Ask a String Theorist

First of all, I’d like to thank Chad for the keys to his internet-house for the next few weeks. If you’re here, you know that one of the things Chad believes in (and is quite good at) is using his weblog for the exposition of science for the general public. While I don’t think I can manage any funny dog stories, I’d like to try to follow his example. I have some ideas already planned (such as, god help me, a three part series on the multiverse), but I thought as an initial post here, I’d go straight to the public. What do you want to hear about? Is there some aspect of string theory, quantum gravity or quantum field theory that you want explained? I can’t guarantee that I’ll know the answer or be able to explain it, but I’ll give it a shot or see if I can con get someone I know to try.

(and if anyone I know sees something they’d like to talk about, thus saving me work, give me an e-mail, he says optimistically)

Comments

  1. #1 Johan Larson
    August 17, 2007

    OK, sure. I’ve seen a lot of flack aimed at string theory criticizing its supposed untestability. What’s the problem here, in your view? Is it just that conducting experiments in this subfield would require inordinately expensive equipment (like particle physics, only more so), or is there some larger issue?

  2. #2 Colin McFaul
    August 17, 2007

    In the hopes that a string theorist might know something about astrophysics, how about Dark Matter? I’ve been a little too lazy to try to find a good introduction to the evidence for it (though, now that I look at it, Wikipedia is doing okay…). So I would pose the question: what is the observational evidence that requires a theory like dark matter, and why do other theories come up short in comparison to dark matter?

  3. #3 Nathan
    August 17, 2007

    Please make sure to invite Lubos Motl to participate in all these discussions.

  4. #4 Aaron Bergman
    August 17, 2007

    Hi Colin,

    This one, I think I can farm out to our friends at Cosmic Variance. In this post, Sean Carroll talks about the Bullet Cluster observation and its implication towards dark matter and alternatives. Sean has also written a cosmology primer that should help.

  5. #5 Moshe
    August 17, 2007

    Welcome Aaron, it would be amusing to read about string theory on these pages. But, more multiverse? why ,oh why? you think the subject did not receive the attention it so richly deserve? or maybe there are arguments and counter-arguments we haven’t heard before (a few times…).

    Seriously, if only I had time to blog I’d try to correct the impression that these discussion is what we do in real life, maybe by giving more examples of what it is that we actually do.

    (sorry to open with a rant, I promise to have more constructive comments later).

  6. #6 Luboš Motl
    August 17, 2007

    I agree with Moshe. So could you please, Aaron, explain how instabilities of the quark Fermi surface arise from the Sakai-Sugimoto holographic QCD model? Thanks. ;-)

  7. #7 Uncle Al
    August 17, 2007

    String theory demands BRST invariance. The effects of a massive body and an accelerating geometry are indistinguishable. Affine, teleparallel, and noncommutative gravitations wholly contain General Relativity. They additionally prescribe empirically measurable anisotropic vacuum background and Equivalence Principle violation without contradicting prior observations in any venue at any scale.

    Though it evinces zero testable predictions, string theory could be falsified in two days’ observation in common commercial equipment. Until such observation is executed, a landscape of 10^1000 allowed vacuum solutions remains absurd. Conservation of angular momentum, GR, QFT, and Lorentz invariance will take their lumps – observation always trumps theory.

  8. #8 Aaron Bergman
    August 17, 2007

    For Moshe, why the multiverse? Because, for better or for worse, people are interested in it, and there’s a lot of misinformation out there. And this way, if I write it all up, I never have to speak of it again :).

    It wasn’t supposed to be three parts, though; it kept growing.

    I’m hoping to do a post about what duality is, at some point, and maybe if I can pull it off, a layman’s introduction to AdS/CFT. That will be a challenge, though. Unfortunately, my own research is esoteric enough that I’m not sure I could manage an expository post on it.

    For Johan, I think I’d like to avoid that subject for now (and possibly for a long time more). I collected many of my thoughts in my review of Peter Woit’s book. I hope you find it interesting.

  9. #9 Moshe
    August 17, 2007

    Pretty funny Lubos, thanks for reading my paper…

    Aaron, sorry again for the unsolicited advice. Let me just say that there is the chicken/egg issue in my mind: maybe people are interested because we don’t seem to be able to stop talking about it? (this applies to other things as well in what passes as string theory discussions). In any event many people, including some of our colleagues seem to have a distorted view of our field. The pieces you mention sound very interesting, and I realize it is more than what I do from my couch here, so I’ll stop now…

  10. #10 Ron
    August 17, 2007

    As you’re fielding topic suggestions related to field theory and gravity, could you elaborate on this topic? I have a hard time wrapping my head around the notion that particles are frame-dependent. Then what are the basic entities? In a related question, we learn both that an accelerating charge radiates and that a local free-falling frame is inertial, so do we expect a electron in freefall to radiate? How does a co-moving observer see a non-radiating static electric field while a stationary observer sees a radiating charge? If we think of the radiation as discrete photons, are they there or not? Or does that question make no sense somehow when formulated precisely?

  11. #11 Alejandro Rivero
    August 17, 2007

    Hmm, is anybody thinking about relaunching the String Caffee Table? Not to speak of s.p.s, in death state.

    If this is an invitation of topics for posts, I’d like to hear something about boundary fermions, Chan-Pato and their brane version. For instance, how many flavours there are really at the ends of the type I open string? 32, 10, or 5?

  12. #12 a
    August 17, 2007

    A joke heard at a conference:

    An experimentalist asks a string theorist “why ghosts are needed for quantization of QCD?”

    The string theorist answers “What is QCD?”

  13. #13 Differential Geometer
    August 17, 2007

    Dear Aaron,

    Can you comment on the status of twistor string theory? In particular:

    Firstly, is the following statement of Witten’s conjecture correct: The only non-zero amplitudes for spin one particle scattering come from configurations of points which lie on algebraic curves in twistor space.

    Second: What is the evidence behind Witten’s conjecture, and what has been done to prove/disprove it? What is the present status?

    Third: Does twistor-string theory extend the Atiyah-Hitchin-Singer theorem about instantons (using generalizations of the Ward theorem) to other cases (quantum corrections)? What are these things, either physically or geometrically?

    Unfortunately I find Witten’s paper very hard to read because I know very little QFT and string theory, but if it isn’t of independent differential geometric interest I’ll eat my hat!

  14. #14 Qalmlea
    August 17, 2007

    I’d like to see a discussion of how (or if?) string theory reconciles the geometric interpretation of gravity with the quantum interpretation. For that matter, I’d love to see a discussion about any other problems that string theory solves, as well as new problems created by the theory.

  15. #15 Doug
    August 17, 2007

    Hi Lubos,

    My screen freezes everytime that I have tried to access your blog over the last couple of weeks.

    I can usually only read the first paragraph of the most recent thread.

    Any hints on how to reslove this problem?

  16. #16 Jack
    August 17, 2007

    As I understand it, the multiverse is created by nucleating new universes as regions of “true vacuum”. Question: what does string theory have to say about this mysterious process? People seem to be very sure that this process can produce a universe like ours. This seems very dubious to me. Question: is there anything in string theory that makes it more plausible that a patch of true vacuum would necessarily or naturally evolve into something like our world? If we cannot answer these questions, should we believe that the landscape is physically relevant?

    I have to say that I’m a bit perturbed by Moshe’s comments above. I can understand that he believes that there is nothing more to be said philosophically [is it really science blah blah blah..]. On the other hand I cannot understand why he thinks that it isn’t interesting scientifically……one constantly hears string theorists complaining, “Hey, we don’t spend all our time thinking about the landscape! We contribute lots of boring papers to the arxiv too!” Oh, well in that case all is forgiven…… :-)

  17. #17 Luboš Motl
    August 18, 2007

    Dear Alejandro, sps is not just “like” in death state. It’s been physically dead for many months because the mail server that was receiving all the e-mail and filtering it went out of business and there were no computer administrators at Harvard who could be fixing it. It’s dead dead!

    Dear Doug, try MSIE7, Safari, Firefox, or newsreaders such as http://www.google.com/reader/view/feed/http://motls.blogspot.com/atom.xml – the latter certainly works (with many other feeds, by the way).

    Moshe: it is almost certain that the multiverse has been discussed in the public more than what would appropriate. But what hasn’t been discussed are the actual reasons why the multiverse has such a strong position and why many leaders in the field believe that it is the answer. They did a poor job in explaining that which is why people who don’t know much about physics rely on their emotions and preconceptions instead.

    Jack: it is not that surprising that a person who is not interested in actual physics will find it boring and will prefer irrational witch hunts and empty philosophical discussions. But unlike you, I don’t think that such a person should be influencing what physicists are doing.

    a: Moshe, for example, knows more about QCD than you with all people you have met in your life combined.

  18. #18 Jack
    August 18, 2007

    Dear Lubos Motl: I interpret your answer as meaning that you cannot answer the questions posed. Do you speak for all string theorists in this matter, or only for those who support the work of the Pilsen brewery?

    Anyway I certainly meant no offence to Moshe, apologies if any was taken. I just wanted to stress that while the philosophical stuff about the multiverse has been said too many times, that does not imply that one can no longer have a meaningful discussion about the science of it. There is far from being too much of that; in fact there is very little of it on the arxiv.

  19. #19 Luboš Motl
    August 18, 2007

    Dear Jack, I am used to treatment like yours so it’s nothing new. Pilsner beer is great, by the way.

    The cosmic bubbles and eternal inflation are concepts rooted in field theory – the long-distance approximation of any theory – and it doesn’t require anything really special about string theory except for string theory’s prediction of a rather complicated configuration space with many minima.

    This prediction enters the long-distance arguments that can otherwise be made by non-string theorists, too. And it is often made by them, indeed.

    I disagree that there has been any meaningful out-or-arxiv debate about the multiverse and I think that the people who are attempting to create such debates are not meaningful debaters themselves. Just like a Jack above, they prefer to repeat and oversell the same meaningless philosophical cliches and dogmas all the time instead of trying to understand some new science and make progress. They also want to ignore the science that actually gives us the main rational arguments about these issues in one way or another, too.

    Sorry to say but that partially includes Aaron Bergman with his planned “three-part series about multiverse” and other things. These are topics that put him into the position of Peter Woit Lite and he certainly doesn’t represent the actual science well.

    If you were able to carefully listen to Moshe or any other real string theorist – people who usually don’t try to be loud – you would understand that constant discussions about general features of the multiverse are simply not the thing that they consider good science. They won’t tell you clearly that these discussions belong to the more low-brow people because they are extremely polite and, in some sense, sissy.

    That’s why I am telling it to you. Yes, my comments do represent the opinions of a vast majority of the people who actually care about the real science instead of stupid media battles popular among cranks and overly self-confident laymen in general. Good that you have asked.

  20. #20 Peter Shor
    August 18, 2007

    I have never understood how string theory manages to stay unitary in the face of the black hole information paradox. Could you say whether this question has been resolved (I have heard differing answers from various string theorists, so I suspect the answer is “no”) and if so, how. I know Hawking paid off on his bet, but I’m not satisfied with this as an answer if he’s the only one who understands the resolution.

  21. #21 Luboš Motl
    August 18, 2007

    Dear Prof Shor,
    one must be careful what the actual question is.

    If the question is whether we have a full mathematical framework that allows to quantify the problems with Hawking’s “proof” of a violation of unitarity, the answer is No. We know that the violations have something to do with non-locality in the presence of horizons – that almost certainly exists since the argument that it stays exact simply rbeak down – but no fully convincing account what happens is known (how much nonlocal it is, how far and quickly one transmits information?), at least it is not known to most people.

    But if you ask whether we know that Hawking evaporation is unitary in quantum gravity, according to string theory, the answer is a resounding Yes. There are many clean setups where it can be answered unambiguously – like in AdS5 x S5 or 11-dimensional flat spacetime. One can show that these spacetimes are equivalent to non-gravitational and manifestly unitary theories (the boundary CFT or Matrix theory) with a Hermitean Hamiltonian.

    The Preskill-Hawking bet was about the latter, Yes/No question, and the answer is demonstrably Yes, the information is preserved. Surely AdS/CFT was the main reason why Hawking finally agreed that it is preserved. That’s why it’s completely correct that Hawking has surrendered in the bet regardless whether his own semi-new explanation why the answer is Yes is comprehensible to others or not. His story is an auxiliary tool that helps him personally to see that loopholes in his previous arguments exist.

    Best
    Lubos

  22. #22 Aaron Bergman
    August 18, 2007

    Please try to be nice, Lubos.

    To Differential Geometer: that’s a bit more technical that I was planning, but if no one shows up to answer your question, I’ll see if I can refresh my memory on the twistor stuff.

    To Jack: As Lubos says, the process of bubble nucleation is actually described in terms of field theory, not string theory. Some people, Tom Banks notably, have argued that string theory may change this picture dramatically, but unfortunately we still don’t to my knowledge have the tools to give an explicit answer in string theory. There are also some interesting questions about when the bubble can actually inflate into a big universe. The calculations that have been done generally assume a high degree of symmetry, but computer simulations seem to show that if you instead end up with something messy, it’s much less apt to inflate.

    To various others: I’ll probably decide early next week what to write a post on, and I’ll try to answer as many questions as I have the energy to.

  23. #23 JohnQPublic
    August 18, 2007

    Aaron,

    I have a very [VERY] basic question about string theory. This may seem stupid, but I’ll bet a lot of lay people who just hear about string theory in the popular press have the same question, so maybe it would be worthwhile for a knowledgable person to address it. I’m not sure if I can express it clearly, or even if the premise of the question is correct, but here goes…

    As I understand it (in my unlearned and simplistic way), in general relativity, gravitation is due to curvature of spacetime. Test particles follow geodesics in curved space, and this accounts for how those particles are affected by gravity. The field equations relate the curvature of spacetime to the distribution of mass, energy, stress. (I hope this synopsis is at least roughly accurate!)

    Now, in string theory, I still hear about spacetime, and even curved spacetime with curled up dimensions, and so on. But this is what confuses me, because if we already have curved spacetime, then we already have gravitation (don’t we?), so what are the “strings” doing? Are we supposed to understand that, somehow, spacetime CONSISTS of strings? Or do strings exist within spacetime? If the latter, is the spacetime allowed to be curved? If so, doesn’t this curvature already imply a kind of gravity? On the other hand, if the answer is that spacetime actually consists of strings, then I’m even more baffled, because all the depictions of “strings” that I’ve ever seen (in popular accounts) seem to show them wiggling around IN spacetime. If we are supposed to understand that spacetime CONSISTS of (or arises from) strings, then it seems to me the popular accounts are all very incorrect and misleading.

    Anyway, hopefully from the above rambling you get the gist of my confusion. I’ve heard that one of the great things about string theory is that it predicts the existence of gravity, but if strings reside in a “pre-existing” curved spacetime (with its own field equations?), then I have trouble understanding the conceptual foundation of it.

    Maybe I can formulate my question more precisely by asking this: In string theory, do the strings reside within spacetime? If so, do we have field equations – analagous to Einstein’s equations – governing the metric of that spacetime? And if so, are those field equations separate from the equations governing the behavior of the strings within spacetime? Do the strings experience “Einsteinian gravity” as they move within this spacetime, and is this different than the gravity that is produced (or embodied or entailed) by the strings themselves?

  24. #24 Jonathan Vos Post
    August 18, 2007

    According to Modern Cosmology: Science or Folktale?
    Current cosmological theory rests on a disturbingly small number of independent observations
    Michael J. Disney
    American Scientist
    http://www.americanscientist.org/template/AssetDetail/assetid/55839?&print=yes

    “The currently fashionable concordance model of cosmology (also known to the cognoscenti as ‘Lambda-Cold Dark Matter,’ or ΛCDM) has 18 parameters, 17 of which are independent. Thirteen of these parameters are well fitted to the observational data; the other four remain floating.”

    What does String Theory say about those 4 free variables?

  25. #25 JKG
    August 18, 2007

    Hi,

    I also would like to ask string theorist a similar question (as JohnQPublic did). What is (quantum) gravity in the string picture?

    In his textbook Joe Polchinski writes that “A curved spacetime is, roughly speaking, a coherent background of gravitons” (vol 1. p. 108). What does it mean exactly? Do you know any reference discussing this statement? In particular, could we (and how) construct a spacetime just from gravitons? If so, will it satisfy Einstein equations?

    Also a more technical question. I understand (but perhaps I’m wrong) that linearized diffeomorphisms (I mean the gauge symmetry of spin 2 field) are symmetries of string theory (on flat background). Now it is known that this symmetry transforms the linearized Schwarzschild metric to the full Schwarzschild metric in particular coordinates (the point mass solution of linearized Einstein equations can be gauge transformed to the metric which solves full Einstein equations). How this fact is interpreted be string theory?

    Thanks

  26. #26 Luboš Motl
    August 18, 2007

    You will find my answers anyway, but here they are.

    http://motls.blogspot.com/2007/08/answering-few-string-related-questions.html

  27. #27 cecil kirksey
    August 18, 2007

    Arron/Lubos:
    I am interested in what are the basic invariants (number of dimensions, if that is a vaible concept, strings, string tension, scalar fields (inflaton, Higgs), etc) that describe the physics prior to one of these vacuum bubbles and inflation. And why wouldn’t the “universe” that gives life to these bubble universes be nothing but another bubble with perhaps a completely different set of basic physics?

    If the multiverse is a viable physical idea would it not be correct that in any other multverse with “intelligent beings” that these beings must also arrive at the same conculsion concerning the multiverse idea based on their own observations and theories? Sense we have zero, nil, nadda experimental or observational data to support the idea of strings or a landscape is there any basis for believing in the multiverse idea?

    Are these questions viable scientific questions in the first place? It used to be that physicists would reflect questions about pre-big bang physics as being not scientific. Are physicists activefully attemping to answer such questions? Or is it mere speculation with no more of a scientific backing than “in the beginning…”?

    Thanks for your time.

  28. #28 JohnQPublic
    August 18, 2007

    I found the answers posted by Lumo (on the other blog) to be quite helpful and illuminating… so naturally they lead me to more questions! Just for easy reference, let me briefly paraphrase the first part of what he wrote (hopefully without mangling the meaning too badly):

    “We start with strings as objects propagating on a pre-existing geometry. Without strings, the geometry is rigid. That changes once you add strings. If you pump a condensate of strings in a certain vibration mode to the pre-existing spacetime, the physical effect on all other strings will be indistinguishable from a deformation of the original geometry. In fact, you could add or subtract strings from spacetime to get all the way to a vanishing metric tensor. Also, the consistency criteria for strings to propagate on a background imply that the background must solve Einstein’s equations (with all the right corrections).”

    Okay, so now my question are:

    (1) Does the original pre-existing rigid geometry have a definite number of dimensions and topology, or doesn’t it matter? For example, does it have some compactified dimensions already, or do those compactifications arise only when strings are added? If adding or subtracting strings can create a VANISHING metric, then can it also change the number of effective dimensions and/or the topology?

    (2) Once the strings are added, as I understand it, they induce an “effective” metric on top of the pre-existing metric… Is the right? If so, I’m confused by the statement that “the background must solve Einstein’s equations”, because I don’t see how the original “rigid” geometry (which I assume is “the background”) can be a non-trivial solution of the field equations. I say this because the original geometry was said to be “rigid”, whereas I don’t think any solution of Einstein’s equations in the presence of any kind of propagating energy can be rigid.

    (3) Assuming the “background” geometry is a solution of Einstein’s equations, then is the “foreground” (i.e., the effective metric induced by the strings) ALSO a solution of Einstein’s equations? If so, are they different solutions? Or are we to understand that these two metrics are one and the same? If so, isn’t there a “chicken and egg” problem here? I mean, we say the effective metric arises from strings propagating in a pre-existing metric, so I don’t see how we can then turn around and say the effective metric serves as the pre-existing metric. But if we don’t identify them with each other, I’m left with two different metrics, both of which apparently are supposed to be solutions of Einstein’s field equations. I’m struggling to formulate a clear question here, and not succeeding… but basically I’m trying to understand how the pre-existing background metric and the effective metric induced by the strings are related to each other (if at all).

    (4) Is the original “pre-existing” geometry observable in any sense? I mean, does it have any consequences? If not, why is it necessary to introduce it in the first place? Could we select any arbitrary background geometry and arrive at effectively the same theory?

    (5) On a slightly different note, all the popular accounts of string theory talk about the strings vibrating and oscilating, which makes me think there must not only be a pre-existing spacetime in which to carry out those oscillations, but also some kind of “inertia” and some kind of tension or restorative force. (If something has no inertia, it can’t oscillate.) In general relativity, inertia and gravitation are very closely identified, but in string theory, if the basic inertia of the strings (or the parts of strings) is a pre-existing attribute, whereas the effective gravitation is a higher-level consequence of vibrating strings, then is there also a higher-level (“foreground”) version of inertia? Or is this another checken and egg, i.e., the inertia that emerges from the behavior of strings is the same inertia that produces the behavior of strings in the first place?

    Again I’m conscious of not being able to articulate very clear questions. I guess I’m so lost and confused that I can’t even figure out what to ask. Any further help that anyone can offer would be appreciated.

  29. #29 Luboš Motl
    August 19, 2007

    Dear JohnQpublic, I think that your questions are good and they should have been asked at many places many times before, but they were not.

    1) Yes, the pre-existing metric is completely classical and has a very definite number of dimensions (in critical string theory it must be 26 or 10, the latter in the more relevant case of superstrings), a very definite topology, and a very definite shape and size. Some of the dimensions may be infinite, others may be compact. All possibilities satisfying Einstein’s equations (with all corrections, if they are nonzero) are allowed. For example, circular dimensions may have an arbitrary length.

    The background geometry is classical and the strings carry the whole quantum nature of everything. It is a standard and crucial method of particle physics to write quantum objects as their vacuum expectation value (a classical value in the “background”, multiplied by the identity operator) plus a quantum fluctuation. In this case, the classical value is ordinary geometry and the fluctuations exist because one can create strings into it.

    However, it turns out that the theories obtained by starting with different geometries are exactly equivalent to each other. If you Taylor-expand a function around a point, the coefficients depend on the point and are not related to each other in any simple way. But if you resum the function, you get the same one. The case of strings is the infinite-dimensional example of the same thing. One can get from any allowed geometry to any other allowed geometries by adding strings and dynamics will be identical. That’s been known for 30 years in the case of continuous transitions and for 10 years in the case of disconnected descriptions (they are equivalent because of dualities) or the case of topology change.

    Yes, it’s been proven that topology of space can change in string theory (see chapters 11,13 of The Elegant Universe for a popular account). Such a change goes through geometries that are singular in general relativity but the full physics of string theory around these points is completely non-singular. The classical geometries I talk about always have 10 dimensions but the effective number of dimensions – those for which normal geometric intuition applies – can dynamically change by adding appropriate string condensates, too. We usually don’t try to change the size of the compact dimensions below the Planck length because by dualities, that would be equivalent to some large dimensions anyway. The “zero size” dimensions were only cited for simplicity: in reality, that’s not where we want to end to prove that space is made out of strings. We want to end at a Planckian (10^{-33} inch) size where classical geometry is a very bad approximation and characteristic stringy phenomena dominate.

    2) The pre-existing background is rigid in the sense that it is classical and once you decide what it is, you should work with this choice all the time and express all deformations of it in terms of created strings. (Analogy: you shouldn’t randomly combine coefficients of Taylor expansions around different points because they’re like apples and oranges.) By saying it is rigid, we don’t mean that it is time-independent. Indeed, it can be time-dependent in which case the calculation is harder but still OK. The geometries may also have a complicated spatial shape. For example, all Calabi-Yau manifolds that we usually use are very curved but Ricci-flat: they obey vacuum Einstein’s equations and can thus be used as backgrounds. There’s a whole lot of an interesting structure in Einstein’s equations once extra compact dimensions are allowed.

    The strings contribute the “operator part” of the metric tensor that can have a nonzero expectation value, for example if you create a “coherent state”. But the expectation value of all fields including the metric is zero in every state with a sharp number of strings; that’s analogous to the statement that the average value of x in N-th excited state of the harmonic oscillator is zero.

    3) The background is a solution of classical Einstein’s equations (for number-valued fields) while the total metric (background plus foreground, as you call it) is a solution of the full Einstein’s equations (imposed upon operators themselves). The latter statement is non-trivially equivalent to the condition that the foreground strings satisfy their dynamical equations of motion in a given background. On the other hand, the “foreground metric” without the background doesn’t satisfy Einstein’s equations, just like you don’t get a solution of GR if you subtract two random solutions.

    There is no contradiction in having two different – and indeed, they are nonequivalent – solutions to Einstein’s equations. For example, think about empty flat space and a space with a gravitational wave added to it. They are not equivalent (even though people used wrong intuition for decades and incorrectly thought that waves could not exist). They are related by a physical process that changes one to another – a deformation of metric i.e. addition of strings in the graviton mode.

    4) Yes, as said above, any consistent pre-existing metric leads to the same theory: the same function can be Taylor-expanded around any point (=geometry) you like. The equivalence between the results with different starting backgrounds is the reason why you really can’t universally measure what the background is (one can only measure the full “field”, background plus foreground, in labs) and why physics of string theory is said to be background-independent. Because the proof of this fact needs some calculation, we say that this background independence is not manifest and we might speculate that there could also exist a manifestly background-independent language to talk about string theory, a hypothesis that could be right or wrong.

    The approach where the strings can be normally visualized as 1-dimensional additions to a pre-existing spacetime always needs some spacetime to start with just like Taylor expansions require you to specify a point around which you expand. In fact, every known definition of string theory has such a preferred background – AdS space, flat space in Matrix theory, and others – but deformations of this background are sometimes representend differently than by adding strings: for example by acting with gauge-theoretical operators in AdS/CFT. For all these approaches, there is a huge body of evidence (or proof) that they define the same, equivalent, theory.

    5) The character of inertia in string theory is identical to the same concept in general relativity. The background geometry is what specifies where the centers of strings want to move (along geodesics) as well as how they respond to the internal tension by vibrating: the worldsheets they span in Minkowski spacetime classically extremizes the proper area measured by the background geometry. We literally talk about normal fundamental strings and what they would do in a general relativistic spacetime.

    What’s new here is that if you promote the locations of points along the string to operators and quantize the theory, you will find out that one of the lowest-lying energy eigenstates of these strings has an indistinguishable physical effect on spacetime – one that is identical to deforming the spacetime geometry. In other words, if you allow (closed) strings to interact (by simply joining and splitting if they cross), a new string moving in a background geometry equipped with a condensate of other strings will have the same motion – or inertia – as if it propagates in a deformed geometry without strings. So I suspect that what you meant by the chicken and egg is right.

    Even if you cared about general relativity itself only, this fact would probably be highly surprising and important for you. Similar statements apply to all other fields and degrees of freedom: the values of all of them can be changed by an appropriate creation of strings in different states (and superpositions of these states). In point-like field theories, different elementary particles are made out of different material. In string theory, everything is made out of the same stuff.

  30. #30 amused
    August 19, 2007

    Hello Lubos,
    in your capacity as representative of the vast majority of the people who actually care about the real science, can you comment on the status of string theory compared to the theory of evolution? Cheers!

  31. #31 Luboš Motl
    August 19, 2007

    Dear cecil, if the Universe is really tiny or in a critical state such as the middle of a bubbling process, none of your quantities is a well-behaved fundamental degree of freedom.

    Scalar and other fields fail at short distances, strings and their tension fail when the coupling is strong, the number of dimensions and the rest of geometry is ill-defined when the geometry is small, and so forth. What are the basic degrees of freedom that describe even these situations well is mostly a mystery. So far we always make some approximation so that fields or strings are still used even under the extreme circumstances.

    The other Universes where we can imagine that life could arise look qualitatively similar to ours, and of course that if they exist, the beings in the life-friendly Universes would also end up finding string theory and the concepts of a multiverse.

    Sense we have zero, nil, nadda experimental or observational data to support the idea of strings or a landscape is there any basis for believing in the multiverse idea?

    This is a completely wrong way of thinking. We have huge, trillion, gadzillion evidence for gauge theories and general relativity and we are confident that string theory is the only mathematically possible theory that can incorporate both. That’s why we can be moderately confident that it has to be the correct theory. One needs to use his brain intensely to achieve this conclusion but brain has been necessary in physics at least for 350 years, it’s just getting more intense as we go deeper and further from easily testable phenomena.

    I’ve personally evaluated the confidence level that string theory can do its task close to 100% and the confidence that it is the right theory of the Universe around 85%. String theory is the only framework in which these questions – is there a multiverse? – can be asked at all. If you throw away all of string theory, you can be sure that what you end up with will be purely irrational, non-quantitative preconceptions and religion. String theory is, to say the least, the only known way to put these questions on a scientific footing and evaluate them by scientific arguments, even if these arguments may look too indirect to some people.

    If you adopted your “experimentally fundamentalist” approach consistently, the only consistent approach for you would be to avoid any discussion about any well-beyond-the-standard-model physics or quantum gravity because no observations are known about them. You’re obviously not doing it. If we’re doing it, we must use the best arguments we have.

    The theoretical arguments in these matters are way more important than the experimental ones that essentially don’t exist. This fact is nothing new, it’s been like that for decades.

    Are these questions viable scientific questions in the first place?

    As has been said many times, most of these questions are completely correct but some of the answers are unknown and some of your answers to other questions are completely wrong.

    All the best
    Lubos

  32. #32 Luboš Motl
    August 19, 2007

    Dear amused, evolution and string theory use different kinds of data and have different goals. The evidence behind evolution is simpler, more material, and more comprehensible to most people, thus much more easily acceptable by nearly 50% of the U.S. population. ;-)

    The evidence behind string theory is more esoteric, mathematical in character, and inaccessible to most people. Just like in the case of relativity or quantum mechanics, the theory in theoretical physics is simply way too much for most people to accept.

    Nevertheless, there is a huge number of rather accurate analogies between the status of these theories and the character of the arguments popular among the critics of these two theories. See e.g.

    http://motls.blogspot.com/2006/06/darwiniana-evolution-and-string-theory.html

    The frameworks of both theories seem inevitable given the known facts when one thinks about it carefully. The key nontrivial effects of both theories – such as strings at the fundamental scale or the evolution of mammals from primitive organisms – can’t be proven in practice because it either requires billions of years of evolution or a collider as large as the Universe. Many interesting details about these theories are unknown in both cases – details about the evolution tree or the choice of the realistic vacuum.

    In both cases, most of the critics of the theories are unfamiliar with very basic facts. In both cases, the critics use philosophical or religious or political arguments instead of a careful, “boring” scientific evaluation of the evidence.

    Many people would probably say that evolution is more well-established as a theory of reality than string theory. I think that one would have to be careful how the confidence is evaluated here.

  33. #33 amused
    August 19, 2007

    Thanks for that, Lubos. I’ld be interested to hear whether the other string theorists here agree with you, especially regarding the huge number of accurate analogies and the inevitability of the string framework. Aaron, Moshe?

  34. #34 Chris
    August 19, 2007

    Dear Aaron and Lubos,

    In QED (and general in QFT I think) there are some commutation relations between field strengths (and as Bohr and Rosenfeld have shown there are certain limits of measurability for those operators which do not commute). I wonder if we can derive these commutation relations using string theory or show that for low energies such relations must hold. Hope you could help me with this (I’m not a field/string theorist sorry if this is a naive question).
    Best wishes,
    Chris

  35. #35 Jack
    August 19, 2007

    Lubos Motl said: “If you were able to carefully listen to Moshe or any other real string theorist – people who usually don’t try to be loud – ”

    God forbid that any string theorist should ever be loud, Lubos. But I promise not to listen to sissies.

    Jeezus H Christ….anyway, back in this Universe,

    Aaron said:

    “There are also some interesting questions about when the bubble can actually inflate into a big universe. The calculations that have been done generally assume a high degree of symmetry, but computer simulations seem to show that if you instead end up with something messy, it’s much less apt to inflate.”

    OK, that is exactly what I had in mind. Could I trouble you for a specific reference? Thanks a lot, that would be very useful!

  36. #36 Aaron Bergman
    August 19, 2007

    Amused — there are plenty of venues where you can play your games. Please don’t do it here.

    Lubos — I would greatly appreciate it if you continued your earlier policy of answering questions at length on your own blog and linking from here. Thank you.

    Jack — Unfortunately, most of my knowledge on this subject comes from talking with various peple, and I can’t remember any references. Let me ask around and see if I can dig something up. Sorry.

  37. #37 Aaron Bergman
    August 19, 2007

    Hi Ron (#10) –

    I like very much the question about the nature of particles in field theory, but I don’t think I’ll be able to pull it off here. Let me instead direct you to the book of Birrell and Davies which has an discussion on just that subject. It should be much, much more approachable than Wald’s famously abstruse book. The question of the nature of particles is somewhat disparate from the infamous question about falling charges. I believe Peierls book, “Surprises in Theoretical Physics” has a nice discussion of that one.

  38. #38 cecil kirksey
    August 19, 2007

    Hi Aaron/ Lubos:
    Let me try again concerning this idea of a multiverse. First let’s assume that string theory and the landscape are correct in describing “our verse”. Now any “intelligent being” in another verse would also eventually conclude the same based on experimental and observational data or mere conjecture. (Note: The idea that intelligent beings in another verse must be like us would seem totally in contradiction with the idea of the landscape. We are looking for the vacuum state that defines OUR verse not someother verse for which we have exactly no knowledge that might support “intelligent life”.)

    If these other beings are to also draw the same conclusions that we do then there must exist some common physic principles in all verses capable of supporting intelligent life. I am asking simply: What are these basic physical principles and what evidence do we have for them?

    Another way of thinking about this is as follows. As string theory was being developed certain assumptions were made along the way: certain type of quantization and associated rules were invoked, conformal invariance, supersymmetry, etc. Now it would seem that these rules must be invariant in all verses if other beings are also to arrive at our version of string theory. Now what evidence do we have, other than pure conjecture, that these conditions exist prior to a bubble inflating to produce our verse?

    As I understand it, the string tension is the key parameter that would allow at least in principle all other constants to be defined. But the tension cannot be derived within the theory. Therefore, if strings existed prior to any bubble expanding then all verses must be able to derive the same string tension. Is this possible?

  39. #39 Tom Foss
    August 19, 2007

    If you’re still answering questions, I have one: a couple of years back, I saw S. James Gates talking about how his team had developed a string model which didn’t require the extra curled-up dimensions that most of the popular variations use. As someone who only became more skeptical of superstrings the more I heard from Brian Greene, this innovation seemed to be a major step towards parsimony. So, has there been any more movement on the four-dimensional front, and has it gained any more popularity than it had the last I heard about it?

  40. #40 Luboš Motl
    August 19, 2007

    I’ve answered most of the newer questions posted here in the fast comments over there:

    http://motls.blogspot.com/2007/08/answering-few-string-related-questions.html

  41. #41 Jonathan Vos Post
    August 19, 2007

    Sorry, I did’t see an answer to my question of comment $24
    [citation omitted]

    “The currently fashionable concordance model of cosmology (also known to the cognoscenti as ‘Lambda-Cold Dark Matter,’ or ΛCDM) has 18 parameters, 17 of which are independent. Thirteen of these parameters are well fitted to the observational data; the other four remain floating.”

    What does String Theory say about those 4 free variables?

  42. #42 Luboš Motl
    August 20, 2007

    Dear Jonathan, string theory as we know today doesn’t predict any cosmological parameter that isn’t predicted by its long-distance approximation.

    The anti-cosmological article by Prof Disney you quoted is really silly, especially the basic thesis that cosmology is based on a small number of observations. Whoever has seen what astonishing amounts of data the experimental cosmologists actually work with must know that the truth is just the opposite.

  43. #43 cecil kirksey
    August 20, 2007

    Hi Lubos:
    Sorry but if possible can you reanswer this question in more general lay terms that would be more clear?

    “First let’s assume that string theory and the landscape are correct in describing “our verse”. Now any “intelligent being” in another verse would also eventually conclude the same based on experimental and observational data or mere conjecture. (Note: The idea that intelligent beings in another verse must be like us would seem totally in contradiction with the idea of the landscape. We are looking for the vacuum state that defines OUR verse not someother verse for which we have exactly no knowledge that might support “intelligent life”.)

    If these other beings are to also draw the same conclusions that we do then there must exist some common physic principles in all verses capable of supporting intelligent life. I am asking simply: What are these basic physical principles and what evidence do we have for them?”

  44. #44 Luboš Motl
    August 21, 2007

    I have already answered your question in completely general lay terms.

    The general principles are the universal laws of string theory including the existence of gravity (dynamical, curved space), postulates of quantum mechanics, the existence of gauge fields, matter, and p-dimensional objects governed by equations of string theory.

    The evidence implying that these principles are correct are composed of millions of experiments that confirm the Standard Model and general relativity and the fact that the framework of string theory is the only mathematically possible framework that incorporates both the Standard Model and General Relativity.

    If one only asks what do the universes that admit life have in common, the answer is “life”. There is no cheap, 3-line description of the sufficient and necessary conditions for intelligent life because life is an extremely complex process.

    What’s exactly unclear about that? Could you please be more specific about your confusion?

  45. #45 immature_amateur
    August 21, 2007

    i just have some very simple questions, perhaps stupid ones: 1)what does string theory tell us about gravity that’s currently missing from general relativity? how does it extend the current standard model? basically i guess i’m asking how string theory ,as currently known, extends what has been experimentally verified? what new surprises and subtleties are to be expected from where our current knowledge is at?
    2) on m-theory , what exactly IS the problem in merging the string theories? how would (if at all possible) you tell a lay person of what string theorists are really trying to achieve as an end result in your concurrent research?

    3) what makes the mathematics of string theory so necessary , that on now having some idea of how the four forces are connected, they can’t be done with the mathematics of either GR or QFT , but requires branes? why branes ?

  46. #46 JohnQPublic
    August 22, 2007

    After pondering the interesting answers the Lumo provided to my previous questions, I find that I’m still struggling to understand a few points (admittedly from a very primitive layman’s perspective). In no particular order, here are some of the things that still puzzle me. Any help will be appreciated.

    (1) The background metric is said to satisfy the vacuum field equations of general relativity, which is to say, they are Ricci-flat (the Ricci tensor vanishes, but the full Riemann curvature tensor need not vanish). A couple of things puzzle me about this. First, I can’t figure out what is supposed to be the “source” of the Riemann curvature, in accord with the field equations. I know the field equations support gravitational waves, but I don’t think anyone is suggesting that something like a Calabi-Yau subspace represents a wave solution (are they?) By comparison, for the plain old vacuum solution of the field equations near a spherically symmetrical mass in ordinary general relativity, I know that the “source” of the curvature is the central mass… but what is the source of the curvature of the background metric in string theory? Do the strings (or membranes?) act as sources? Surely they have energy, so they ought to act as sources, but then we wouldn’t be dealing with vacuum solutions, would we?

    (2) Another thing that puzzles me is that we seem to have two physically very distinct ways of getting effective spacetime curvature. We have the classical background spacetime itself, which is curved, and then we have the effective metric, which is the net result of the background metric and the forground metric, the latter being the product of the strings. Lumo commented that neither of these is individually observable, i.e., we can only observe the net effect of the two, and he also indicated (I think) that, starting with a different background, we could get to the same net result simply by postulating a different stringy foreground. Hence the individual natures of the background and foreground my be (in some sense) just an artifact of our choice of the point at which to expand the Taylor series (to use Lumo’s analogy). Nevertheless…

    I’m bothered by the fact that a theory that is supposed to explain the curvature of spacetime in terms of strings, still needs to invoke classical curvature of the “raw” background spacetime, which is the very thing it is trying to explain. In fact, as Lumo explained it, “the background geometry is what specifies where the centers of strings want to move (along geodesics)”, so it sounds like we already have general relativity and a theory of gravity before we even add the effect of the strings. If the background spacetime is posited to be a solution of the field equations, prior to any string ingredients being added, then it seems (to my befuddled brain) that spacetime curvature (and inertia and the tendency of mass-energy to follow geodesics) already exist without strings, so we haven’t really explained anything unless we can totally eliminate that classical background spacetime. Am I reading too much into the background spacetime? Or are we supposed to postulate some sort of Meta-string theory to account for the background spacetime dynamics? And then an infinite regress of meta-meta string theories?

    (3) I feel as if I’m being told two contradictory things about the background spacetime. On one hand, I hear that it is unobservable and ultimately unimportant, like choosing a point about which to expand a function, since the resulting sums will always be the same (assuming convergence), and this extends even to the topology and number of dimensions, because all of these can be compensated by suitable arrangement of strings. But on the other hand, I’m being told that the background spacetime must satisfy some very strict conditions, such as having exactly 11 (or exactly 26) dimensions, and so on. So I’m perplexed. If the characteristics of the background spacetime ultimately don’t matter, and can be compensated for by a suitable arrangement of strings, then why is it so essential to postulate a background of 11 (or 26) dimensions? I feel like I’m missing something here. Either the characteristics of the background spacetime matter or they don’t. Which is it?

    Hmmm… I’m having one of those déjà vu moments right now… About I remember a debate about 10 years ago on the subject of general relativity and Poincare’s conventionalism. Recall that Poincare talked about observable experience as being the net sum of two individually unobservable components, namely, the posited background geometry G, and the posited physical laws P. He argued that the true nature of geometry is ultimately unknowable, or rather conventional, because we never observe G (or P) individually, we only observe the sum G+P. For example, we could maintain that the Earth’s surface is flat, provided we were willing to posit physical laws that entail distortions of measuring rods, lines of sight, etc., in order to yield the appearance of living on a spherical surface. In general (Poincare argued), we can postulate any G we like, provided we are willing to augment it with whatever (possibly outlandish) physical laws P are necessary to give the same net G+P. Of course, Poincare advised chosing G so that P is as simple as possible, but he insisted that this is just a matter of taste and convenience, not a logical necessity.

    Okay, so when I mentioned this (ten years ago), a lot of people jumped all over me, saying things like “That’s clearly invalid, you moron, because no physics could ever alter the dimensionality or topology of the geometry”. I felt duty-bound to defend Poincare’s honor, so I suggested various ways in which changes in both the effective topology and dimensionality could result from suitable physical premises, but one fellow in particular was vehement that I was spouting pure nonsense. He was adament that you could not possibly simulate topological or dimensional differences by means of physical processes. If I recall correctly (and I do), the gentleman’s name was Jacques Distler, who I later learned was/is a string theorist. Hmmm… I wonder if he endorses Lumo’s comment that the “topology of space can change in string theory… the effective number of dimensions can dynamically change by adding appropriate string condensates too… That’s been known for 30 years in the case of continuous transitions and for 10 years in the case of disconnected descriptions or the case of topology change.” Hmmm… If this has been so well known for so long, then why did poor JohnQPublic (not to mention Poincare) get ridiculed for even suggesting that such a thing was conceivable? But I digress…

  47. #47 Luboš Motl
    August 26, 2007

    I am answering these great questions here:

    http://motls.blogspot.com/2007/08/answering-few-string-related-questions.html

    Fast comments.

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    September 6, 2007

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