. One cannot do justice to all of them, but the greatest justice I could probably do to many of them is to not mention them here.

What the notion of large or possibly infinite extra dimensions has done is borrow some of the facets of string theory while ignoring the bulk of the theory (forgive the pun), about which, as I have explained, we have only the vaguest notions. It seems to me to be a very big long shot that an apparently ad hoc choice of what to keep and what to ignore will capture the essential physics of our universe.

This [the Landscape] has resulted in yet another fascinating sociological metamorphosis of the theory, with warts becoming beauty marks.

… the anthropic principle is something that physicists play around with when they don’t have any fundamental theory to work with, and they drop it like a hot potato if they find one.

This finally brings up back to M-theory. Faced with the prospect that the theory may ultimately predict a virtually uncountable set of possible universes, some string theorists did a 180-degree about-face. Instead of heralding a unique Theory of Everything that could produce calculable predictions, they are now resorting to what even a decade ago they may have called the last refuge of scoundrels. But, when string theorists take a position, they do it with flair.

…if the landscape turns out to be the main physical implication of the grand edifice of string theory or M-theory… we might be left with the mere suggestion that anything goes. What was touted twenty years ago as a Theory of Everything would then instead have turned quite literally into a Theory of Nothing.

Krauss ends his book with an epilogue describing conversations with Gross, Wilczek and Witten about string theory. Wilczek is a skeptic, annoyed by the excessive claims made for the theory. Witten is quoted as saying that string theory “is a remarkably simple way of getting a rough draft of particle physics unified with gravity. There are, however, uncomfortably many ways to reach such a rough draft, and it is frustratingly difficult to get a second draft.” He justifies work on string theory partly through progress it has led to in the understanding of strongly coupled gauge theories.

Gross is described as convinced “that the theory is simply too beautiful not to be true”, an attitude that strikes Krauss “as sounding like religion more than science.” With this, Krauss ends his book by quoting Hermann Weyl:

My work always tried to unite the true and the beautiful, but when I had to choose one or the other, I usually chose the beautiful.

and concludes:

So it is that mathematicians, poets, writers, and artists almost always choose beauty over truth. Scientists, alas, do not have this luxury, and can only hope that we do not have to make this choice.

Here, to some extent I part ways with Krauss. As I’ve explained elsewhere, I don’t find the 10 dimensional heterotic superstring compactified on a Calabi-Yau to be in any sense beautiful, and attempts to connect string theory with physics lead to appallingly ugly constructions, strong evidence that they are on the wrong track. Absent useful experimental results, the pursuit of compelling new mathematically beautiful insights into fundamental physics is one of the few promising ways forward. But to go down this road successfully you have to be honest about what is mathematically beautiful and what isn’t.

All in all, this is by far the best book that I know of on the topic of recent speculative work on fundamental particle physics, and I strongly recommend that anyone who enjoys reading about this should get themselves a copy.

Update: An interview with Krauss about the book just appeared in the Cleveland Plain Dealer.

Update: It was pointed out to me that the way I compared Krauss’s book to Randall’s here wasn’t really fair to hers since she was trying to do something different, so for non-specialist readers, the books have different functions. I submitted this review to Amazon, and edited it a bit so that it would be more appropriate for people looking for a comparison of the two books. The main change was the addition of the following paragraph:

“While they are ultimately concerned with the same speculative ideas about extra dimensions, Krauss and Randall’s books are in many ways different. Randall is writing about her own research work, so on the one hand she is a partisan for these ideas, on the other she gets to tell the inside story of exactly how she came up with them. She goes to a lot of trouble to dig in and try and explain in as simple terms as possible the details of the physics that motivates this research, as well as exactly what it is trying to achieve, how it has evolved in recent years and where it seems to be going. Krauss also covers these topics, but is (justifiably in my view) more of a skeptic, and sets the whole story in a wider context of the long history of this kind of speculation. If you’ve read Randall’s book, you should seriously consider reading Krauss for a different point of view. If you read Krauss and want a much more extended exposition on some of these topics, Randall is the place to go.”

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41 Responses to Hiding in the Mirror

  1. MathPhys says:

    “I don’t find the 10 dimensional heterotic superstring compactified on a Calabi-Yau to be in any sense beautiful.”

    I’ve read the above statement many times on this blog, but now it strikes me that I agree with you. The whole structure, looked at from a distance, seems unnatural and contrived: You start in 10 dimensions with lots of symmetries, then you have to get rid of 6 dimensions and most of the symmetries.

    On the other hand, starting with a type II string that has no internal symmetries in 10 dimensions, and obtaining these at the expense of the extra dimensions looks better. At this moment.

  2. Lubos Motl says:

    Dear Peter,

    are you serious that this book covers “very much the same material” as the Warped Passages? I find such a statement incredible. First of all, Krauss understands physics of extra dimensions roughly as well as you do, he’s never worked or thought about them seriously, so it is physically impossible for him to write anything meaningful about them. Maybe you wanted to say that it tries to cover very much the same material as Abbott’s Flatland?

    Best wishes
    Lubos

  3. woit says:

    Hi Lubos,

    Yes, I’m very serious that the book covers the same material as Warped Passages, but does a better job. I was going to put something in the posting about how string theorists’ reaction to the book would be to denounce Krauss as incompetent, even before they read it…

  4. blank says:

    “… they are now resorting to what even a decade ago they may have called the last refuge of scoundrels.”

    That sums it up pretty well. Particle theory over the past decade has been marked not by objective progress, but rather receeding standards.

  5. Anonymous says:

    The piling up of symmetries and dimensions that one has to then discard to match the real world resembles the cycles upon epicycles needed in the Ptolemaic theory of the solar system, ’cause circular motion was sacrosanct. Oh, for a Kepler!

  6. Tony Smith says:

    Peter, as you and Krauss noted, “… Marcel Duchamp’s famous piece The Bride Stripped Bare by Her Bachelors, Even (also known as the Large Glass), was heavily influenced by ideas about projecting from four dimensions …”. Here are some (in my opinion) relevant quotes from Duchamp, as found in the book Dialogues with Marcel Duchamp, 1966 interview with Pierre Cabanne, Plenum (Da Capo) (1971, 1987):

    “… I never was the scientific type. … What we were interested in at the time was the fourth dimension. … Povolowski … was a publisher, in the rue Bonaparte. … He had written some article in a magazine popularizing the fourth dimension, to explain that there were flat beings who have only two dimensions, etc. … That was working in my head while I worked, although I almost never put any calculations into the “Large Glass”. Simply, I thought of the idea of a projection, of an invisible fourth dimension, something you couldn’t see with your eyes. … I thought that … the fourth dimension could project an object of three dimensions, or, to put it another way, any three-dimensional object, which we see dispassionately, is a projection of something four-dimensional, something we’re not familiar with. It was a bit of sophism, but still it was possible. “The Bride” in the “Large Glass” was based on this, as it were the projection of a four-dimensional object. … Only the “Large Glass” interested me, … I wanted to be free of any material obligation, so I began a career as a librarian, which was a sort of excuse for not being obliged to show up socially. … I … went to take courses at the School of Paleography and Librarianship. … I knew very well that I would never be able to pass the examination at the school, but I went there as a matter of form. It was a sort of grip on an intellectual position, against the manual servitude of the artist. At the same time, I was doing my calculations for the “Large Glass”. …
    The “Large Glass” constitutes a rehabilitation of perspective, which had then been completely ignored and disparaged. For me, perspective became absolutely scientific. … It’s a mathematical, scientific perspective. …”.

    Could the “… completely ignored and disparaged …” perspective in art correspond, in today’s world of physics, to the 1970s Standard Model plus Gravity view of physics based on detailed contact with experimental results ?

    Has the superstring community completely ignored and disparaged the building of physics models based on detailed contact with experimental results ?

    Does today’s world of physics need a new Duchamp to rehabilitate the theoretical physics by building models based on detailed contact with experimental results from a “… mathematical, scientific perspective …” ?

    Tony Smith
    http://www.valdostamuseum.org/hamsmith/

  7. steve says:

    My only problem with Krauss was in one of his popular books on physics in science fiction. He claimed that the giant flying saucers in the movie Independence Day wouldn’t have been able to levitate over the Earth without flattening everything beneath. I have no problem with F=MA, but hasn’t he heard about neutrino drives? All the propulsive efficiency with none of that annoying matter interaction! (He also didn’t stop to consider that the saucers could be made of single-molecule-ply superstrong materials with ultra-high strength to mass, but I wouldn’t expect a particle guy to think about advanced materials.)

  8. D R Lunsford says:

    Most talk of extra dimensions is idle speculation, because the spine of physics, irreducibility, is optional.

    -drl

  9. Aaron says:

    “string theorists”

    Be careful with those generalizations, please.

  10. woit says:

    Hi Aaron,

    Point taken, I should have mentioned that I was thinking of the reaction of certain string theorists, not all of them. I’m certainly curious to see how string theorists in general will react to Krauss’s book. Will they respond to it with the seriousness it deserves, or like Lubos, just attack the author as not knowing what he is talking about? So far the count is 0-1. But the book isn’t even quite in stores yet….

  11. Tung says:

    RT Cox, as mentioned here, had done important work on the foundation of probability theory, which has become the cornerstone of the view that probability is a kind of generalisation of aristotelian logic.

  12. Quantoken says:

    Lubos said: “…so it is physically impossible for him to write anything meaningful about them”

    Absolutely correct! It is physically impossible for ANYONE to say anything meaningful about extra dimentions. Because extra dimentions are simply imaginative and none-physical. How could any one say anything physical about something that’s pure imaginative? There is not the slightest evidence that any extra dimention exists in nature.

    And I object to Peter using the term “science of extra dimentions”. There is no “science” of extra dimentions. Because extra dimentions are simply not qualified to be scientific. You can say “research of extra dimentions”, but it’s not science. Not all research activities are science.

    Quantoken

  13. Shantanu says:

    FWIW, Spires hepnames page indicates that Lawrence Krauss was the thesis
    advisor of Raman Sundrum (of Randall/Sundrum)
    See http://www.slac.stanford.edu/spires/hepnames/

  14. Richard says:

    So, Lubos, it is not possible to say meaningful things about things you are not professionally working on? Oh. So tell me, which is your latest paper about global warming?

  15. The Anti-Lubos says:

    I’ve asked it before, but I’ll ask it again.

    Does anyone like him? And if so, how and why?

  16. plato says:

    I for one, find this a very important blog entry from the perspective of responsibility, in explaining these extra dimensions.

    I sense this in Peter’s blog entry, and of course, the underlying skepticism about this is still no secret. There have been attempts to define this issue much clearer and directly, in experimental fashion.

    So it is not without some historical implications that early thoughts could have been exceeded, to relate this issue, and try to make sense of it. It is still a responsible function that we recognize as necessary.

    The artistic implicatons of “cubism” is one I found related to discrete measures, and to see this developing aspect in relation to science, is no less important as we engage how such extra dimensions might be seen as a continuity in topological form?

    Would this be incorrect?

  17. Wolfgang says:

    Anti-Lubos,

    > I’ve asked it before, but I’ll ask it again.
    > Does anyone like him? And if so, how and why?

    Are you saying you do not like his songs ?
    http://schwinger.harvard.edu/~motl/sf/frames.html

    PS: I like Lubos.

  18. plato says:

    Dissident:If you perform an experiment in which some of the energy you put in seems to disappear somewhere, unaccounted for, then yes, you have some explaining to do. Conservation of energy is not something we’d give up lightly; rewriting all those textbooks would be exhausting… but large extra dimensions would certainly not top the list of things to consider.

    First of all, “missing energy? is a normal feature of collider experiments, since you can’t expect to catch all the stuff that comes out of them. You have two particle beams banging into each other inside a tunnel of finite width; any decay products flying off into the tunnel are lost. Around the collision point, you have detectors which, while huge and most impressive, also have blind angles and – most importantly – finite size.

    http://cosmicvariance.com/2005/09/05/dark-matter-and-extra-dimensional-modifications-of-gravity/#comment-4160

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  20. Dan says:

    Quantoken,

    your extra-dementia clearly determines your opinion about extra-dimentions. How’s your GUITAR?

  21. Quantoken says:

    Dan:
    I am making pretty good progress in GUITAR but I have decided not to talk about it until I can figure out the whole thing in one piece.
    Privately I wish large extra dimentions exist. It will make life much easier. Surgical incisions will not be needed for a doctor to operate on a patient’s internal organs, for example. They can be reached through extra dimentions, without having to cut up the patient’s chest. But there may be other inconveniences. Prison inmates may escape through extra dimentions without having to dig a secret tunnel. And compressed air within a tire could leak out through extra dimentions, even though the surface of the tire is perfectly tight.
    Super String Theorists could save their time and energy in their invain effort to search for extra dimentions, by humbly begging the teaching of magicians, who are the only people who have figured extra dimentions out already. For there is no other rational explanation how they managed to cross one metal ring into another one and then remove them freely, without breaking the rings to do that. The topology simply does not allow that unless there is extra dimentions :-)
    Of course, that is not science.

    Quantoken

  22. ksh95 says:

    Quantoken said:

    For there is no other rational explanation how they managed to cross one metal ring into another one and then remove them freely, without breaking the rings to do that. The topology simply does not allow that unless there is extra dimentions.

    Hmmm, that’s not obvious to me. It’s obvious that you could escape from prison through extra dimensions, but I’m not sure you could pull rings apart in any dimension.

    I’m sure some one here has some insight into this.

  23. D R Lunsford says:

    IIRC knots are only possible in 3d (Klein and others).

    -drl

  24. ks says:

    Maybe L. Krauss and Peters books will be the last critical examinations of ST by ST outsiders before dropout literature enters the market? Until than ST does not have to harm about an “objective enemy” ( Stalin ). By the way I find Lubos attitude towards Krauss somehow strange for a person who criticises climate research as a well informed ousider. If sectarianism or closed society counts so much one may ask for the amount of scientific papers he published in this area.

  25. Thomas Larsson says:

    Hmmm, that’s not obvious to me. It’s obvious that you could escape from prison through extra dimensions, but I’m not sure you could pull rings apart in any dimension.

    Manifolds of dimension m and n embedded in D-dimensional space generically intersect along an (m+n-D)-dimensional manifold (i.e. codimensions add). They are knotted if m+n-D = -1. E.g., two curves (m=n=1) are knotted in D=3 dimensions, two 2D surfaces are knotted in D=5 embedding dimensions but intersect along a 1D curve in D=3, etc.

  26. Bryan says:

    ‘Maybe L. Krauss and Peters books will be the last critical examinations of ST by ST outsiders…’ KS

    I disagree, because when details come out next March there may be a Congressional inquiry into what went wrong with ST…

  27. Kris says:

    Brian, what are you expecting in March? Seems you have something specific in mind…

  28. Bryan says:

    Kris: was thinking of the publication of a book about ST being “Not Even Wrong”. Think it might stir up trouble!

  29. Juan R. says:

    ks Said:

    By the way I find Lubos attitude towards Krauss somehow strange for a person who criticises climate research as a well informed ousider. If sectarianism or closed society counts so much one may ask for the amount of scientific papers he published in this area.

    Well, perhaps, you forget that many particle physicists, and by extension string theorists, believe that they can talk about everything since are -they believe- more intelligent that other guys.

    Newer have you heard abut fist class and second class scientists? Unfortunately some physicists still believe that a chemist is a kind of ‘second-class physicist’.

    This would imply -of course, it is a completely nonsense- that a physicist ‘can’ talk about physics, chemistry, biology, environment whereas chemists or biologists cannot talk about physics.

    Some time ago, when i was in the Colegio official de químicos de Galicia, an ‘iluminated’ group of physicists proposed that, in Spain, physicists could gave courses of both physics AND chemistry in Schools but chemists can only gave courses on chemistry!

    Of course, was a nonsense and the corresponding law newer was approved…

    When people like Gross, Witten, Greene, Weinberg, Anderson, or even Gell-Mann talk about chemistry only say either irrelevant/wrong things or outdated stuff.

    Juan R.

    Center for CANONICAL |SCIENCE)

  30. Bryan says:

    http://www.indiadaily.com/editorial/5061.asp

    The article above reports the discovery of extra dimensions. Is this premature, like cold fusion, or real. It mentions that the extra dimensions are really big so they will enable us to do the things Quantoken suggests, like operations without any need to cut skin or tissue at all, and it may account for punctures in tyres where you can’t immediately see a hole. ;)

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  32. Nigel says:

    Juan – I think Lubos is not the bad guy really, he has just got mixed up with the wrong crowd. The only reason he asserts views on every aspect of everything is that he is qualified to do this, since string theory – his expertise area – is a ‘theory of everything’!

  33. Arun says:

    Now that I have Roger Penrose’s “Road to Reality” in hand, I see that he has a plethora of objections to string theory. Are there available any coherent replies to Penrose’s doubts?

  34. Wolfgang says:

    Arun,

    Lubos Motl stated that the objections of Roger Penrose are “obvious nonsense”, but from what he wrote it is clear that he never read the relevant parts of the book.

    Some of the doubts have been expressed also by Lee Smolin and Peter (e.g the question if string theory is indeed finite and consistent) and have provoked some responses from string theorists.

    I am not aware that the main argument of Penrose (M4xCY is unstable against perturbations, in particular in a classical approximation) has ever been seriously discussed or shown to be incorrect.

    I am personally not too impressed by his argument(s), but I cannot say if his classical approximation is relevant or not.
    Also, I am not convinced of his discussion of quantum theory in general.

  35. Arun says:

    Wolfgang,

    Motl’s remarks don’t help me, they don’t count as a coherent reply. Obviously, there is plenty of room for disagreement with Penrose.

    What I’d like is the following type analysis, hopefully that addresses the same audience that Penrose is addressing; or if not, to Penrose himself, and he can tell us if he is adequately answered.

    1. For some objections, Penrose is making an unwarranted assumption about the nature of reality, or he has utter misunderstood string theory.

    2. For some objections, Penrose is on the mark, and this is an area where string theorists have to do further research to meet his challenge.

    3. For some objections, there is a good physical argument, even if no mathematical proof, that resolves Penrose’s objection.

  36. Steve Myers says:

    It’s long been known that adding dimensions drives volume to the surface (it’s called “The Curse of Dimensions”). So how does that affect a field?
    Also remember you can always get a symmetry by adding a dimension — but there’s no reason it is physically real.

  37. bryan2 says:

    Thomas Larsson Said:
    “Manifolds of dimension m and n embedded in D-dimensional space generically intersect along an (m+n-D)-dimensional manifold (i.e. codimensions add). They are knotted if m+n-D = -1. E.g., two curves (m=n=1) are knotted in D=3 dimensions, two 2D surfaces are knotted in D=5 embedding dimensions but intersect along a 1D curve in D=3, etc.”

    An easy way to visualize this is the case where m=n=0, and D=1. m and n are each 2 points separated by a fixed distance. They are knotted when a point from one is in between the point of the other. When D=2, m and n are no longer knotted since they have another direction to move in.

  38. Juan R. says:

    Nigel note i do not said that Lubos or other string theorists were “bad guys”. I simply said that are a bit confounded.

    Yes they believe that are working in the TOE, but this is false.

    See my recent post on sci.physics.research.

    I wait a hot debate on this

    Juan R.

    Center for CANONICAL |SCIENCE)

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  40. Juan R. says:

    Sorry, i made a typo.

    Instead of

    “See my recent post on sci.physics.research.”

    would read

    “See my recent post on sci.physics.strings.”

    Juan R.

    Center for CANONICAL |SCIENCE)

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