Why does string theory require 10 or 11 spacetime dimensions? The answer at a technical level is well-known, but it’s hard to bring it down to earth. By reading economics blogs by people who check out political theory blogs, I stumbled across an attempt at making it clear — by frequent CV commenter Moshe Rozali, writing in Scientific American. After explaining a bit about supersymmetry, Moshe concludes:
A guide in this pursuit is a theorem devised/put forth by physicists Steven Weinberg and Edward Witten, which proves that theories containing particles with spin higher than 2 are trivial. Remember each supersymmetry changes the spin by one half. If we want the spin to be between -2 and 2, we cannot have more than eight supersymmetries. The resulting theory contains a spin -2 boson, which is just what is needed to convey the force of gravitation and thereby unite all physical interactions in a single theory. This theory–called N=8 supergravity–is the maximally symmetric theory possible in four dimensions and it has been a subject of intense research since the 1980s.
Another type of symmetry occurs when an object remains the same despite being rotated in space. Because there is no preferred direction in empty space, rotations in three dimensions are symmetric. Suppose the universe had a few extra dimensions. That would lead to extra symmetries because there would be more ways to rotate an object in this extended space than in our three-dimensional space. Two objects that look different from our vantage point in the three visible dimensions might actually be the same object, rotated to different degrees in the higher-dimensional space. Therefore all properties of these seemingly different objects will be related to each other; once again, simplicity would underlie the complexity of our world.
These two types of symmetry look very different but modern theories treat them as two sides of the same coin. Rotations in a higher-dimensional space can turn one supersymmetry into another. So the limit on the number of supersymmetries puts a limit on the number of extra dimensions. The limit turns out to be 6 or 7 dimensions in addition to the four dimensions of length, width, height and time, both possibilities giving rise to exactly eight supersymmetries (M-theory is a proposal to further unify both cases). Any more dimensions would result in too much supersymmetry and a theoretical structure too simple to explain the complexity of the natural world.
This is reminiscent of Joe Polchinski’s argument (somewhat tongue-in-cheek, somewhat serious) that all attempts to quantize gravity should eventually lead to string theory. According to Joe, whenever you sit around trying to quantize gravity, you will eventually realize that your task is made easier by supersymmetry, which helps cancel divergences. Once you add supersymmetry to your theory, you’ll try to add as much as possible, which leads you to N=8 in four dimensions. Then you’ll figure out that this theory has a natural interpretation as a compactification of maximal supersymmetry in eleven dimensions. Gradually it will dawn on you that 11-dimensional supergravity contains not only fields, but two-dimensional membranes. And then you will ask what happens if you compactify one of those dimensions on a circle, and you’ll see that the membranes become superstrings. Voila!
sisyphys, that formula is valid in flat spacetime, where Lorentz invariance is a symmetry of the entire universe. In any curved spacetime, the interval will be a different function of the coordinates. Curved spacetimes are generally less symmetric than flat ones, although certain special examples might be equally symmetric, just in a different way.
Oh! The invariant interval formula! Sorry sisyphus, your terminology was fine….I was distracted by other things and did not make the connection, stupidly enough. Looks like Sean has answered you.
-cvj
Thanks, Sean. I’ll work on it.
Apropos of something else: Feyerabend may have been a tad radical, but maybe he got it right when he suggested that the slavish observation of a particular methodology can stifle discovery.
Thanks again.
Thanks, Clifford. I’m aware of your loss.
sisyphus:- in addition to the possibility that the spacetime has a non-trivial metric, mentioned by Sean, another common way of changing things quite drastically is to have other dynamical fields switched on in some directions, but not others. The classic example is a linear dilaton…. i.e. a spacetime field generated by the string, the “dilaton”, has a non-trivial dependence (linear in this case) on just one direction in spacetime….. the rather singles out that direction as being rather special as compared to the others, a possiblity not allowed for in the critical string constructions. This is one example of how you can have string theories that live in dimensions other than the “critical” ones.
-cvj
Thanks, Clifford. This is a bit to chew on. I’ll print it out and do a little research.
This is a fascinating post!
There is not string theory just a program named “string theory” devoted to search of anything that can be called “string theory”.
I find particulary interesting the above claim of string theorists that old “axiom” “string theory requires 10D” is not rigorous (i would wait they agree that nothing in string theory research can be considered rigorous).
I find really amazing the dozens of talks, books and articles devoted to critize Loop quantum gravity and others aproaches because they work in the “old” 4D framework. Once i read from a string theorist that LQG was wrong because was 4D and non-supersimmetric!!!!
Many string theorists popularly stated that universe WAS 10-11D and NOT 4D. Public is completely misinformed about the real status of string theory in modern science. It is a kind of cancer…
I find also amazing that many of my predictions in the recent past begin to see accepted by some people. For example, In my Oct 21 post “String theory is not a TOE” in moderated newsgroup sci.physics.strings i did a joke about the infinite malleability of string theory and how even with that infinite malleability string theory was an dead way. By dead way i mean dead for doing science, real science; of course, “string theory” and the Landscape and all stuff will survive during decades as a kind of postmodern religion or metaphysics, as it has done in last decade or so.
I said in page 2 of my April non-technical article cited in the newsgroup:
The notation “[string, M)” means the “sequence” of dozens of different versions of “string theory” proposed as the Final theory during the last 3-4 decades. Note that i leave open “)” the sequence by the right hand!!!
Yes, public reading my post may be skeptic because theorists as Witten or B. Greene newer said them that different versions of string theory were proposed in literature and none of them worked even minimally.
Please, by the sanity of science, do not forget the real history of field which is not covered in Witten popular essays in Nature or in Greene’s The Elegant Universe!
Robert B. Laughlin, 1998 Nobel Prize-winning physicist said last year
Return to the history of dimensions: 4D,… 26D, 10D, 11D, 12D?, 4D again. It appears to be a syntom of being doing research in circles, Right?
Now, i am preparing a formal rebuttal to last Witten Essay in Nature, which i consider completely distort the reality of the field and is based in beliefs.
I am also considering the possibility for an open letter (signed by specialists in many fields) explaining to public last “advances” in string theory and why string theory is completely wrong as candidate to TOE since have a wrong mathematical structure.
In fact, i personally doubt that even in the restricted field of particle physics and quantum gravity we can wait some good from string M-theory in a future.
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Juan R.
Center for CANONICAL |SCIENCE)
Once i read from a string theorist that LQG was wrong because was 4D and non-supersimmetric!!!!
gr-qc/9710008, footnote on page 2.
Btw, it’s supersymmetry.
Tanks by reference and by the correction!!!
I did several other errors in the post: “newer” instead of “never”, “have” instead of “has”…
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Juan R.
Center for CANONICAL |SCIENCE)
There are more fundamental errors than just typos.
For example, I believe Brian Greene did discuss different string theories (type I, IIA, IIB etc) in “The Elegant Universe”.
Critical string theory in 26D is a bosonic theory only, and I’m sure no-one has ever suggested that this represented a “theory of everything”.
As for the footnote referenced, since that is not credited to anyone in particular, it does not seem to me to be good evidence that this was ever put forward as a serious argument against LQG.
Poppycock,
It is good to know that. I believe that the perfect post has been still not invented. It is good and needed to make errors. My criticism ot string theorists is not by making errors, just by ignoring the last near four-decades criticism and by their obvious attempt to distort the history of the field.
I would emphasize “near four-decades” because in your blog you write
In a pair of years, string theory will be 40 years-old. Somewhat as many people is misinformed about real status of string theory, I believe that many people would be perplexed when know that your “twenty-sometimes” means near the double of years: 40.
Now, let us see if it is true you are claiming. You said
I never said the contrary! That i said was that The Elegant Universe presented to the public a distorted version of the history of string theory research. Moreover, by different versions of string theory i was not refering just to the five (2, 10) versions of string theories usually named by the collective name of “superstring theory”. By different versions of string theory i refer to dozens of versions published in literature you apparently have not read the list of different versions i cited in my April work.
However, your appeal to superstring theory is good, because now i can add some i said not in my previous post: that some time ago many physicists claimed that ONE of the five known superstring versions WAS the correct final theory.
In fact, the community of string theorists (“stringers”) thought then that our universe was just described by, and only by, (2, 10) points in the “branescan”. Now, they admit that were wrong in the past which reinforces my thesis history of string theory is the history of sucessive failure. It is more even now it is admited that string is not fundamental…
It is amazing to write at one hand all past claims of stringers and, at the other hand, our current understanding of topics. Allmost all was claimed in the past has been shown to be wrong.
I never said or even suggested that!
I said that in the past it WAS suggested that universe WAS 26D. Of course this idea was inspired in critical dimension of bosonic theory. Nobody claimed that a theory of 26D lacking fermionic modes could be considered a candidate to TOE. However, stringers believed that a fermionic corrected theory would be also 26D, because in the contrary case they would say: “NO, universe is not 26D; 16D are just an artifact of current formulation of the theory“.
el of classical theory, but on attempting to promote it to a quantum theory, researchers discovered that the total number of spacetime dimensions is fixed uniquely to be 26. So, quantum strings could exist only in a world with 25 (rather than 3) spatial dimensions, plus time. The excitement of finding — for the first time — a mathematical consistency condition that determines the number of spacetime dimensions, rather than treating this number as an experimental input, was somewhat tempered by the absurd value predicted for this number.
Nobody predicted a reduction 26D –> 10D via generalization to fermionic modes of the bosonic somewhat as nobody recently predicted the adittion of a new dimension outside the (2, 10) “traditional” regime.
In fact, i have seen some early work and ideas about compactification 26D –> 4D which now are considered outdated since the number of dimension is assumed to be 10D in superstring (CY) and 11D in M-theory (G2).
And YES, stringers claimed in public that superstring theory was the searched TOE and universe WAS 10D already in the 80s (i.e. 30 years ago). But 10D was not a correct number again.
I repeat the history of dimensions: 4D, 26D, 10D, 11D, 12D?, 4D again…
If i write E= mc^2 in this blog i think that i do not need to reference a 1905 paper for suporting it. We do not usually reference material is well-known for readers we are focusing. Above preprint was focused to people who already know (you apparently do not) the history of the field.
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Juan R.
Center for CANONICAL |SCIENCE)
Sure is nice to have the opportunities to rebuff the current state of affairs Juan R. 🙂
While these models appear abstract, how is it that you could marry such thoughts to “proposed experimental processes” with which to deal with the consequences of such abstract thoughts?
Was it wrong to go down certain avenues, then find that such experimental processes “stupid” after the fact, or was there real science being looked at?
Taking in the current state of affairs, to such analogistics levels of scientific validation, is just one more aspect of model assumption?
The contributors here are providing a service instead of the ole rant(yada yada), yet, we do hear of the 10 or 11 with some clarifications?:) Your contribution is helpful? Thanks. I’m learning a lot from a historical perspective, and after the fact.:)
Your thoughts on ICECUBE, in a weak field and it’s manifestation?
Beautiful and deep reply Plato 😉
During a brief instant (perhaps at Planck scale) your reply resembled the deep vision launched by the classical philosophers that your nick evokes.
Yes, during that brief instant, I was tempted to become a believer.
Unfortunately for the believers, the history of the field is very different of is said in talks focused to young and impressionable minds or in books dealing with laymen. Unfortunately for believers, it is a hard task to try to convince to real scientists that there is some serious below the stringy hype far from three decades arrogant claims of being working with the Final Theory, a theory that could explain everything.
Unfortunately, today string theory continues being so far from any realistic TOE as was 40 years ago. Unfortunately, each little time a new “prediction” of string theory is shown to be false. Last, I remember was the observation some days ago of the so called cosmological strings that were not so string after all…
Unfortunately, even with the infinite malleability of string theory, in which you can say anything and the contrary of anything (each claim founding a new version of string theory) all of us would recognize (even believers!) that after of all Nature does not like beauty 🙂
Stringy of course…
About the ICECUBE i prefer to follow “solid” Witten philosphy in gravity and talk of postdictions. Therefore, when you obtain some data contact with me.
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Juan R.
Center for CANONICAL |SCIENCE)
Juan R. (1R?)
hmmmm….
each little time a new “prediction” of string theory is shown to be false.
How is this possible? As a lay person such an example was important to me, that if such predictions are made and falsified, this was being handled properly?
Postdiction? Ah so you are saying any model assumption, or effort to use this model currently, is postdiction?
So lets say on mathematics alone then, is there any consistancy?
A side note? War on SeaGull: Any of you know? 🙂 Beer and Present Danger, was actually a good one.
Layman ponders.
Anyway, what is this “new physics” that might house dimensional perspective?
Multiverses. Really! How would such “funnels” provide for new beginnings? A geometrodynamical view of bubble technologies? :)Ronald Mallet’s dream of travelling back in time and making way for new things?
Maybe Joanne in another thread created could give us some more information and the relationship to dimenional attributes with neutrino considerations??
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